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Title: Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 2 - "Hydromechanics" to "Ichnography"
Author: Various
Language: English
As this book started as an ASCII text book there are no pictures available.
Copyright Status: Not copyrighted in the United States. If you live elsewhere check the laws of your country before downloading this ebook. See comments about copyright issues at end of book.

*** Start of this Doctrine Publishing Corporation Digital Book "Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 2 - "Hydromechanics" to "Ichnography"" ***

This book is indexed by ISYS Web Indexing system to allow the reader find any word or number within the document.



Transcriber's notes:

(1) Numbers following letters (without space) like C2 were originally
      printed in subscript. Letter subscripts are preceded by an
      underscore, like C_n.

(2) Characters following a carat (^) were printed in superscript.

(3) Side-notes were relocated to function as titles of their respective
      paragraphs.

(4) Macrons and breves above letters and dots below letters were not
      inserted.

(5) [root] stands for the root symbol; [alpha], [beta], etc. for greek
      letters.

(6) The following typographical errors have been corrected:

    ARTICLE HYDROMECHANICS: "... and [omega] the angular velocity
      about it generated by an impulse couple M, and M' is the couple
      required to set the surrounding medium in motion ..." 'impulse'
      amended from 'impluse'.

    ARTICLE HYMENOPTERA: "... see P. Cameron's British Phytophagous
      Hymenoptera (4 vols., London, Roy. Soc., 1882-1893)." 'Roy'
      amended from 'Ray'.

    ARTICLE HYRCANUS: "During its later years his reign was much
      disturbed, however, by the contentions for ascendancy which arose
      between the Pharisees and Sadducees, the two rival sects or
      parties which then for the first time (under those names at least)
      came into prominence." 'disturbed' amended from 'distrubed'.

    ARTICLE ICELAND: "Iceland is emphatically a land of proverbs,
      while of folk-tales, those other keys to the people's heart, there
      is plentiful store." 'people's' amended from 'poeple's'.



          ENCYCLOPAEDIA BRITANNICA

  A DICTIONARY OF ARTS, SCIENCES, LITERATURE
           AND GENERAL INFORMATION

              ELEVENTH EDITION


            VOLUME XIV, SLICE II

        Hydromechanics to Ichnography



ARTICLES IN THIS SLICE:


  HYDROMECHANICS          HYTHE
  HYDROMEDUSAE            I
  HYDROMETER              IAMBIC
  HYDROPATHY              IAMBLICHUS (Greek philosopher)
  HYDROPHOBIA             IAMBLICHUS (Greek romance writer)
  HYDROSPHERE             IANNINA
  HYDROSTATICS            IAPETUS
  HYDROXYLAMINE           IAPYDES
  HYDROZOA                IATROCHEMISTRY
  HYENA                   IAZYGES
  HYÈRES                  IBADAN
  HYGIEIA                 IBAGUÉ
  HYGIENE                 IBARRA
  HYGINUS (eighth pope)   IBERIANS
  HYGINUS (Latin writer)  IBEX
  HYGINUS, GAIUS JULIUS   IBIS
  HYGROMETER              IBLIS
  HYKSOS                  IBN 'ABD RABBIHI
  HYLAS                   IBN 'ARABI
  HYLOZOISM               IBN ATHIR
  HYMEN                   IBN BATUTA
  HYMENOPTERA             IBN DURAID
  HYMETTUS                IBN FARADI
  HYMNS                   IBN FARID
  HYPAETHROS              IBN GABIROL
  HYPALLAGE               IBN HAUKAL
  HYPATIA                 IBN HAZM
  HYPERBATON              IBN HISHAM
  HYPERBOLA               IBN ISHAQ
  HYPERBOLE               IBN JUBAIR
  HYPERBOREANS            IBN KHALDUN
  HYPEREIDES              IBN KHALLIKAN
  HYPERION                IBN QUTAIBA
  HYPERSTHENE             IBN SA'D
  HYPERTROPHY             IBN TIBBON
  HYPNOTISM               IBN TUFAIL
  HYPOCAUST               IBN USAIBI'A
  HYPOCHONDRIASIS         IBO
  HYPOCRISY               IBRAHIM AL-MAUSILI
  HYPOSTASIS              IBRAHIM PASHA
  HYPOSTYLE               IBSEN, HENRIK
  HYPOSULPHITE OF SODA    IBYCUS
  HYPOTHEC                ICA
  HYPOTHESIS              ICE
  HYPOTRACHELIUM          ICEBERG
  HYPSOMETER              ICELAND
  HYRACOIDEA              ICELAND MOSS
  HYRCANIA                ICE-PLANT
  HYRCANUS                ICE-YACHTING
  HYSSOP                  I-CH'ANG
  HYSTASPES               ICHNEUMON
  HYSTERESIS              ICHNEUMON-FLY
  HYSTERIA                ICHNOGRAPHY
  HYSTERON-PROTERON



HYDROMECHANICS ([Greek: hydromêchanika]), the science of the mechanics
of water and fluids in general, including _hydrostatics_ or the
mathematical theory of fluids in equilibrium, and _hydromechanics_, the
theory of fluids in motion. The practical application of hydromechanics
forms the province of hydraulics (q.v.).

  _Historical._--The fundamental principles of hydrostatics were first
  given by Archimedes in his work [Greek: Peri tôn ochoumenôn], or _De
  iis quae vehuntur in humido_, about 250 B.C., and were afterwards
  applied to experiments by Marino Ghetaldi (1566-1627) in his _Promotus
  Archimedes_ (1603). Archimedes maintained that each particle of a
  fluid mass, when in equilibrium, is equally pressed in every
  direction; and he inquired into the conditions according to which a
  solid body floating in a fluid should assume and preserve a position
  of equilibrium.

  In the Greek school at Alexandria, which flourished under the auspices
  of the Ptolemies, the first attempts were made at the construction of
  hydraulic machinery, and about 120 B.C. the fountain of compression,
  the siphon, and the forcing-pump were invented by Ctesibius and Hero.
  The siphon is a simple instrument; but the forcing-pump is a
  complicated invention, which could scarcely have been expected in the
  infancy of hydraulics. It was probably suggested to Ctesibius by the
  _Egyptian Wheel_ or _Noria_, which was common at that time, and which
  was a kind of chain pump, consisting of a number of earthen pots
  carried round by a wheel. In some of these machines the pots have a
  valve in the bottom which enables them to descend without much
  resistance, and diminishes greatly the load upon the wheel; and, if we
  suppose that this valve was introduced so early as the time of
  Ctesibius, it is not difficult to perceive how such a machine might
  have led to the invention of the forcing-pump.

  Notwithstanding these inventions of the Alexandrian school, its
  attention does not seem to have been directed to the motion of fluids;
  and the first attempt to investigate this subject was made by Sextus
  Julius Frontinus, inspector of the public fountains at Rome in the
  reigns of Nerva and Trajan. In his work _De aquaeductibus urbis Romae
  commentarius_, he considers the methods which were at that time
  employed for ascertaining the quantity of water discharged from
  ajutages, and the mode of distributing the waters of an aqueduct or a
  fountain. He remarked that the flow of water from an orifice depends
  not only on the magnitude of the orifice itself, but also on the
  height of the water in the reservoir; and that a pipe employed to
  carry off a portion of water from an aqueduct should, as circumstances
  required, have a position more or less inclined to the original
  direction of the current. But as he was unacquainted with the law of
  the velocities of running water as depending upon the depth of the
  orifice, the want of precision which appears in his results is not
  surprising.

  Benedetto Castelli (1577-1644), and Evangelista Torricelli
  (1608-1647), two of the disciples of Galileo, applied the discoveries
  of their master to the science of hydrodynamics. In 1628 Castelli
  published a small work, _Della misura dell' acque correnti_, in which
  he satisfactorily explained several phenomena in the motion of fluids
  in rivers and canals; but he committed a great paralogism in supposing
  the velocity of the water proportional to the depth of the orifice
  below the surface of the vessel. Torricelli, observing that in a jet
  where the water rushed through a small ajutage it rose to nearly the
  same height with the reservoir from which it was supplied, imagined
  that it ought to move with the same velocity as if it had fallen
  through that height by the force of gravity, and hence he deduced the
  proposition that the velocities of liquids are as the square root of
  the head, apart from the resistance of the air and the friction of the
  orifice. This theorem was published in 1643, at the end of his
  treatise _De motu gravium projectorum_, and it was confirmed by the
  experiments of Raffaello Magiotti on the quantities of water
  discharged from different ajutages under different pressures (1648).

  In the hands of Blaise Pascal (1623-1662) hydrostatics assumed the
  dignity of a science, and in a treatise on the equilibrium of liquids
  (_Sur l'équilibre des liqueurs_), found among his manuscripts after
  his death and published in 1663, the laws of the equilibrium of
  liquids were demonstrated in the most simple manner, and amply
  confirmed by experiments.

  The theorem of Torricelli was employed by many succeeding writers, but
  particularly by Edmé Mariotte (1620-1684), whose _Traité du mouvement
  des eaux_, published after his death in the year 1686, is founded on a
  great variety of well-conducted experiments on the motion of fluids,
  performed at Versailles and Chantilly. In the discussion of some
  points he committed considerable mistakes. Others he treated very
  superficially, and in none of his experiments apparently did he attend
  to the diminution of efflux arising from the contraction of the liquid
  vein, when the orifice is merely a perforation in a thin plate; but he
  appears to have been the first who attempted to ascribe the
  discrepancy between theory and experiment to the retardation of the
  water's velocity through friction. His contemporary Domenico
  Guglielmini (1655-1710), who was inspector of the rivers and canals at
  Bologna, had ascribed this diminution of velocity in rivers to
  transverse motions arising from inequalities in their bottom. But as
  Mariotte observed similar obstructions even in glass pipes where no
  transverse currents could exist, the cause assigned by Guglielmini
  seemed destitute of foundation. The French philosopher, therefore,
  regarded these obstructions as the effects of friction. He supposed
  that the filaments of water which graze along the sides of the pipe
  lose a portion of their velocity; that the contiguous filaments,
  having on this account a greater velocity, rub upon the former, and
  suffer a diminution of their celerity; and that the other filaments
  are affected with similar retardations proportional to their distance
  from the axis of the pipe. In this way the medium velocity of the
  current may be diminished, and consequently the quantity of water
  discharged in a given time must, from the effects of friction, be
  considerably less than that which is computed from theory.

  The effects of friction and viscosity in diminishing the velocity of
  running water were noticed in the _Principia_ of Sir Isaac Newton, who
  threw much light upon several branches of hydromechanics. At a time
  when the Cartesian system of vortices universally prevailed, he found
  it necessary to investigate that hypothesis, and in the course of his
  investigations he showed that the velocity of any stratum of the
  vortex is an arithmetical mean between the velocities of the strata
  which enclose it; and from this it evidently follows that the velocity
  of a filament of water moving in a pipe is an arithmetical mean
  between the velocities of the filaments which surround it. Taking
  advantage of these results, Henri Pitot (1695-1771) afterwards showed
  that the retardations arising from friction are inversely as the
  diameters of the pipes in which the fluid moves. The attention of
  Newton was also directed to the discharge of water from orifices in
  the bottom of vessels. He supposed a cylindrical vessel full of water
  to be perforated in its bottom with a small hole by which the water
  escaped, and the vessel to be supplied with water in such a manner
  that it always remained full at the same height. He then supposed this
  cylindrical column of water to be divided into two parts,--the first,
  which he called the "cataract," being an hyperboloid generated by the
  revolution of an hyperbola of the fifth degree around the axis of the
  cylinder which should pass through the orifice, and the second the
  remainder of the water in the cylindrical vessel. He considered the
  horizontal strata of this hyperboloid as always in motion, while the
  remainder of the water was in a state of rest, and imagined that there
  was a kind of cataract in the middle of the fluid. When the results of
  this theory were compared with the quantity of water actually
  discharged, Newton concluded that the velocity with which the water
  issued from the orifice was equal to that which a falling body would
  receive by descending through half the height of water in the
  reservoir. This conclusion, however, is absolutely irreconcilable with
  the known fact that jets of water rise nearly to the same height as
  their reservoirs, and Newton seems to have been aware of this
  objection. Accordingly, in the second edition of his _Principia_,
  which appeared in 1713, he reconsidered his theory. He had discovered
  a contraction in the vein of fluid (_vena contracta_) which issued
  from the orifice, and found that, at the distance of about a diameter
  of the aperture, the section of the vein was contracted in the
  subduplicate ratio of two to one. He regarded, therefore, the section
  of the contracted vein as the true orifice from which the discharge of
  water ought to be deduced, and the velocity of the effluent water as
  due to the whole height of water in the reservoir; and by this means
  his theory became more conformable to the results of experience,
  though still open to serious objections. Newton was also the first to
  investigate the difficult subject of the motion of waves (q.v.).

  In 1738 Daniel Bernoulli (1700-1782) published his _Hydrodynamica seu
  de viribus et motibus fluidorum commentarii_. His theory of the motion
  of fluids, the germ of which was first published in his memoir
  entitled _Theoria nova de motu aquarum per canales quocunque
  fluentes_, communicated to the Academy of St Petersburg as early as
  1726, was founded on two suppositions, which appeared to him
  conformable to experience. He supposed that the surface of the fluid,
  contained in a vessel which is emptying itself by an orifice, remains
  always horizontal; and, if the fluid mass is conceived to be divided
  into an infinite number of horizontal strata of the same bulk, that
  these strata remain contiguous to each other, and that all their
  points descend vertically, with velocities inversely proportional to
  their breadth, or to the horizontal sections of the reservoir. In
  order to determine the motion of each stratum, he employed the
  principle of the _conservatio virium vivarum_, and obtained very
  elegant solutions. But in the absence of a general demonstration of
  that principle, his results did not command the confidence which they
  would otherwise have deserved, and it became desirable to have a
  theory more certain, and depending solely on the fundamental laws of
  mechanics. Colin Maclaurin (1698-1746) and John Bernoulli (1667-1748),
  who were of this opinion, resolved the problem by more direct methods,
  the one in his _Fluxions_, published in 1742, and the other in his
  _Hydraulica nunc primum detecta, et demonstrata directe ex fundamentis
  pure mechanicis_, which forms the fourth volume of his works. The
  method employed by Maclaurin has been thought not sufficiently
  rigorous; and that of John Bernoulli is, in the opinion of Lagrange,
  defective in clearness and precision. The theory of Daniel Bernoulli
  was opposed also by Jean le Rond d'Alembert. When generalizing the
  theory of pendulums of Jacob Bernoulli (1654-1705) he discovered a
  principle of dynamics so simple and general that it reduced the laws
  of the motions of bodies to that of their equilibrium. He applied this
  principle to the motion of fluids, and gave a specimen of its
  application at the end of his _Dynamics_ in 1743. It was more fully
  developed in his _Traité des fluides_, published in 1744, in which he
  gave simple and elegant solutions of problems relating to the
  equilibrium and motion of fluids. He made use of the same suppositions
  as Daniel Bernoulli, though his calculus was established in a very
  different manner. He considered, at every instant, the actual motion
  of a stratum as composed of a motion which it had in the preceding
  instant and of a motion which it had lost; and the laws of equilibrium
  between the motions lost furnished him with equations representing the
  motion of the fluid. It remained a desideratum to express by equations
  the motion of a particle of the fluid in any assigned direction. These
  equations were found by d'Alembert from two principles--that a
  rectangular canal, taken in a mass of fluid in equilibrium, is itself
  in equilibrium, and that a portion of the fluid, in passing from one
  place to another, preserves the same volume when the fluid is
  incompressible, or dilates itself according to a given law when the
  fluid is elastic. His ingenious method, published in 1752, in his
  _Essai sur la résistance des fluides_, was brought to perfection in
  his _Opuscules mathématiques_, and was adopted by Leonhard Euler.

  The resolution of the questions concerning the motion of fluids was
  effected by means of Euler's partial differential coefficients. This
  calculus was first applied to the motion of water by d'Alembert, and
  enabled both him and Euler to represent the theory of fluids in
  formulae restricted by no particular hypothesis.

  One of the most successful labourers in the science of hydrodynamics
  at this period was Pierre Louis Georges Dubuat (1734-1809). Following
  in the steps of the Abbé Charles Bossut (_Nouvelles Experiences sur la
  résistance des fluides_, 1777), he published, in 1786, a revised
  edition of his _Principes d'hydraulique_, which contains a
  satisfactory theory of the motion of fluids, founded solely upon
  experiments. Dubuat considered that if water were a perfect fluid, and
  the channels in which it flowed infinitely smooth, its motion would be
  continually accelerated, like that of bodies descending in an inclined
  plane. But as the motion of rivers is not continually accelerated, and
  soon arrives at a state of uniformity, it is evident that the
  viscosity of the water, and the friction of the channel in which it
  descends, must equal the accelerating force. Dubuat, therefore,
  assumed it as a proposition of fundamental importance that, when water
  flows in any channel or bed, the accelerating force which obliges it
  to move is equal to the sum of all the resistances which it meets
  with, whether they arise from its own viscosity or from the friction
  of its bed. This principle was employed by him in the first edition of
  his work, which appeared in 1779. The theory contained in that edition
  was founded on the experiments of others, but he soon saw that a
  theory so new, and leading to results so different from the ordinary
  theory, should be founded on new experiments more direct than the
  former, and he was employed in the performance of these from 1780 to
  1783. The experiments of Bossut were made only on pipes of a moderate
  declivity, but Dubuat used declivities of every kind, and made his
  experiments upon channels of various sizes.

  The theory of running water was greatly advanced by the researches of
  Gaspard Riche de Prony (1755-1839). From a collection of the best
  experiments by previous workers he selected eighty-two (fifty-one on
  the velocity of water in conduit pipes, and thirty-one on its velocity
  in open canals); and, discussing these on physical and mechanical
  principles, he succeeded in drawing up general formulae, which
  afforded a simple expression for the velocity of running water.

  J. A. Eytelwein (1764-1848) of Berlin, who published in 1801 a
  valuable compendium of hydraulics entitled _Handbuch der Mechanik und
  der Hydraulik_, investigated the subject of the discharge of water by
  compound pipes, the motions of jets and their impulses against plane
  and oblique surfaces; and he showed theoretically that a water-wheel
  will have its maximum effect when its circumference moves with half
  the velocity of the stream.

  J. N. P. Hachette (1769-1834) in 1816-1817 published memoirs
  containing the results of experiments on the spouting of fluids and
  the discharge of vessels. His object was to measure the contracted
  part of a fluid vein, to examine the phenomena attendant on additional
  tubes, and to investigate the form of the fluid vein and the results
  obtained when different forms of orifices are employed. Extensive
  experiments on the discharge of water from orifices (_Expériences
  hydrauliques_, Paris, 1832) were conducted under the direction of the
  French government by J. V. Poncelet (1788-1867) and J. A. Lesbros
  (1790-1860). P. P. Boileau (1811-1891) discussed their results and
  added experiments of his own (_Traité de la mésure des eaux
  courantes_, Paris, 1854). K. R. Bornemann re-examined all these
  results with great care, and gave formulae expressing the variation of
  the coefficients of discharge in different conditions (_Civil
  Ingénieur_, 1880). Julius Weisbach (1806-1871) also made many
  experimental investigations on the discharge of fluids. The
  experiments of J. B. Francis (_Lowell Hydraulic Experiments_, Boston,
  Mass., 1855) led him to propose variations in the accepted formulae
  for the discharge over weirs, and a generation later a very complete
  investigation of this subject was carried out by H. Bazin. An
  elaborate inquiry on the flow of water in pipes and channels was
  conducted by H. G. P. Darcy (1803-1858) and continued by H. Bazin, at
  the expense of the French government (_Recherches hydrauliques_,
  Paris, 1866). German engineers have also devoted special attention to
  the measurement of the flow in rivers; the _Beiträge zur Hydrographie
  des Königreiches Böhmen_ (Prague, 1872-1875) of A. R. Harlacher
  (1842-1890) contained valuable measurements of this kind, together
  with a comparison of the experimental results with the formulae of
  flow that had been proposed up to the date of its publication, and
  important data were yielded by the gaugings of the Mississippi made
  for the United States government by A. A. Humphreys and H. L. Abbot,
  by Robert Gordon's gaugings of the Irrawaddy, and by Allen J. C.
  Cunningham's experiments on the Ganges canal. The friction of water,
  investigated for slow speeds by Coulomb, was measured for higher
  speeds by William Froude (1810-1879), whose work is of great value in
  the theory of ship resistance (_Brit. Assoc. Report._, 1869), and
  stream line motion was studied by Professor Osborne Reynolds and by
  Professor H. S. Hele Shaw.     (X.)


HYDROSTATICS

Hydrostatics is a science which grew originally out of a number of
isolated practical problems; but it satisfies the requirement of perfect
accuracy in its application to phenomena, the largest and smallest, of
the behaviour of a fluid. At the same time, it delights the pure
theorist by the simplicity of the logic with which the fundamental
theorems may be established, and by the elegance of its mathematical
operations, insomuch that hydrostatics may be considered as the
Euclidean pure geometry of mechanical science.

1. _The Different States of a Substance or Matter._--All substance in
nature falls into one of the two classes, solid and fluid; a solid
substance, the land, for instance, as contrasted with a fluid, like
water, being a substance which does not flow of itself.

A _fluid_, as the name implies, is a substance which flows, or is
capable of flowing; water and air are the two fluids distributed most
universally over the surface of the earth.

Fluids again are divided into two classes, termed a liquid and a gas, of
which water and air are the chief examples.

A _liquid_ is a fluid which is incompressible or practically so, i.e. it
does not change in volume sensibly with change of pressure.

A _gas_ is a compressible fluid, and the change in volume is
considerable with moderate variation of pressure.

Liquids, again, can be poured from one open vessel into another, and can
be kept in an uncovered vessel, but a gas tends to diffuse itself
indefinitely and must be preserved in a closed reservoir.

The distinguishing characteristics of the three kinds of substance or
states of matter, the solid, liquid and gas, are summarized thus in O.
Lodge's _Mechanics_:--

  A solid has both size and shape.
  A liquid has size but not shape.
  A gas has neither size nor shape.

2. _The Change of State of Matter._--By a change of temperature and
pressure combined, a substance can in general be made to pass from one
state into another; thus by gradually increasing the temperature a solid
piece of ice can be melted into the liquid state of water, and the water
again can be boiled off into the gaseous state as steam. Again, by
raising the temperature, a metal in the solid state can be melted and
liquefied, and poured into a mould to assume any form desired, which is
retained when the metal cools and solidifies again; the gaseous state of
a metal is revealed by the spectroscope. Conversely, a combination of
increased pressure and lowering of temperature will, if carried far
enough, reduce a gas to a liquid, and afterwards to the solid state; and
nearly every gaseous substance has now undergone this operation.

A certain critical temperature is observed in a gas, above which the
liquefaction is impossible; so that the gaseous state has two
subdivisions into (i.) a true gas, which cannot be liquefied, because
its temperature is above the critical temperature, (ii.) a vapour, where
the temperature is below the critical, and which can ultimately be
liquefied by further lowering of temperature or increase of pressure.

3. _Plasticity and Viscosity._--Every solid substance is found to be
plastic more or less, as exemplified by punching, shearing and cutting;
but the plastic solid is distinguished from the viscous fluid in that a
plastic solid requires a certain magnitude of stress to be exceeded to
make it flow, whereas the viscous liquid will yield to the slightest
stress, but requires a certain length of time for the effect to be
appreciable.

According to Maxwell (_Theory of Heat_) "When a continuous alteration of
form is produced only by a stress exceeding a certain value, the
substance is called a solid, however soft and plastic it may be. But
when the smallest stress, if only continued long enough, will cause a
perceptible and increasing change of form, the substance must be
regarded as a viscous fluid, however hard it may be." Maxwell
illustrates the difference between a soft solid and a hard liquid by a
jelly and a block of pitch; also by the experiment of supporting a
candle and a stick of sealing-wax; after a considerable time the
sealing-wax will be found bent and so is a fluid, but the candle remains
straight as a solid.

4. _Definition of a Fluid._--A fluid is a substance which yields
continually to the slightest tangential stress in its interior; that is,
it can be divided very easily along any plane (given plenty of time if
the fluid is viscous). It follows that when the fluid has come to rest,
the tangential stress in any plane in its interior must vanish, and the
stress must be entirely normal to the plane. This mechanical axiom of
the _normality of fluid pressure_ is the foundation of the mathematical
theory of hydrostatics.

The theorems of hydrostatics are thus true for all stationary fluids,
however viscous they may be; it is only when we come to hydrodynamics,
the science of the motion of a fluid, that viscosity will make itself
felt and modify the theory; unless we begin by postulating the perfect
fluid, devoid of viscosity, so that the principle of the _normality of
fluid pressure_ is taken to hold when the fluid is in movement.

  5. _The Measurement of Fluid Pressure._--The pressure at any point of
  a plane in the interior of a fluid is the intensity of the normal
  thrust estimated per unit area of the plane.

  Thus, if a thrust of P lb. is distributed uniformly over a plane area
  of A sq. ft., as on the horizontal bottom of the sea or any reservoir,
  the pressure at any point of the plane is P/A lb. per sq. ft., or
  P/144A lb. per sq. in. (lb./ft.² and lb./in.², in the Hospitalier
  notation, to be employed in the sequel). If the distribution of the
  thrust is not uniform, as, for instance, on a vertical or inclined
  face or wall of a reservoir, then P/A represents the average pressure
  over the area; and the actual pressure at any point is the average
  pressure over a small area enclosing the point. Thus, if a thrust
  [Delta]P lb. acts on a small plane area [Delta]A ft.² enclosing a
  point B, the pressure p at B is the limit of [Delta]P/[Delta]A; and

    p = lt([Delta]P/[Delta]A) = dP/dA,   (1)

  in the notation of the differential calculus.

  6. _The Equality of Fluid Pressure in all Directions._--This
  fundamental principle of hydrostatics follows at once from the
  principle of the normality of fluid pressure implied in the definition
  of a fluid in § 4. Take any two arbitrary directions in the plane of
  the paper, and draw a small isosceles triangle abc, whose sides are
  perpendicular to the two directions, and consider the equilibrium of a
  small triangular prism of fluid, of which the triangle is the cross
  section. Let P, Q denote the normal thrust across the sides bc, ca,
  and R the normal thrust across the base ab. Then, since these three
  forces maintain equilibrium, and R makes equal angles with P and Q,
  therefore P and Q must be equal. But the faces bc, ca, over which P
  and Q act, are also equal, so that the pressure on each face is equal.
  A scalene triangle abc might also be employed, or a tetrahedron.

  [Illustration: FIG. 1a.]

  It follows that the pressure of a fluid requires to be calculated in
  one direction only, chosen as the simplest direction for convenience.

  7. _The Transmissibility of Fluid Pressure._--Any additional pressure
  applied to the fluid will be transmitted equally to every point in the
  case of a liquid; this principle of the _transmissibility of pressure_
  was enunciated by Pascal, 1653, and applied by him to the invention of
  the _hydraulic press_.

  This machine consists essentially of two communicating cylinders (fig.
  1a), filled with liquid and closed by pistons. If a thrust P lb. is
  applied to one piston of area A ft.², it will be balanced by a thrust
  W lb. applied to the other piston of area B ft.², where

    p = P/A = W/B,   (1)

  the pressure p of the liquid being supposed uniform; and, by making
  the ratio B/A sufficiently large, the mechanical advantage can be
  increased to any desired amount, and in the simplest manner possible,
  without the intervention of levers and machinery.

  Fig. 1b shows also a modern form of the hydraulic press, applied to
  the operation of covering an electric cable with a lead coating.

  8. _Theorem._--In a fluid at rest under gravity the pressure is the
  same at any two points in the same horizontal plane; in other words, a
  surface of equal pressure is a horizontal plane.

  This is proved by taking any two points A and B at the same level, and
  considering the equilibrium of a thin prism of liquid AB, bounded by
  planes at A and B perpendicular to AB. As gravity and the fluid
  pressure on the sides of the prism act at right angles to AB, the
  equilibrium requires the equality of thrust on the ends A and B; and
  as the areas are equal, the pressure must be equal at A and B; and so
  the pressure is the same at all points in the same horizontal plane.
  If the fluid is a liquid, it can have a free surface without diffusing
  itself, as a gas would; and this free surface, being a surface of zero
  pressure, or more generally of uniform atmospheric pressure, will also
  be a surface of equal pressure, and therefore a horizontal plane.

  [Illustration: FIG. 1b.]

  Hence the _theorem_.--The free surface of a liquid at rest under
  gravity is a horizontal plane. This is the characteristic
  distinguishing between a solid and a liquid; as, for instance, between
  land and water. The land has hills and valleys, but the surface of
  water at rest is a horizontal plane; and if disturbed the surface
  moves in waves.

  9. _Theorem._--In a homogeneous liquid at rest under gravity the
  pressure increases uniformly with the depth.

  This is proved by taking the two points A and B in the same vertical
  line, and considering the equilibrium of the prism by resolving
  vertically. In this case the thrust at the lower end B must exceed the
  thrust at A, the upper end, by the weight of the prism of liquid; so
  that, denoting the cross section of the prism by [alpha] ft.², the
  pressure at A and By by p0 and p lb./ft.², and by w the density of the
  liquid estimated in lb./ft.³,

    p[alpha] - p0[alpha] = w[alpha]·AB,   (1)

    p = w·AB + p0.   (2)

  Thus in water, where w = 62.4lb./ft.³, the pressure increases 62.4
  lb./ft.², or 62.4 ÷ 144 = 0.433 lb./in.² for every additional foot of
  depth.

  10. _Theorem._--If two liquids of different density are resting in
  vessels in communication, the height of the free surface of such
  liquid above the surface of separation is inversely as the density.

  For if the liquid of density [sigma] rises to the height h and of
  density [rho] to the height k, and p0 denotes the atmospheric
  pressure, the pressure in the liquid at the level of the surface of
  separation will be [sigma]h + p0 and [rho]k + p0, and these being
  equal we have

    [sigma]h = [rho]k.   (1)

  The principle is illustrated in the article BAROMETER, where a column
  of mercury of density [sigma] and height h, rising in the tube to the
  Torricellian vacuum, is balanced by a column of air of density [rho],
  which may be supposed to rise as a homogeneous fluid to a height k,
  called the height of the homogeneous atmosphere. Thus water being
  about 800 times denser than air and mercury 13.6 times denser than
  water,

    k/h = [sigma]/[rho] = 800 × 13.6 = 10,880;   (2)

  and with an average barometer height of 30 in. this makes k 27,200
  ft., about 8300 metres.

  11. _The Head of Water or a Liquid._--The pressure [sigma]h at a depth
  h ft. in liquid of density [sigma] is called the pressure due to a
  _head_ of h ft. of the liquid. The atmospheric pressure is thus due to
  an average head of 30 in. of mercury, or 30 × 13.6 ÷ 12 = 34 ft. of
  water, or 27,200 ft. of air. The pressure of the air is a convenient
  unit to employ in practical work, where it is called an "atmosphere";
  it is made the equivalent of a pressure of one kg/cm²; and one
  ton/inch², employed as the unit with high pressure as in artillery,
  may be taken as 150 atmospheres.

  12. _Theorem._--A body immersed in a fluid is buoyed up by a force
  equal to the weight of the liquid displaced, acting vertically upward
  through the centre of gravity of the displaced liquid.

  For if the body is removed, and replaced by the fluid as at first,
  this fluid is in equilibrium under its own weight and the thrust of
  the surrounding fluid, which must be equal and opposite, and the
  surrounding fluid acts in the same manner when the body replaces the
  displaced fluid again; so that the resultant thrust of the fluid acts
  vertically upward through the centre of gravity of the fluid
  displaced, and is equal to the weight.

  When the body is floating freely like a ship, the equilibrium of this
  liquid thrust with the weight of the ship requires that the weight of
  water displaced is equal to the weight of the ship and the two centres
  of gravity are in the same vertical line. So also a balloon begins to
  rise when the weight of air displaced is greater than the weight of
  the balloon, and it is in equilibrium when the weights are equal. This
  theorem is called generally the _principle of Archimedes_.

  It is used to determine the density of a body experimentally; for if W
  is the weight of a body weighed in a balance in air (strictly _in
  vacuo_), and if W´ is the weight required to balance when the body is
  suspended in water, then the upward thrust of the liquid or weight of
  liquid displaced is W - W´, so that the _specific gravity_ (S.G.),
  defined as the ratio of the weight of a body to the weight of an equal
  volume of water, is W/(W - W´).

  As stated first by Archimedes, the principle asserts the obvious fact
  that a body displaces its own volume of water; and he utilized it in
  the problem of the determination of the adulteration of the crown of
  Hiero. He weighed out a lump of gold and of silver of the same weight
  as the crown; and, immersing the three in succession in water, he
  found they spilt over measures of water in the ratio 1/14 : 4/77 :
  2/21 or 33 : 24 : 44; thence it follows that the gold : silver alloy
  of the crown was as 11 : 9 by weight.

  13. _Theorem._--The resultant vertical thrust on any portion of a
  curved surface exposed to the pressure of a fluid at rest under
  gravity is the weight of fluid cut out by vertical lines drawn round
  the boundary of the curved surface.

  _Theorem._--The resultant horizontal thrust in any direction is
  obtained by drawing parallel horizontal lines round the boundary, and
  intersecting a plane perpendicular to their direction in a plane
  curve; and then investigating the thrust on this plane area, which
  will be the same as on the curved surface.

  The proof of these theorems proceeds as before, employing the
  normality principle; they are required, for instance, in the
  determination of the liquid thrust on any portion of the bottom of a
  ship.

  In casting a thin hollow object like a bell, it will be seen that the
  resultant upward thrust on the mould may be many times greater than
  the weight of metal; many a curious experiment has been devised to
  illustrate this property and classed as a hydrostatic paradox (Boyle,
  _Hydrostatical Paradoxes_, 1666).

  [Illustration: FIG. 2.]

  Consider, for instance, the operation of casting a hemispherical bell,
  in fig. 2. As the molten metal is run in, the upward thrust on the
  outside mould, when the level has reached PP´, is the weight of metal
  in the volume generated by the revolution of APQ; and this, by a
  theorem of Archimedes, has the same volume as the cone ORR´, or 1/3
  [pi]y³, where y is the depth of metal, the horizontal sections being
  equal so long as y is less than the radius of the outside hemisphere.
  Afterwards, when the metal has risen above B, to the level KK´, the
  additional thrust is the weight of the cylinder of diameter KK´ and
  height BH. The upward thrust is the same, however thin the metal may
  be in the interspace between the outer mould and the core inside; and
  this was formerly considered paradoxical.

  _Analytical Equations of Equilibrium of a Fluid at rest under any
  System of Force._

  14. Referred to three fixed coordinate axes, a fluid, in which the
  pressure is p, the density [rho], and X, Y, Z the components of
  impressed force per unit mass, requires for the equilibrium of the
  part filling a fixed surface S, on resolving parallel to Ox,
      _  _         _  _  _
     /  /         /  /  /
     |  | lp dS = |  |  | [rho]X dx dy dz,   (1)
    _/ _/        _/ _/ _/

  where l, m, n denote the direction cosines of the normal drawn outward
  of the surface S.

  But by Green's transformation
      _  _         _  _  _
     /  /         /  /  / dp
     |  | lp dS = |  |  | -- dx dy dz,   (2)
    _/ _/        _/ _/ _/ dx

  thus leading to the differential relation at every point

    dp           dp           dp
    -- = [rho]X, -- = [rho]Y, -- = [rho]Z.   (3)
    dx           dy           dz

  The three equations of equilibrium obtained by taking moments round
  the axes are then found to be satisfied identically.

  Hence the space variation of the pressure in any direction, or the
  _pressure-gradient_, is the resolved force per unit volume in that
  direction. The resultant force is therefore in the direction of the
  steepest pressure-gradient, and this is normal to the surface of equal
  pressure; for equilibrium to exist in a fluid the lines of force must
  therefore be capable of being cut orthogonally by a system of
  surfaces, which will be surfaces of equal pressure.

  Ignoring temperature effect, and taking the density as a function of
  the pressure, surfaces of equal pressure are also of equal density,
  and the fluid is stratified by surfaces orthogonal to the lines of
  force;

      1   dp    1   dp    1   dp
    ----- --, ----- --, ----- --, or X, Y, Z   (4)
    [rho] dx  [rho] dy  [rho] dz

  are the partial differential coefficients of some function P, =
  [int]dp/[rho], of x, y, z; so that X, Y, Z must be the partial
  differential coefficients of a potential -V, such that the force in
  any direction is the downward gradient of V; and then

    dP   dV
    -- + -- = 0, or P + V = constant,   (5)
    dx   dx

  in which P may be called the hydrostatic head and V the head of
  potential.

  With variation of temperature, the surfaces of equal pressure and
  density need not coincide; but, taking the pressure, density and
  temperature as connected by some relation, such as the gas-equation,
  the surfaces of equal density and temperature must intersect in lines
  lying on a surface of equal pressure.

  15. As an example of the general equations, take the simplest case of
  a uniform field of gravity, with Oz directed vertically downward;
  employing the gravitation unit of force,

      1   dp        1   dp        1   dp
    ----- -- = 0, ----- -- = 0, ----- -- = 1,  (1)
    [rho] dx      [rho] dy      [rho] dz
         _
        /
    P = | dp/[rho] = z + a constant.   (2)
       _/

  When the density [rho] is uniform, this becomes, as before in (2) § 9

    p = [rho]z + p0.   (3)

  Suppose the density [rho] varies as some nth power of the depth below
  O, then

    dp/dz = [rho] = [mu]z^n   (4)

            z^(n+1)   [rho]z   [rho]  /[rho]\^1/n
    p = [mu]------- = ------ = ----- ( ----- )   ,  (5)
             n + 1     n + 1   n + 1  \[mu] /

  supposing p and [rho] to vanish together.

  These equations can be made to represent the state of convective
  equilibrium of the atmosphere, depending on the gas-equation

    p = [rho]k = R[rho][theta],   (6)

  where [theta] denotes the absolute temperature; and then

     d[theta]    d  / p   \      1
    R-------- = -- ( ----- ) = -------,   (7)
        dz      dz  \[rho]/    (n + 1)

  so that the temperature-gradient d[theta]/dz is constant, as in
  convective equilibrium in (11).

  From the gas-equation in general, in the atmosphere

      1   dp    1  dp      1    d[theta]   [rho]      1    d[theta]    1       1    d[theta]
    ----- -- = --- -- - ------- -------- = ----- - ------- -------- = --- - ------- --------,  (8)
    [rho] dz    p  dz   [theta]    dz        p     [theta]    dz       k    [theta]    dz

  which is positive, and the density [rho] diminishes with the ascent,
  provided the temperature-gradient d[theta]/dz does not exceed
  [theta]/k.

  With uniform temperature, taking k constant in the gas-equation,

    dp/dz = [rho] = p/k, p = p0e^(z/k),   (9)

  so that in ascending in the atmosphere of thermal equilibrium the
  pressure and density diminish at compound discount, and for pressures
  p1 and p2 at heights z1 and z2

    (z1 - z2)/k = log e (p2/p1) = 2.3 log10 (p2/p1).   (10)

  In the convective equilibrium of the atmosphere, the air is supposed
  to change in density and pressure without exchange of heat by
  conduction; and then

    [rho]/[rho]0 = ([theta]/[theta]0)^n, p/p0 =
      ([theta]/[theta]0)^(n+1),   (11)

       dz        1      dp                   p                       1
    -------- = ----- -------- = (n + 1)------------R, [gamma] = 1 + ---,
    d[theta]   [rho] d[theta]          [rho][theta]                  n

  where [gamma] is the ratio of the specific heat at constant pressure
  and constant volume.

  In the more general case of the convective equilibrium of a spherical
  atmosphere surrounding the earth, of radius a,

      dp             p0   d[theta]      a²
    ----- = (n + 1)------ -------- = - --- dr,   (12)
    [rho]          [rho]0 [theta]0      r²

  gravity varying inversely as the square of the distance r from the
  centre; so that, k = p0/[rho]0, denoting the height of the homogeneous
  atmosphere at the surface, [theta] is given by

    (n + 1) k (1 - [theta]/[theta]0) = a(1 - a/r),   (13)

  or if c denotes the distance where [theta] = 0,

    [theta]     a    c - r
    -------- = --- · -----.   (14)
    [theta]0    r    c - a

  When the compressibility of water is taken into account in a deep
  ocean, an experimental law must be employed, such as

    p - p0 = k([rho] - [rho]0), or [rho]/[rho]0 = 1
      + (p - p0)/[lambda], [lambda] = k[rho]0, (15)

  so that [lambda] is the pressure due to a head k of the liquid at
  density [rho]0 under atmospheric pressure p0; and it is the gauge
  pressure required on this law to double the density. Then

    dp/dz = kd[rho]/dz = [rho], [rho] = [rho]0e^(z/k),
      p - p0 = k[rho]0(e^(z/k) - 1); (16)

  and if the liquid was incompressible, the depth at pressure p would be
  (p - p0)/p0, so that the lowering of the surface due to compression is

    ke^(z/k) - k - z = ½z²/k, when k is large. (17)

  For sea water, [lambda] is about 25,000 atmospheres, and k is then
  25,000 times the height of the water barometer, about 250,000 metres,
  so that in an ocean 10 kilometres deep the level is lowered about 200
  metres by the compressibility of the water; and the density at the
  bottom is increased 4%.

  On another physical assumption of constant cubical elasticity
  [lambda],

    dp = [lambda]d[rho]/[rho], (p - p0)/[lambda] = log([rho]/[rho]0), (18)

    dp   [lambda]  d[rho]                   /  1        1  \           [rho]0    z
    -- = --------  ------ = [rho], [lambda]( ------ - ----- ) = z, 1 - ------ = ---, [lambda] = k[rho]0,  (19)
    zd    [rho]      dz                     \[rho]0   [rho]/            [rho]    k

  and the lowering of the surface is

    p - p0             [rho]               /     z \                z²
    ------ - z = k log ------ - z = k log ( 1 - --- ) - z [approx] ---  (20)
    [rho]0             [rho]0              \     k /                2k

  as before in (17).

  16. _Centre of Pressure._--A plane area exposed to fluid pressure on
  one side experiences a single resultant thrust, the integrated
  pressure over the area, acting through a definite point called the
  centre of pressure (C.P.) of the area.

  Thus if the plane is normal to Oz, the resultant thrust
         _ _
        / /
    R = | |pdxdy,   (1)
       _/_/

  and the coordinates [=x], [=y] of the C.P. are given by
             _ _                   _ _
            / /                   / /
    [=x]R = | | xp dx dy, [=y]R = | | yp dx dy.   (2)
           _/_/                  _/_/

  The C·P. is thus the C·G. of a plane lamina bounded by the area, in
  which the surface density is p.

  If p is uniform, the C·P. and C·G. of the area coincide.

  For a homogeneous liquid at rest under gravity, p is proportional to
  the depth below the surface, i.e. to the perpendicular distance from
  the line of intersection of the plane of the area with the free
  surface of the liquid.

  If the equation of this line, referred to new coordinate axes in the
  plane area, is written

  x cos [alpha] + y sin [alpha] - h = 0,   (3)
         _ _
        / /
    R = | | [rho](h - x cos [alpha] - y sin [alpha]) dx dy,   (4)
       _/_/
             _ _
            / /
    [=x]R = | | [rho]x(h - x cos [alpha] - y sin [alpha]) dx dy,   (5)
           _/_/
             _ _
            / /
    [=y]R = | | [rho]y(h - x cos [alpha] - y sin [alpha]) dx dy.
           _/_/

  Placing the new origin at the C.G. of the area A,
      _ _              _ _
     / /              / /
     | | xd x dy = 0, | | y dx dy = 0,   (6)
    _/_/             _/_/

    R = [rho]hA,   (7)
                           _ _                     _ _
                          / /                     / /
    [=x]hA = -cos [alpha] | | x² dA - sin [alpha] | | xy dA,   (8)
                         _/_/                    _/_/
                           _ _                     _ _
                          / /                     / /
    [=y]hA = -cos [alpha] | | xy dA - sin [alpha] | | y² dA.   (9)
                         _/_/                    _/_/

  Turning the axes to make them coincide with the principal axes of the
  area A, thus making [int][int] xy dA = 0,

    [=x]h = -a² cos [alpha], [=y]h = -b² sin [alpha],   (10)

  where
      _ _              _ _
     / /              / /
     | | x² dA = Aa², | | y² dA = Ab²,   (11)
    _/_/             _/_/

  a and b denoting the semi-axes of the momental ellipse of the area.

  This shows that the C.P. is the antipole of the line of intersection
  of its plane with the free surface with respect to the momental
  ellipse at the C.G. of the area.

  Thus the C.P. of a rectangle or parallelogram with a side in the
  surface is at 2/3 of the depth of the lower side; of a triangle with a
  vertex in the surface and base horizontal is ¾ of the depth of the
  base; but if the base is in the surface, the C·P. is at half the depth
  of the vertex; as on the faces of a tetrahedron, with one edge in the
  surface.

  The _core_ of an area is the name given to the limited area round its
  C.G. within which the C·P. must lie when the area is immersed
  completely; the boundary of the core is therefore the locus of the
  antipodes with respect to the momental ellipse of water lines which
  touch the boundary of the area. Thus the core of a circle or an
  ellipse is a concentric circle or ellipse of one quarter the size.

  The C.P. of water lines passing through a fixed point lies on a
  straight line, the antipolar of the point; and thus the core of a
  triangle is a similar triangle of one quarter the size, and the core
  of a parallelogram is another parallelogram, the diagonals of which
  are the middle third of the median lines.

  In the design of a structure such as a tall reservoir dam it is
  important that the line of thrust in the material should pass inside
  the core of a section, so that the material should not be in a state
  of tension anywhere and so liable to open and admit the water.

[Illustration: FIG. 3.]

17. _Equilibrium and Stability of a Ship or Floating Body. The
Metacentre._--The principle of Archimedes in § 12 leads immediately to
the conditions of equilibrium of a body supported freely in fluid, like
a fish in water or a balloon in the air, or like a ship (fig. 3)
floating partly immersed in water and the rest in air. The body is in
equilibrium under two forces:--(i.) its weight W acting vertically
downward through G, the C.G. of the body, and (ii.) the buoyancy of the
fluid, equal to the weight of the displaced fluid, and acting vertically
upward through B, the C.G. of the displaced fluid; for equilibrium these
two forces must be equal and opposite in the same line.

The conditions of equilibrium of a body, floating like a ship on the
surface of a liquid, are therefore:--

(i.) the weight of the body must be less than the weight of the total
volume of liquid it can displace; or else the body will sink to the
bottom of the liquid; the difference of the weights is called the
"reserve of buoyancy."

(ii.) the weight of liquid which the body displaces in the position of
equilibrium is equal to the weight W of the body; and

(iii.) the C.G., B, of the liquid displaced and G of the body, must lie
in the same vertical line GB.

18. In addition to satisfying these conditions of equilibrium, a ship
must fulfil the further condition of stability, so as to keep upright;
if displaced slightly from this position, the forces called into play
must be such as to restore the ship to the upright again. The stability
of a ship is investigated practically by inclining it; a weight is moved
across the deck and the angle is observed of the heel produced.

  Suppose P tons is moved c ft. across the deck of a ship of W tons
  displacement; the C.G. will move from G to G1 the reduced distance
  G1G2 = c(P/W); and if B, called the centre of buoyancy, moves to B1,
  along the curve of buoyancy BB1, the normal of this curve at B1 will
  be the new vertical B1G1, meeting the old vertical in a point M, the
  centre of curvature of BB1, called the _metacentre_.

  If the ship heels through an angle [theta] or a slope of 1 in m,

    GM = GG1cot[theta] = mc(P/W),   (1)

  and GM is called the metacentric height; and the ship must be
  ballasted, so that G lies below M. If G was above M, the tangent drawn
  from G to the evolute of B, and normal to the curve of buoyancy, would
  give the vertical in a new position of equilibrium. Thus in H.M.S.
  "Achilles" of 9000 tons displacement it was found that moving 20 tons
  across the deck, a distance of 42 ft., caused the bob of a pendulum 20
  ft. long to move through 10 in., so that

         240         20
    GM = --- × 42 × ---- = 2.24 ft.;   (2)
          10        9000

  also

    cot [theta] = 24, [theta] = 2°24´.   (3)

  In a diagram it is conducive to clearness to draw the ship in one
  position, and to incline the water-line; and the page can be turned if
  it is desired to bring the new water-line horizontal.

  Suppose the ship turns about an axis through F in the water-line area,
  perpendicular to the plane of the paper; denoting by y the distance of
  an element dA if the water-line area from the axis of rotation, the
  change of displacement is [sum]ydA tan[theta], so that there is no
  change of displacement if [sum]ydA = 0, that is, if the axis passes
  through the C.G. of the water-line area, which we denote by F and call
  the centre of flotation.

  The righting couple of the wedges of immersion and emersion will be

    [Sigma]wy dA tan [theta]·y = w tan [theta] [Sigma] y² dA
      = w tan [theta]·Ak² ft. tons,   (4)

  w denoting the density of water in tons/ft.³, and W = wV, for a
  displacement of V ft.³

  This couple, combined with the original buoyancy W through B, is
  equivalent to the new buoyancy through B, so that

    W.BB1 = wAk² tan [theta],   (5)

    BM = BB1 cot [theta] = Ak²/V,   (6)

  giving the radius of curvature BM of the curve of buoyancy B, in terms
  of the displacement V, and Ak² the moment of inertia of the water-line
  area about an axis through F, perpendicular to the plane of
  displacement.

  An inclining couple due to moving a weight about in a ship will heel
  the ship about an axis perpendicular to the plane of the couple, only
  when this axis is a principal axis at F of the momental ellipse of the
  water-line area A. For if the ship turns through a small angle [theta]
  about the line FF´, then b1, b2, the C·G. of the wedge of immersion
  and emersion, will be the C·P. with respect to FF´ of the two parts of
  the water-line area, so that b1b2 will be conjugate to FF´ with
  respect to the momental ellipse at F.

  The naval architect distinguishes between the _stability of form_,
  represented by the righting couple W.BM, and the _stability of
  ballasting_, represented by W.BG. Ballasted with G at B, the righting
  couple when the ship is heeled through [theta] is given by W.BM.
  tan[theta]; but if weights inside the ship are raised to bring G above
  B, the righting couple is diminished by W.BG.tan[theta], so that the
  resultant righting couple is W·GM·tan[theta]. Provided the ship is
  designed to float upright at the smallest draft with no load on board,
  the stability at any other draft of water can be arranged by the
  stowage of the weight, high or low.

  19. Proceeding as in § 16 for the determination of the C.P. of an
  area, the same argument will show that an inclining couple due to the
  movement of a weight P through a distance c will cause the ship to
  heel through an angle [theta] about an axis FF´ through F, which is
  conjugate to the direction of the movement of P with respect to an
  ellipse, not the momental ellipse of the water-line area A, but a
  confocal to it, of squared semi-axes

    a² - hV/A, b² - hV/A,   (1)

  h denoting the vertical height BG between C.G. and centre of buoyancy.
  The varying direction of the inclining couple Pc may be realized by
  swinging the weight P from a crane on the ship, in a circle of radius
  c. But if the weight P was lowered on the ship from a crane on shore,
  the vessel would sink bodily a distance P/wA if P was deposited over
  F; but deposited anywhere else, say over Q on the water-line area, the
  ship would turn about a line the antipolar of Q with respect to the
  confocal ellipse, parallel to FF´, at a distance FK from F

    FK = (k² - hV/A)/FQ sin QFF´   (2)

  through an angle [theta] or a slope of one in m, given by

                   1      P      P        V
    sin [theta] = --- = ----- = --- · -------- FQ sin QFF´,   (3)
                   m    wA·FK    W    Ak² - hV

  where k denotes the radius of gyration about FF´ of the water-line
  area. Burning the coal on a voyage has the reverse effect on a
  steamer.


HYDRODYNAMICS

20. In considering the motion of a fluid we shall suppose it
non-viscous, so that whatever the state of motion the stress across any
section is normal, and the principle of the normality and thence of the
equality of fluid pressure can be employed, as in hydrostatics. The
practical problems of fluid motion, which are amenable to mathematical
analysis when viscosity is taken into account, are excluded from
treatment here, as constituting a separate branch called "hydraulics"
(q.v.). Two methods are employed in hydrodynamics, called the Eulerian
and Lagrangian, although both are due originally to Leonhard Euler. In
the Eulerian method the attention is fixed on a particular point of
space, and the change is observed there of pressure, density and
velocity, which takes place during the motion; but in the Lagrangian
method we follow up a particle of fluid and observe how it changes. The
first may be called the statistical method, and the second the
historical, according to J. C. Maxwell. The Lagrangian method being
employed rarely, we shall confine ourselves to the Eulerian treatment.


_The Eulerian Form of the Equations of Motion._

21. The first equation to be established is the _equation of
continuity_, which expresses the fact that the increase of matter within
a fixed surface is due to the flow of fluid across the surface into its
interior.

  In a straight uniform current of fluid of density [rho], flowing with
  velocity q, the flow in units of mass per second across a plane area
  A, placed in the current with the normal of the plane making an angle
  [theta] with the velocity, is [rho]Aq cos [theta], the product of the
  density [rho], the area A, and q cos [theta] the component velocity
  normal to the plane.

  Generally if S denotes any closed surface, fixed in the fluid, M the
  mass of the fluid inside it at any time t, and [theta] the angle which
  the outward-drawn normal makes with the velocity q at that point,

    dM/dt = rate of increase of fluid inside the surface,   (1)

          = flux across the surface into the interior
               _ _
              / /
          = - | | [rho]q cos [theta] dS,
             _/_/

  the integral equation of continuity.

  In the Eulerian notation u, v, w denote the components of the velocity
  q parallel to the coordinate axes at any point (x, y, z) at the time
  t; u, v, w are functions of x, y, z, t, the independent variables; and
  d is used here to denote partial differentiation with respect to any
  one of these four independent variables, all capable of varying one at
  a time.

  To transfer the integral equation into the differential equation of
  continuity, Green's transformation is required again, namely,
      _ _ _                                         _ _
     / / /  /d[xi]   d[eta]   d[zeta] \            / /
     | | | ( ----- + ------ + -------  )dx dy dz = | | (l[xi] + m[eta] + n[zeta]) dS,   (2)
    _/_/_/  \  dx      dy        dz   /           _/_/

  or individually
      _ _ _                   _ _
     / / /  d[xi]            / /
     | | |  ----- dx dy dz = | | l[xi] dS,...,   (3)
    _/_/_/   dx             _/_/

  where the integrations extend throughout the volume and over the
  surface of a closed space S; l, m, n denoting the direction cosines of
  the outward-drawn normal at the surface element dS, and [xi], [eta],
  [zeta] any continuous functions of x, y, z.

  The integral equation of continuity (1) may now be written
      _ _ _                   _ _
     / / /  d[rho]           / /
     | | |  ----- dx dy dz = | | (l[rho]u + m[rho]v + n[rho]w) dS = 0,   (4)
    _/_/_/    dt            _/_/

  which becomes by Green's transformation
    _ _ _
   / / /  /d[rho]   d([rho]u)   d([rho]v)   d([rho]w)\
   | | | ( ------ + --------- + --------- + --------  ) dx dy dz = 0,   (5)
  _/_/_/  \  dt        dx          dy          dz    /

  leading to the differential equation of continuity when the
  integration is removed.

22. The equations of motion can be established in a similar way by
considering the rate of increase of momentum in a fixed direction of the
fluid inside the surface, and equating it to the momentum generated by
the force acting throughout the space S, and by the pressure acting over
the surface S.

  Taking the fixed direction parallel to the axis of x, the time-rate of
  increase of momentum, due to the fluid which crosses the surface, is
       _ _                            _ _
      / /                            / /
    - | | [rho]uq cos [theta] dS = - | | (l[rho]u² + m[rho]uv + n[rho]uw) dS,  (1)
     _/_/                           _/_/

  which by Green's transformation is
       _ _ _
      / / /  /d([rho]u²)   d([rho]uv)   d([rho]uw)\
    - | | | (---------- + ---------- + ----------  ) dx dy dz.   (2)
     _/_/_/  \    dx           dy           dz    /

  The rate of generation of momentum in the interior of S by the
  component of force, X per unit mass, is
      _ _ _
     / / /
     | | | [rho]X dx dy dz,   (3)
    _/_/_/

  and by the pressure at the surface S is
       _ _           _ _ _
      / /           / / / dp
    - | | lp dS = - | | | -- dx dy dz,   (4)
     _/_/          _/_/_/ dx

  by Green's transformation.

  The time rate of increase of momentum of the fluid inside S is
      _ _ _
     / / / d([rho]u)
     | | | --------- dx dy dz;   (5)
    _/_/_/    dt

  and (5) is the sum of (1), (2), (3), (4), so that
      _ _ _
     / / /  /d[rho]u   d[rho]u²   d[rho]uv   d[rho]uw            dp \
     | | | ( ------- + -------- + -------- + -------- - [rho]X + --  ) dx dy dz = 0,   (6)
    _/_/_/  \  dt         dx         dy         dz               dx /

  leading to the differential equation of motion

    d[rho]u   d[rho]u²   d[rho]uv,  d[rho]uw            dp
    ------- + -------- + -------- + -------- = [rho]X - --,   (7)
      dt         dx         dy         dz               dx

  with two similar equations.

  The absolute unit of force is employed here, and not the gravitation
  unit of hydrostatics; in a numerical application it is assumed that
  C.G.S. units are intended.

  These equations may be simplified slightly, using the equation of
  continuity (5) § 21; for

    d[rho]u   d[rho]u²   d[rho]uv   d[rho]uw
    ------- + -------- + -------- + --------
      dt         dx         dy         dz

             /du    du    du    du \
    = [rho] ( -- + u-- + v-- + w--  )
             \dt    dx    dy    dz /

         /d[rho]   d[rho]u   d[rho]v   d[rho]w \
    + u ( ------ + ------- + ------- + -------  ),   (8)
         \  dt        dx        dy        dz   /

  reducing to the first line, the second line vanishing in consequence
  of the equation of continuity; and so the equation of motion may be
  written in the more usual form

    du    du    du    du         1   dp
    -- + u-- + v-- + w-- = X - ----- --,   (9)
    dt    dx    dy    dz       [rho] dx

  with the two others

    dv    dv    dv    dv         1   dp
    -- + u-- + v-- + w-- = Y - ----- --,   (10)
    dt    dx    dy    dz       [rho] dy

    dw    dw    dw    dw         1   dp
    -- + u-- + v-- + w-- = Z - ----- --.   (11)
    dt    dx    dy    dz       [rho] dz



23. As a rule these equations are established immediately by determining
the component acceleration of the fluid particle which is passing
through (x, y, z) at the instant t of time considered, and saying that
the reversed acceleration or kinetic reaction, combined with the
impressed force per unit of mass and pressure-gradient, will according
to d'Alembert's principle form a system in equilibrium.

  To determine the component acceleration of a particle, suppose F to
  denote any function of x, y, z, t, and investigate the time rate of F
  for a moving particle; denoting the change by DF/dt,

    DF      F(x + u[delta]t, y + v[delta]t, z + w[delta]t, t + [delta]t) - F(x, y, z, t)
    -- = lt·----------------------------------------------------------------------------
    dt                                       [delta]t

      dF    dF    dF    dF
    = -- + u-- + v-- + w--;   (1)
      dt    dx    dy    dz

  and D/dt is called particle differentiation, because it follows the
  rate of change of a particle as it leaves the point x, y, z; but

    dF/dt, dF/dx, dF/dy, dF/dz   (2)

  represent the rate of change of F at the time t, at the point, x, y,
  z, fixed in space.

  The components of acceleration of a particle of fluid are consequently

    Du   du    du    du    du
    -- = -- + u-- + v-- + w--,   (3)
    dt   dt    dx    dy    dz

    Dv   dv    dv    dv    dv
    -- = -- + u-- + v-- + w--,  (4)
    dt   dt    dx    dy    dz

    Dw   dw    dw    dw    dw
    -- = -- + u-- + v-- + w--,  (5)
    dt   dt    dx    dy    dz

  leading to the equations of motion above.

  If F (x, y, z, t) = 0 represents the equation of a surface containing
  always the same particles of fluid,

    DF         dF    dF    dF    dF
    -- = 0, or -- + u-- + v-- + w-- = 0,   (6)
    dt         dt    dx    dy    dz

  which is called the differential equation of the _bounding surface_. A
  bounding surface is such that there is no flow of fluid across it, as
  expressed by equation (6). The surface always contains the same fluid
  inside it, and condition (6) is satisfied over the complete surface,
  as well as any part of it.

  But turbulence in the motion will vitiate the principle that a
  bounding surface will always consist of the same fluid particles, as
  we see on the surface of turbulent water.

  24. To integrate the equations of motion, suppose the impressed force
  is due to a potential V, such that the force in any direction is the
  rate of diminution of V, or its downward gradient; and then

    X = -dV/dx, Y = -dV/dy, Z = -dV/dz;   (1)

  and putting

    dw   dv          du   dw           dv   du
    -- - -- = 2[xi], -- - -- = 2[eta], -- - -- = 2[zeta],   (2)
    dy   dz          dz   dx           dx   dy

    d[xi]   d[eta]   d[zeta]
    ----- + ------ + ------- = 0,   (3)
     dx       dy       dz

  the equations of motion may be written

    du                        dH
    -- - 2v[zeta] + 2w[eta] + -- = 0,   (4)
    dt                        dx

    dv                       dH
    -- - 2w[xi] + 2u[zeta] + -- = 0,   (5)
    dt                       dy

    dw                      dH
    -- - 2u[eta] + 2w[xi] + -- = 0,   (6)
    dt                      dz

  where
         _
        /
    H = | dp/[rho] + V + ½q²,   (7)
       _/

    q² = u² + v² + w²,   (8)

  and the three terms in H may be called the pressure head, potential
  head, and head of velocity, when the gravitation unit is employed and
  ½q² is replaced by ½q²/g.

  Eliminating H between (5) and (6)

    D[xi]       du        dv         dw        / du   dv   dw \
    ----- - [xi]-- - [eta]-- - [zeta]-- + [xi](  -- + -- + --  ) = 0,   (9)
     dt         dx        dx         dx        \ dx   dy   dz /

  and combining this with the equation of continuity

      1   D[rho]   du   dv   dw
    ----- ------ + -- + -- + -- = 0,   (10)
    [rho]   dt     dx   dy   dz

  we have

     D  /[xi] \    [xi]  du   [eta] dv   [zeta] dw
    -- ( ----- ) - ----- -- - ----- -- - ------ -- = 0,   (11)
    dt  \[rho]/    [rho] dx   [rho] dx   [rho]  dx

  with two similar equations.

  Putting

    [omega]² = [xi]² + [eta]² + [zeta]²,   (12)

  a _vortex line_ is defined to be such that the tangent is in the
  direction of [omega], the resultant of [xi], [eta], [zeta], called the
  components of molecular rotation. A small sphere of the fluid, if
  frozen suddenly, would retain this angular velocity.

  If [omega] vanishes throughout the fluid at any instant, equation (11)
  shows that it will always be zero, and the fluid motion is then called
  _irrotational_; and a function [phi] exists, called the _velocity
  function_, such that

    udx + vdy + wdz = -d[phi],   (13)

  and then the velocity in any direction is the space-decrease or
  downward gradient of [phi].

  25. But in the most general case it is possible to have three
  functions [phi], [psi], m of x, y, z, such that

    udx + vdy + wdz = -d[phi] - md[psi],   (1)

  as A. Clebsch has shown, from purely analytical considerations
  (_Crelle_, lvi.); and then

             d([psi], m)            d([psi], m)             d([psi], m)
    [xi] = ½ -----------, [eta] = ½ -----------, [zeta] = ½ -----------,   (2)
               d(y, z)                d(z, x)                 d(x, y)

  and

        d[psi]        d[psi]         d[psi]          dm        dm         dm
    [xi]------ + [eta]------ + [zeta]------ = 0, [xi]-- + [eta]-- + [zeta]-- = 0,   (3)
          dx            dy             dz            dx        dy         dz

  so that, at any instant, the surfaces over which [psi] and m are
  constant intersect in the vortex lines.

  Putting

         d[phi]     d[psi]
    H -  ------ - m ------ = K,   (4)
           dt         dt
  the equations of motion (4), (5), (6) § 24 can be written

    dK                        d([psi],m)
    -- - 2u[zeta] + 2w[eta] - ---------- = 0, ..., ...;   (5)
    dx                          d(x,t)

  and therefore

        dK        dK         dK
    [xi]-- + [eta]-- + [zeta]-- = 0.   (6)
        dx        dy         dz

  Equation (5) becomes, by a rearrangement,

    dK   d[psi]  /dm    dm    dm    dm \
    -- - ------ ( -- + u-- + v-- + w--  )
    dx     dx    \dt    dx    dy    dz /

        dm  / d[psi]    d[psi]    d[psi]    d[psi] \
      + -- (  ------ + u------ + v------ + w------  ) = 0, ..., ...,   (7)
        dx  \   dt        dx        dy        dz   /

    dK   d[psi] Dm   dm D[psi]
    -- - ------ -- + -- ------ = 0, ..., ...,   (8)
    dx     dx   dt   dx   dt

  and as we prove subsequently (§ 37) that the vortex lines are composed
  of the same fluid particles throughout the motion, the surface m and
  [psi] satisfies the condition of (6) § 23; so that K is uniform
  throughout the fluid at any instant, and changes with the time only,
  and so may be replaced by F(t).

  26. When the motion is _steady_, that is, when the velocity at any
  point of space does not change with the time,

    dK
    -- - 2v[zeta] + 2w[eta] = 0, ..., ...   (1)
    dx

        dK        dK         dK       dK    dK    dK
    [xi]-- + [eta]-- + [zeta]-- = 0, u-- + v-- + w-- = 0,   (2)
        dx        dy         dz       dx    dy    dz
  and
         _
        /
    K = | dp/[rho] + V + ½q² = H   (3)
       _/

  is constant along a vortex line, and a _stream line_, the path of a
  fluid particle, so that the fluid is traversed by a series of H
  surfaces, each covered by a network of stream lines and vortex lines;
  and if the motion is irrotational H is a constant throughout the
  fluid.

  Taking the axis of x for an instant in the normal through a point on
  the surface H = constant, this makes u = 0, [xi] = 0; and in steady
  motion the equations reduce to

    dH/d[nu] = 2v[zeta] - 2w[eta] = 2q[omega] sin [theta],   (4)

  where [theta] is the angle between the stream line and vortex line;
  and this holds for their projection on any plane to which d[nu] is
  drawn perpendicular.

  In plane motion (4) reduces to

     dH                   / dQ    q  \
    ----- = 2q[zeta] = q (  -- + ---  ),   (5)
    d[nu]                 \ dv    r  /

  if r denotes the radius of curvature of the stream line, so that

     1     dp      dV      dH     d½q²     q²
    ----- ----- + ----- = ----- - ----- = ---,   (6)
    [rho] d[nu]   d[nu]   d[nu]   d[nu]    r

  the normal acceleration.

  The osculating plane of a stream line in steady motion contains the
  resultant acceleration, the direction ratios of which are

     du    du    du   d½q²                        d½q²   dH
    u-- + v-- + w-- = ---- - 2v[zeta] + 2w[eta] = ---- - --, ...,   (7)
     dx    dy    dz    dx                          dx    dx

  and when q is stationary, the acceleration is normal to the surface H
  = constant, and the stream line is a geodesic.

  Calling the sum of the pressure and potential head the statical head,
  surfaces of constant statical and dynamical head intersect in lines on
  H, and the three surfaces touch where the velocity is stationary.

  Equation (3) is called Bernoulli's equation, and may be interpreted as
  the balance-sheet of the energy which enters and leaves a given tube
  of flow.

  If homogeneous liquid is drawn off from a vessel so large that the
  motion at the free surface at a distance may be neglected, then
  Bernoulli's equation may be written

    H = p/[rho] + z + q²/2g = P/[rho] + h,   (8)

  where P denotes the atmospheric pressure and h the height of the free
  surface, a fundamental equation in hydraulics; a return has been made
  here to the gravitation unit of hydrostatics, and Oz is taken
  vertically upward.

  In particular, for a jet issuing into the atmosphere, where p = P,

    q²/2g = h - z,   (9)

  or the velocity of the jet is due to the head k - z of the still free
  surface above the orifice; this is Torricelli's theorem (1643), the
  foundation of the science of hydrodynamics.

  27. _Uniplanar Motion._--In the uniplanar motion of a homogeneous
  liquid the equation of continuity reduces to

    du   dv
    -- + -- = 0,   (1)
    dx   dy

  so that we can put

    u = -d[psi]/dy, v = d[psi]/dx,   (2)

  where [psi] is a function of x, y, called the stream- or
  current-function; interpreted physically, [psi] - [psi]0, the
  difference of the value of [psi] at a fixed point A and a variable
  point P is the flow, in ft.³/second, across any curved line AP from A
  to P, this being the same for all lines in accordance with the
  continuity.

  Thus if d[psi] is the increase of [psi] due to a displacement from P
  to P´, and k is the component of velocity normal to PP´, the flow
  across PP´ is d[psi] = k·PP´; and taking PP´ parallel to Ox, d[psi] =
  vdx; and similarly d[psi]= -udy with PP´ parallel to Oy; and generally
  d[psi]/ds is the velocity across ds, in a direction turned through a
  right angle forward, against the clock.

  In the equations of uniplanar motion

              dv   du   d²[psi]  d²[psi]
    2[zeta] = -- - -- = ------ + ------ = -[Nabla]²[psi], suppose,   (3)
              dx   dy     dx²      dy²

  so that in steady motion

    dH                d[psi]      dH                d[psi]        dH
    -- + [Nabla]²[psi]------ = 0, -- + [Nabla]²[psi]------ = 0, ------ + [Nabla]²[psi] = 0,   (4)
    dx                  dx        dy                  dy        d[psi]

  and [Nabla]²[psi] must be a function of [psi].

  If the motion ia irrotational,

          d[phi]     d[psi]        d[phi]  d[psi]
    u = - ------ = - ------, v = - ----- = ------,   (5)
            dx         dy            dy      dx´

  so that [psi] and [phi] are conjugate functions of x and y,

    [phi] + [psi]i = [f](x + yi), [Nabla]²[psi] = 0, [Nabla]²[phi] = 0;   (6)

  or putting

    [phi] + [psi]i = w, x + yi = z, w = [f](z).

  The curves [phi] = constant and [psi] = constant form an orthogonal
  system; and the interchange of [phi] and [psi] will give a new state
  of uniplanar motion, in which the velocity at every point is turned
  through a right angle without alteration of magnitude.

  For instance, in a uniplanar flow, radially inward towards O, the flow
  across any circle of radius r being the same and denoted by 2[pi]m,
  the velocity must be m/r, and

    [phi] = m log r, [psi] = m[theta],
      [phi] + [psi]i = m log re^(i[theta]), w = m log z.   (7)

  Interchanging these values

    [psi] = m log r, [phi] = m[theta],
      [psi] + [phi]i = m log re^(i[theta])   (8)

  gives a state of vortex motion, circulating round Oz, called a
  straight or columnar vortex.

  A single vortex will remain at rest, and cause a velocity at any point
  inversely as the distance from the axis and perpendicular to its
  direction; analogous to the magnetic field of a straight electric
  current.

  If other vortices are present, any one may be supposed to move with
  the velocity due to the others, the resultant stream-function being

    [psi] = [Sigma]m log r = log [Pi]r^m;   (9)

  the path of a vortex is obtained by equating the value of [psi] at the
  vortex to a constant, omitting the r^m of the vortex itself.

  When the liquid is bounded by a cylindrical surface, the motion of a
  vortex inside may be determined as due to a series of vortex-images,
  so arranged as to make the flow zero across the boundary.

  For a plane boundary the image is the optical reflection of the
  vortex. For example, a pair of equal opposite vortices, moving on a
  line parallel to a plane boundary, will have a corresponding pair of
  images, forming a rectangle of vortices, and the path of a vortex will
  be the Cotes' spiral

    r sin 2[theta] = 2a, or x^(-2) + y^(-2) = a^(-2);   (10)

  this is therefore the path of a single vortex in a right-angled
  corner; and generally, if the angle of the corner is [pi]/n, the path
  is the Cotes' spiral

    r sin n[theta] = na.   (11)

  A single vortex in a circular cylinder of radius a at a distance c
  from the centre will move with the velocity due to an equal opposite
  image at a distance a²/c, and so describe a circle with velocity

    mc/(a² - c²) in the periodic time 2[pi](a² - c²)/m.   (12)

  Conjugate functions can be employed also for the motion of liquid in a
  thin sheet between two concentric spherical surfaces; the components
  of velocity along the meridian and parallel in colatitude [theta] and
  longitude [lambda] can be written

     d[phi]         1        d[psi]         1         d[psi]       d[psi]
    -------- = ----------- ---------,  -----------  --------- = - --------,   (13)
    d[theta]   sin [theta] d[lambda]   sin [theta]  d[lambda]     d[theta]

  and then

    [phi] + [psi]i = F(tan ½[theta]·e^([lambda]i)).   (14)

  28. _Uniplanar Motion of a Liquid due to the Passage of a Cylinder
  through it._--A stream-function [psi] must be determined to satisfy
  the conditions

    [Nabla]²[psi] = 0, throughout the liquid;   (1)

    [psi] = constant, over any fixed boundary;   (2)

    d[psi]/ds = normal velocity reversed over a solid boundary,   (3)

  so that, if the solid is moving with velocity U in the direction Ox,
  d[psi]/ds = -Udy/ds, or [psi] + Uy = constant over the moving
  cylinder; and [psi] + Uy = [psi]´ is the stream function of the
  relative motion of the liquid past the cylinder, and similarly [psi] -
  Vx for the component velocity V along Oy; and generally

    [psi]´ = [psi] + Uy - Vx   (4)

  is the relative stream-function, constant over a solid boundary moving
  with components U and V of velocity.

  If the liquid is stirred up by the rotation R of a cylindrical body,

    d[psi]/ds = normal velocity reversed

                   dx     dy
              = -Rx-- - Ry--,   (5)
                   ds     ds

    [psi] + ½R(x² + y²) = [psi]´,   (6)

  a constant over the boundary; and [psi]´ is the current-function of
  the relative motion past the cylinder, but now

    V²[psi]´ + 2R = 0,   (7)

  throughout the liquid.

  Inside an equilateral triangle, for instance, of height h,

    [psi]´ = -2R[alpha][beta][gamma]/h,   (8)

  where [alpha], [beta], [gamma] are the perpendiculars on the sides of
  the triangle.

  In the general case [psi]´ = [psi] + Uy - Vx + ½R(x² + y²) is the
  relative stream function for velocity components, U, V, R.

  29. _Example 1._--Liquid motion past a circular cylinder.

  Consider the motion given by

    [omega] = U(z + a²/z), (1)

  so that

               /    a²\                   /    a² \
    [phi] = U ( r + -- ) cos [theta] = U ( 1 + --  )x,   (2)
               \    r /                   \    r² /

               /    a²\                   /    a² \
    [psi] = U ( r - -- ) sin [theta] = U ( 1 - --  )y.
               \    r /                   \    r² /

  Then [psi] = 0 over the cylinder r = a, which may be considered a
  fixed post; and a stream line past it along which [psi] = Uc, a
  constant, is the curve

     /    a²\
    ( r - -- ) sin [theta] = c, (x² + y²)(y - c) - a²y = 0   (3)
     \    r /

  a cubic curve (C3).

  Over a concentric cylinder, external or internal, of radius r = b,

                               /     a²\
    [psi]´ = [psi] + U1y = [U ( 1 - --- ) + U1] y,   (4)
                               \     b²/

  and [psi]´ is zero if

    U1/U = (a² - b²)/b²;   (5)

  so that the cylinder may swim for an instant in the liquid without
  distortion, with this velocity U1, and [omega] in (1) will give the
  liquid motion in the interspace between the fixed cylinder r = a and
  the concentric cylinder r = b, moving with velocity U1.

  When b = 0, U1 = [oo]; and when b = [oo], U1 = -U, so that at infinity
  the liquid is streaming in the direction xO with velocity U.

  If the liquid is reduced to rest at infinity by the superposition of
  an opposite stream given by [omega] = -Uz, we are left with

    [omega] = Ua²/z,   (6)

    [phi] = U(a²/r) cos [theta] = Ua²x/(x² + y²),   (7)

    [psi] = -U(a²/r) sin [theta] = -Ua²y/(x² + y²),   (8)

  giving the motion due to the passage of the Cylinder r = a with
  velocity U through the origin O in the direction Ox.

  If the direction of motion makes an angle [theta]´ with Ox,

                  d[phi] / d[phi]    2xy
    tan[theta]´ = ----- /  ----- = ------ = tan 2[theta], [theta] = ½[theta]´,   (9)
                    dy /     dx    x² - y²

  and the velocity is Ua²/r².

  Along the path of a particle, defined by the C3 of (3),

                        y²     y(y - c)
    sin² ½[theta]´ = ------- = -------,   (10)
                     x² + y²      a²

                   d[theta]´   2y - c dy
    ½ sin [theta]´ --------- = ------ --,   (11)
                      ds         a²   ds

  on the radius of curvature is ¼a²/(y - ½c), which shows that the curve
  is an Elastica or Lintearia. (J. C. Maxwell, _Collected Works_, ii.
  208.)

  If [phi]1 denotes the velocity function of the liquid filling the
  cylinder r = b, and moving bodily with it with velocity U1,

    [phi]1 = -U1x,   (12)

  and over the separating surface r = b

      [phi]       U   /    a²\    a² + b²
    --------- = - -- ( 1 + -- ) = -------,   (13)
     [phi]1       U1  \    b²/    a² - b²

  and this, by § 36, is also the ratio of the kinetic energy in the
  annular interspace between the two cylinders to the kinetic energy of
  the liquid moving bodily inside r = b.

  Consequently the inertia to overcome in moving the cylinder r = b,
  solid or liquid, is its own inertia, increased by the inertia of
  liquid (a² + b²)/(a² - b²) times the volume of the cylinder r = b;
  this total inertia is called the effective inertia of the cylinder r =
  b, at the instant the two cylinders are concentric.

  With liquid of density [rho], this gives rise to a kinetic reaction to
  acceleration dU/dt, given by

                  a² + b² dU   a² + b²   dU
    [pi][rho]b²   ------- -- = ------- M´--,   (14)
                  a² - b² dt   a² - b²   dt

  if M´ denotes the mass of liquid displaced by unit length of the
  cylinder r = b. In particular, when a = [oo], the extra inertia is M´.

  When the cylinder r = a is moved with velocity U and r = b with
  velocity U1 along Ox,

                 a²    / b²    \                     b²    /     a²\
    [phi] = U ------- ( --- + r ) cos [theta] - U1------- ( r + --- ) cos [theta],   (15)
              b² - a²  \ r     /                  b² - a²  \     r /

                  a²    / b²    \                    b²     /     a²\
    [psi] = -U ------- ( --- - r ) sin [theta] - U1------- ( r - --- ) sin [theta];   (16)
               b² - a²  \ r     /                  b² - a²  \     r /

  and similarly, with velocity components V and V1 along Oy

                 a²    / b²    \                     b²    /     a²\
    [phi] = V ------- ( --- + r ) sin [theta] - V1------- ( r + --- ) sin [theta],   (17)
              b² - a²  \ r     /                  b² - a²  \     r /

                 a²    / b²    \                    b²     /     a²\
    [psi] = V ------- ( --- - r ) cos [theta] + V1------- ( r - --- ) cos [theta],   (18)
              b² - a²  \ r     /                  b² - a²  \     r /

  and then for the resultant motion
                     a²      z        a²b²  U + Vi
    w  = (U² + V²) ------- ------ + ------- ------
                   b² - a² U + Vi   b² - a²    z

                      a²      z         a²b²  U1 + V1i
      -(U1² + V1²) ------- -------- + ------- --------.   (19)
                   b² - a² U1 + V1i   b² - a²     z

  The resultant impulse of the liquid on the cylinder is given by the
  component, over r = a (§ 36),
         _
        /                                                 /  b² + a²        2b²  \
    X = | [rho][phi] cos [theta]·ad[theta] = [pi][rho]a² ( U ------- - U1 ------- );   (20)
       _/                                                 \  b² - a²      b² - a²/

  and over r = b
          _
         /                                                 /    2a²      b² + a² \
    X1 = | [rho][phi] cos [theta]·bd[theta] = [pi][rho]b² ( U ------ - U1-------  ),   (21)
        _/                                                 \  b² - a²    b² - a² /

  and the difference X - X1 is the component momentum of the liquid in
  the interspace; with similar expressions for Y and Y1.

  Then, if the outside cylinder is free to move

             V1     2a²                      b² - a²
    X1 = 0,  -- = -------,  X = [pi][rho]a²U -------.   (22)
             U    b² + a²                    b² + a²

  But if the outside cylinder is moved with velocity U1, and the inside
  cylinder is solid or filled with liquid of density [sigma],

                        U1              2[rho]b²
    X = -[pi][rho]a²U,  -- = --------------------------------,
                        U    [rho](b² + a²) + [sigma](b² - a²)

    U - U1      ([rho] - [sigma])(b² - a²)
    ------ = ---------------------------------,   (23)
      U1     [rho](b² + a²) + [sigma](b² - a²)

  and the inside cylinder starts forward or backward with respect to the
  outside cylinder, according as [rho] > or < [sigma].

  30. The expression for [omega] in (1) § 29 may be increased by the
  addition of the term

    im log z = -m[theta] + im log r,   (1)

  representing vortex motion circulating round the annulus of liquid.

  Considered by itself, with the cylinders held fixed, the vortex sets
  up a circumferential velocity m/r on a radius r, so that the angular
  momentum of a circular filament of annular cross section dA is
  [rho]mdA, and of the whole vortex is [rho]m[pi](b² - a²).

  Any circular filament can be started from rest by the application of a
  circumferential impulse [pi][rho]mdr at each end of a diameter; so
  that a mechanism attached to the cylinders, which can set up a uniform
  distributed impulse [pi][rho]m across the two parts of a diameter in
  the liquid, will generate the vortex motion, and react on the cylinder
  with an impulse couple -[rho]m[pi]a² and [rho]m[pi]b², having
  resultant [rho]m[pi](b² - a²), and this couple is infinite when b =
  [oo], as the angular momentum of the vortex is infinite. Round the
  cylinder r = a held fixed in the U current the liquid streams past
  with velocity

    q´ = 2U sin [theta] + m/a;   (2)

  and the loss of head due to this increase of velocity from U to q´ is

    q´² - U²   (2U sin [theta] + m/a)² - U²
    -------- = ----------------------------,   (3)
      2g                    2g

  so that cavitation will take place, unless the head at a great
  distance exceeds this loss.

  The resultant hydrostatic thrust across any diametral plane of the
  cylinder will be modified, but the only term in the loss of head which
  exerts a resultant thrust on the whole cylinder is 2mU sin[theta]/ga,
  and its thrust is 2[pi][rho]mU absolute units in the direction Cy, to
  be counteracted by a support at the centre C; the liquid is streaming
  past r = a with velocity U reversed, and the cylinder is surrounded by
  a vortex. Similarly, the streaming velocity V reversed will give rise
  to a thrust 2[pi][rho]mV in the direction xC.

  Now if the cylinder is released, and the components U and V are
  reversed so as to become the velocity of the cylinder with respect to
  space filled with liquid, and at rest at infinity, the cylinder will
  experience components of force per unit length

  (i.) - 2[pi][rho]mV, 2[pi][rho]mU, due to the vortex motion;

  (ii.) - [pi][rho]a² dU/dt, -[pi][rho]a² dV/dt, due to the kinetic
  reaction of the liquid;

  (iii.) 0, -[pi]([sigma] - [rho])a²g, due to gravity,

  taking Oy vertically upward, and denoting the density of the cylinder
  by [sigma]; so that the equations of motion are

               dU                dU
    [pi][rho]a²-- = - [pi][rho]a²-- - 2[pi][rho]mV,   (4)
               dt                dt

               dV                dV
    [pi][rho]a²-- = - [pi][rho]a²-- + 2[pi][rho]mV - [pi]([sigma] - [rho])a²g,   (5)
               dt                dt

  or, putting m = a²[omega], so that the vortex velocity is due to an
  angular velocity [omega] at a radius a,

    ([sigma] + [rho])dU/dt + 2[rho][omega]V = 0,   (6)

    ([sigma] + [rho])dV/dt - 2[rho][omega]U + ([sigma] - [rho])g = 0.   (7)

  Thus with g = 0, the cylinder will describe a circle with angular
  velocity 2[rho][omega]/([sigma] + [rho]), so that the radius is
  ([sigma] + [rho])v/2[rho][omega], if the velocity is v. With [sigma] =
  0, the angular velocity of the cylinder is 2[omega]; in this way the
  velocity may be calculated of the propagation of ripples and waves on
  the surface of a vertical whirlpool in a sink.

  Restoring [sigma] will make the path of the cylinder a trochoid; and
  so the swerve can be explained of the ball in tennis, cricket,
  baseball, or golf.

  Another explanation may be given of the sidelong force, arising from
  the velocity of liquid past a cylinder, which is encircled by a
  vortex. Taking two planes x = ± b, and considering the increase of
  momentum in the liquid between them, due to the entry and exit of
  liquid momentum, the increase across dy in the direction Oy, due to
  elements at P and P´ at opposite ends of the diameter PP´, is

      [rho]dy (U - Ua²r^(-2) cos 2[theta] + mr^(-1) sin [theta])(Ua²r^(-2) sin 2[theta] + mr^(-1) cos [theta])
    + [rho]dy (- U + Ua²r^(-2) cos 2[theta] + mr^(-1) sin [theta])(Ua²r^(-2) sin 2[theta] - mr^(-1) cos [theta])
    = 2[rho]dymUr^(-1)(cos [theta] - a^2r^(-2)cos 3[theta]),   (8)

  and with y = b tan [theta], r = b sec [theta], this is

    2[rho]mUd[theta] (1 - a²b^(-2) cos 3[theta] cos [theta]),   (9)

  and integrating between the limits [theta] = ±½[pi], the resultant, as
  before, is 2[pi][rho]mU.

  31. _Example 2.--Confocal Elliptic Cylinders._--Employ the elliptic
  coordinates [eta], [xi], and [zeta] = [eta] + [xi]i, such that

    z = c ch[zeta], x = c ch [eta] cos [xi], y = c sh [eta] sin [zeta];   (1)

  then the curves for which [eta] and [xi] are constant are confocal
  ellipses and hyperbolas, and

        d(x, y)
    J = -------, [xi]) = c²(ch²[eta] - cos² [xi])
        d([eta]

      = ½c²(ch 2[eta] - cos 2[xi]) = r1r2 = OD²,   (2)

  if OD is the semi-diameter conjugate to OP, and r1, r2 the focal
  distances,

    r1, r2 = c(ch[eta] ± cos [xi]);   (3)

    r² = x² + y² = c²(ch²[eta] - sin² [xi])

       = ½c²(ch 2[eta] + cos 2[xi]).   (4)

  Consider the streaming motion given by

    w = m ch([zeta] - [gamma]), [gamma] = [alpha] + [beta]i, (5)

    [phi] = m ch([eta] - [alpha]) cos ([xi] - [beta]),
    [psi] = m sh([eta] - [alpha]) sin ([xi] - [beta]).   (6)

  Then [psi] = 0 over the ellipse [eta] = [alpha], and the hyperbola
  [xi] = [beta], so that these may be taken as fixed boundaries; and
  [psi] is a constant on a C4.

  Over any ellipse [eta], moving with components U and V of velocity,

    [psi]´ = [psi] + Uy - Vx = [m sh([eta] - [alpha]) cos [beta] + Uc sh[eta]] sin [xi]

      -[m sh ([eta] - [alpha]) sin [beta] + Vc ch [eta] cos [xi];   (7)

  so that [psi]´ = 0, if

           m  sh([eta] - [alpha])                    m    sh([eta] - [alpha])
    U = - --- ------------------- cos [beta], V = - --- - ------------------- sin [beta],   (8)
           c         sh[eta]                         c          ch[eta]

  having a resultant in the direction PO, where P is the intersection of
  an ellipse [eta] with the hyperbola [beta]; and with this velocity the
  ellipse [eta] can be swimming in the liquid, without distortion for an
  instant.

  At infinity

           m                          m
    U = - --- e^(-a) cos [beta] = - ----- cos [beta],
           c                        a - b

           m                          m
    V = - --- e^(-a) sin [beta] = - ----- sin [beta],   (9)
           c                        a + b

  a and b denoting the semi-axes of the ellipse [alpha]; so that the
  liquid is streaming at infinity with velocity Q = m/(a + b) in the
  direction of the asymptote of the hyperbola [beta].

  An ellipse interior to [eta] = [alpha] will move in a direction
  opposite to the exterior current; and when [eta] = 0, U = [oo], but V
  = (m/c) sh [alpha] sin [beta].

  Negative values of [eta] must be interpreted by a streaming motion on
  a parallel plane at a level slightly different, as on a double Riemann
  sheet, the stream passing from one sheet to the other across a cut SS´
  joining the foci S, S´. A diagram has been drawn by Col. R. L.
  Hippisley.

  The components of the liquid velocity q, in the direction of the
  normal of the ellipse [eta] and hyperbola [xi], are

    -mJ^(-1)sh([eta] - [alpha]) cos([xi] - [beta]),
     mJ^(-1)ch([eta] - [alpha]) sin ([xi] - [beta]).   (10)

  The velocity q is zero in a corner where the hyperbola [beta] cuts the
  ellipse [alpha]; and round the ellipse [alpha] the velocity q reaches
  a maximum when the tangent has turned through a right angle, and then

             [root](ch 2[alpha] - cos 2[beta])
    q = Qe^a ---------------------------------;   (11)
                        sh 2[alpha]

  and the condition can be inferred when cavitation begins.

  With [beta] = 0, the stream is parallel to x0, and

  [phi] = m ch([eta] - [alpha])cos [xi]

        = -Uc ch([eta] - [alpha])sh [eta] cos [xi]/sh([eta] - [alpha])   (12)

  over the cylinder [eta], and as in (12) § 29,

    [phi]1 = -Ux = -Uc ch [eta] cos [xi],   (13)

  for liquid filling the cylinder; and

     [phi]         th [eta]
    ------ = --------------------,   (14)
    [phi]1   th ([eta] - [alpha])

  over the surface of [eta]; so that parallel to Ox, the effective
  inertia of the cylinder [eta], displacing M´ liquid, is increased by
  M´th [eta]/th([eta]- [alpha]), reducing when [alpha] = [oo] to M´th
  [eta] = M´(b/a).

  Similarly, parallel to Oy, the increase of effective inertia is M´/th
  [eta] th([eta] - [alpha]), reducing to M´/th [eta] = M´(a/b), when
  [alpha] = [oo], and the liquid extends to infinity.

  32. Next consider the motion given by

    [phi] = m ch 2([eta] - [alpha]) sin 2[xi],
    [psi] = -m sh 2([eta] - [alpha]) cos 2[xi];   (1)

  in which [psi] = 0 over the ellipse [alpha], and

    [psi]´ = [psi] + ½R(x² + y²)
           = [-m sh 2([eta] - [alpha]) + ¼Rc²] cos 2[xi] + ¼Rc² ch 2[eta],   (2)

  which is constant over the ellipse [eta] if

    ¼Rc² = m sh 2([eta] - [alpha]);   (3)

  so that this ellipse can be rotating with this angular velocity R for
  an instant without distortion, the ellipse [alpha] being fixed.

  For the liquid filling the interior of a rotating elliptic cylinder of
  cross section

    x²/a² + y²/b² = 1,   (4)

    [psi]1´ = m1(x²/a² + y²/b²)   (5)

  with

    [nabla]²[psi]1´ = -2R = -2m1(1/a² + 1/b²),

    [psi]1 = m1(x²/a² + y²/b²) - ½R(x² + y²)
           = -½R(x² - y²)(a² - b²)/(a² + b²),   (6)

    [phi]1 = Rxy(a² - b²)/(a² + b²),

    w1 = [phi]1 + [psi]1i = -½iR(x + yi)²(a² - b²)/(a² + b²).

  The velocity of a liquid particle is thus (a² - b²)/(a² + b²) of what
  it would be if the liquid was frozen and rotating bodily with the
  ellipse; and so the effective angular inertia of the liquid is (a² -
  b²)²/(a² + b²)² of the solid; and the effective radius of gyration,
  solid and liquid, is given by

    k² = ¼(a² + b²), and ¼(a² - b²)²/(a² + b²).   (7)

  For the liquid in the interspace between [alpha] and [eta],

    [phi]         m ch 2([eta] - [alpha]) sin 2[xi]
    ------ = -------------------------------------------
    [phi]1   ¼Rc² sh 2[eta] sin 2[xi](a² - b²)/(a² + b²)

           = 1/th 2([eta] - [alpha])th 2[eta];   (8)

  and the effective k² of the liquid is reduced to

    ¼c²/th 2([eta] - [alpha]) sh 2[eta],   (9)

  which becomes ¼c²/sh 2[eta] = 1/8 (a² - b²)/ab, when [alpha] = [oo],
  and the liquid surrounds the ellipse [eta] to infinity.

  An angular velocity R, which gives components -Ry, Rx of velocity to a
  body, can be resolved into two shearing velocities, -R parallel to Ox,
  and R parallel to Oy; and then [psi] is resolved into [psi]1 + [psi]2,
  such that [psi]1 + ½Rx² and [psi]2 + ½Ry² is constant over the
  boundary.

  Inside a cylinder

    [phi]1 + [psi]1i = -½iR(x + yi)²a²/(a² + b²),   (10)

    [phi]2 + [psi]2i = ½iR(x + yi)²b²/(a² + b²),   (11)

  and for the interspace, the ellipse [alpha] being fixed, and [alpha]1
  revolving with angular velocity R

    [phi]1 + [psi]1i = -1/8 iRc²sh 2([eta] - [alpha]
      + [xi]i)(ch 2[alpha] + 1)/sh 2([alpha]1 - [alpha]),   (12)

    [phi]2 + [psi]2i = 1/8 iRc²sh 2([eta] - [alpha]
      + [xi]i)(ch 2[alpha] - 1)/sh 2([alpha]1 - [alpha]),   (13)

  satisfying the condition that [psi]1 and [psi]2 are zero over [eta] =
  [alpha], and over [eta] = [alpha]1

    [psi]1 + ½Rx² = 1/8 Rc²(ch 2[alpha]1 + 1),   (14)

    [psi]2 + ½Ry² = 1/8 Rc²(ch 2[alpha]1 - 1),   (15)

  constant values.

  In a similar way the more general state of motion may be analysed,
  given by

    w = m ch 2([zeta] - [gamma]), [gamma] = [alpha] + [beta]i,   (16)

  as giving a homogeneous strain velocity to the confocal system; to
  which may be added a circulation, represented by an additional term
  m[zeta] in w.

  Similarly, with

    x + yi = c[root][sin ([xi] + [eta]i)]   (17)

  the function

    [psi] = Qc sh ½([eta] - [alpha]) sin ½([xi] - [beta])   (18)

  will give motion streaming past the fixed cylinder [eta] = [alpha],
  and dividing along [xi] = [beta]; and then

    x² - y² = c² sin [xi] ch [eta], 2xy = c² cos [xi] sh [eta].   (19)

  In particular, with sh [alpha] = 1, the cross-section of [eta] =
  [alpha] is

    x^4 + 6x²y² + y^4 = 2c^4, or x^4 + y^4 = c^4   (20)

  when the axes are turned through 45°.

  33. _Example 3._--Analysing in this way the rotation of a rectangle
  filled with liquid into the two components of shear, the stream
  function [psi]1 is to be made to satisfy the conditions

  (i.) [nabla]²[psi]1 = 0,

  (ii.) [psi]1 + ½Rx² = ½Ra², or [psi]1 = 0 when x = ±a,

  (iii.) [psi]1 + ½Rx² = ½Ra², [psi]1 = ½R(a² - x²), when y = ± b.

  Expanded in a Fourier series,

               32       __  cos (2n + 1) ½[pi]x/a
    a² - x² = ----- a² \    ---------------------,   (1)
              [pi]³    /__         (2n + 1)³

  so that

               16       __  cos (2n + 1) ½[pi]x/a · ch(2n + 1) ½[pi]y/a)
    [psi]1 =  ----- a² \   ---------------------------------------------,
              [pi]³    /__        (2n + 1)^3 · ch(2n + 1) ½[pi]b/a


                                16    __     cos (2n + 1) ½[pi]z/a
    w1 = [phi]1 + [psi]1i = iR ----- \   ------------------------------,   (2)
                               [pi]³ /__ (2n + 1)^3 ch(2n + 1) ½[pi]b/a

  an elliptic-function Fourier series; with a similar expression for
  [psi]2 with x and y, a and b interchanged; and thence [psi] = [psi]1 +
  [psi]2.

  _Example 4._--Parabolic cylinder, axial advance, and liquid streaming
  past.

  The polar equation of the cross-section being

    r^½ cos ½[theta] = a^½, or r + x = 2a,   (3)

  the conditions are satisfied by

    [psi]´ = Ur sin [theta] - 2Ua^½ r^½ sin ½[theta]
           = 2Ur^½ sin ½[theta](r^½ cos ½[theta] - a^½),   (4)

    [psi] = 2Ua^½ r^½ sin ½[theta] = -U[root][2a(r-x)],   (5)

    w = -2Ua^½ z^½,   (6)

  and the resistance of the liquid is 2[pi][rho]aV²/2g.

  A relative stream line, along which [psi]´ = Uc, is the quartic curve

                                   (4a²y² - (y - c)^4       4a²y² + (y-c)^4
    y - c = [root][2a(r - x)], x = -------------------, r = ---------------,   (7)
                                       (4a(y - c)²             4a(y - c)²

  and in the absolute space curve given by [psi],

    dy     (y - c)²         2ac
    -- = - --------, x = - ----- 2a log (y - c).   (8)
    dx       2ay           y - c

  34. _Motion symmetrical about an Axis._--When the motion of a liquid
  is the same for any plane passing through Ox, and lies in the plane, a
  function [psi] can be found analogous to that employed in plane
  motion, such that the flux across the surface generated by the
  revolution of any curve AP from A to P is the same, and represented by
  2[pi]([psi] - [psi]0); and, as before, if d[psi] is the increase in
  [psi] due to a displacement of P to P´, then k the component of
  velocity normal to the surface swept out by PP´ is such that
  2[pi]d[psi] = 2[pi]yk.PP´; and taking PP´ parallel to Oy and Ox,

    u = -d[psi]/ydy, v = d[psi]/ydx,   (1)

  and [psi] is called after the inventor, "Stokes's stream or current
  function," as it is constant along a stream line (_Trans. Camb. Phil.
  Soc._, 1842; "Stokes's Current Function," R. A. Sampson, _Phil.
  Trans._, 1892); and d[psi]/yds is the component velocity across ds in
  a direction turned through a right angle forward.

  In this symmetrical motion

                                   d   / 1  d[psi] \    d   / 1  d[psi]\
    [xi] = 0, [eta] = 0, 2[zeta] = -- ( --- ------  ) + -- ( --- ------ )
                                   dx  \ y    dx   /    dy  \ y    dy  /

         1   /d²[psi]   d²[psi]    1  d[psi]\       1
      = --- ( ------- + ------- - --- ------ ) = - ---[nabla]²[psi],   (2)
         y   \  dx²       dy²      y    dy  /       y

  suppose; and in steady motion,

     dH    1  d[psi]                   dH    1  d[psi]
     -- + --- ----- [nabla]²[psi] = 0, -- + --- ------ [nabla]²[psi] = 0,   (3)
     dx    y²   dx                     dy    y²   dy

  so that

    2[zeta]/y = -y^(-2)[nabla]²[psi] = dH/d[psi]   (4)

  is a function of [psi], say [f]´([psi]), and constant along a stream line;

    dH/dv = 2q[zeta], H - [f]([psi]) = constant,   (5)

  throughout the liquid.

  When the motion is irrotational,

                      d[phi]      1  d[psi]        d[phi]    1  d[psi]
    [zeta] = 0, u = - ------ = - --- ------, v = - ------ = --- ------,   (6)
                        dx        y    dy            dy      y    dx

                          d²[psi]   d²[psi]    1  d[psi]
    [nabla]²[psi] = 0, or ------- + ------- - --- ------ = 0.   (7)
                            dx²       dy²      y    dy

  Changing to polar coordinates, x = r cos[theta], y = r sin[theta], the
  equation (2) becomes, with cos[theta] = [mu],

      d²[psi]               d²[psi]
    r²------- + (1 - [mu]²) ------- = 2[zeta]r³ sin [theta],   (8)
        dr²                  d[mu]²

  of which a solution, when [zeta] = 0, is

             /            B  \               dPn     /              B    \     dPn
    [psi] = ( Ar^(n+1) + ---  ) (1 - [mu]²) ----- = ( Ar^(n-1) + -------  ) y²-----,   (9)
             \           r^n /              d[mu]    \           r^(n+2) /    d[mu]

    [phi] = {(n + 1)Ar^n - nBr^(-n-1)} Pn,   (10)

  where Pn denotes the zonal harmonic of the nth order; also, in the
  exceptional case of

    [psi] = A0 cos[theta], [phi] = A0/r;

    [psi] = B0r, [phi] = -B0 log tan ½[theta]
                       = -½B0 sh(-1) x/y.   (11)

  Thus cos[theta] is the Stokes' function of a point source at O, and PA
  - PB of a line source AB.

  The stream function [psi] of the liquid motion set up by the passage
  of a solid of revolution, moving with axial velocity U, is such that

     1  d[psi]      dy
    --- ------ = -U --, [psi] + ½Uy² = constant,   (12)
     y    ds        ds

  over the surface of the solid; and [psi] must be replaced by [psi]´ =
  [psi] + ½Uy² in the general equations of steady motion above to obtain
  the steady relative motion of the liquid past the solid.

  For instance, with n = 1 in equation (9), the relative stream function
  is obtained for a sphere of radius a, by making it

    [psi]´ = [psi] + ½Uy² = ½U(r² - a³/r) sin² [theta],
    [psi] = -½Ua³ sin² [theta]/r;   (13)

  and then

    [phi]´ = Ux(1 + ½a³/r²), [phi] = ½Ua³ cos [theta]/r²,   (14)

      d[phi]     a³                 d[phi]        a³
    - ------ = U -- cos [theta], - --------- = ½U -- sin [theta],   (15)
        dr       r³                rd[theta]      r³

  so that, if the direction of motion makes an angle [psi] with Ox,

    tan ([psi] - [theta]) = ½ tan [theta],
    tan [psi] = 3 tan [theta]/(2 - tan² [theta]),   (16)

  Along the path of a liquid particle [psi]´ is constant, and putting it
  equal to ½Uc²,

    (r² - a³/r) sin² [theta] = c², sin² [theta] = c²r/(r³ - a³),   (17)

  the polar equation; or

    y² = c²r³/(r³ - a³), r³ = a³y²/(y² - c²),   (18)

  a curve of the 10th degree (C10).

  In the absolute path in space

    cos [psi] = (2 - 3 sin² [theta])/[root](4 - sin² [theta]),
      and sin³ [theta] = (y³ - c²y)/a³,   (19)

  which leads to no simple relation.

  The velocity past the surface of the sphere is

         1       d[psi]´       /     a³ \  sin² [theta]
    ------------ ------- = ½U ( 2r + --  ) ------------- = 3/2 U sin [theta], when r = a;   (20)
    r sin[theta]   dr          \     r² /  r sin [theta]

  so that the loss of head is

    (9/4 sin² [theta] - 1) U²/2g, having a maximum 5/4 U²/2g,   (21)

  which must be less than the head at infinite distance to avoid
  cavitation at the surface of the sphere.

  With n = 2, a state of motion is given by

    [psi] = -½Uy²a^4[mu]/r^4, [psi]´ = ½Uy²(1 - a^4[mu]/r^4),   (22)

    [phi]´ = Ux + [phi], [phi] = -1/3 U(a^4/r³)P2, P2 = 3/2 [mu]² - ½,   (23)

  representing a stream past the surface r^4 = a^4[mu].

35. A circular vortex, such as a smoke ring, will set up motion
symmetrical about an axis, and provide an illustration; a half vortex
ring can be generated in water by drawing a semicircular blade a short
distance forward, the tip of a spoon for instance. The vortex advances
with a certain velocity; and if an equal circular vortex is generated
coaxially with the first, the mutual influence can be observed. The
first vortex dilates and moves slower, while the second contracts and
shoots through the first; after which the motion is reversed
periodically, as if in a game of leap-frog. Projected perpendicularly
against a plane boundary, the motion is determined by an equal opposite
vortex ring, the optical image; the vortex ring spreads out and moves
more slowly as it approaches the wall; at the same time the molecular
rotation, inversely as the cross-section of the vortex, is seen to
increase. The analytical treatment of such vortex rings is the same as
for the electro-magnetic effect of a current circulating in each ring.

  36. _Irrotational Motion in General._--Liquid originally at rest in a
  singly-connected space cannot be set in motion by a field of force due
  to a single-valued potential function; any motion set up in the liquid
  must be due to a movement of the boundary, and the motion will be
  irrotational; for any small spherical element of the liquid may be
  considered a smooth solid sphere for a moment, and the normal pressure
  of the surrounding liquid cannot impart to it any rotation.

  The kinetic energy of the liquid inside a surface S due to the
  velocity function [phi] is given by
                _ _ _  _                                    _
               / / /  |  /d[phi]\²    /d[phi]\²    /d[phi]\² |
    T = ½[rho] | | |  | ( ------ ) + ( ------ ) + ( ------ ) | dx dy dz,
              _/_/_/  |_ \  dx  /     \  dy  /     \  dz  / _|
                _ _
               / /       d[phi]
      = ½[rho] | | [phi] ------ dS   (1)
              _/_/        d[nu]

  by Green's transformation, d[nu] denoting an elementary step along the
  normal to the exterior of the surface; so that d[phi]/d[nu] = 0 over
  the surface makes T = 0, and then

     /d[phi]\²    /d[phi]\²    /d[phi]\²      d[phi]      d[phi]      d[phi]
    ( ------ ) + ( ------ ) + ( ------ ) = 0, ------ = 0, ------ = 0, ------ = 0   (2)
     \  dx  /     \  dy  /     \  dz  /         dx          dy          dz

  If the actual motion at any instant is supposed to be generated
  instantaneously from rest by the application of pressure impulse over
  the surface, or suddenly reduced to rest again, then, since no natural
  forces can act impulsively throughout the liquid, the pressure impulse
  [~[omega]] satisfies the equations

      1   d[~omega]         1   d[~omega]         1   d[~omega]
    ----- --------- = -u, ----- --------- = -v, ----- --------- = -[~omega],   (3)
    [rho]     dx          [rho]     dy          [rho]     dz

    [~omega] = [rho][phi] + a constant,   (4)

  and the constant may be ignored; and Green's transformation of the
  energy T amounts to the theorem that the work done by an impulse is
  the product of the impulse and average velocity, or half the velocity
  from rest.

  In a multiply connected space, like a ring, with a multiply valued
  velocity function [phi], the liquid can circulate in the circuits
  independently of any motion of the surface; thus, for example,

    [phi] = m[theta] = m tan^(-1) y/x   (5)

  will give motion to the liquid, circulating in any ring-shaped figure
  of revolution round Oz.

  To find the kinetic energy of such motion in a multiply connected
  space, the channels must be supposed barred, and the space made
  acyclic by a membrane, moving with the velocity of the liquid; and
  then if k denotes the cyclic constant of [phi] in any circuit, or the
  value by which [phi] has increased in completing the circuit, the
  values of [phi] on the two sides of the membrane are taken as
  differing by k, so that the integral over the membrane
      _ _                     _ _
     / /       d[phi]        / /  d[phi]
     | | [phi] ------ dS = k | |  ------ dS,   (6)
    _/_/        d[nu]       _/_/   d[nu]

  and this term is to be added to the terms in (1) to obtain the
  additional part in the kinetic energy; the continuity shows that the
  integral is independent of the shape of the barrier membrane, and its
  position. Thus, in (5), the cyclic constant k = 2[pi]m.

  In plane motion the kinetic energy per unit length parallel to Oz
                _ _  _                       _                  _ _  _                       _
               / /  |  /d[phi]\²    /d[phi]\² |                / /  |  /d[psi]\²    /d[psi]\² |
    T = ½[rho] | |  | ( ------ ) + ( ------ ) | dx dy = ½[rho] | |  | ( ------ ) + ( ------ ) | dx dy
              _/_/  |_ \  dx  /     \  dy  / _|               _/_/  |_ \  dx  /     \  dy  / _|
                _                          _
               /       d[phi]             /       d[phi]
      = ½[rho] | [phi] ------ ds = ½[rho] | [psi] ------ ds.   (7)
              _/        d[nu]            _/        d[nu]

  For example, in the equilateral triangle of (8) § 28, referred to
  coordinate axes made by the base and height,

    [psi]´ = -2R[alpha][beta][gamma]/h = -½Ry[(h - y)² - 3x²]/h   (8)

    [psi] = [psi]´ - ½R [(1/3h - y)² + x²]

          = -½R [½h³ + 1/3 h²y + h) (x² - y²) - 3x²y + y³] /h   (9)

  and over the base y = 0,

    dx/d[nu] = -dx/dy = + ½R(1/3 h² - 3x²)/h, [psi] = -½R(1/9 h² + x²).   (10)

  Integrating over the base, to obtain one-third of the kinetic energy
  T,
                    _
                   / h/[root]3
    1/3 T = ½[rho] |            ¼R²(3x^4 - 1/27 h^4) dx/h
                  _/ -h/[root]3

          = [rho]R²h^4/135[root]3   (11)

  so that the effective k² of the liquid filling the triangle is given
  by

    k² = T/½[rho]R²A = 2h²/45

       = 2/5 (radius of the inscribed circle)²,   (12)

  or two-fifths of the k² for the solid triangle.

  Again, since

    d[phi]/d[nu] = d[psi]/ds, d[phi]/ds = -d[psi]/d[nu],   (13)
                _                        _
               /                        /
    T = ½[rho] | [phi] d[psi] = -½[rho] | [psi] d[phi].   (14)
              _/                       _/

  With the Stokes' function [psi] for motion symmetrical about an
  axis.
                _                                    _
               /       d[psi]                       /
    T = ½[rho] | [phi] ------ 2[pi]y ds = [pi][rho] | [phi] d[psi].   (15)
              _/         yds                       _/

  37. _Flow, Circulation, and Vortex Motion._--The line integral of the
  tangential velocity along a curve from one point to another, defined
  by
      _                           _
     /  / dx    dy    dz \       /
     | ( u-- + v-- + w--  ) ds = | (u dx + v dy + z dz),   (1)
    _/  \ ds    ds    ds /      _/

  is called the "flux" along the curve from the first to the second
  point; and if the curve closes in on itself the line integral round
  the curve is called the "circulation" in the curve.

  With a velocity function [phi], the flow
       _
      /
    - | d[phi] = [phi]1 - [phi]2,   (2)
     _/

  so that the flow is independent of the curve for all curves mutually
  reconcilable; and the circulation round a closed curve is zero, if the
  curve can be reduced to a point without leaving a region for which
  [phi] is single valued.

  If through every point of a small closed curve the vortex lines are
  drawn, a tube is obtained, and the fluid contained is called a _vortex
  filament_.

  By analogy with the spin of a rigid body, the component spin of the
  fluid in any plane at a point is defined as the circulation round a
  small area in the plane enclosing the point, divided by twice the
  area. For in a rigid body, rotating about Oz with angular velocity
  [zeta], the circulation round a curve in the plane xy is
      _
     /         /  dy     dx \
     | [zeta] ( x -- - y --  ) ds = [zeta] times twice the area.   (3)
    _/         \  ds     ds /

  In a fluid, the circulation round an elementary area dxdy is equal to

           /     dv  \       /     du  \             / dv  du \
    udx + ( v + --dx  )dy - ( u + --dy  )dx - vdy = ( -- - --  )dx dy,   (4)
           \     dx  /       \     dy  /             \ dx  dy /

  so that the component spin is

       / dv   du \
    ½ (  -- - --  ) = [zeta],   (5)
       \ dx   dy /

  in the previous notation of § 24; so also for the other two components
  [xi] and [eta].

  Since the circulation round any triangular area of given aspect is the
  sum of the circulation round the projections of the area on the
  coordinate planes, the composition of the components of spin, [xi],
  [eta], [zeta], is according to the vector law. Hence in any
  infinitesimal part of the fluid the circulation is zero round every
  small plane curve passing through the vortex line; and consequently
  the circulation round any curve drawn on the surface of a vortex
  filament is zero.

  If at any two points of a vortex line the cross-section ABC, A´B´C´ is
  drawn of the vortex filament, joined by the vortex line AA´, then,
  since the flow in AA´ is taken in opposite directions in the complete
  circuit ABC AA´B´C´ A´A, the resultant flow in AA´ cancels, and the
  circulation in ABC, A´B´C´ is the same; this is expressed by saying
  that at all points of a vortex filament [omega][alpha] is constant
  where [alpha] is the cross-section of the filament and [omega] the
  resultant spin (W. K. Clifford, _Kinematic_, book iii.).

  So far these theorems on vortex motion are kinematical; but
  introducing the equations of motion of § 22,

    Du   dQ      Dv   dQ      Dw   dQ
    -- + -- = 0, -- + -- = 0, -- + -- = 0,   (6)
    dt   dx      dt   dy      dt   dz
         _
        /
    Q = | dp/[rho] + V,   (7)
       _/

  and taking dx, dy, dz in the direction of u, v, w, and

    dx : dy : dz = u : v : w,

    D   /                 \    Du        D dx
    -- (u dx + v dy + w dz ) = -- dx + u ---- + ... = -dQ + ½dq²,   (8)
    dt  \                 /    dt         dt

  and integrating round a closed curve
          _
     D   /
     --  | (u dx + v dy + w dz) = 0,   (9)
     dt _/

  and the circulation in any circuit composed of the same fluid
  particles is constant; and if the motion is differential irrotational
  and due to a velocity function, the circulation is zero round all
  reconcilable paths. Interpreted dynamically the normal pressure of the
  surrounding fluid on a tube cannot create any circulation in the tube.

  The circulation being always zero round a small plane curve passing
  through the axis of spin in vortical motion, it follows conversely
  that a vortex filament is composed always of the same fluid particles;
  and since the circulation round a cross-section of a vortex filament
  is constant, not changing with the time, it follows from the previous
  kinematical theorem that [alpha][omega] is constant for all time, and
  the same for every cross-section of the vortex filament.

  A vortex filament must close on itself, or end on a bounding surface,
  as seen when the tip of a spoon is drawn through the surface of water.

  Denoting the cross-section [alpha] of a filament by dS and its mass by
  dm, the quantity [omega]dS/dm is called the _vorticity_; this is the
  same at all points of a filament, and it does not change during the
  motion; and the vorticity is given by [omega] cos[epsilon]dS/dm, if dS
  is the oblique section of which the normal makes an angle [epsilon]
  with the filament, while the aggregate vorticity of a mass M inside a
  surface S is
             _
            /
     M^(-1) | [omega] cos [epsilon] dS.
           _/

  Employing the equation of continuity when the liquid is homogeneous,

      / d[zeta]    d[eta]\                                  d²    d²    d²
    2(  ------ -  ------  ) = [nabla]²u, ... , [nabla]² = - --- - --- - ---,   (10)
      \   dy         dz  /                                  dx²   dy²   dz²

  which is expressed by

    [nabla]²(u,v,w) = 2 curl ([xi], [eta], [zeta]),
      ([xi], [eta], [zeta]) = ½ curl (u, v, w).   (11)

  38. _Moving Axes in Hydrodynamics._--In many problems, such as the
  motion of a solid in liquid, it is convenient to take coordinate axes
  fixed to the solid and moving with it as the movable trihedron frame
  of reference. The components of velocity of the moving origin are
  denoted by U, V, W, and the components of angular velocity of the
  frame of reference by P, Q, R; and then if u, v, w denote the
  components of fluid velocity in space, and u´, v´, w´ the components
  relative to the axes at a point (x, y, z) fixed to the frame of
  reference, we have

    u = U + u´ - yR + zQ,   (1)
    v = V + v´- zP + xR,
    w = W + w´ - xQ + yP.

  Now if k denotes the component of absolute velocity in a direction
  fixed in space whose direction cosines are l, m, n,

    k = lu + mv + nw;   (2)

  and in the infinitesimal element of time dt, the coordinates of the
  fluid particle at (x, y, z) will have changed by (u´, v´, w´)dt; so
  that

    Dk   dl    dm    dn
    -- = --u + --v + --w
    dt   dt    dt    dt

        / du     du     du     du \
    + l(  -- + u´-- + v´-- + w´--  )
        \ dt     dx     dy     dz /

        / dv     dv     dv     dv \
    + m(  -- + u´-- + v´-- + w´--  )
        \ dt     dx     dy     dz /

        / dw     dw     dw     dw \
    + n(  -- + u´-- + v´-- + w´--  ).   (3)
        \ dt     dx     dy     dz /

  But as l, m, n are the direction cosines of a line fixed in space,

    dl            dm            dn
    -- = mR - nQ, -- = nP - lR, -- = lQ - mP; (4)
    dt            dt            dt

  so that

    Dk     / du               du     du     du \
    -- = l(  -- - vR + wQ + u´-- + v´-- + w´--  ) + m(...) + n(...)
    dt     \ dt               dx     dy     dz /

           /    1  dp \      /     1  dp \      /     1  dp \
       = l( X- --- --  ) + m( Y - --- --  ) + n( Z - --- --  ),   (5)
           \    p  dx /      \     p  dy /      \     p  dz /

  for all values of l, m, n, leading to the equations of motion with
  moving axes.

  When the motion is such that

          d[phi]    d[psi]        d[phi]    d[psi]        d[phi]    d[psi]
    u = - ------ - m------, v = - ------ - m------, w = - ------ - m------,   (6)
            dx        dx            dy        dy             dz        dz

  as in §25 (1), a first integral of the equations in (5) may be written
      _
     /  dp               d[phi]    d[psi]             / d[phi]    d[psi] \
     | ----- + V + ½q² - ------ - m------ + (u - u´) ( ------ + m------   )
    _/ [rho]               dt        dt               \  dx         dx   /

               / d[phi]    d[psi] \             / d[phi]    d[psi] \
    + (v - v´)(  ------ + m------  ) + (w - w´)(  ------ + m------  ) = F(t),   (7)
               \   dy        dy   /             \   dz        dz   /
  in which

    d[phi]           d[phi]          d[phi]           d[phi]
    ------ - (u - u´)------ - (v -v´)------ - (w - w´)------
      dt               dx              dy               dz

      d[phi]                d[phi]                d[phi]                d[phi]
    = ------ - (U - yR + zQ)------ - (V - zP + xR)------ - (W - xQ + yP)------   (8)
        dt                    dx                    dy                    dz

  is the time-rate of change of [phi] at a point fixed in space, which
  is left behind with velocity components u - u´, v - v´, w - w´.

  In the case of a steady motion of homogeneous liquid symmetrical about
  Ox, where O is advancing with velocity U, the equation (5) of § 34

    p/[rho] + V + ½q´² - [f]([psi]´) = constant   (9)

  becomes transformed into

      p                U  d[psi]
    ----- + V + ½q² - --- ------ + ½U² - [f]([psi] + ½Uy²) = constant,   (10)
    [rho]              y    dy

    [psi]´ = [psi] + ¼U²,   (11)

  subject to the condition, from (4) §34,

    y^(-2)[nabla]²[psi]´ = -[f]´([psi]´),
    y^(-2)[nabla]²[psi]  = -[f]´([psi] + ½Uy²).   (12)

  Thus, for example, with

    [psi]´ = ¾Uy²(r²a^(-2) - 1), r² = x² + y²,   (13)

  for the space inside the sphere r = a, compared with the value of
  [psi]´ in §34 (13) for the space outside, there is no discontinuity of
  the velocity in crossing the surface.

  Inside the sphere

               d   / 1  d[psi]´\     d   / 1  d[psi]´\    15    y
    2[zeta] = --- ( --- ------- ) + --- ( --- ------- ) = ---U ---,   (14)
              dx   \ y    dx   /    dy   \ y     dy  /     2    a²

  so that §34 (4) is satisfied, with

                  15                        15
    [f]´([psi]´)= ---Ua^(-2), [f]([psi]´) = ---U[psi]´a^(-2);   (15)
                   2                         2

  and (10) reduces to
                      _                        _
      p          9   |  / x²   \²    / y²    \² |
    ----- + V - ---U | ( --- -1 ) - ( --- - ½ ) | = constant;   (16)
    [rho]        8   |_ \ a²   /     \ a²    / _|

  this gives the state of motion in M. J. M. Hill's spherical vortex,
  advancing through the surrounding liquid with uniform velocity.

  39. As an application of moving axes, consider the motion of liquid
  filling the ellipsoidal case

     x²    y²    z²
    --- + --- + --- = 1;   (1)
     a²    b²    c²

  and first suppose the liquid to be frozen, and the ellipsoid to be
  rotating about the centre with components of angular velocity [xi],
  [eta], [zeta]; then

    u = - y[zeta] + z[eta], v = - z[xi] + x[zeta],
    w = - x[eta] + y[xi].   (2)

  Now suppose the liquid to be melted, and additional components of
  angular velocity [Omega]1, [Omega]2, [Omega]3 communicated to the
  ellipsoidal case; the additional velocity communicated to the liquid
  will be due to a velocity-function

                       b² - c²               c² - a²              a² - b²
    [phi] = - [Omega]1 ------- yz - [Omega]2 -------zx - [Omega]3 -------xy,   (3)
                       b² + c²               c² + a²              a² + b²

  as may be verified by considering one term at a time.

  If u´, v´, w´ denote the components of the velocity of the liquid
  relative to the axes,

                         2a²                  2a²
    u´ = u + yR - zQ = ------- [Omega]3 y - ------- [Omega]2 z,   (4)
                       a² + b²              c² + a²

                         2b²                  2b²
    v´ = v + zP - xR = ------- [Omega]1 z - ------- [Omega]3 x,   (5)
                       b² + c²              a² + b²

                         2c²                  2c²
    w´ = w + xQ - yP = ------- [Omega]2 x - ------- [Omega]1 y,   (6)
                       c² + a²              b² + c²

    P = [Omega]1 + [xi], Q = [Omega]2 + [eta], R = [Omega]3 + [zeta].   (7)

  Thus

        x        y        z
    u´ --- + v´ --- + w´ --- = 0,   (8)
       a2       b2       c2

  so that a liquid particle remains always on a similar ellipsoid.

  The hydrodynamical equations with moving axes, taking into account the
  mutual gravitation of the liquid, become

      1   dp                  du               du     du     du
    ----- -- + 4[pi][rho]Ax + -- - vR + wQ + u´-- + v´-- + w´-- = 0, ... , ... ,   (9)
    [rho] dx                  dt               dx     dy     dz

  where
               _
              / [oo]                abcd[lambda]
    A, B, C = |     ----------------------------------------------
             _/ 0   (a² + [lambda], b² + [lambda], c² + [lambda])P

    P² = 4(a² + [lambda]) (b² + [lambda]) (c² + [lambda]).   (10)

  With the values above of u, v, w, u´, v´, w´, the equations become of
  the form

      1   dp
    ----- -- + 4[pi][rho]Ax + [alpha]x + hy + gz = 0,   (11)
    [rho] dx

      1   dp
    ----- -- + 4[pi][rho]By + hx + [beta]y + fz = 0,   (12)
    [rho] dy

      1   dp
    ----- -- + 4[pi][rho]Cz + gx + fy + [gamma]z = 0,   (13)
    [rho] dz

  and integrating

    p[rho]^(-1) + 2[pi][rho](Ax² + By² + Cz²)

      + ½([alpha]x² + [beta]y² + [gamma]z² + 2fyz + 2gzx + 2hxy) = const.,   (14)

  so that the surfaces of equal pressure are similar quadric surfaces,
  which, symmetry and dynamical considerations show, must be coaxial
  surfaces; and f, g, h vanish, as follows also by algebraical
  reduction; and

              4c²(c² - a²)             / c² - a²                \²
    [alpha] = ------------[Omega]2² - (  -------[Omega]2 - [eta] )
               (c² + a²)²              \ c² + a²                /

            4b²(a² - b²)             / a² - b²                 \²
          - ------------[Omega]3² - (  -------[Omega]3 - [zeta] ),   (15)
             (a² + b²)²              \ a² + b²                 /

  with similar equations for [beta] and [gamma].

  If we can make

    (4[pi][rho]A + [alpha])x² = (4[pi][rho]B + [beta])b²
      = (4[pi][rho]C + [gamma])c²,   (16)

  the surfaces of equal pressure are similar to the external case, which
  can then be removed without affecting the motion, provided [alpha],
  [beta], [gamma] remain constant.

  This is so when the axis of revolution is a principal axis, say Oz;
  when

    [Omega]1 = 0, [Omega]2 = 0, [xi] = 0, [eta] = 0.   (17)

  If [Omega]3 = 0 or [theta]3 = [zeta] in addition, we obtain the
  solution of Jacobi's ellipsoid of liquid of three unequal axes,
  rotating bodily about the least axis; and putting a = b, Maclaurin's
  solution is obtained of the rotating spheroid.

  In the general motion again of the liquid filling a case, when a = b,
  [Omega]3 may be replaced by zero, and the equations, hydrodynamical
  and dynamical, reduce to

    d[xi]       2c²                   d[eta]     2a²
    ----- = - -------[Omega]2 [zeta], ------ = -------[Omega]1 [zeta],
     dt       a² + c²                   dt     a² + c²

      d[zeta]     2c²
      ------- = -------([Omega]2 [xi] - [Omega]2 [eta])   (18)
        dt      a² + c²

    d[Omega]1                     a² + c²
    --------- = [Omega]2 [zeta] + -------[eta][zeta],
        dt                        a² - c²

      d[Omega]2                     a² + c²
      --------- = [Omega]1 [zeta] + -------[xi][zeta];   (19)
         dt                         a² - c²

  of which three integrals are

                         a²
    [xi]² + [eta]² = L - --[zeta]²,   (20)
                         c²

                                 (a² + c²)²
    [Omega]1² + [Omega]2² = M + ------------ [zeta]²,   (21)
                                2c²(a² - c²)

                                        a² + c²
    [Omega]1 [xi] + [Omega]2 [eta]N = + ------- [zeta]²;   (22)
                                          4c²
  and then

     / d[zeta]\²     4c^4
    (  ------- ) = --------- ([Omega]2[xi] - [Omega]1²[eta])²
     \   dt   /    (a² + c²)

        4c^4
    = ---------- [([xi]² + [eta]²)([Omega)1² + [Omega]2²) -([Omega]1[xi] + [Omega]2[eta])²]
      (a² + c²)²
                  _
         4c^4    |            /  (a² + c²)²       a²     (a² + c²)\
    = ---------- | LM - N² + ( L------------ - M --- - N --------- ) [zeta]²
      (a² + c²)² |_           \ 2c²(a² + c²)      c²        2c²   /
                                  _
      (a² + c²)(9a² - c²)          |
    - ------------------- [zeta]^4 | = Z,   (23)
        16c^4(a² - c²)            _|

  where Z is a quadratic in [zeta]², so that [zeta] is an elliptic
  function of t, except when c = a, or 3a.

    Put [Omega]1 = [Omega] cos [phi], [Omega]2 = -[Omega] sin [phi],

             d[phi]   d[Omega]1                      d[Omega]2                    (a² + c²)
    [Omega]2 ------ = -----------[Omega]2 - [Omega]1 --------- = [Omega]²[zeta] - ---------([Omega]1 [xi] + [Omega]2 [eta])[zeta],   (24)
               dt          dt                            dt                       (a² - c²)

                                            a² + c²
                                        N + -------
    d[phi]            (a² + c²)               4c²
    ------ = [zeta] - --------- · -------------------------,   (25)
      dt              (a² - c²)         (a² + c²)²
                                  M +  ------------[zeta]²
                                       2c²(a² - c²)

                                          a² + c²
             _                    _   N + -------[zeta]²
            / [zeta]d   a² + c²  /          4c²               [zeta] d[zeta]
    [phi] = | ------- - -------  | ------------------------ · --------------,   (26)
           _/ [root]Z   a² - c² _/      (a² + c²)²                [root]Z
                                   M + ------------[zeta]²
                                       2c²(a² - c²)

  which, as Z is a quadratic function of [zeta]², are non-elliptic
  integrals; so also for [psi], where [xi] = [omega] cos [psi], [eta] =
  -[omega] sin [psi].

  In a state of steady motion

    d[zeta]      [Omega]1   [Omega]2
    ------- = 0, -------- = --------,   (27)
       dt          [xi]       [eta]

    [phi] = [psi] = nt, suppose,   (28)

    [Omega]1[xi] + [Omega]2 [eta] = [Omega][omega],   (29)

    d[phi]           a² + c² [omega]
    ------ = [zeta]- ------- -------[zeta],   (30)
      dt             a² - c² [Omega]

    d[psi]       2a²   [Omega]
    ------ = - ------- -------[zeta],   (31)
      dt       a² + c² [omega]

        a² + c² [omega]       2a²   [Omega]
    1 - ------- ------- = - ------- -------,   (32)
        a² - c² [Omega]     a² + c² [omega]

     / [omega]     a² + c² \²   (a² - c²)(9a² - c²)
    (  ------- - ½ -------  ) = -------------------,   (33)
     \ [Omega]     a² - c² /        4(a² + c²)

  and a state of steady motion is impossible when 3a > c > a.

An experiment was devised by Lord Kelvin for demonstrating this, in
which the difference of steadiness was shown of a copper shell filled
with liquid and spun gyroscopically, according as the shell was slightly
oblate or prolate. According to the theory above the stability is
regained when the length is more than three diameters, so that a modern
projectile with a cavity more than three diameters long should fly
steadily when filled with water; while the old-fashioned type, not so
elongated, would be highly unsteady; and for the same reason the gas
bags of a dirigible balloon should be over rather than under three
diameters long.

40. _A Liquid Jet._--By the use of the complex variable and its
conjugate functions, an attempt can be made to give a mathematical
interpretation of problems such as the efflux of water in a jet or of
smoke from a chimney, the discharge through a weir, the flow of water
through the piers of a bridge, or past the side of a ship, the wind
blowing on a sail or aeroplane, or against a wall, or impinging jets of
gas or water; cases where a surface of discontinuity is observable, more
or less distinct, which separates the running stream from the dead water
or air.

  Uniplanar motion alone is so far amenable to analysis; the velocity
  function [phi] and stream function [psi] are given as conjugate
  functions of the coordinates x, y by

    w = [f](z) where z = x + yi, w = [phi] + [psi]i,   (1)

  and then

    dw   d[phi]    d[psi]
    -- = ------ + i------ = -u + vi;   (2)
    dz     dx        dx

  so that, with u = q cos [theta], v = q sin [theta], the function

                dz      Q        Q             Q
    [zeta] = -Q -- = -------- = ---(u + vi) = --- (cos [theta] + i sin [theta]),   (3)
                dw   (u - vi)    q²            q

  gives [zeta] as a vector representing the reciprocal of the velocity q
  in direction and magnitude, in terms of some standard velocity Q.

  To determine the motion of a jet which issues from a vessel with plane
  walls, the vector [zeta] must be Constructed so as to have a constant
  direction [theta] along a plane boundary, and to give a constant skin
  velocity over the surface of a jet, where the pressure is constant.

  It is convenient to introduce the function

    [Omega] = log [zeta] = log(Q/q) + [theta]i   (4)

  so that the polygon representing [Omega] conformally has a boundary
  given by straight lines parallel to the coordinate axes; and then to
  determine [Omega] and w as functions of a variable u (not to be
  confused with the velocity component of q), such that in the conformal
  representation the boundary of the [Omega] and w polygon is made to
  coincide with the real axis of u.

  [Illustration: FIG. 4.]

  It will be sufficient to give a few illustrations.

  Consider the motion where the liquid is coming from an infinite
  distance between two parallel walls at a distance xx´ (fig. 4), and
  issues in a jet between two edges A and A´; the wall xA being bent at
  a corner B, with the external angle [beta] = ½[pi]/n.

  The theory of conformal representation shows that the motion is given
  by
              _                                           _
             | [root](b - a´·u - a) + [root](b - a·u - a´) |^1/n
    [zeta] = | ------------------------------------------- |     , u = ae^(-[pi]w/m);   (5)
             |_           [root](a - a´·u - b)            _|

  where u = a, a´ at the edge A, A¹; u = b at a corner B; u = 0 across
  xx´ where [phi] = [oo]; and u = [oo], [phi] = [oo] across the end JJ´
  of the jet, bounded by the curved lines APJ, A´P´J´, over which the
  skin velocity is Q. The stream lines xBAJ, xA´J´ are given by [psi] =
  0, m; so that if c denotes the ultimate breadth JJ´ of the jet, where
  the velocity may be supposed uniform and equal to the skin velocity Q,

    m = Qc, c = m/Q.

  If there are more B corners than one, either on xA or x´A´, the
  expression for [zeta] is the product of corresponding factors, such as
  in (5).

  Restricting the attention to a single corner B,

                / Q \^n                                  [root](b - a´·u - a) + [root](b - a·u - a´)
    [zeta]^n = ( --- )  (cos n[theta] + i sin n[theta] = -------------------------------------------,   (6)
                \ q /                                                 [root](a - a´.u - b)

                         / Q \^n                          / Q \^n
    ch n[omega] = ch log( --- )  cos n[theta] + i sh log ( --- )  sin n[theta]
                         \ q /                            \ q /

                                       /b - a´     /u - a´
      = ½([zeta]^n + [zeta]^(-n)) =   / ------    / ------   (7)
                                    \/  a - a´  \/  u - b´

                          / Q \                           / Q \^n
    sh n[Omega] = sh log ( --- ) cos n[theta] + i ch log ( --- )  sin n[theta]
                          \ q /                           \ q /

                                       /b - a´    /u - a´
      = ½([zeta]^n - [zeta]^(-n)) =   / ------   / ------   (8)
                                    \/  a - a´ \/  u - b´

    [oo] > a > b > 0 > a´ > -[oo]   (9)

  and then

    d[Omega]     1     [root](b - a´·b - a´)     dw       m
    -------- = - -- ---------------------------, -- = - ------   (10)
       du        2n (u - b)[root](a - a·u - a´)  du     [pi]u´

  the formulas by which the conformal representation is obtained.

  For the [Omega] polygon has a right angle at u = a, a´, and a zero
  angle at u = b, where [theta] changes from 0 to ½[pi]/n and [Omega]
  increases by ½i[pi]/n; so that

    d[Omega]               A                          [root](b - a·b - a´)
    -------- = ---------------------------, where A = --------------------.   (11)
       du      (u - b)[root](u - a·u - a´)                     2n

  And the w polygon has a zero angle at u = 0, [oo], where [psi] changes
  from 0 to m and back again, so that w changes by im, and

    dw    B                m
    -- = ---, where B = - ----.   (12)
    du    u               [pi]

  Along the stream line xBAPJ,

    [psi] = 0, u = ae^(-[pi][phi]/m);   (13)

  and over the jet surface JPA, where the skin velocity is Q,

    d[phi]
    ------ = -q = -Q, u = ae^([pi]sQ/m) = ae^([pi]s/c),   (14)
      ds

  denoting the arc AP by s, starting at u = a;

                                    /b - a´    /u - a´
    ch n[Omega] = cos n[theta] =   / -----    / ------   (15)
                                 \/  a - a´ \/  u - b´

                                        /a - b     /u - a´
    sh n[Omega] = i sin n[theta] = i   / ------   / ------   (16)
                                     \/  a - a´ \/  u - b´

    [oo] > u = ae^([pi]s/c) > a,   (17)

  and this gives the intrinsic equation of the jet, and then the radius
  of curvature

                ds        1   d[phi]     i    dw       i  dw   / d[Omega]
    [rho] = - -------- = --- -------- = --- ------- = --- --  /  -------
              d[theta]    Q  d[theta]    Q  d[Omega]   Q  du /      du

             c     u - b [root](u - a·u - a´)
          = ----·2n----- --------------------,   (18)
            [pi]     u   [root](a - b·b - a´)

  not requiring the integration of (11) and (12)

  If [theta] = [alpha] across the end JJ´ of the jet, where u = [oo], q
  = Q,

                                    /b - a´                                   /a - b
    ch n[Omega] = cos n[alpha] =   /-------, sh n[Omega] = i sin n[alpha]=   / ------,   (19)
                                 \/  a - a´                                \/  a - a´

  Then

                                     a - b·b - a´                   a - a´
    cos 2n[alpha] - cos 2n[theta] = 2------------ = ½ sin² 2n[alpha]------
                                     a - a´·u - b                   u - b

                     [root](a - b.b - a´)[root](u - a·u - b´)
    sin 2n[theta] = 2----------------------------------------   (20)
                                  a - a´·u - b

                                 [root](a - a·b - a´)
                  = sin 2n[alpha]--------------------;
                                         u - b

     2n     c      /      b  \  [root](a - b·b - a´)
    ----- ----- = ( 1 + ----- ) --------------------   (21)
    [phi] [rho]    \    u - b/  [root](u - a·u - a´)

      a - a´ + (a + a´) cos 2n[alpha] - [a + a´ + (a - a´) cos 2n[alpha] cos 2n[theta]
    = --------------------------------------------------------------------------------
                               (a - a´) sin² 2n[alpha]

                                  cos 2n[alpha] - cos 2n[theta]
                                × -----------------------------
                                          sin 2n[theta]

  Along the wall AB, cos n[theta] = 0, sin n[theta] = 1,

    a > u > b,    (22)

                            / Q \^n         /b - a´    /a - u
    ch n[Omega] = i sh log ( --- )   = i   / ------   / ------   (23)
                            \ q /        \/  a - a´ \/  u - b´

                            / Q \^n         /a - b     /u - a´
    sh n[Omega] = i ch log ( --- )   = i   / ------   / ------   (24)
                            \ q /        \/  a - a´ \/  u - b´

    ds     ds   d[phi]     m       c   Q
    -- = ------ ------ = ------ = ---  --   (25)
    du   d[phi]   dt     [pi]qu   [pi] qu
              _
        AB   / a  Q  du
    [pi]-- = |   --- --
        c   _/ b  q  u
         _  _                                                         _
        /  | [root](a - b)[root](u - a´) + [root](b - a´)[root](a - u) |^1/n du
      = |  | --------------------------------------------------------- |     --.   (26)
       _/  |_             [root](a - a´)[root](u - b´)                _|     u

  Along the wall Bx, cos n[theta] = 1, sin n[theta] = 0,

    b > u > 0   (27)

                          / Q \^n       /b - a´    /a - u
    ch n[Omega] = ch log ( --- )   =   / ------   / ------   (28)
                          \ q /      \/  a - a´ \/  b - u´

                          / Q \^n       /a - b     /u - a´
    sh n[Omega] = sh log ( --- )   =   / ------   / ------.   (29)
                          \ q /      \/  a - a´ \/  b - u

  At x where [phi] = [oo], u = 0, and q = q0,

     / Q  \^n       /b - a´    / a       /a - b     / -a´
    ( ---  )   =   / ------   / --- +   / ------   /  ---.   (30)
     \ q0 /      \/  a - a´ \/   b    \/  a - a´ \/    q

  In crossing to the line of flow x´A´P´J´, [psi] changes from 0 to m,
  so that with q = Q across JJ´, while across xx´ the velocity is q0, so
  that

    m = q0.xx´ = Q.JJ´   (31)
                 _                                         _
    JJ´   q0    |     /b - a´    / a       /a - b     / -a´ |^1/n
    -- =  --- = |    / ------   / --- -   / ------   /  --- |     ,   (32)
    xx´    Q    |_ \/  a - a´ \/   b    \/  a - a´ \/    q _|

  giving the contraction of the jet compared with the initial breadth of
  the stream.

  Along the line of flow x´A´P´J´, [psi] = m, u = a´e^(-[pi][phi]/m),
  and from x´ to A´, cos n[theta] = 1, sin n[theta] = 0,

                          / Q \^n       /b - a´    /a - u
    ch n[Omega] = ch log ( --- )   =   / ------   / ------,   (33)
                          \ q /      \/  a - a´ \/  b - u´

                          / Q \^n       /a - b     /u - a´
    sh n[Omega] = sh log ( --- )   =   / ------   / ------.   (34)
                          \ q /      \/  a - a´ \/  b - u´

    0 > u > a´.   (35)

  Along the jet surface A´J´, q = Q,

                                    /b - a´    /a - u
    ch n[Omega] = cos n[theta] =   / ------   / ------,   (36)
                                 \/  a - a´ \/  b - u´

                                       /a - b     /a´ - u
    sh n[Omega] = i sin n[theta] = i  / ------   / ------,   (37)
                                    \/  a - a´ \/  b - u´

    a´ > u = a´e^([pi]/sc) > -[oo],   (38)

  giving the intrinsic equation.

  41. The first problem of this kind, worked out by H. v. Helmholtz, of
  the efflux of a jet between two edges A and A1 in an infinite wall, is
  obtained by the symmetrical duplication of the above, with n = 1, b =
  0, a´ = -[oo], as in fig. 5,

                    /u - a                 / -a
    ch [Omega] =   / -----, sh [Omega] =  /  ---;   (1)
                 \/    u                \/    u

  and along the jet APJ, [oo] > u = ae^([pi]s/c) > a,

    sh [Omega] = i sin [theta] - i[root](a/u) = ie^(-½[pi]s/c),   (2)
          _                      _
         / [oo]                 /                      c                     c
    PM = |     sin [theta] ds = | e^(-½[pi]s/c) ds = ----- e^(-½[pi]s/c) = ----- sin [theta],   (3)
        _/ s                   _/                    ½[pi]                 ½[pi]

  so that PT = c/½[pi], and the curve AP is the tractrix; and the
  coefficient of contraction, or

      breadth of the jet       [pi]
    ---------------------- = --------.   (4)
    breadth of the orifice   [pi] + 2

  A change of [Omega] and [theta] into n[Omega] and n[theta] will give
  the solution for two walls converging symmetrically to the orifice AA1
  at an angle [pi]/n. With n = ½, the reentrant walls are given of
  Borda's mouthpiece, and the coefficient of contraction becomes ½.
  Generally, by making a´ = - [oo], the line x´A´ may be taken as a
  straight stream line of infinite length, forming an axis of symmetry;
  and then by duplication the result can be obtained, with assigned n,
  a, and b, of the efflux from a symmetrical converging mouthpiece, or
  of the flow of water through the arches of a bridge, with wedge-shaped
  piers to divide the stream.

  [Illustration: FIG. 5.]

  [Illustration: FIG. 6.]

  42. Other arrangements of the constants n, a, b, a´ will give the
  results of special problems considered by J. M. Michell, _Phil.
  Trans._ 1890.

  Thus with a´ = 0, a stream is split symmetrically by a wedge of angle
  [pi]/n as in Bobyleff's problem; and, by making a = [oo], the wedge
  extends to infinity; then

                     /  b                     /  n
    ch n[Omega] =   / -----, sh n[Omega] =   / -----.   (1)
                  \/  b - u                \/  b - u

  Over the jet surface [psi] = m, q = Q,

    u = - e^([pi][phi]/m) = - be^([pi]²/c),

                                   /       1                                            /  e^([pi]²/c)
    ch [Omega] = cos n[theta] =   / ---------------, sh [Omega] = i sin n[theta] = i   / ---------------,   (2)
                                \/  e^([pi]²/c) + 1                                  \/  e^([pi]²/c) + 1

                                 ½[pi]    ds            2n
    e^(½[pi]²/c) = tan n[theta], ----- -------- = -------------.   (3)
                                   c   d[theta]   sin 2n[theta]

  For a jet impinging normally on an infinite plane, as in fig. 6, n = 1,

    e^(½[pi]²/c) = tan [theta], ch (½[pi]s/c) sin 2[theta] = 1,   (4)

    sh ½[pi]x/c = cot [theta], sh ½[pi]y/c = tan [theta],

    sh ½[pi]x/c sh ½[pi]y/c = 1, e^(½[pi](x + y)/c) = e^(½[pi]x/c) + e^(½[pi]y/c) + 1.   (5)

  With n = ½, the jet is reversed in direction, and the profile is the
  catenary of equal strength.

  In Bobyleff's problem of the wedge of finite breadth,

                     / b     /u - a                   /b - a    /  u
    ch n[Omega] =   / ---   / -----, sh n[Omega] =   / -----   / -----,   (6)
                  \/   a  \/  u - b                \/    a   \/  u - b

                      / b                     /a - b
    cos n[alpha] =   / ---, sin n[alpha] =   / -----,   (7)
                   \/   a                  \/    a

  and along the free surface APJ, q = Q, [psi] = 0, u = e^(-[pi][phi]/m) = ae^([pi]s/c),

                                   /      e^([pi]²/c) - 1
    cos n[theta] = cos n[alpha]   / ---------------------------,
                                \/  e^([pi]²/c) - cos² n[alpha]

                   cos² n[alpha] sin² n[theta]
    e^([pi]²/c) = -----------------------------,   (8)
                  sin² n[theta] - sin² n[alpha]

  the intrinsic equation, the other free surface A´P´J´ being given by

                   cos² n[alpha] sin² n[theta]
    e^([pi]²/c) = -----------------------------.   (9)
                  sin² n[alpha] - sin² n[theta]

  Putting n = 1 gives the case of a stream of finite breadth disturbed
  by a transverse plane, a particular case of Fig. 7.

  When a = b, [alpha] = 0, and the stream is very broad compared with
  the wedge or lamina; so, putting w = w´(a - b)/a in the penultimate
  case, and

    u = ae^(-w) [asympt] a - (a - b)w´,   (10)

                     /w´ + 1                   /   1
    ch n[Omega] =   / ------, sh n[Omega] =   / --------,   (11)
                  \/    w´                  \/  [root]w´

  in which we may write

    w´ = [phi] + [psi]i. (12)

  Along the stream line xABPJ, [psi] = 0; and along the jet surface APJ,
  -1 > [phi] > -[oo]; and putting [phi] = -[pi]s/c - 1, the intrinsic
  equation is

    [pi]s/c = cot² n[theta],   (13)

  which for n = 1 is the evolute of a catenary.

  [Illustration: FIG. 7.]

  43. When the barrier AA´ is held oblique to the current, the stream
  line xB is curved to the branch point B on AA´ (fig. 7), and so must
  be excluded from the boundary of u; the conformal representation is
  made now with

    d[Omega]         [root](b - a·b - a´)
    -------- = - ----------------------------   (1)
       du        (u - b) [root](u - a·u - a´)

    dw      m     1      m´    1        m + m´       u - b
    -- = - ---- ----- - ---- -----, = - ------ · -------------,
    du     [pi] u - j   [pi] u - j       [pi]     u - j·u - j´

        mj´ + m´j
    b = ---------,   (2)
          m + m´

  taking u = [oo] at the source where [phi] = [oo], u = b at the branch
  point B, u = j, j´ at the end of the two diverging streams where [phi]
  = -[oo]; while [psi] = 0 along the stream line which divides at B and
  passes through A, A´; and [psi] = m, -m´ along the outside boundaries,
  so that m/Q, m´/Q is the final breadth of the jets, and (m + m´)/Q is
  the initial breadth, c1 of the impinging stream. Then

                     /b - a´    /u - a                   /b - a     /u - a´
    ch ½[Omega] =   / ------   / -----, sh ½[Omega] =   / ------   / ------,   (3)
                  \/  a - a´ \/  u - b                \/  a - a´ \/  u - b

                 2b - a - a´    N
    ch [Omega] = ----------- - -----,
                    a - a´     u - b

                    / [root](2·a - u·u - a´)
    sh [Omega] =   / N----------------------,
                 \/            u - b

         a - b·b - a´
    N = 2------------.   (4)
            a - a´

  Along a jet surface, q = Q, and

    ch[Omega] = cos [theta] = cos [alpha] - ½sin² [alpha](a - a´)/(u - b),   (5)

  if [theta] = [alpha] at the source x of the jet xB, where u = [oo];
  and supposing [theta] = [beta], [beta]´ at the end of the streams
  where u = j, j´,

    u - b        ½ sin² [alpha]        u - j                                cos[theta] - cos[beta]
    ----- = -------------------------, ------ = ½ sin² [alpha]-----------------------------------------------------,
    a - a´  cos [alpha] - cos [theta]  a - a´                 (cos [alpha] - cos [beta])(cos [alpha] - cos [theta])

    u - j´                               cos [theta] - cos [beta]´
    -----  = ½ sin² [alpha]------------------------------------------------------;   (6)
    a - a´                 (cos [alpha] - cos [beta]´)(cos [alpha] - cos [theta])

  and [psi] being constant along a stream line

    d[phi]   dw       ds       d[phi]    dw    du
    ------ = --, Q -------- = -------- = -- --------,
      du     du    d[theta]   d[theta]   du d[theta]

    [pi]Q     ds      [pi]    ds               (cos [alpha] - cos [beta])(cos [alpha] - cos [beta]´)sin[theta]
    ------ -------- = ---- -------- = ---------------------------------------------------------------------------------,
    m + m´ d[theta]    c   d[theta]   (cos [alpha] - cos [theta])(cos [theta] - cos [beta])(cos [theta] - cos [alpha]´)

             sin [theta]          cos [alpha] - cos [beta]´         sin [theta]
    = ------------------------- + ------------------------- · ------------------------
      cos [alpha] - cos [theta]    cos [beta] - cos [beta]´   cos [theta] - cos [beta]

    cos [alpha] - cos [beta]          sin [theta]
    ------------------------ · -------------------------,   (7)
    cos [beta] - cos [beta]´   cos [theta] - cos [beta]´

  giving the intrinsic, equation of the surface of a jet, with proper
  attention to the sign.

  From A to B, a > u > b, [theta] = 0,

                         Q                                 a - a´
    ch [Omega] = ch log --- = cos [alpha] - ½ sin² [alpha] ------
                         q                                 a - b

                         Q    [root](a - u·u - a´)
    sh [Omega] = sh log --- = -------------------- sin [alpha]
                         q            u - b

     Q    (u - b) cos [alpha] - ½(a - a´) sin² [alpha] + [root](a - u·u - a´)sin[alpha]
    --- = -----------------------------------------------------------------------------   (8)
     q                                       u - b

      ds       ds   d[phi]      Q  dw
    Q -- = Q ------ ------ = - --- --
      du     d[phi]   du        q  du

      m + m´   (u - b) cos [alpha] - ½(a - a´) sin² [alpha] + [root](a - u·u - a´) sin [alpha]
    = ------ · -------------------------------------------------------------------------------   (9)
       [pi]                                   j - u·u - j´
               _
        AB    / a  (2b - a - a´)(u - b) - 2(a - b)(b - a´) + 2[root](a - b·b -a´·a - u·u -a´)
    [pi]-- =  |    -------------------------------------------------------------------------- du,   (10)
        c    _/ b                             a - a´·j - u·u - j´

  with a similar expression for BA´.

  The motion of a jet impinging on an infinite barrier is obtained by
  putting j = a, j´ = a´; duplicated on the other side of the barrier,
  the motion reversed will represent the direct collision of two jets of
  unequal breadth and equal velocity. When the barrier is small compared
  with the jet, [alpha] = [beta] = [beta]´, and G. Kirchhoff's solution
  is obtained of a barrier placed obliquely in an infinite stream.

  Two corners B1 and B2 in the wall xA, with a´ = -[oo], and n = 1, will
  give the solution, by duplication, of a jet issuing by a reentrant
  mouthpiece placed symmetrically in the end wall of the channel; or
  else of the channel blocked partially by a diaphragm across the
  middle, with edges turned back symmetrically, problems discussed by J.
  H. Michell, A. E. H. Love and M. Réthy.

  When the polygon is closed by the walls joining, instead of reaching
  back to infinity at xx´, the liquid motion must be due to a source,
  and this modification has been worked out by B. Hopkinson in the
  _Proc. Lond. Math. Soc._, 1898.

  Michell has discussed also the hollow vortex stationary inside a
  polygon (_Phil. Trans._, 1890); the solution is given by

    ch n[Omega] = sn w, sh n[Omega] = i cn w   (11)

  so that, round the boundary of the polygon, [psi] = K´, sin n[theta] =
  0; and on the surface of the vortex [psi] = 0, q = Q, and

    cos n[theta] = sn [phi], n[theta] = ½[pi] - am s/c,   (12)

  the intrinsic equation of the curve.

  This is a closed Sumner line for n = 1, when the boundary consists of
  two parallel walls; and n = ½ gives an Elastica.

  44. _The Motion of a Solid through a Liquid._--An important problem in
  the motion of a liquid is the determination of the state of velocity
  set up by the passage of a solid through it; and thence of the
  pressure and reaction of the liquid on the surface of the solid, by
  which its motion is influenced when it is free.

  Beginning with a single body in liquid extending to infinity, and
  denoting by U, V, W, P, Q, R the components of linear and angular
  velocity with respect to axes fixed in the body, the velocity function
  takes the form

    [phi] = U_[phi]1 + V_[phi]2 + W_[phi]3 + P_[chi]1 + Q_[chi]2 + R_[chi]3,   (1)

  where the [phi]'s and [chi]'s are functions of x, y, z, depending on
  the shape of the body; interpreted dynamically, C - [rho][phi]
  represents the impulsive pressure required to stop the motion, or C +
  [rho][phi] to start it again from rest.

  The terms of [phi] may be determined one at a time, and this problem
  is purely kinematical; thus to determine [phi]1, the component U alone
  is taken to exist, and then l, m, n, denoting the direction cosines of
  the normal of the surface drawn into the exterior liquid, the function
  [phi]1 must be determined to satisfy the conditions

  (i.) [nabla]²[phi]1 = 0. throughout the liquid;

  (ii.) d[ph]1/d[upsilon] = -l, the gradient of [phi] down the normal at
  the surface of the moving solid;

  (iii.) d[ph]1/d[upsilon] = 0, over a fixed boundary, or at infinity;

  similarly for [phi]2 and [phi]3.

  To determine [chi]1 the angular velocity P alone is introduced, and
  the conditions to be satisfied are

  (i.) [nabla]²[chi]1 = 0, throughout the liquid;

  (ii.) d[chi]1/d[upsilon] = mz - ny, at the surface of the moving body,
  but zero over a fixed surface, and at infinity; the same for [chi]2
  and [chi]3.

  For a cavity filled with liquid in the interior of the body, since the
  liquid inside moves bodily for a motion of translation only,

    [phi]1 = -x, [phi]2 = -y, [phi]3 = -z;   (2)

  but a rotation will stir up the liquid in the cavity, so that the
  [chi]'s depend on the shape of the surface.

  The ellipsoid was the shape first worked out, by George Green, in his
  _Research on the Vibration of a Pendulum in a Fluid Medium_ (1833);
  the extension to any other surface will form an important step in this
  subject.

  A system of confocal ellipsoids is taken

          x²              y²             z²
    ------------- + ------------- + ------------- = 1   (3)
    a² + [lambda]   b² + [lambda]   c² + [lambda]

  and a velocity function of the form

    [phi] = x[psi],   (4)

  where [psi] is a function of [lambda] only, so that [psi] is constant
  over an ellipsoid; and we seek to determine the motion set up, and the
  form of [psi] which will satisfy the equation of continuity.

  Over the ellipsoid, p denoting the length of the perpendicular from
  the centre on a tangent plane,

              px                 py                pz
    l = -------------, m = -------------, n = -------------   (5)
        a² + [lambda]      b² + [lambda]      c² + [lambda]

              p²x²               p²y²               p²z²
    1 = ---------------- + ---------------- + ----------------,   (6)
        (a² + [lambda])²   (b² + [lambda])²   (c² + [lambda])²

    p² = (a² + [lambda])l² + (b² + [lambda])m² + (c² + [lambda])n²,   (7)
       = a²l² + b²m² + c²n² + [lambda],

      dp   d[lambda]
    2p-- = ---------;   (8)
      ds      ds

  Thence

    d[phi]   dx         d[psi]
    ------ = --[psi] + x------
      ds     ds           ds

             dx                         d[psi]    dp
           = --[psi] + 2(a² + [lambda])--------- l--,   (9)
             ds                        d[lambda]  ds

  so that the velocity of the liquid may be resolved into a component
  -[psi] parallel to Ox, and -2(a² + [lambda])l d[psi]/d[lambda] along
  the normal of the ellipsoid; and the liquid flows over an ellipsoid
  along a line of slope with respect to Ox, treated as the vertical.

  Along the normal itself

    d[phi]   /                          d[psi]   \
    ----- = ( [psi] + 2(a² + [lambda])--------    )l,   (10)
     ds      \                         d[lambda] /

  so that over the surface of an ellipsoid where [lambda] and [psi] are
  constant, the normal velocity is the same as that of the ellipsoid
  itself, moving as a solid with velocity parallel to Ox

                                  d[psi]
    U = -[psi] - 2(a² + [lambda])---------,   (11)
                                 d[lambda]

  and so the boundary condition is satisfied; moreover, any ellipsoidal
  surface [lambda] may be supposed moving as if rigid with the velocity
  in (11), without disturbing the liquid motion for the moment.

  The continuity is secured if the liquid between two ellipsoids
  [lambda] and [lambda]1, moving with the velocity U and U1 of equation
  (11), is squeezed out or sucked in across the plane x = 0 at a rate
  equal to the integral flow of the velocity [psi] across the annular
  area [alpha]1 - [alpha] of the two ellipsoids made by x = 0; or if
                              _
                             / [lambda]1     d[alpha]
    [alpha]U - [alpha]1U1 =  |          [psi]-------- d[lambda],   (12)
                            _/ [lambda]      d[lambda]

    [alpha] = [pi][root](b² + [lambda]·c² + [lambda]).   (13)

  Expressed as a differential relation, with the value of U from (11),
               _                                                _
        d     |                                        d[psi]    |        d[alpha]
    --------- | [alpha][psi] + 2(a² + [lambda])[alpha]---------  | - [psi]--------- = 0,   (14)
    d[lambda] |_                                      d[lambda] _|        d[lambda]

              d[psi]                       d      /        d[psi]  \
    3[alpha]--------- + 2(a² + [lambda])-------- ( [alpha]--------  ) = 0,   (15)
            d[lambda]                   d[lambda] \       d[lambda]/

  and integrating

                                d[psi]
    (a² + [lambda])^3/2 [alpha]-------- = a constant,   (16)
                               d[lambda]

  so that we may put
             _
            /     Md[lambda]
    [psi] = | ----------------,   (17)
           _/ (a² + [lambda])P

    P² = 4(a² + [lambda])(b² + [lambda])(c² + [lambda]),   (18)

  where M denotes a constant; so that [psi] is an elliptic integral of
  the second kind.

  The quiescent ellipsoidal surface, over which the motion is entirely
  tangential, is the one for which

                     d[psi]
    2(a² + [lambda])--------- + [psi] = 0,   (19)
                    d[lambda]

  and this is the infinite boundary ellipsoid if we make the upper limit
  [lambda]1 = [oo].

  The velocity of the ellipsoid defined by [lambda] = 0 is then

             d[psi]0
    U = -2a²--------- - [psi]0
            d[lambda]
                _
         M     / [oo]   Md[lambda]
      = --- -  |     ----------------
        abc   _/ 0   (a² + [lambda])P

         M
      = --- (1 - A0),   (20)
        abc

  with the notation
                        _
                       / [oo]      abc d[lambda]
    A or A_[lambda] =  |         ----------------
                      _/[lambda] (a² + [lambda])P
                                _
                            d  / [oo]    d[lambda]
                    = -2abc--- |         ---------,   (21)
                           da²_/ [lambda]    P

  so that in (4)

             M       UxA             xA_[lambda]
    [phi] = ---xA = ------, [phi]1 = -----------,   (22)
            abc     1 - A0              1 - A0

  in (1) for an ellipsoid.

  The impulse required to set up the motion in liquid of density [rho]
  is the resultant of an impulsive pressure [rho][phi] over the surface
  S of the ellipsoid, and is therefore
      _ _                               _ _
     / /                               / /
     | | [rho][phi]l dS = [rho][psi]0  | | xl dS
    _/_/                              _/_/

      = [rho][psi]0 (volume of the ellipsoid) = [psi]0 W´,   (23)

  where W´ denotes the weight of liquid displaced.

  Denoting the effective inertia of the liquid parallel to Ox by
  [alpha]W´. the momentum

    [alpha]W´U = [psi]0W´   (24)

              [psi]0     A0
    [alpha] = ------ = ------;   (25)
                 U     1 - A0

  in this way the air drag was calculated by Green for an ellipsoidal
  pendulum.

  Similarly, the inertia parallel to Oy and Oz is

                 B0                     C0
    [beta]W´ = ------ W´, [gamma]W´ = ------ W´,   (26)
               1 - B0                 1 - C0
                              _
                             / [oo]             abc d[lambda]
    B_[lambda], C_[lambda] = |         -------------------------------;   (27)
                            _/[lambda] (b² + [lambda], c² + [lambda])P

  and

    A + B + C = abc/½P, A0 + B0 + C0 = 1.   (28)

  For a sphere

    a = b = c, A0 = B0 = C0 = 1/3, [alpha] = [beta] = [gamma] = ½,   (29)

  so that the effective inertia of a sphere is increased by half the
  weight of liquid displaced; and in frictionless air or liquid the
  sphere, of weight W, will describe a parabola with vertical
  acceleration

     W - W´
    ------- g.   (30)
    W + ½W´

  Thus a spherical air bubble, in which W/W´ is insensible, will begin
  to rise in water with acceleration 2g.

  45. When the liquid is bounded externally by the fixed ellipsoid
  [lambda] = [lambda]1, a slight extension will give the velocity
  function [phi] of the liquid in the interspace as the ellipsoid
  [lambda] = 0 is passing with velocity U through the confocal position;
  [phi] must now take the form x([psi] + N), and will satisfy the
  conditions in the shape
                                                   _
                                         abc      /[lambda]1    abcd[lambda]
                                        ------ +  |           ----------------
                  A + B1 + C1           a1b1c1   _/ [lambda]  (a² + [lambda])P
    [phi] = Ux ----------------- = Ux ------------------------------------------,   (1)
               B0 + C0 - B1 - C1           abc      /[lambda]1    abcd[lambda]
                                      1 - ------ -  |           ----------------
                                          a1b1c1   _/0          (a² + [lambda])P

  and any confocal ellipsoid defined by [lambda], internal or external
  to [lambda] = [lambda]1, may be supposed to swim with the liquid for
  an instant, without distortion or rotation, with velocity along Ox

      B_[lambda] + C_[lambda]  - B1 - C1
    U ----------------------------------
              B0 + C0 - B1 - C1

  Since - Ux is the velocity function for the liquid W´ filling the
  ellipsoid [lambda] = 0, and moving bodily with it, the effective
  inertia of the liquid in the interspace is

       A0 + B1 + C1
    ----------------- W´.   (2)
    B0 + C0 - B1 - C1

  If the ellipsoid is of revolution, with b = c,

                A + 2B1
    [phi] = ½Ux -------,   (3)
                B0 - B1

  and the Stokes' current function [psi] can be written down

                   B - B1
    [psi] = - ½Uy² -------;   (4)
                   B0 - B1

  reducing, when the liquid extends to infinity and B1 = 0, to
                A                  B
    [phi] = ½Ux --, [psi] = - ½Uy² --;   (5)
                B0                 B0

  so that in the relative motion past the body, as when fixed in the
  current U parallel to xO,

                  /    A  \                    /    B  \
    [phi]´ = ½Ux ( 1 + --  ),   [psi]´ = ½Uy² ( 1 - --  ).   (6)
                  \    B0 /                    \    B0 /

  Changing the origin from the centre to the focus of a prolate
  spheroid, then putting b² = pa, [lambda] = [lambda]´a, and proceeding
  to the limit where a = [oo], we find for a paraboloid of revolution

                p        B          p
    B = ½ -------------, -- = -------------,   (7)
          p + [lambda]´  B0   p + [lambda]´

          y²
    ------------- = p + [lambda]´ - 2x,   (8)
    p + [lambda]´

  with [lambda]´ = 0 over the surface of the paraboloid; and then

    [psi]´ = ½U [y² - p[root](x² + y²) + px];   (9)

    [psi]  = -½Up [[root](x² + y²) - x];   (10)

    [phi]  = -½Up log [ [root](x² + y²) + x].   (11)

  The relative path of a liquid particle is along a stream line

    [psi]´ = ½Uc², a constant,   (12)

        p²y² - (y² - c²)²                    p²y² - (y² - c²)²
    x = -----------------, [root](x² + y²) = -----------------   (13)
           2p(y² - c²)                          2p(y² - c²)

  a C4; while the absolute path of a particle in space will be given by

    dy     r - x   y² - c²
    -- = - ----- = -------,   (14)
    dx       y       2py

    y² - c² = a²e^(-x/p).   (15)

  46. Between two concentric spheres, with

    a² + [lambda] = r², a² + [lambda]1 = a1²,   (1)

    A = B = C = a³/3r³,

                a³      a³                a³     a³
                -- + 2 ---                -- + 2 ---
                r³     a1³                r³     a1³
    [phi] = ½Ux -----------, [psi] = ½Uy² ----------;   (2)
                1 - a^4/a1²               1 - a³/a1³

  and the effective inertia of the liquid in the interspace is

     A0 + 2A1        a1³ + 2a³
    --------- W´ = ½ --------- W´.   (3)
    2A0 - 2A1        a1³ - a³

  When the spheres are not concentric, an expression for the effective
  inertia can be found by the method of images (W. M. Hicks, _Phil.
  Trans._, 1880).

  The image of a source of strength [mu] at S outside a sphere of radius
  a is a source of strength [mu]a/[f] at H, where OS = [f], OH = a²/f,
  and a line sink reaching from the image H to the centre O of line
  strength - [mu]/a; this combination will be found to produce no flow
  across the surface of the sphere.

  Taking Ox along OS, the Stokes' function at P for the source S is [mu]
  cos PSx, and of the source H and line sink OH is [mu](a/[f]) cos PHx
  and -([mu]/a)(PO - PH); so that

                  /          a            PO - PH \
    [psi] = [mu] (cos PSx + --- cos PHx - -------  ),   (4)
                  \         [f]              a    /

  and [psi] = -[mu], a constant, over the surface of the sphere, so that
  there is no flow across.

  When the source S is inside the sphere and H outside, the line sink
  must extend from H to infinity in the image system; to realize
  physically the condition of zero flow across the sphere, an equal sink
  must be introduced at some other internal point S´.

  When S and S´ lie on the same radius, taken along Ox, the Stokes'
  function can be written down; and when S and S´ coalesce a doublet is
  produced, with a doublet image at H.

  For a doublet at S, of moment m, the Stokes' function is

     d               y²
    m-- cos PSx = -m---;   (5)
     df             PS³

  and for its image at H the Stokes' function is

     d              a³  y²
    m-- cos PHx = -m-- ---;   (6)
     df             f³ PH³

  so that for the combination

                 /a³  1     1 \     y²  / a³    f³\
    [psi] = my² ( -- --- - --- ) = m-- ( --- - --- ),   (7)
                 \f³ PH³   PS³/     f³  \PH³   PS³/

  and this vanishes over the surface of the sphere.

  There is ao Stokes' function when the axis of the doublet at S does
  not pass through O; the image system will consist of an inclined
  doublet at H, making an equal angle with OS as the doublet S, and of a
  parallel negative line doublet, extending from H to O, of moment
  varying as the distance from O.

  A distribution of sources and doublets over a moving surface will
  enable an expression to be obtained for the velocity function of a
  body moving in the presence of a fixed sphere, or inside it.

  The method of electrical images will enable the stream function [psi]´
  to be inferred from a distribution of doublets, finite in number when
  the surface is composed of two spheres intersecting at an angle
  [pi]/m, where m is an integer (R. A. Herman, _Quart. Jour. of Math._
  xxii.).

  Thus for m = 2, the spheres are orthogonal, and it can be verified
  that

                   /    a1³   a2³   a³ \
    [psi]´ = ½Uy² ( 1 - --- - --- + --  ),   (8)
                   \    r1³   r2³   r³ /

  where a1, a2, a = a1a2/[root](a1² + a2²) is the radius of the spheres
  and their circle of intersection, and r1, r2, r the distances of a
  point from their centres.

  The corresponding expression for two orthogonal cylinders will be

                 /    a1²   a2²   a² \
    [psi]´ = Uy ( 1 - --- - --- + --  ).   (9)
                 \    r1²   r2²   r² /

  With a2 = [oo], these reduce to

                   /    a^5 \   x          /    a^4 \   x
    [psi]´ = ½Uy² ( 1 - ---  ) ---, or Uy ( 1 - ---  ) ---,   (10)
                   \    r^5 /   a          \    r^4 /   a

  for a sphere or cylinder, and a diametral plane.

  Two equal spheres, intersecting at 120°, will require
                   _                                              _
                  |  x     a³    a^4(a - 2x)    a³    a^4(a + 2x)  |
    [psi]´ = ½Uy² | --- - ---- + ----------- + ---- - -----------  |,   (11)
                  |_ a    2r1³      2r1^5      2r2³      2r2^5    _|

  with a similar expression for cylinders; so that the plane x = 0 may
  be introduced as a boundary, cutting the surface at 60°. The motion of
  these cylinders across the line of centres is the equivalent of a line
  doublet along each axis.

  47. The extension of Green's solution to a rotation of the ellipsoid
  was made by A. Clebsch, by taking a velocity function

    [phi] = xy[chi]   (1)

  for a rotation R about Oz; and a similar procedure shows that an
  ellipsoidal surface [lambda] may be in rotation about Oz without
  disturbing the motion if

           /      1              1        \              dx
          (  ------------ + ------------   ) [chi] + 2---------
           \ a² + [lambda]  b² + [lambda] /           d[lambda]
    R = - -----------------------------------------------------,   (2)
                   1/(b² + [lambda] - 1/(a² = [lambda])

  and that the continuity of the liquid is secured if

                                                              d[chi]
    (a² + [lambda])^3/2 (b² + [lambda])^3/2 (c² + [lambda]) ½--------- = constant,   (3)
                                                             d[lambda]
              _
             / [oo]               Nd[lambda]              N    B_[lambda] - A_[lambda]
    [chi] =  |         ------------------------------- = --- . -----------------------;   (4)
            _/[lambda] (a² + [lambda])(b² + [lambda])P   abc            a² - b²

  and at the surface [lambda] = 0,

           / 1    1\   N  B0 - A0    N   1
          ( -- + -- ) --- ------- - --- ----
           \a²   b²/  abc a² - b²   abc a²b²
    R = - ----------------------------------,   (5)
                      1/b² - 1/a²

     N             1/b² - 1/a²
    --- = R --------------------------,   (6)
    abc      1      / 1    1\  B0 - A0
            ---- - ( -- + -- ) -------
            a²b²    \a²   b²/  a² - b²

             (a² - b²)²/(a² + b²)
    = R -------------------------------.
        (a² - b²)/(a² + b²) - (B0 - A0)

  The velocity function of the liquid inside the ellipsoid [lambda] = 0
  due to the same angular velocity will be

    [phi]1 = Rxy(a² - b²)/(a² + b²),   (7)

  and on the surface outside

                           N  B0 - A0
    [phi]0 = xy[chi]0 = xy--- -------,   (8)
                          abc a² - b²

  so that the ratio of the exterior and interior value of [phi] at the
  surface is

    [phi]0              B0 - A0
    ------ = -------------------------------,   (9)
    [phi]1   (a² - b²)/(a² + b²) - (B0 - A0)

  and this is the ratio of the effective angular inertia of the liquid,
  outside and inside the ellipsoid [lambda] = 0.

  The extension to the case where the liquid is bounded externally by a
  fixed ellipsoid [lambda] = [lambda]1 is made in a similar manner, by
  putting

    [phi] = xy([chi] + M),   (10)

  and the ratio of the effective angular inertia in (9) is changed to

                                a1² - b1²  abc
        (B0 - A0) - (B1 - A1) + --------- ------
                                a1² + b1² a1b1c1
    --------------------------------------------------.   (11)
    a² - b²   a1² - b1²  abc
    ------- - --------- ------ - (B0 - A0) + (B1 - A1)
    a² + b²   a1² + b1² a1b1c1

  Make c = [oo] for confocal elliptic cylinders; and then
                 _
                /[oo]                              ab                               ab     /       /b² + [lambda] \
    A[lambda] = |         ----------------------------------------------------- = ------- ( 1 -   / -------------  ),   (12)
               _/[lambda] (a² + [lambda])[root]([4·a² + [lambda]·b² + [lambda])   a² - b²  \    \/  a² + [lambda] /

                  ab     /    /a² + [lambda]    \
    B[lambda] = ------- (    / ------------- - 1 ), C[lambda]= 0;
                a² - b²  \ \/  b² + [lambda]    /

  and then as above in § 31, with

    a = c ch [alpha], b = c sh [alpha],
    a1 = [root](a² + [lambda]) = c ch [alpha]1, b1 = c sh [alpha]1   (13)

  the ratio in (11) agrees with § 31 (6).

  As before in § 31, the rotation may be resolved into a shear-pair, in
  planes perpendicular to Ox and Oy.

  A torsion of the ellipsoidal surface will give rise to a velocity
  function of the form [phi] = xyz[Omega], where [Omega] can be
  expressed by the elliptic integrals A_[lambda], B_[lambda],
  C_[lambda], in a similar manner, since
                 _
                / [oo]
    [Omega] = L |        d[lambda]/P³
               _/ [lambda]

  48. The determination of the [phi]'s and [chi]'s is a kinematical
  problem, solved as yet only for a few cases, such as those discussed
  above.

  But supposing them determined for the motion of a body through a
  liquid, the kinetic energy T of the system, liquid and body, is
  expressible as a quadratic function of the components U, V, W, P, Q,
  R. The partial differential coefficient of T with respect to a
  component of velocity, linear or angular, will be the component of
  momentum, linear or angular, which corresponds.

  Conversely, if the kinetic energy T is expressed as a quadratic
  function of x1, x2, x3, y1, y2, y3, the components of momentum, the
  partial differential coefficient with respect to a momentum component
  will give the component of velocity to correspond.

  These theorems, which hold for the motion of a single rigid body, are
  true generally for a flexible system, such as considered here for a
  liquid, with one or more rigid bodies swimming in it; and they express
  the statement that the work done by an impulse is the product of the
  impulse and the arithmetic mean of the initial and final velocity; so
  that the kinetic energy is the work done by the impulse in starting
  the motion from rest.

  Thus if T is expressed as a quadratic function of U, V, W, P, Q, R,
  the components of momentum corresponding are

         dT       dT       dT
    x1 = --, x2 = --, x3 = --,   (1)
         dU       dV       dW

         dT       dT       dT
    y1 = --, y2 = --, y3 = --;
         dP       dQ       dR

  but when it is expressed as a quadratic function of x1, x2, x3, y1,
  y2, y3,

        dT       dT       dT
    U = ---, V = ---, W = ---,   (2)
        dx1      dx2      dx3

        dT       dT       dT
    P = ---, Q = ---, R = ---.
        dy1      dy2      dy3

  The second system of expression was chosen by Clebsch and adopted by
  Halphen in his _Fonctions elliptiques_; and thence the dynamical
  equations follow

        dx1     dT      dT
    X = --- - x2--- + x3---, Y = ..., Z = ...,   (3)
        dt      dy3     dy2

        dy1     dT      dT      dT      dT
    L = --- - y2--- + y3--- - x2--- + x2---, M = ..., N = ...,   (4)
        dt      dy3     dy2     dx3     dx2

  where X, Y, Z, L, M, N denote components of external applied force on
  the body.

  These equations are proved by taking a line fixed in space, whose
  direction cosines are l, m, n, then

    dl            dm            dn
    -- = mR - nQ, -- = nP - lR, -- = lQ - mP.   (5)
    dt            dt            dt

  If P denotes the resultant linear impulse or momentum in this
  direction

    P = lx1 + mx2 + nx3,   (6)

    dP   dl     dm     dn
    -- = --x1 + --x2 + --x3
    dt   dt     dt     dt

          dx1    dx2    dx3
       + l--- + m--- + n---,
          dt     dt     dt

            / dx1            \
       = l (  --- - x2R + x3Q )
            \ dt             /

            / dx2            \
       + m (  --- - x3P + x1R )
            \ dt             /

            / dx3            \
       + n (  --- - x1Q + x2P )
            \ dt             /

       = lX + mY + nZ,   (7)

  for all values of l, m, n.

  Next, taking a fixed origin [Omega] and axes parallel to Ox, Oy, Oz
  through O, and denoting by x, y, z the coordinates of O, and by G the
  component angular momentum about [Omega] in the direction (l, m, n)

    G = l(y1 - x2z + x3y)
      + m(y2 - x3x + x1z)
      + n(y3 - x1y + x2x).   (8)

  Differentiating with respect to t, and afterwards moving the fixed
  origin up to the moving origin O, so that

                       dx      dy      dz
    x = y = z = 0, but -- = U, -- = V, -- = W,
                       dt      dt      dt

    dG      / dy1                         \
    -- = l (  --- - y2R + y3Q - x2W + x3V  )
    dt      \ dt                          /

            / dy2                         \
       + m (  --- - y3P + y1R - x3U + x1W  )
            \ dt                          /

            / dy3                         \
       + n (  --- - y1Q + y2P - x1V + x2U  )
            \ dt                          /

       = lL + mM + nN,   (9)

  for all values of l, m, n.

  When no external force acts, the case which we shall consider, there
  are three integrals of the equations of motion

  (i.) T = constant,

  (ii.) x1² + x2² + x3² = F², a constant,

  (iii.) x1y1 + x2y2 + x3y3 = n = GF, a constant;

  and the dynamical equations in (3) express the fact that x1, x2, x3
  are the components of a constant vector having a fixed direction;
  while (4) shows that the vector resultant of y1, y2, y3 moves as if
  subject to a couple of components

    x2W - x3V, x3U - x1W, x1V - x2U,   (10)

  and the resultant couple is therefore perpendicular to F, the
  resultant of x1, x2, x3, so that the component along OF is constant,
  as expressed by (iii).

  If a fourth integral is obtainable, the solution is reducible to a
  quadrature, but this is not possible except in a limited series of
  cases, investigated by H. Weber, F. Kötter, R. Liouville, Caspary,
  Jukovsky, Liapounoff, Kolosoff and others, chiefly Russian
  mathematicians; and the general solution requires the double-theta
  hyperelliptic function.

  49. In the motion which can be solved by the elliptic function, the
  most general expression of the kinetic energy was shown by A. Clebsch
  to take the form

    T = ½p(x1² + x2²) + ½p´x3²
      + q(x1y1 + x2y2) + q´x3y3
      + ½r(y1² + y2²) + ½r´y3²   (1)

  so that a fourth integral is given by

    dy3/dt = 0, y3 = constant;   (2)

    dx3
    --- = x1(qx2 + ry2) - x2(qx1 + ry1) = r(x1y2 - x2y1),   (3)
    dt

    1   / dx3 \²
    -- (  ---  ) = (x1² + x2²)(y1² + y2²) - (x1y1 + x2y2)²
    r²  \ dt  /

                 = (x1² + x2²)(y1² + y2²) - (FG - x3y3)²
                 = (x1² + x2²)(y1² + y2² + y3² - G²) - (Gx3 - Fy3)²,   (4)

  in which

    x1² + x2² = F² - x3², x1y1 + x2y2 = FG - x3y3,   (5)

    r(y1² + y2²) = 2T - p(x1² + x2²) - p´x3²
                 - 2q(x1y1 + x2y2) - 2q´x3y3 - r´y3²
                 = (p - p´)x3² + 2(q - q´)x3y3 + m1,   (6)

    m1 - 2T - pF² - 2qFG - r1y3²   (7)

  so that

    1   / dx3 \²
    -- (  ---  ) = X3   (8)
    r²  \ dt  /

  where X3 is a quartic function of x3, and thus t is given by an
  elliptic integral of the first kind; and by inversion x3 is in
  elliptic function of the time t. Now

  (x1 - x2i)(y1 + y2i) = x1y1 + x2y2 + i(x1y2 - x2y1)
                       = FG - xy3y3 + i[V-]X3,   (9)

    y1 + y2i   FG - x3y3 + i[root]X3
    -------- = --------------------- ,   (10)
    x1 + x2i         x1² + x2²

    d
    -- (x1 + x2i) = -i[(q´ - q)x3 + r´y3] + irx3(y1 + y2i),   (11)
    dt

     d                                             FG - x3y3 + i[root]X3
    --- log (x1 + x2i) = dti -(q´ - q)x - r´y + rx ---------------------,   (12)
    dti                                                   F² - x3²

     d          /x1 + x2i                                Fy3 - Gx3
    --- log \  / -------- = -(q´ - q)x3 - (r´ - r)y3 - Fr---------,   (13)
    dti      \/  x1 - x2i                                 F² - x3²

  requiring the elliptic integral of the third kind; thence the
  expression of x1 + x2i and y1 + y2i.

  Introducing Euler's angles [theta], [phi], [psi],

    x1 = F sin [theta] sin [phi], x2 = F sin [theta] cos [phi],

    x1 + x2i = iF sin [theta][epsilon]^(-[psi]i), x3 = F cos [theta];   (14)

                d[psi]
    sin [theta] ------ = P sin [phi] + Q cos[phi],   (15)
                  dt

                  d[psi]   dT       dT
    F sin²[theta] ------ = --- x1 + --- x2
                    dt     dy1      dy2

                         = (qx1 + ry1)x1 + (qx2 + ry2)x2

                         = qx1² + x2²) + r (x1y1 + x2y2)

                         = gF² sin² [theta] + r(FG - x3y3),   (16)
                   _
                  / FG - x3y3   Fr dx3
    [psi] - qFt = | ---------  --------,   (17)
                 _/  F² - x3²  [root]X3

  elliptic integrals of the third kind.

  Employing G. Kirchhoff's expressions for X, Y, Z, the coordinates of
  the centre of the body,
                __          __          __
    FX = y1 cos xY + y2 cos yY + y3 cos zY,   (18)
                 __          __          __
    FY = -y1 cos xX + y2 cos yX + y3 cos zX,   (19)
               __          __          __
    G = y1 cos xZ + y2 cos yZ + y3 cos zZ,   (20)

    F²(X² + Y²) = y1² + y2² + y3² - G²,   (21)

                Fy3 - Gx3 + i[root]X3
    F(X + Yi) = --------------------- [epsilon]^[psi]_i.   (22)
                   [root](F² - x3²)

  Suppose x3 - F is a repeated factor of X3, then y3 = G, and
                    _                                       _
                   | p´ - p             q´ - q               |
    X3 = (x3 - F)² | ------(x3 + F)² + 2------G(x3 + F) - G² |,   (23)
                   |_  r                   r                _|

  and putting x3 - F = y,
                     _
     / dy \²        |   p´ - p        q´ - q
    (  --  ) = r²y² | 4 ------ F² + 4 ------ FG - G²
     \ dt /         |_     r             r
                                                   _
             /  p´ - p     q´ - q  \      p´ - p    |
        + 2 ( 2 ------ F + ------ G ) y + ------ y² |,   (24)
             \    r          r     /        r      _|

  so that the stability of this axial movement is secured if

          p´ - p       q´ - q
    A = 4 ------F² + 4 ------FG - G²   (25)
            r            r

  is negative, and then the axis makes r[V-](-A)/[pi] nutations per
  second. Otherwise, if A is positive
          _
         /          dy
    rt = | ----------------------
        _/ y[root](A + 2By + Cy²)

           1    sh^(-1) [root]A[root](A + 2By + Cy²)      1    ch^(-1)      A + By
      = -------         ---------------------------- = -------         ---------------,   (26)
        [root]A ch^(-1)       y[root](B² ~ AC)         [root]A sh^(-1) y[root](B² ~ AC)

  and the axis falls away ultimately from its original direction.

  A number of cases are worked out in the American Journal of
  Mathematics (1907), in which the motion is made algebraical by the use
  of the pseudo-elliptic integral. To give a simple instance, changing
  to the stereographic projection by putting tan ½[theta] = x,

    (Nxe[psi]i)^3/2 = (x + 1)[root]X1 + i(x - 1)[root]X2,   (27)

    X1
    -- = ±ax^4 + 2ax³ ± 3(a + b)x² + 2bx ± b,   (28)
    X2

    N³ = -8(a + b),   (29)

  will give a possible state of motion of the axis of the body; and the
  motion of the centre may then be inferred from (22).

50. The theory preceding is of practical application in the
investigation of the stability of the axial motion of a submarine boat,
of the elongated gas bag of an airship, or of a spinning rifled
projectile. In the steady motion under no force of such a body in a
medium, the centre of gravity describes a helix, while the axis
describes a cone round the direction of motion of the centre of gravity,
and the couple causing precession is due to the displacement of the
medium.

In the absence of a medium the inertia of the body to translation is the
same in all directions, and is measured by the weight W, and under no
force the C.G. proceeds in a straight line, and the axis of rotation
through the C.G. preserves its original direction, if a principal axis
of the body; otherwise the axis describes a cone, right circular if the
body has uniaxial symmetry, and a Poinsot cone in the general case.

But the presence of the medium makes the effective inertia depend on the
direction of motion with respect to the external shape of the body, and
on W´ the weight of fluid medium displaced.

  Consider, for example, a submarine boat under water; the inertia is
  different for axial and broadside motion, and may be represented by

    c1 = W + W´[alpha], c2 = W + W´[beta],   (1)

  where [alpha], [beta] are numerical factors depending on the external
  shape; and if the C.G. is moving with velocity V at an angle [phi]
  with the axis, so that the axial and broadside component of velocity
  is u = V cos [phi], v = V sin [phi], the total momentum F of the
  medium, represented by the vector OF at an angle [theta] with the
  axis, will have components, expressed in sec. lb.,

                        u                     V                                  v                    V
    F cos [theta] = c1 --- = (W + W´[alpha]) --- cos [phi], F sin [theta] = c2 --- = (W + W´[beta]) --- sin [phi].   (2)
                        g                     g                                  g                    g

  Suppose the body is kept from turning as it advances; after t seconds
  the C.G. will have moved from O to O´, where OO´ = Vt; and at O´ the
  momentum is the same in magnitude as before, but its vector is
  displaced from OF to O´F´.

  For the body alone the resultant of the components of momentum

       V                   V                  V
    W --- cos [phi] and W --- sin [phi] is W --- sec. lb.,   (3)
       g                   g                  g

  acting along OO´, and so is unaltered.

  But the change of the resultant momentum F of the medium as well as of
  the body from the vector OF to O´F´ requires an impulse couple,
  tending to increase the angle FOO´, of magnitude, in sec. foot-pounds

    F·OO´·sin FOO´ = FVt sin ([theta] - [phi]),   (4)

  equivalent to an incessant couple

    N = FV sin ([theta] - [phi])
      = (F sin [theta] cos [phi] - F cos [theta] sin [phi])V
      = (c2 - c1)(V²/g) sin [phi] cos [phi]
      = W´([beta] - [alpha]uv/g).   (5)

  This N is the couple in foot-pounds changing the momentum of the
  medium, the momentum of the body alone remaining the same; the medium
  reacts on the body with the same couple N in the opposite direction,
  tending when c2-c1 is positive to set the body broadside to the
  advance.

  An oblate flattened body, like a disk or plate, has c2 - c1 negative,
  so that the medium steers the body axially; this may be verified by a
  plate dropped in water, and a leaf or disk or rocket-stick or piece of
  paper falling in air. A card will show the influence of the couple N
  if projected with a spin in its plane, when it will be found to change
  its aspect in the air.

  An elongated body like a ship has c2-c1 positive, and the couple N
  tends to disturb the axial movement and makes it unstable, so that a
  steamer requires to be steered by constant attention at the helm.

  Consider a submarine boat or airship moving freely with the direction
  of the resultant momentum horizontal, and the axis at a slight
  inclination [theta]. With no reserve of buoyancy W = W´, and the
  couple N, tending to increase [theta], has the effect of diminishing
  the metacentric height by h ft. vertical, where

                                  c1  u²
    Wh tan[theta] = N = (c2 - c1) -- --- tan [theta],   (6)
                                  c2  g

        c2 - c1 c1  u²                     1 + [alpha]  u²
    h = ------- -- --- = ([beta] - [alpha] ----------- ---.   (7)
           W    c2  g                      1 + [beta]   g

51. An elongated shot is made to preserve its axial flight through the
air by giving it the spin sufficient for stability, without which it
would turn broadside to its advance; a top in the same way is made to
stand upright on the point in the position of equilibrium, unstable
statically but dynamically stable if the spin is sufficient; and the
investigation proceeds in the same way for the two problems (see
GYROSCOPE).

  The effective angular inertia of the body in the medium is now
  required; denote it by C1 about the axis of the figure, and by C2
  about a diameter of the mean section. A rotation about the axis of a
  figure of revolution does not set the medium in motion, so that C1 is
  the moment of inertia of the body about the axis, denoted by Wk1². But
  if Wk2² is the moment of inertia of the body about a mean diameter,
  and [omega] the angular velocity about it generated by an impulse
  couple M, and M´ is the couple required to set the surrounding medium
  in motion, supposed of effective radius of gyration k´,

    Wk2²[omega] = M - M´, W´k´²[omega] = M´,   (1)

    Wk2² + W´k´²[omega] = M,   (2)

    C2 = Wk2² + W´k´² = (W + W´[epsilon])k2²,   (3)

  in which we have put k´² = [epsilon]k², where [epsilon] is a numerical
  factor depending on the shape.

  If the shot is spinning about its axis with angular velocity p, and is
  preceding steadily at a rate [mu] about a line parallel to the
  resultant momentum F at an angle [theta], the velocity of the vector
  of angular momentum, as in the case of a top, is

    C1p[mu] sin [theta] - C2[mu]² sin [theta] cos [theta];   (4)

  and equating this to the impressed couple (multiplied by g), that is,
  to

                  c1
    gN = (c1 - c2)-- u² tan [theta],   (5)
                  c2

  and dividing out sin[theta], which equated to zero would imply perfect
  centring, we obtain

                                             c1
    C2[mu]² cos [theta] - C1p[mu] + (c2 - c1)-- u² sec [theta] = 0.   (6)
                                             c2

  The least admissible value of p is that which makes the roots equal of
  this quadratic in [mu], and then

             C1
    [mu] = ½ --p sec [theta],   (7)
             C2

  the roots would be imaginary for a value of p smaller than given by

                      c1
    C1²p² - 4(c2 - c1)-- C2u² = 0,   (8)
                      c2

    p²               c1 C2
    -- = 4 (c2 - c1) -- ---.   (9)
    u²               c2 C1²

  _Table of Rifling for Stability of an Elongated Projectile, x Calibres
  long, giving [delta] the Angle of Rifling, and n the Pitch of Rifling
  in Calibres._

    +-----------------------+-----------------+-----------------+-----------------+-----------------+
    |                       | Cast-iron Common| Palliser Shell  |   Solid Steel   |   Solid Lead    |
    |                       | Shell [f] = 2/3,| [f] = ½, S.G. 8.|     Bullet      | Bullet [f] = 0, |
    |                       |     S.G. 7.2.   |                 | [f] = 0, S.G. 8.|    S.G. 10.9.   |
    +--------+--------------+--------+--------+--------+--------+--------+--------+--------+--------+
    |   x    |[beta]-[alpha]|[delta] |   n    |[delta] |   n    |[delta] |   n    |[delta] |   n    |
    +--------+--------------+--------+--------+--------+--------+--------+--------+--------+--------+
    |  1.0   |    0.0000    |  0°  0´|Infinity|  0°  0´|Infinity|  0°  0´|Infinity|  0°  0´|Infinity|
    |  2.0   |    0.4942    |  2  49 | 63.87  |  2  32 | 71.08  |  2  29 | 72.21  |  2  08 | 84.29  |
    |  2.5   |    0.6056    |  3  46 | 47.91  |  3  23 | 53.32  |  3  19 | 54.17  |  2  51 | 63.24  |
    |  3.0   |    0.6819    |  4  41 | 38.45  |  4  13 | 42.79  |  4  09 | 43.47  |  3  38 | 50.74  |
    |  3.5   |    0.7370    |  5  35 | 32.13  |  5  02 | 35.75  |  4  58 | 36.33  |  4  15 | 42.40  |
    |  4.0   |    0.7782    |  6  30 | 27.60  |  5  51 | 30.72  |  5  45 | 31.21  |  4  56 | 36.43  |
    |  4.5   |    0.8100    |  7  24 | 24.20  |  6  40 | 26.93  |  6  32 | 27.36  |  5  37 | 31.94  |
    |  5.0   |    0.8351    |  8  16 | 21.56  |  7  28 | 23.98  |  7  21 | 24.36  |  6  18 | 28.44  |
    |  6.0   |    0.8721    | 10  05 | 17.67  |  9  04 | 19.67  |  8  56 | 19.98  |  7  40 | 23.33  |
    |  10.0  |    0.9395    | 16  57 | 10.31  | 15  19 | 11.47  | 15  05 | 11.65  | 13  00 | 13.60  |
    |Infinity|    1.0000    | 90  00 | 0.00   | 90  00 | 0.00   | 90  00 | 0.00   | 90  00 | 0.00   |
    +--------+--------------+--------+--------+--------+--------+--------+--------+--------+--------+

  If the shot is moving as if fired from a gun of calibre d inches, in
  which the rifling makes one turn in a pitch of n calibres or nd
  inches, so that the angle [delta] of the rifling is given by

    tan [delta] = [pi]d/nd = ½ dp/u,   (10)

  which is the ratio of the linear velocity of rotation ½dp to u, the
  velocity of advance,

                                                   c1 C2d²
    tan² [delta] = [pi]²/n² = d²p²/4u² = (c2 - c1) -- ----
                                                   c2  C1²

                                  W´            /     W´         \   / k2 \²
                             1 + --- [alpha]   ( 1 + ---[epsilon] ) (  --  )
       W´                         W             \     W          /   \ d  /
    = --- ([beta] - [alpha]) --------------- · -----------------------------.   (11)
       W                           W´                     / k1 \^4
                              1 + ---[beta]              (  --  )
                                   W                      \ d  /

  For a shot in air the ratio W´/W is so small that the square may be
  neglected, and formula (11) can be replaced for practical purpose in
  artillery by

                  [pi]²    W´                     / k2 \²  / / k1 \^4
    tan²[delta] = ----- = --- ([beta] - [alpha]) (  --  ) / (  --  ),   (12)
                    n²     W                      \ d  / /   \ d  /

  if then we can calculate [beta], [alpha], or [beta] - [alpha] for the
  external shape of the shot, this equation will give the value of
  [delta] and n required for stability of flight in the air.

  The ellipsoid is the only shape for which [alpha] and [beta] have so
  far been determined analytically, as shown already in § 44, so we must
  restrict our calculation to an egg-shaped bullet, bounded by a prolate
  ellipsoid of revolution, in which, with b = c,
          _                                                               _
         / [oo]                       ab² d[lambda]                      / [oo]           ab² d[lambda]
    A0 = |     ------------------------------------------------------- = |    -----------------------------------,   (13)
        _/ 0   (a² + [lambda])[root][4(a² + [lambda])(b² + [lambda])²]  _/ 0  2(a² + [lambda])^3/2 (b² + [lambda])

    A0 + 2B0 = 1,   (14)

                A0               B0     1 - A0        1
    [alpha] = ------, [beta] = ------ = ------ = ------------.   (15)
              1 - A0           1 - B0   1 + A0   1 + 2[alpha]

  The length of the shot being denoted by l and the calibre by d, and
  the length in calibres by x

    l/d = 2a/2b = x,   (16)

              x                   1
    A0 = ----------- ch^(-1)x - ------,   (17)
         (x²- 1)^3/2            x² - 1

              -x                   x²
    2B0 = ----------- ch^(-1)x + ------,   (18)
          x² - 1)^3/2            x² + 1

                 x sh^(-1) [root](x²-1)        x
    x²A0 + 2B0 = ---------------------- = ------------ log [x + [root](x² - 1)].   (19)
                       [root](x²-1)       [root](x²-1)

  If [sigma] denotes the density of the metal, and if the shell has a
  cavity homothetic with the external ellipsoidal shape, a fraction f of
  the linear scale; then the volume of a round shot being 1/6 [pi] d^3,
  and 1/6 [pi] d^3 x of a shot x calibres long

    W = 1/6 [pi] d^3 x (i - f^3) [sigma],   (20)

                          d²
    Wk1² = 1/6 [pi] d^3 x -- (1 - f^5) [sigma],   (21)
                          10

                           l² + d²
    Wk2² = 1/6 [pi] d^3 x  ------- (1 - f^5) [sigma].   (22)
                              20

  If [rho] denotes the density of the air or medium

    W´ = 1/6 [pi] d^3 x [rho],   (23)

     W´     1     [rho]
    --- = ------ -------,   (24)
     W    1 - f³ [sigma]

    k1²    1  1 - f^5   k2²   x² + 1
    --- = --- -------, ---- = ------,   (25)
    d²    10   1 - f³   k1²     2

                    [rho]                       x² + 1
    tan² [delta] = ------- ([beta] - [alpha])-------------,   (26)
                   [sigma]                   1/5 (1 - f^5)

  in which [sigma]/[rho] may be replaced by 800 times the S.G. of the
  metal, taking water as 800 times denser than air on the average, in
  round numbers, and formula (10) may be written n tan [delta] = [pi],
  or n[delta] = 180, when [delta] is a small angle, and given in
  degrees.

  From this formula (26) the table following has been calculated by A.
  G. Hadcock, and the results are in agreement with practical
  experience.

  52. In the steady motion the centre of the shot describes a helix,
  with axial velocity

                                    /    c1             \
    u cos [theta]= v sin [theta] = ( l + -- tan² [theta] ) u cos [theta] [asympt] u sec [theta],   (1)
                                    \    c2             /

  and transverse velocity

                                     /    c1 \
    u sin [theta] - v cos [theta] = ( l - --  ) u sin [theta] [asympt] ([beta] - [alpha]) u sin [theta];   (2)
                                     \    c2 /

  and the time of completing a turn of the spiral is 2[pi]/[mu].

  When [mu] has the critical value in (7),

    2[pi]   4[pi] C2               2[pi]
    ----- = ----- -- cos [theta] = ----- (x² + 1) cos [theta],   (3)
    [mu]      p   C1                 p

  which makes the circumference of the cylinder on which the helix
  is wrapped

    2[pi]                                 2[pi]u
    -----(u sin [theta] - v cos [theta] = ------ ([beta] - [alpha]) (x² + 1) sin² [theta] cos [theta]
    [mu]                                     p

       = nd ([beta] - [alpha]) (x² + 1) sin [theta] cos [theta],   (4)

  and the length of one turn of the helix

    2[pi]
    ----- (u cos [theta] + v sin [theta] ) = nd(x² + 1);   (5)
    [mu]

  thus for x = 3, the length is 10 times the pitch of the rifling.

  53. _The Motion of a Perforated Solid in Liquid._--In the preceding
  investigation, the liquid stops dead when the body is brought to rest;
  and when the body is in motion the surrounding liquid moves in a
  uniform manner with respect to axes fixed in the body, and the force
  experienced by the body from the pressure of the liquid on its surface
  is the opposite of that required to change the motion of the liquid;
  this has been expressed by the dynamical equations given above. But if
  the body is perforated, the liquid can circulate through a hole, in
  reentrant stream lines linked with the body, even while the body is at
  rest; and no reaction from the surface can influence this circulation,
  which may be supposed started in the ideal manner described in § 29,
  by the application of impulsive pressure across an ideal membrane
  closing the hole, by means of ideal mechanism connected with the body.
  The body is held fixed, and the reaction of the mechanism and the
  resultant of the impulsive pressure on the surface are a measure of
  the impulse, linear [xi], [eta], [zeta], and angular [lambda], [mu],
  [nu], required to start the circulation.

  This impulse will remain of constant magnitude, and fixed relatively
  to the body, which thus experiences an additional reaction from the
  circulation which is the opposite of the force required to change the
  position in space of the circulation impulse; and these extra forces
  must be taken into account in the dynamical equations.

  An article may be consulted in the _Phil. Mag._, April 1893, by G. H.
  Bryan, in which the analytical equations of motion are deduced of a
  perforated solid in liquid, from considerations purely hydrodynamical.

  The effect of an external circulation of vortex motion on the motion
  of a cylinder has been investigated in § 29; a similar procedure will
  show the influence of circulation through a hole in a solid, taking as
  the simplest illustration a ring-shaped figure, with uniplanar motion,
  and denoting by [xi] the resultant axial linear momentum of the
  circulation.

  As the ring is moved from O to O´ in time t, with velocity Q, and
  angular velocity R, the components of liquid momentum change from

    [alpha]M´U + [xi] and [beta]M´V along Ox and Oy

  to

    [alpha]M´U´ + [xi] and [beta]M´V´ along O´x´ and O´y´,   (1)

  the axis of the ring changing from Ox to O´x´; and

    U = Q cos [theta], V = Q sin [theta],

    U´ = Q cos ([theta] - Rt), V´ = Q sin ([theta] - Rt),   (2)

  so that the increase of the components of momentum, X1, Y1, and N1,
  linear and angular, are

    X1 = ([alpha]M´U´ + [xi])[cos] Rt - [alpha]M´U - [xi] - [beta]M´V´ sin Rt
       = ([alpha] - [beta])M´Q sin ([theta] - Rt) sin Rt - [xi] ver Rt   (3)

    Y1 = ([alpha]M´U´ + [xi]) sin Rt + [beta]M´V´ cos Rt - [beta]M´V
       = ([alpha] - [beta])M´Q cos ([theta] - Rt) sin Rt + [xi] sin RT,   (4)

    N1 = [ -([alpha]M´U´ + [xi]) sin ([theta] - Rt) + [beta]M´V´ cos ([theta] - Rt)OO´
       = [ -([alpha] - [beta])´Q cos ([theta] - Rt) sin ([theta] - Rt) - [xi] sin ([theta] - Rt)]Qt.   (5)

  The components of force, X, Y, and N, acting on the liquid at O, and
  reacting on the body, are then

    X = lt. X1/t = ([alpha] - [beta])M´QR sin [theta] = ([alpha] - [beta])M´VR,   (6)

    Y = lt. Y1/t = ([alpha] - [beta])M´QR cos [theta] + [xi]R = ([alpha] - [beta])M´UR + [xi]R,   (7)

    Z = lt. Z1/t = -([alpha] - [beta])M´Q² sin [theta]cos[theta] - [xi]Q sin [theta]
      = [-([alpha] - [beta])M´U + [xi]]V.   (8)

  Now suppose the cylinder is free; the additional forces acting on the
  body are the components of kinetic reaction of the liquid

                / dU     \              / dV     \              dR
    -[alpha]M´ (  -- - VR ), -[beta]M´ (  -- + UR ), [epsilon]C´--,   (9)
                \ dt     /              \ dt     /              dt

  so that its equations of motion are

       / dU    \                / dU     \
    M (  -- -VR ) = -[alpha]M´ (  -- - VR ) - ([alpha] - [beta])M´VR,   (10)
       \ dt    /                \ dt     /

       / dV     \               / dV     \
    M (  -- + UR ) = -[beta]M´ (  -- + UR ) - ([alpha] - [beta])M´UR - [xi]R,   (11)
       \ dt     /               \ dt     /

     dR               dR
    C-- = -[epsilon]C´-- + ([alpha] - [beta])M´UV + [xi]V;   (12)
     dt               dt

  and putting as before

    M + [alpha]M´ = c1, M + [beta]M´ = c2, C + [epsilon]C´ = C3,   (13)

      dU
    c1-- - c2 VR = 0,   (14)
      dt

      dV
    c2-- + (c1 U + [xi])R = 0,   (15)
      dt

      dR
    c3-- - (c1U + [xi] - c2 U)V = 0;   (16)
      dt

  showing the modification of the equations of plane motion, due to the
  component [xi] of the circulation.

  The integral of (14) and (15) may be written

    c1U + [xi] = F cos [theta], c2V = - F sin [theta],   (17)

    dx                                   F cos² [theta]   F sin² [theta]   [xi]
    -- = U cos [theta] - V sin [theta] = -------------- + -------------- - ---- cos [theta],   (18)
    dt                                         c1               c2          c1

    d[mu]                                    / F    F  \                            [xi]
    ----- = U sin [theta] + V cos [theta] = (  -- - --  ) sin [theta] cos [theta] - ---- sin [theta],   (19)
     dt                                      \ c1   c2 /                             c1

      d²[theta]    / F²   F² \                            F[xi]                d[mu]
    C3--------- = (  -- - --  ) sin [theta] cos [theta] - ----- sin [theta] = F-----,   (20)
         dt²       \ c1   c2 /                             c1                   dt
                           _                                                            _
      d[theta]          / |   F² cos² [theta]   F² sin² [theta]    F[xi]                 |
    C3-------- = Fy =  /  | - --------------- - --------------- + 2----- cos [theta] + H |;   (21)
         dt          \/   |_         c1               c2            c1                  _|

  so that cos [theta] and y is an elliptic function of the time.

  When [xi] is absent, dx/dt is always positive, and the centre of the
  body cannot describe loops; but with [xi], the influence may be great
  enough to make dx/dt change sign, and so loops occur, as shown in A.
  B. Basset's _Hydrodynamics_, i. 192, resembling the trochoidal curves,
  which can be looped, investigated in § 29 for the motion of a cylinder
  under gravity, when surrounded by a vortex.

  The branch of hydrodynamics which discusses wave motion in a liquid or
  gas is given now in the articles SOUND and WAVE; while the influence
  of viscosity is considered under HYDRAULICS.

  REFERENCES.--For the history and references to the original memoirs
  see _Report to the British Association_, by G. G. Stokes (1846), and
  W. M. Hicks (1882). See also the _Fortschritte der Mathematik_, and A.
  E. H. Love, "Hydrodynamik" in the _Encyklöpadie der mathematischen
  Wissenschaften_ (1901).     (A. G. G.)



HYDROMEDUSAE, a group of marine animals, recognized as belonging to the
Hydrozoa (q.v.) by the following characters. (1) The polyp (hydropolyp)
is of simple structure, typically much longer than broad, without
ectodermal oesophagus or mesenteries, such as are seen in the anthopolyp
(see article ANTHOZOA); the mouth is usually raised above the peristome
on a short conical elevation or hypostome; the ectoderm is without cilia.
(2) With very few exceptions, the polyp is not the only type of
individual that occurs, but alternates in the life-cycle of a given
species, with a distinct type, the medusa (q.v.), while in other cases
the polyp-stage may be absent altogether, so that only medusa-individuals
occur in the life-cycle.

The Hydromedusae represent, therefore, a sub-class of the Hydrozoa. The
only other sub-class is the Scyphomedusae (q.v.). The Hydromedusae
contrast with the Scyphomedusae in the following points. (1) The polyp,
when present, is without the strongly developed longitudinal retractor
muscles, forming ridges (_taeniolae_) projecting into the digestive
cavity, seen in the scyphistoma or scyphopolyp. (2) The medusa, when
present, has a velum and is hence said to be _craspedote_; the nervous
system forms two continuous rings running above and below the velum; the
margin of the umbrella is not lobed (except in Narcomedusae) but entire;
there are characteristic differences in the sense-organs (see below, and
SCYPHOMEDUSAE); and gastral filaments (phacellae), subgenital pits, &c.,
are absent. (3) The gonads, whether formed in the polyp or the medusa,
are developed in the ectoderm.

The Hydromedusae form a widespread, dominant and highly differentiated
group of animals, typically marine, and found in all seas and in all
zones of marine life. Fresh-water forms, however, are also known, very
few as regards species or genera, but often extremely abundant as
individuals. In the British fresh-water fauna only two genera, _Hydra_
and _Cordylophora_, are found; in America occurs an additional genus,
_Microhydra_. The paucity of fresh-water forms contrasts sharply, with
the great abundance of marine genera common in all seas and on every
shore. The species of _Hydra_, however, are extremely common and
familiar inhabitants of ponds and ditches.

In fresh-water Hydromedusae the life-cycle is usually secondarily
simplified, but in marine forms the life-cycle may be extremely
complicated, and a given species often passes in the course of its
history through widely different forms adapted to different habitats and
modes of life. Apart from larval or embryonic forms there are found
typically two types of person, as already stated, the polyp and the
medusa, each of which may vary independently of the other, since their
environment and life-conditions are usually quite different. Hence both
polyp and medusa present characters for classification, and a given
species, genus or other taxonomic category may be defined by
polyp-characters or medusa-characters or by both combined. If our
knowledge of the life-histories of these organisms were perfect, their
polymorphism would present no difficulties to classification; but
unfortunately this is far from being the case. In the majority of cases
we do not know the polyp corresponding to a given medusa, or the medusa
that arises from a given polyp.[1] Even when a medusa is seen to be
budded, from a polyp under observation in an aquarium, the difficulty is
not always solved, since the freshly-liberated, immature medusa may
differ greatly from the full-grown, sexually-mature medusa after several
months of life on the high seas (see figs. 11, B, C, and 59, a, b, c).
To establish the exact relationship it is necessary not only to breed
but to rear the medusa, which cannot always be done in confinement. The
alternative is to fish all stages of the medusa in its growth in the
open sea, a slow and laborious method in which the chance of error is
very great, unless the series of stages is very complete.

At present, therefore, classifications of the Hydromedusae have a more
or less tentative character, and are liable to revision with increased
knowledge of the life-histories of these organisms. Many groups bear at
present two names, the one representing the group as defined by
polyp-characters, the other as defined by medusa-characters. It is not
even possible in all cases to be certain that the polyp-group
corresponds exactly to the medusa-group, especially in minor systematic
categories, such as families.

The following is the main outline of the classification that is Adopted
in the present article. Groups founded on polyp-characters are printed
in ordinary type, those founded on medusa-characters in italics. For
definitions of the groups see below.

  Sub-class Hydromedusae (_Hydrozoa Craspedota_).

  Order   I.  Eleutheroblastea.
    "    II.  Hydroidea (_Leptolinae_).
      Sub-order 1. Gymnoblastea (_Anthomedusae_).
          "     2. Calyptoblastea (_Leptomedusae_).
  Order III. Hydrocorallinae.
    "    IV. Graptolitoidea.
    "     V. Trachylinae.
      Sub-order 1. _Trachomedusae_.
          "     2. _Narcomedusae_.
  Order  VI. Siphonophora.
      Sub-order 1. Chondrophorida.
          "     2. Calycophorida.
          "     3. Physophorida.
          "     4. Cystophorida.


  _Organization and Morphology of the Hydromedusae._

As already stated, there occur in the Hydromedusae two distinct types of
person, the polyp and the medusa; and either of them is capable of
non-sexual reproduction by budding, a process which may lead to the
formation of colonies, composed of more or fewer individuals combined
and connected together. The morphology of the group thus falls naturally
into four sections--(1) the hydropolyp, (2) the polyp-colony, (3) the
hydromedusa, (4) the medusa-colonies. Since, however, medusa-colonies
occur only in one group, the Siphonophora, and divergent views are held
with regard to the morphological interpretation of the members of a
siphonophore, only the first three of the above subdivisions of
hydromedusa morphology will be dealt with here in a general way, and the
morphology of the Siphonophora will be considered under the heading of
the group itself.

  [Illustration: FIG. 1.--Diagram of a typical Hydropolyp.

    a, Hydranth;
    b, Hydrocaulus;
    c, Hydrorhiza;
    t, Tentacle;
    ps, Perisarc, forming in the region of the hydranth a cup or
      hydrotheca (h, t),--which, however, is only found in polyps of the
      order Calyptoblastea.]

  1. _The Hydropolyp_ (fig. 1)--The general characters of this organism
  are described above and in the articles HYDROZOA and POLYP. It is
  rarely free, but usually fixed and incapable of locomotion. The foot
  by which it is attached often sends out root-like processes--the
  _hydrorhiza_ (c). The column (b) is generally long, slender and
  stalk-like (_hydrocaulus_). Just below the crown of tentacles,
  however, the body widens out to form a "head," termed, the _hydranth_
  (a), containing a stomach-like dilatation of the digestive cavity. On
  the upper face of the hydranth the crown of tentacles (t) surrounds
  the peristome, from which rises the conical hypostome, bearing the
  mouth at its extremity. The general ectoderm covering the surface of
  the body has entirely lost the cilia present in the earlier larval
  stages (planula), and may be naked, or clothed in a cuticle or
  exoskeleton, the perisarc (ps), which in its simplest condition is a
  chitinous membrane secreted by the ectoderm. The perisarc when present
  invests the hydrorhiza and hydrocaulus; it may stop short below the
  hydranth, or it may extend farther. In general there are two types of
  exoskeleton, characteristic of the two principal divisions of the
  Hydroidea. In the Gymnoblastea the perisarc either stops below the
  hydranth, or, if continued on to it, forms a closely-fitting
  investment extending as a thin cuticle as far as the bases of the
  tentacles (e.g. _Bimeria_, see G. J. Allman [1],[2] pl. xii. figs, 1
  and 3). In the Calyptoblastea the perisarc is always continued above
  the hydrocaulus, and forms a cup, the hydrangium or hydrotheca (h, t),
  standing off from the body, into which the hydranth can be retracted
  for shelter and protection.

  [Illustration: From Allman's _Gymnoblastic Hydroids_, by permission of
  the Council of the Ray Society.

  FIG. 2.--_Stauridium productum_, portion of the colony magnified; p,
  polyp; rh, hydrorhiza.]

  [Illustration: FIG. 3.--Diagram of _Corymorpha_. A, A hydriform person
  giving rise to medusiform persons by budding from the margin of the
  disk; B, free swimming medusa (_Steenstrupia_ of Forbes) detached from
  the same, with manubrial genitalia, (_Anthomedusae_) and only one
  tentacle. (After Allman).]

  The architecture of the hydropolyp, simple though it be, furnishes a
  long series of variations affecting each part of the body. The
  greatest variation, however, is seen in the tentacles. As regards
  number, we find in the aberrant forms _Protohydra_ and _Microhydra_
  tentacles entirely absent. In the curious hydroid _Monobrachium_ a
  single tentacle is present, and the same is the case in _Clathrozoon_;
  in _Amphibrachium_ and in _Lar_ (fig. 11, A) the polyp bears two
  tentacles only. The reduction of the tentacles in all these forms may
  be correlated with their mode of life, and especially with living in a
  constant current of water, which brings food-particles always from one
  direction and renders a complete whorl or circle of tentacles
  unnecessary. Thus _Microhydra_ lives amongst Bryozoa, and appears to
  utilize the currents produced by these animals. _Protohydra_ occurs in
  oyster-banks and _Monobrachium_ also grows on the shells of bivalves,
  and both these hydroids probably fish in the currents produced by the
  lamellibranchs. _Amphibrachium_ grows in the tissues of a sponge,
  _Euplectella_, and protrudes its hydranth into the canal-system of the
  sponge; and _Lar_ grows on the tubes of the worm _Sabella_. With the
  exception of these forms, reduced for the most part in correlation
  with a semi-parasitic mode of life, the tentacles are usually
  numerous. It is rare to find in the polyp a regular, symmetrical
  disposition of the tentacles as in the medusa. The primitive number of
  four in a whorl is seen, however, in _Stauridium_ (fig. 2) and
  _Cladonema_ (Allman [1], pl. xvii.), and in _Clavatella_ each whorl
  consists regularly of eight (Allman, _loc. cit._ pl. xviii.). As a
  rule, however, the number in a whorl is irregular. The tentacles may
  form a single whorl, or more than one; thus in _Corymorpha_ (fig. 3)
  and _Tubularia_ (fig. 4) there are two circlets; in _Stauridium_ (fig.
  2) several; in _Coryne_ and _Cordylophora_ the tentacles are scattered
  irregularly over the elongated hydranth.

  As regards form, the tentacles show a number of types, of which the
  most important are (1) filiform, _i.e._ cylindrical or tapering from
  base to extremity, as in _Clava_ (fig. 5); (2) capitate, i.e. knobbed
  at the extremity, as in _Coryne_ (see Allman, loc. cit. pl. iv.); (3)
  branched, a rare form in the polyp, but seen in _Cladocoryne_ (see
  Allman, loc. cit. p. 380, fig. 82). Sometimes more than one type of
  form is found in the same polyp; in _Pennaria_ and _Stauridium_ (fig.
  2) the upper whorls are capitate, the lower filiform. Finally, as
  regards structure, the tentacles may retain their primitive hollow
  nature, or become solid by obliteration of the axial cavity.

  The hypostome of the hydropolyp may be small, or, on the other hand,
  as in _Eudendrium_ (Allman, loc. cit. pls. xiii., xiv.), large and
  trumpet-shaped. In the curious polyp _Myriothela_ the body of the
  polyp is differentiated into nutritive and reproductive portions.

  [Illustration: FIG. 4.--Diagram of _Tubularia indivisa_. A single
  hydriform person a bearing a stalk carrying numerous degenerate
  medusiform persons or sporosacs b. (After Allman.)]

  _Histology._--The ectoderm of the hydropolyp is chiefly sensory,
  contractile and protective in function. It may also be glandular in
  places. It consists of two regions, an external epithelial layer and a
  more internal sub-epithelial layer.

  The epithelial layer consists of (1) so-called "indifferent" cells
  secreting the perisarc or cuticle and modified to form glandular cells
  in places; for example, the adhesive cells in the foot. (2) Sensory
  cells, which may be fairly numerous in places, especially on the
  tentacles, but which occur always scattered and isolated, never
  aggregated to form sense-organs as in the medusa. (3) Contractile or
  myo-epithelial cells, with the cell prolonged at the base into a
  contractile muscle-fibre (fig. 6, B). In the hydropolyp the ectodermal
  muscle-fibres are always directed longitudinally. Belonging primarily
  to the epithelial layer, the muscular cells may become secondarily
  sub-epithelial.

  [Illustration: From Allman's _Gymnoblastic Hydroids_, by permission of
  the Council of the Ray Society.

  FIG. 5.--Colonies of _Clava_. A, _Clava squamata_, magnified. B, _C.
  multicornis_, natural size; p, _polyp_; _gon_, gonophores; rh,
  hydrorhiza.]

  The sub-epithelial layer consists primarily of the so-called
  interstitial cells, lodged between the narrowed basal portions of the
  epithelial cells. From them are developed two distinct types of
  histological elements; the genital cells and the cnidoblasts or
  mother-cells of the nematocysts. The sub-epithelial layer thus
  primarily constituted may be recruited by immigration from without of
  other elements, more especially by nervous (ganglion) cells and
  muscle-cells derived from the epithelial layer. In its fullest
  development, therefore, the sub-epithelial layer consists of four
  classes of cell-elements.

  [Illustration: FIG. 6 A.--Portion of the body-wall of _Hydra_, showing
  ectoderm cells above, separated by "structureless lamella" from three
  flagellate endoderm cells below. The latter are vacuolated, and
  contain each a nucleus and several dark granules. In the middle
  ectoderm cell are seen a nucleus and three nematocysts, with trigger
  hairs projecting beyond the cuticle. A large nematocyst, with everted
  thread, is seen in the right-hand ectodermal cell. (After F. E.
  Schulze.)]

  The genital cells are simple wandering cells (archaeocytes), at first
  minute and without any specially distinctive features, until they
  begin to develop into germ-cells. According to Wulfert [60] the
  primitive germ-cells of _Gonothyraea_ can be distinguished soon after
  the fixation of the planula, appearing amongst the interstitial cells
  of the ectoderm. The germ-cells are capable of extensive migrations,
  not only in the body of the same polyp, but also from parent to bud
  through many non-sexual generations of polyps in a colony (A. Weismann
  [58]).

  [Illustration: FIG. 6 B.--Epidermo-muscular cells of _Hydra_. m,
  muscular-fibre processes. (After Kleinenberg, from Gegenbaur.)]

  The cnidoblasts are the mother-cells of the nematocysts, each cell
  producing one nematocyst in its interior. The complete nematocyst
  (fig. 7) is a spherical or oval capsule containing a hollow thread,
  usually barbed, coiled in its interior. The capsule has a double wall,
  an outer one (o.c.), tough and rigid in nature, and an inner one
  (i.c.) of more flexible consistence. The outer wall of the capsule is
  incomplete at one pole, leaving an aperture through which the thread
  is discharged. The inner membrane is continuous with the wall of the
  hollow thread at a spot immediately below the aperture in the outer
  wall, so that the thread itself (f) is simply a hollow prolongation of
  the wall of the inner capsule inverted and pushed into its cavity. The
  entire nematocyst is enclosed in the cnidoblast which formed it. When
  the nematocyst is completely developed, the cnidoblast passes outwards
  so as to occupy a superficial position in the ectoderm, and a delicate
  protoplasmic process of sensory nature, termed the _cnidocil_ (cn)
  projects from the cnidoblast like a fine hair or cilium. Many points
  in the development and mechanism of the nematocyst are disputed, but
  it is tolerably certain (1) that the cnidocil is of sensory nature,
  and that stimulation, by contact with prey or in other ways, causes a
  reflex discharge of the nematocyst; (2) that the discharge is an
  explosive change whereby the in-turned thread is suddenly everted and
  turned inside out, being thus shot through the opening in the outer
  wall of the capsule, and forced violently into the tissues of the
  prey, or, it may be, of an enemy; (3) that the thread inflicts not
  merely a mechanical wound, but instils an irritant poison, numbing and
  paralysing in its action. The points most in dispute are, first, how
  the explosive discharge is brought about, whether by pressure exerted
  external to the capsule (i.e. by contraction of the cnidoblast) or by
  internal pressure. N. Iwanzov [27] has brought forward strong grounds
  for the latter view, pointing out that the cnidoblast has no
  contractile mechanism and that measurements show discharged capsules
  to be on the average slightly larger than undischarged ones. He
  believes that the capsule contains a substance which swells very
  rapidly when brought into contact with water, and that in the
  undischarged condition the capsule has its opening closed by a plug of
  protoplasm (x, fig. 7) which prevents access of water to the contents;
  when the cnidocil is stimulated it sets in action a mechanism or
  perhaps a series of chemical changes by which the plug is dissolved or
  removed; as a result water penetrates into the capsule and causes its
  contents to swell, with the result that the thread is everted
  violently. A second point of dispute concerns the spot at which the
  poison is lodged. Iwanzov believes it to be contained within the
  thread itself before discharge, and to be introduced into the tissues
  of the prey by the eversion of the thread. A third point of dispute is
  whether the nematocysts are formed _in situ_, or whether the
  cnidoblasts migrate with them to the region where they are most
  needed; the fact that in _Hydra_, for example, there are no
  interstitial cells in the tentacles, where nematocysts are very
  abundant, is certainly in favour of the view that the cnidoblasts
  migrate on to the tentacles from the body, and that like the genital
  cells the cnidoblasts are wandering cells.

  [Illustration: FIG. 7.--Diagrams to show the structure of Nematocysts
  and their mode of working. (After Iwanzov.)

    a,   Undischarged nematocyst.
    b,   Commencing discharge.
    c,   Discharge complete.
    cn,  Cnidocil.
    N,   Nucleus of cnidoblast.
    o.c, Outer capsule.
    x,   Plug closing the opening of the outer capsule.
    i.c., Inner capsule, continuous with the wall of the filament, f.
    b,    Barbs.]

  The muscular tissue consists primarily of processes from the bases of
  the epithelial cells, processes which are contractile in nature and
  may be distinctly striated. A further stage in evolution is that the
  muscle-cells lose their connexion with the epithelium and come to lie
  entirely beneath it, forming a sub-epithelial contractile layer,
  developed chiefly in the tentacles of the polyp. The evolution of the
  ganglion-cells, is probably similar; an epithelial cell develops
  processes of nervous nature from the base, which come into connexion
  with the bases of the sensory cells, with the muscular cells, and with
  the similar processes of other nerve-cells; next the nerve-cell loses
  its connexion with the outer epithelium and becomes a sub-epithelial
  ganglion-cell which is closely connected with the muscular layer,
  conveying stimuli from the sensory cells to the contractile elements.
  The ganglion-cells of Hydromedusae are generally very small. In the
  polyp the nervous tissue is always in the form of a scattered plexus,
  never concentrated to form a definite nervous system as in the medusa.

  [Illustration: From Gegenbaur's _Elements of Comparative Anatomy_.

  FIG. 8.--Vacuolated Endoderm Cells of cartilaginous consistence from
  the axis of the tentacle of a Medusa (_Cunina_).]

  The endoderm of the polyp is typically a flagellated epithelium of
  large cells (fig. 6), from the bases of which arise contractile
  muscular processes lying in the plane of the transverse section of the
  body. In different parts of the coelenteron the endoderm may be of
  three principal types--(1) digestive endoderm, the primitive type,
  with cells of large size and considerably vacuolated, found in the
  hydranth; some of these cells may become special glandular cells,
  without flagella or contractile processes; (2) circulatory endoderm,
  without vacuoles and without basal contractile processes, found in the
  hydrorhiza and hydrocaulus; (3) supporting endoderm (fig. 8), seen in
  solid tentacles as a row of cubical vacuolated cells, occupying the
  axis of the tentacle, greatly resembling notochordal tissue,
  particularly that of _Amphioxus_ at a certain stage of development; as
  a fourth variety of endodermal cells excretory cells should perhaps be
  reckoned, as seen in the pores in the foot of _Hydra_ and elsewhere
  (cf. C. Chun, HYDROZOA [1], pp. 314, 315).

  The mesogloea in the hydropolyp is a thin elastic layer, in which may
  be lodged the muscular fibres and ganglion cells mentioned above, but
  which never contains any connective tissue or skeletogenous cells or
  any other kind of special mesogloeal corpuscles.

  [Illustration: From Allman's _Gymnoblastic Hydroids_, by permission of
  the Council of the Ray Society.

  FIG. 9.--Colony of _Hydractinia echinata_, growing on the Shell of a
  Whelk. Natural size.]

  [Illustration: From Allman's _Gymnoblastic Hydroids_, by permission of
  the Council of the Ray Society.

  FIG. 10.--Polyps from a Colony of _Hydractinia_, magnified. dz,
  dactylozoid; gz, gastrozoid: b, blastostyle; gon, gonophores; rh,
  hydrorhiza.]

  2. _The Polyp-colony._--All known hydropolyps possess the power of
  reproduction by budding, and the buds produced may become either
  polyps or medusae. The buds may all become detached after a time and
  give rise to separate and independent individuals, as in the common
  _Hydra_, in which only polyp-individuals are produced and sexual
  elements are developed upon the polyps themselves; or, on the other
  hand, the polyp-individuals produced by budding may remain permanently
  in connexion with the parent polyp, in which case sexual elements are
  never developed on polyp-individuals but only on medusa-individuals,
  and a true colony is formed. Thus the typical hydroid colony starts
  from a "founder" polyp, which in the vast majority of cases is fixed,
  but which may be floating, as in _Nemopsis_, _Pelagohydra_, &c. The
  founder-polyp usually produces by budding polyp-individuals, and these
  in their turn produce other buds. The polyps are all non-sexual
  individuals whose function is purely nutritive. After a time the
  polyps, or certain of them, produce by budding medusa-individuals,
  which sooner or later develop sexual elements; in some cases, however,
  the founder-polyp remains solitary, that is to say, does not produce
  polyp-buds, but only medusa-buds, from the first (_Corymorpha_, fig.
  3, _Myriothela_, &c.). In primitive forms the medusa-individuals are
  set free before reaching sexual maturity and do not contribute
  anything to the colony. In other cases, however, the
  medusa-individuals become sexually mature while still attached to the
  parent polyp, and are then not set free at all, but become appanages
  of the hydroid colony and undergo degenerative changes leading to
  reduction and even to complete obliteration of their original medusan
  structure. In this way the hydroid colony becomes composed of two
  portions of different function, the nutritive "trophosome," composed
  of non-sexual polyps, and the reproductive "gonosome," composed of
  sexual medusa-individuals, which never exercise a nutritive function
  while attached to the colony. As a general rule polyp-buds are
  produced from the hydrorhiza and hydrocaulus, while medusa-buds are
  formed on the hydranth. In some cases, however, medusa-buds are formed
  on the hydrorhiza, as in Hydrocorallines.

  In such a colony of connected individuals, the exact limits of the
  separate "persons" are not always clearly marked out. Hence it is
  necessary to distinguish between, first, the "zooids," indicated in
  the case of the polyps by the hydranths, each with mouth and
  tentacles; and, secondly, the "coenosarc," or common flesh, which
  cannot be assigned more to one individual than another, but consists
  of a more or less complicated network of tubes, corresponding to the
  hydrocaulus and hydrorhiza of the primitive independent
  polyp-individual. The coenosarc constitutes a system by which the
  digestive cavity of any one polyp is put into communication with that
  of any other individual either of the trophosome or gonosome. In this
  manner the food absorbed by one individual contributes to the welfare
  of the whole colony, and the coenosarc has the function of circulating
  and distributing nutriment through the colony.

  The hydroid colony shows many variations in form and architecture
  which depend simply upon differences in the methods in which polyps
  are budded.

  [Illustration: After Hincks, Forbes, and Browne. A and B modified from
  Hincks; C modified from Forbes's _Brit. Naked-eyed Medusae_.

  FIG. 11.--_Lar sabellarum_ and two stages of its Medusa, _Willia
  stellata_. A, colony of _Lar_; B and C, young and adult medusae.]

  In the first place, buds may be produced only from the hydrorhiza,
  which grows out and branches to form a basal _stolon_, typically
  net-like, spreading over the substratum to which the founder-polyp
  attached itself. From the stolon the daughter-polyps grow up
  vertically. The result is a spreading or creeping colony, with the
  coenosarc in the form of a root-like horizontal network (fig. 5, B;
  11, A). Such a colony may undergo two principal modifications. The
  meshes of the basal network may become very small or virtually
  obliterated, so that the coenosarc becomes a crust of tubes tending to
  fuse together, and covered over by a common perisarc. Encrusting
  colonies of this kind are seen in _Clava squamata_ (fig. 5, A) and
  _Hydractinia_ (figs. 9, 10), the latter having the perisarc calcified.
  A further very important modification is seen when the tubes of the
  basal perisarc do not remain spread out in one plane, but grow in all
  planes forming a felt-work; the result is a massive colony, such as is
  seen in the so-called Hydrocorallines (fig. 60), where the interspaces
  between the coenosarcal tubes are filled up with calcareous matter, or
  _coenosteum_, replacing the chitinous perisarc. The result is a stony,
  solid mass, which contributes to the building up of coral reefs. In
  massive colonies of this kind no sharp distinction can be drawn
  between hydrorhiza and hydrocaulus in the coenosarc; it is practically
  all hydrorhiza. Massive colonies may assume various forms and are
  often branching or tree-like. A further peculiarity of this type of
  colony is that the entire coenosarcal complex is covered externally by
  a common layer of ectoderm; it is not clear how this covering layer is
  developed.

  [Illustration: FIG. 12.--Colony of _Bougainvillea fruticosa_, natural
  size, attached to the underside of a piece of floating timber. (After
  Allman.)]

  In the second place, the buds may be produced from the hydrocaulus,
  growing out laterally from it; the result is an arborescent, tree-like
  colony (figs. 12, 13). Budding from the hydrocaulus may be combined
  with budding from the hydrorhiza, so that numerous branching colonies
  arise from a common basal stolon. In the formation of arborescent
  colonies, two sharply distinct types of budding are found, which are
  best described in botanical terminology as the monopodial or racemose,
  and the sympodial or cymose types respectively; each is characteristic
  of one of the two sub-orders of the Hydroidea, the Gymnoblastea and
  Calyptoblastea.

  In the monopodial method (figs. 12, 14) the founder-polyp is,
  theoretically, of unlimited growth in a vertical direction, and as it
  grows up it throws out buds right and left alternately, so that the
  first bud produced by it is the lowest down, the second bud is above
  the first, the third above this again, and so on. Each bud produced by
  the founder proceeds to grow and to bud in the same way as the founder
  did, producing a side branch of the main stem. Hence, in a colony of
  gymnoblastic hydroids, the oldest polyp of each system, that is to
  say, of the main stem or of a branch, is the topmost polyp; the
  youngest polyp of the system is the one nearest to the topmost polyp;
  and the axis of the system is a true axis.

  [Illustration: FIG. 13.--Portion of colony of _Bougainvillea
  fruticosa_ (_Anthomedusae-Gymnoblastea_) more magnified. (From
  Lubbock, after Allman.)]

  [Illustration: FIG. 14.--Diagrams of the monopodial method of budding,
  shown in five stages (1-5). F, the founder-polyp; 1, 2, 3, 4, the
  succession of polyps budded from the founder-polyp; a´, b´, c´, the
  succession of polyps budded from 1; a², b², polyps budded from 2; a³,
  polyp budded from 3.]

  In the sympodial method of budding, on the other hand, the
  founder-polyp is of limited growth, and forms a bud from its side,
  which is also of limited growth, and forms a bud in its turn, and so
  on (figs. 15, 16). Hence, in a colony of calyptoblastic hydroids, the
  oldest polyp of a system is the lowest; the youngest polyp is the
  topmost one; and the axis of the system is a false axis composed of
  portions of each of the consecutive polyps. In this method of budding
  there are two types. In one, the biserial type (fig. 15), the polyps
  produce buds right and left alternately, so that the hydranths are
  arranged in a zigzag fashion, forming a "scorpioid cyme," as in
  _Obelia_ and _Sertularia_. In the other, the uniserial type (fig. 16),
  the buds are formed always on the same side, forming a "helicoid
  cyme," as in _Hydrallmania_, according to H. Driesch, in which,
  however, the primitively uniserial arrangement becomes masked later by
  secondary torsions of the hydranths.

  [Illustration: FIG. 15.--Diagram of sympodial budding, biserial type,
  shown in five stages (1-5). F, founder-polyp; 1, 2, 3, 4, 5, 6,
  succession of polyps budded from the founder; a, b, c, second series
  of polyps budded from the founder; a³, b³, series budded from 3.]

  [Illustration: FIG. 16.--Diagram of sympodial budding, uniserial type,
  shown in four stages (1-4). F, founder-polyp; 1, 2, 3, succession of
  polyps budded from the founder.]

  In a colony formed by sympodial budding, a polyp always produces first
  a bud, which contributes to the system to which it belongs, i.e.
  continues the stem or branch of which its parent forms a part. The
  polyp may then form a second bud, which becomes the starting point of
  a new system, the beginning, that is, of a new branch; and even a
  third bud, starting yet another system, may be produced from the same
  polyp. Hence the colonies of Calyptoblastea may be complexly branched,
  and the budding may be biserial throughout, uniserial throughout, or
  partly one, partly the other. Thus in _Plumularidae_ (figs. 17, 18)
  there is formed a main stem by biserial budding; each polyp on the
  main stem forms a second bud, which usually forms a side branch or
  _pinnule_ by uniserial budding. In this way are formed the familiar
  feathery colonies of _Plumularia_, in which the pinnules are all in
  one plane, while in the allied _Antennularia_ the pinnules are
  arranged in whorls round the main biserial stem. The pinnules never
  branch again, since in the uniserial mode of budding a polyp never
  forms a second polyp-bud. On the other hand, a polyp on the main stem
  may form a second bud which, instead of forming a pinnule by uniserial
  budding, produces by biserial budding a branch, from which pinnules
  arise as from the main stem (fig. 18--3, 6). Or a polyp on the main
  stem, after having budded a second time to form a pinnule, may give
  rise to a third bud, which starts a new biserial system, from which
  uniserial pinnules arise as from the main stem--type of _Aglaophenia_
  (fig. 19). The laws of budding in hydroids have been worked out in an
  interesting manner by H. Driesch [13], to whose memoirs the reader
  must be referred for further details.

  [Illustration: FIG. 17.--Diagram of sympodial budding, simple
  unbranched _Plumularia_-type. F, founder; 1-8, main axis formed by
  biserial budding from founder; a-e, pinnule formed by uniserial
  budding from founder; a¹-d¹, branch formed by similar budding from 1;
  a²-d² from 2, and so forth.]

  _Individualization of Polyp-Colonies._--As in other cases where animal
  colonies are formed by organic union of separate individuals, there is
  ever a tendency for the polyp-colony as a whole to act as a single
  individual, and for the members to become subordinated to the needs of
  the colony and to undergo specialization for particular functions,
  with the result that they simulate organs and their individuality
  becomes masked to a greater or less degree. Perhaps the earliest of
  such specializations is connected with the reproductive function.
  Whereas primitively any polyp in a colony may produce medusa-buds, in
  many hydroid colonies medusae are budded only by certain polyps termed
  _blastostyles_ (fig. 10, b). At first not differing in any way from
  other polyps (fig. 5), the blastostyles gradually lose their nutritive
  function and the organs connected with it; the mouth and tentacles
  disappear, and the blastostyle obtains the nutriment necessary for its
  activity by way of the coenosarc. In the Calyptoblastea, where the
  polyps are protected by special capsules of the perisarc, the
  _gonothecae_ enclosing the blastostyles differ from the hydrothecae
  protecting the hydranths (fig. 54).

  [Illustration: FIG. 18.--Diagram showing method of branching in the
  _Plumularia_-type; compare with fig. 17. Polyps 3 and 6, instead of
  producing uniserial pinnules, have produced biserial branches (3¹, 3²,
  3³, 3^4; 6¹-6³), which give off uniserial branches in their turn.]

  In other colonies the two functions of the nutritive polyp, namely,
  capture and digestion of food, may be shared between different polyps
  (fig. 10). One class of polyps, the _dactylozoids_ (dz), lose their
  mouth and stomach, and become elongated and tentacle-like, showing
  great activity of movement. Another class, the _gastrozoids_ (gz),
  have the tentacles reduced or absent, but have the mouth and stomach
  enlarged. The dactylozoids capture food, and pass it on to the
  gastrozoids, which swallow and digest it.

  [Illustration: FIG. 19.--Diagram showing method of branching in the
  _Aglaophenia_-type. Polyp 7 has produced as its first bud, 8; as its
  second bud, a^7, which starts a uniserial pinnule; and as a third bud
  I^7, which starts a biserial branch (II^7-VI^7) that repeats the
  structure of the main stem and gives off pinnules. The main stem is
  indicated by-·-·-·, the new stem by ······.]

  Besides the three types of individual above mentioned, there are other
  appendages of hydroid colonies, of which the individuality is
  doubtful. Such are the "guard-polyps" (machopolyps) of _Plumularidae_,
  which are often regarded as individuals of the nature of dactylozoids,
  but from a study of the mode of budding in this hydroid family Driesch
  concluded that the guard-polyps were not true polyp-individuals,
  although each is enclosed in a small protecting cup of the perisarc,
  known as a nematophore. Again, the spines arising from the basal crust
  of _Podocoryne_ have been interpreted by some authors as reduced
  polyps.

  3. _The Medusa._--In the Hydromedusae the medusa-individual occurs, as
  already stated, in one of two conditions, either as an independent
  organism leading a true life in the open seas, or as a subordinate
  individuality in the hydroid colony, from which it is never set free;
  it then becomes a mere reproductive appendage or _gonophore_, losing
  successively its organs of sense, locomotion and nutrition, until its
  medusoid nature and organization become scarcely recognizable. Hence
  it is convenient to consider the morphology of the medusa from these
  two aspects.

  (a) _The Medusa as an Independent Organism._--The general structure
  and characteristics of the medusa are described elsewhere (see
  articles HYDROZOA and MEDUSA), and it is only necessary here to deal
  with the peculiarities of the Hydromedusa.

  [Illustration: From Allman's _Gymnoblastic Hydroids_, by permission of
  the Council of the Ray Society.

  FIG. 20.--_Cladonema radiatum_, the medusa walking on the basal
  branches of its tentacles (t), which are turned up over the body.]

  [Illustration: From Allman's _Gymnoblastic Hydroids_, by permission of
  the Council of the Ray Society.

  FIG. 21.--_Clavatella prolifera_, ambulatory medusa. t, tentacles; oc,
  ocelli.]

  As regards habit of life the vast majority of Hydromedusae are pelagic
  organisms, floating on the surface of the open sea, propelling
  themselves feebly by the pumping movements of the umbrella produced by
  contraction of the sub-umbral musculature, and capturing their prey
  with their tentacles. The genera _Cladonema_ (fig. 20) and
  _Clavatella_ (fig. 21), however, are ambulatory, creeping forms,
  living in rock-pools and walking, as it were, on the tips of the
  proximal branches of each of the tentacles, while the remaining
  branches serve for capture of food. _Cladonema_ still has the typical
  medusan structure, and is able to swim about, but in _Clavatella_ the
  umbrella is so much reduced, that swimming is no longer possible. The
  remarkable medusa _Mnestra parasites_ is ecto-parasitic throughout
  life on the pelagic mollusc _Phyllirrhoe_, attached to it by the
  sub-umbral surface, and its tentacles have become rudimentary or
  absent. It is interesting to note that _Mnestra_ has been shown by J.
  W. Fewkes [15] and R. T. Günther [19] to belong to the same family
  (_Cladonemidae_) as _Cladonema_ and _Clavatella_, and it is reasonable
  to suppose that the non-parasitic ancestor of _Mnestra_ was, like the
  other two genera, an ambulatory medusa which acquired louse-like
  habits. In some species of the genus _Cunina_ (Narcomedusae) the
  youngest individuals (actinulae) are parasitic on other medusae (see
  below), but in later life the parasitic habit is abandoned. No other
  instances are known of sessile habit in Hydromedusae.

  [Illustration: After E. T. Browne, from _Proc. Zool. Soc. of London_.

  FIG. 22.--_Corymorpha nutans_, adult female Medusa. Magnified 10
  diameters.]

  The external form of the Hydromedusae varies from that of a deep bell
  or thimble, characteristic of the Anthomedusae, to the shallow
  saucer-like form characteristic of the Leptomedusae. It is usual for
  the umbrella to have an even, circular, uninterrupted margin; but in
  the order Narcomedusae secondary down-growths between the tentacles
  produce a lobed, indented margin to the umbrella. The marginal
  tentacles are rarely absent in non-parasitic forms, and are typically
  four in number, corresponding to the four perradii marked by the
  radial canals. Interradial tentacles may be also developed, so that
  the total number present may be increased to eight or to an
  indefinitely large number. In _Willia_, _Geryonia_, &c., however, the
  tentacles and radial canals are on the plan of six instead of four
  (figs. 11 and 26). On the other hand, in some cases the tentacles are
  less in number than the perradii; in _Corymorpha_ (figs. 3 and 22)
  there is but a single tentacle, while two are found in _Amphinema_ and
  _Gemmaria_ (Anthomedusae), and in _Solmundella bitentaculata_ (fig.
  67) and _Aeginopsis hensenii_ (fig. 23) (Narcomedusae). The tentacles
  also vary considerably in other ways than in number: first, in form,
  being usually simple, with a basal bulb, but in _Cladonemidae_ they
  are branched, often in complicated fashion; secondly, in grouping,
  being usually given off singly, and at regular intervals from the
  margin of the umbrella, but in _Margelidae_ and in some Trachomedusae
  they are given off in tufts or bunches (fig. 24); thirdly, in position
  and origin, being usually implanted on the extreme edge of the
  umbrella, but in Narcomedusae they become secondarily shifted and are
  given off high up on the ex-umbrella (figs. 23 and 25); and, fourthly,
  in structure, being hollow or solid, as in the polyp. In some medusae,
  for instance, the remarkable deep-sea family _Pectyllidae_, the
  tentacles may bear suckers, by which the animal may attach itself
  temporarily. It should be mentioned finally that the tentacles are
  very contractile and extensible, and may therefore present themselves,
  in one and the same individual, as long, drawn-out threads, or in the
  form of short corkscrew-like ringlets; they may stream downwards from
  the sub-umbrella, or be held out horizontally, or be directed upwards
  over the ex-umbrella (fig. 23). Each species of medusa usually has a
  characteristic method of carrying its tentacles.

  [Illustration: After O. Maas, _Die craspedoten Medusen der Plankton
  Expedition_, by permission of Lipsius and Tischer.

  FIG. 23.--_Aeginopsis hensenii_, slightly magnified, showing the
  manner in which the tentacles are carried in life.]

  [Illustration: After O. Maas, _Craspedoten Medusen der
  Siboga-Expedition_, by permission of E. S. Brill & Co.

  FIG. 24.--_Rathkea octonemalis._]

  The sub-umbrella invariably shows a velum as an inwardly projecting
  ridge or rim at its margin, within the circle of tentacles; hence the
  medusae of this sub-class are termed craspedote. The manubrium is
  absent altogether in the fresh-water medusa _Limnocnida_, in which the
  diameter of the mouth exceeds half that of the umbrella; on the other
  hand, the manubrium may attain a great length, owing to the centre of
  the sub-umbrella with the stomach being drawn into it, as it were, to
  form a long proboscis, as in _Geryonia_. The mouth may be a simple,
  circular pore at the extremity of the manubrium, or by folding of the
  edges it may become square or shaped like a Maltese cross, with four
  corners and four lips. The corners of the mouth may then be drawn out
  into lobes or lappets, which may have a branched or fringed outline
  (fig. 27), and in _Margelidae_ the subdivisions of the fringe simulate
  tentacles (fig. 24).

  [Illustration: After O. Maas, _Medusae_, in Prince of Monaco's series.

  FIG. 25.--_Aeginura grimaldii._]

  The internal anatomy of the Hydromedusae shows numerous variations.
  The stomach may be altogether lodged in the manubrium, from which the
  radial canals then take origin directly as in _Geryonia_
  (Trachomedusae); it may be with or without gastric pouches. The radial
  canals may be simple or branched, primarily four, rarely six in
  number. The ring-canal is drawn out in Narcomedusae into festoons
  corresponding with the lobes of the margin, and may be obliterated
  altogether (_Solmaris_). In this order the radial canals are
  represented only by wide gastric pouches, and in the family Solmaridae
  are suppressed altogether, so that the tentacles and the festoons of
  the ring-canal arise directly from the stomach. In _Geryonia_,
  centripetal canals, ending blindly, arise from the ring-canal and run
  in a radial direction towards the centre of the umbrella (fig. 26).

  _Histology of the Hydromedusa._--The histology described above for the
  polyp may be taken as the primitive type, from which that of the
  medusa differs only in greater elaboration and differentiation of the
  cell-elements, which are also more concentrated to form distinct
  tissues.

  [Illustration: FIG. 26.--_Carmarina (Geryonia) hastata_, one of the
  _Trachomedusae_. (After Haeckel.)

    a, Nerve ring,
    a´, Radial nerve.
    b, Tentaculocyst.
    c, Circular canal.
    e, Radiating canal,
    g´´. Ovary.
    h, Peronia or cartilaginous process ascending from the cartilaginous
      margin of the disk centripetally in the outer surface of the
      jelly-like disk; six of these are perradial, six interradial,
      corresponding to the twelve solid larval tentacles, resembling those
      of _Cunina_.
    k, Dilatation (stomach) of the manubrium.
    l, Jelly of the disk.
    p, Manubrium.
      t, Tentacle (hollow and tertiary, i.e. preceded by six perradial and
      six interradial solid larval tentacles).
    u, Cartilaginous margin of the disk covered by thread-cells.
    v. Velum.]

  The ectoderm furnishes the general epithelial covering of the body,
  and the muscular tissue, nervous system and sense-organs. The external
  epithelium is flat on the ex-umbral surface, more columnar on the
  sub-umbral surface, where it forms the muscular tissue of the
  sub-umbrella and the velum. The nematocysts of the ectoderm may be
  grouped to form batteries on the tentacles, umbrellar margin and oral
  lappets. In places the nematocysts may be crowded so thickly as to
  form a tough, supporting, "chondral" tissue, resembling cartilage,
  chiefly developed at the margin of the umbrella and forming streaks or
  bars supporting the tentacles ("Tentakelspangen," _peronia_) or the
  tentaculocysts ("Gehörspangen," _otoporpae_).

  [Illustration: After O. Maas in _Results of the "Albatross"
  Expedition_, Museum of Comparative Zoology, Cambridge, Mass., U.S.A.

  FIG. 27.--_Stomotoca divisa_, one of the _Tiaridae_ (Anthomedusae).]

  The muscular tissue of the Hydromedusae is entirely ectodermal. The
  muscle-fibres arise as processes from the bases of the epithelial
  cells; such cells may individually become sub-epithelial in position,
  as in the polyp; or, in places where muscular tissue is greatly
  developed, as in the velum or sub-umbrella, the entire muscular
  epithelium may be thrown into folds in order to increase its surface,
  so that a deeper sub-epithelial muscular layer becomes separated
  completely from a more superficial body-epithelium.

  In its arrangement the muscular tissue forms two systems: the one
  composed of striated fibres arranged circularly, that is to say,
  concentrically round the central axis of the umbrella; the other of
  non-striated fibres running longitudinally, that is to say, in a
  radial direction from, or (in the manubrium) parallel to, the same
  ideal axis. The circular system is developed continuously over the
  entire sub-umbral surface, and the velum represents a special local
  development of this system, at a region where it is able to act at the
  greatest mechanical advantage in producing the contractions of the
  umbrella by which the animal progresses. The longitudinal system is
  discontinuous, and is subdivided into proximal, medial and distal
  portions. The proximal portion forms the retractor muscles of the
  manubrium, or proboscis, well developed, for example, in _Geryonia_.
  The medial portion forms radiating tracts of fibres, the so-called
  "bell-muscles" running underneath, and parallel to, the radial canals;
  when greatly developed, as in _Tiaridae_, they form ridges, so-called
  mesenteries, projecting into the sub-umbral cavity. The distal
  portions form the muscles of the tentacles. In contrast with the
  polyp, the longitudinal muscle-system is entirely ectodermal, there
  being no endodermal muscles in craspedote medusae.

  [Illustration: FIG. 28.--Muscular Cells of Medusae (_Lizzia_). The
  uppermost is a purely muscular cell from the sub-umbrella; the two
  lower are epidermo-muscular cells from the base of a tentacle; the
  upstanding nucleated portion forms part of the epidermal mosaic on the
  free surface of the body. (After Hertwig.)]

  The nervous system of the medusa consists of sub-epithelial
  ganglion-cells, which form, in the first place, a diffuse plexus of
  nervous tissue, as in the polyp, but developed chiefly on the
  sub-umbral surface; and which are concentrated, in the second place,
  to form a definite central nervous system, never found in the polyp.
  In Hydromedusae the central nervous system forms two concentric
  nerve-rings at the margin of the umbrella, near the base of the velum.
  One, the "upper" or ex-umbral nerve-ring, is derived from the ectoderm
  on the ex-umbral side of the velum; it is the larger of the two rings,
  containing more numerous but smaller ganglion-cells, and innervates
  the tentacles. The other, the "lower" or sub-umbral nerve-ring, is
  derived from the ectoderm on the sub-umbral side of the velum; it
  contains fewer but larger ganglion-cells and innervates the muscles of
  the velum (see diagram in article MEDUSAE). The two nerve-rings are
  connected by fibres passing from one to the other.

  [Illustration: After O. Maas, _Craspedoten Medusen der Siboga
  Expedition_, by permission of E. S. Brill & Co.

  FIG. 29.--_Tiaropsis rosea_ (Ag. and Mayer) showing the eight adradial
  Statocysts, each close to an Ocellus. Cf. fig. 30.]

  The sensory cells are slender epithelial cells, often with a cilium or
  stiff protoplasmic process, and should perhaps be regarded as the only
  ectoderm-cells which retain the primitive ciliation of the larval
  ectoderm, otherwise lost in all Hydrozoa. The sense-cells form, in the
  first place, a diffuse system of scattered sensory cells, as in the
  polyp, developed chiefly on the manubrium, the tentacles and the
  margin of the umbrella, where they form a sensory ciliated epithelium
  covering the nerve-centres; in the second place, the sense-cells are
  concentrated to form definite sense-organs, situated always at the
  margin of the umbrella, hence often termed "marginal bodies." The
  possession of definite sense-organs at once distinguishes the medusa
  from the polyp, in which they are never found.

  The sense-organs of medusae are of two kinds--first, organs sensitive
  to light, usually termed _ocelli_ (fig. 29); secondly, organs commonly
  termed _otocysts_, on account of their resemblance to the auditory
  vesicles of higher animals, but serving for the sense of balance and
  orientation, and therefore given the special name of _statocysts_
  (fig. 30). The sense-organs may be _tentaculocysts_, i.e.
  modifications of a tentacle, as in Trachylinae, or developed from the
  margin of the umbrella, in no connexion with a tentacle (or, if so
  connected, not producing any modification in the tentacle), as in
  Leptolinae. In Hydromedusae the sense-organs are always exposed at the
  umbrellar margin (hence _Gymnophthalmata_), while in Scyphomedusae
  they are covered over by flaps of the umbrellar margin (hence
  _Steganophthalmata_).

  [Illustration: Modified after Linko, _Traveaux Soc. Imp. Nat._, St.
  Petersbourg, xxix.

  FIG. 30.--Section of a Statocyst and Ocellus of _Tiaropsis diademata_;
  cf. fig. 29.

    ex, Ex-umbral ectoderm.
    sub, Sub-umbral ectoderm.
    c.c, Circular canal.
    v, Velum.
    st.e, Cavity of statocyst.
    con, Concrement-cell with otolith.]

  The _statocysts_ present in general the structure of either a knob or
  a closed vesicle, composed of (1) indifferent supporting epithelium:
  (2) sensory, so-called auditory epithelium of slender cells, each
  bearing at its free upper end a stiff bristle and running out at its
  base into a nerve-fibre; (3) concrement-cells, which produce
  intercellular concretions, so-called otoliths. By means of vibrations
  or shocks transmitted through the water, or by displacements in the
  balance or position of the animal, the otoliths are caused to impinge
  against the bristles of the sensory cells, now on one side, now on the
  other, causing shocks or stimuli which are transmitted by the basal
  nerve-fibre to the central nervous system. Two stages in the
  development of the otocyst can be recognized, the first that of an
  open pit on a freely-projecting knob, in which the otoliths are
  exposed, the second that of a closed vesicle, in which the otoliths
  are covered over. Further, two distinct types of otocyst can be
  recognized in the Hydromedusae: that of the Leptolinae, in which the
  entire organ is ectodermal, concrement-cells and all, and the organ is
  not a tentaculocyst; and that of the Trachylinae, in which the organ
  is a tentaculocyst, and the concrement-cells are endodermal, derived
  from the endoderm of the modified tentacle, while the rest of the
  organ is ectodermal.

  [Illustration: Modified after O. and R, Hertwig, _Nervensystem und
  Sinnesorgane der Medusen_, by permission of F. C. W. Vogel.

  FIG. 31.--Section of a Statocyst of _Mitrocoma annae_.

    sub, Sub-umbral ectoderm.
    c.c, Circular canal.
    v, Velum.
    st.c,. Cavity of statocyst.
    con, Concrement-cell with otolith.]

  [Illustration: Modified after O. and R, Hertwig, _Nervensystem und
  Sinnesorgane der Medusen_, by permission of F. C. W. Vogel.

  FIG. 32.--Section of a Statocyst of _Phialidium_.

    ex, Ex-umbral ectoderm.
    sub, Sub-umbral ectoderm.
    v, Velum.
    st.c, Cavity of statocyst.
    con, Concrement-cell with otolith.]

  [Illustration: Modified after O. and R, Hertwig, _Nervensystem und
  Sinnesorgane der Medusen_, by permission of F. C. W. Vogel.

  FIG. 33.--Optical Section of a Statocyst of _Octorchis_.

    con, Concrement-cell with otolith.
    st.c, Cavity of statocyst.]

  In the Leptolinae the otocysts are seen in their first stage in
  _Mitrocoma annae_ (fig. 31) and _Tiaropsis_ (figs. 29, 30) as an open
  pit at the base of the velum, on its sub-umbral side. The pit has its
  opening turned towards the sub-umbral cavity, while its base or fundus
  forms a bulge, more or less pronounced, on the ex-umbral side of the
  velum. At the _fundus_ are placed the concrement-cells with their
  conspicuous otoliths (_con_) and the inconspicuous auditory cells,
  which are connected with. the sub-umbral nerve-ring. From the open
  condition arises the closed condition very simply by closing up of the
  aperture of the pit. We then find the typical otocyst of the
  Leptomedusae, a vesicle bulging on the ex-umbral side of the velum
  (figs. 32, 33). The otocysts are placed on the outer wall of the
  vesicle (the fundus of the original pit) or on its sides; their
  arrangement and number vary greatly and furnish useful characters for
  distinguishing genera. The sense-cells are innervated, as before, from
  the sub-umbral nerve-ring. The inner wall of the vesicle (region of
  closure) is frequently thickened to form a so-called "sense-cushion,"
  apparently a ganglionic offshoot from the sub-umbral nerve-ring. In
  many Leptomedusae the otocysts are very small, inconspicuous and
  embedded completely in the tissues; hence they may be easily
  overlooked in badly-preserved material, and perhaps are present in
  many cases where they have been said to have been wanting.

  [Illustration: After O. and R, Hertwig, _Nervensystem und Sinnesorgane
  der Medusen_, by permission of F. C. W. Vogel.

  FIG. 34.--Tentaculocyst (statorhabd) of _Cunina solmaris_. n.c,
  Nerve-cushion; end, endodermal concrement-cells; con, otolith.]

  [Illustration: After O. and R, Hertwig, _Nervensystem und Sinnesorgane
  der Medusen_, by permission of F. C. W. Vogel.

  FIG. 35.--Tentaculocyst of _Cunina lativentris_.

    ect, Ectoderm.
    n.c, Nerve-cushion.
    end, Endodermal concrement-cells.
    con, Otolith.]

  In the Trachylinae the simplest condition of the otocyst is a freely
  projecting club, a so-called _statorhabd_ (figs. 34, 35), representing
  a tentacle greatly reduced in size, covered with sensory ectodermal
  epithelium (_ect._), and containing an endodermal core (_end._), which
  is at first continuous with the endoderm of the ring-canal, but later
  becomes separated from it. In the endoderm large concretions are
  formed (_con._). Other sensory cells with long cilia cover a sort of
  cushion (_n.c._) at the base of the club; the club may be long and the
  cushion small, or the cushion large and the club small. The whole
  structure is innervated, like the tentacles, from the ex-umbral
  nerve-ring. An advance towards the second stage is seen in such a form
  as _Rhopalonema_ (fig. 36), where the ectoderm of the cushion rises up
  in a double fold to enclose the club in a protective covering forming
  a cup or vesicle, at first open distally; finally the opening closes
  and the closed vesicle may sink inwards and be found far removed from
  the surface, as in _Geryonia_ (fig. 37).

  [Illustration: FIG. 36.--Simple tentaculocyst of _Rhopalonema
  velatum_. The process carrying the otolith or concretion hk, formed by
  endoderm cells, is enclosed by an upgrowth forming the "vesicle,"
  which is not yet quite closed in at the top. (After Hertwig.)]

  The _ocelli_ are seen in their simplest form as a pigmented patch of
  ectoderm, which consists of two kinds of cells--(1) pigment-cells,
  which are ordinary indifferent cells of the epithelium containing
  pigment-granules, and (2) visual cells, slender sensory epithelial
  cells of the usual type, which may develop visual cones or rods at
  their free extremity. The ocelli occur usually either on the inner or
  outer sides of the tentacles; if on the inner side, the tentacle is
  turned upwards and carried over the ex-umbrella, so as to expose the
  ocellus to the light; if the ocellus be on the outer side of a
  tentacle, two nerves run round the base of the tentacle to it. In
  other cases ocelli may occur between tentacles, as in _Tiaropsis_
  (fig. 29).

  The simple form of ocellus described in the foregoing paragraph may
  become folded into a pit or cup, the interior of which becomes filled
  with a clear gelatinous secretion forming a sort of vitreous body. The
  distal portion of the vitreous body may project from the cavity of the
  cup, forming a non-cellular lens as in _Lizzia_ (fig. 28). Beyond this
  simple condition the visual organs of the Hydromedusae do not advance,
  and are far from reaching the wonderful development of the eyes of
  Scyphomedusae (_Charybdaea_).

  [Illustration: After O. and R, Hertwig, _Nervensystem und Sinnesorgane
  der Medusen_, by permission of F. C. W. Vogel.

  FIG. 37.--Section of statocyst of _Geryonia_ (_Carmarina hastata_).

    st.c, Statocyst containing the minute tentaculocyst.
    nr1, Ex-umbral nerve-ring.
    nr2, Sub-umbral nerve-ring.
    ex, Ex-umbral ectoderm.
    sub, Sub-umbral ectoderm.
    c.c, Circular canal.
    v, Velum.]

  Besides the ordinary type of ocellus just described, there is found in
  one genus (_Tiaropsis_) a type of ocellus in which the visual elements
  are inverted, and have their cones turned away from the light, as in
  the human retina (fig. 30). In this case the pigment-cells are
  endodermal, forming a cup of pigment in which the visual cones are
  embedded. A similar ocellus is formed in _Aurelia_ among the
  Scyphomedusae (q.v.).

  Other sense organs of Hydromedusae are the so-called _sense-clubs_ or
  _cordyli_ found in a few Leptomedusae, especially in those genera in
  which otocysts are inconspicuous or absent (fig. 39). Each cordylus is
  a tentacle-like structure with an endodermal axis containing an axial
  cavity which may be continuous with the ring-canal, or may be
  partially occluded. Externally the cordylus is covered, by very
  flattened ectoderm, and bears no otoliths or sense-cells, but the base
  of the club rests upon the ex-umbral nerve-ring. Brooks regards these
  organs as sensory, serving for the sense of balance, and representing
  a primitive stage of the tentaculocysts of Trachylinae; Linko, on the
  other hand, finding no nerve-elements connected with them, regards
  them as digestive (?) in function.

  The sense-organs of the two fresh-water medusae _Limnocodium_ and
  _Limnocnida_ are peculiar and of rather doubtful nature (see E. T.
  Browne [10]).

  FIG. 38.--Ocellus of _Lizzia koellikeri_. oc, Pigmented ectodermal
  cells; l, lens. (After Hertwig.)

  The endoderm of the medusa shows the same general types of structure
  as in the polyp, described above. We can distinguish (1) digestive
  endoderm, in the stomach, often with special glandular elements; (2)
  circulatory endoderm, in the radial and ring-canals; (3) supporting
  endoderm in the axes of the tentacles and in the endoderm-lamella; the
  latter is primitively a double layer of cells, produced by
  concrescence of the ex-umbral and sub-umbral layers of the
  coelenteron, but it is usually found as a single layer of flattened
  cells (fig. 40); in _Geryonia_, however, it remains double, and the
  centripetal canals arise by parting of the two layers; (4) excretory
  endoderm, lining pores at the margin of the umbrella, occurring in
  certain Leptomedusae as so-called "marginal tubercles," opening, on
  the one hand, into the ring-canal and, on the other hand, to the
  exterior by "marginal funnels," which debouch into the sub-umbral
  cavity above the velum. As has been described above, the endoderm may
  also contribute to the sense-organs, but such contributions are always
  of an accessory nature, for instance, concrement-cells in the
  otocysts, pigment in the ocelli, and never of sensory nature,
  sense-cells being in all cases ectodermal.

  The reproductive cells may be regarded as belonging primarily to
  neither ectoderm nor endoderm, though lodged in the ectoderm in all
  Hydromedusae. As described for the polyp, they are wandering cells
  capable of extensive migrations before reaching the particular spot at
  which they ripen. In the Hydromedusae they usually, if not invariably,
  ripen in the ectoderm, but in the neighbourhood of the main sources of
  nutriment, that is to say, not far from the stomach. Hence the gonads
  are found on the manubrium in Anthomedusae generally; on the base of
  the manubrium, or under the gastral pouches, or in both these
  situations (_Octorchidae_), or under the radial canals, in
  Trachomedusae; under the gastral pouches or radial canals, in
  Narcomedusae. When ripe, the germ-cells are dehisced directly to the
  exterior.

  [Illustration: After W. K. Brooks, _Journal of Morphology_, x., by
  permission of Ginn & Co.

  FIG. 39.--Section of a Cordylus of _Laodice_.

    c.c, Circular canal.
    v, Velum.
    t, Tentacle.
    c, Cordylus, composed of flattened ectoderm ec covering a large-celled
      endodermal axis en.]

  Hydromedusae are of separate sexes, the only known exception being
  _Amphogona apsteini_, one of the Trachomedusae (Browne [9]). Moreover,
  all the medusae budded from a given hydroid colony are either male or
  female, so that even the non-sexual polyp must be considered to have a
  latent sex. (In _Hydra_, on the other hand, the individual is usually
  hermaphrodite.) The medusa always reproduces itself sexually, and in
  some cases non-sexually also. The non-sexual reproduction takes the
  form of fission, budding or sporogony, the details of which are
  described below. Buds may be produced from the manubrium, radial
  canals, ring-canal, or tentacle-bases, or from an aboral stolon
  (Narcomedusae). In all cases only medusa-buds are produced, never
  polyp-buds.

  The mesogloea of the medusa is largely developed and of great
  thickness in the umbrella. The sub-epithelial tissues, i.e. the
  nervous and muscular cells, are lodged in the mesogloea, but in
  Hydromedusae it never contains tissue-cells or mesogloeal corpuscles.

  (b) _The Medusae as a Subordinate Individuality._--It has been shown
  above that polyps are budded only from polyps and that the medusae may
  be budded either from polyps or from medusae. In any case the
  daughter-individuals produced from the buds may be imagined as
  remaining attached to the parent and forming a colony of individuals
  in organic connexion with one another, and thus three possible cases
  arise. The first case gives a colony entirely composed of polyps, as
  in many Hydroidea. The second case gives a colony partly composed of
  polyp-individuals, partly of medusa-individuals, a possibility also
  realized in many colonies of Hydroidea. The third case gives a colony
  entirely composed of medusa-individuals, a possibility perhaps
  realized in the Siphonophora, which will be discussed in dealing with
  this group.

  [Illustration: FIG. 40.--Portions of Sections through the Disk of
  Medusae--the upper one of _Lizzia_, the lower of _Aurelia_. (After
  Hertwig.)

    el, Endoderm lamella.
    m, Muscular processes of the ectoderm-cells in cross section.
    d, Ectoderm.
    en, Endoderm lining the enteric cavity.
    e, Wandering endoderm cells of the gelatinous substance.]

  The first step towards the formation of a mixed hydroid colony is
  undoubtedly a hastening of the sexual maturity of the
  medusa-individual. Normally the medusae are liberated in quite an
  immature state; they swim away, feed, grow and become adult mature
  individuals. From the bionomical point of view, the medusa is to be
  considered as a means of spreading the species, supplementing the
  deficiencies of the sessile polyp. It may be, however, that increased
  reproductiveness becomes of greater importance to the species than
  wide diffusion; such a condition will be brought about if the medusae
  mature quickly and are either set free in a mature condition or remain
  in the shelter of the polyp-colony, protected from risks of a free
  life in the open sea. In this way the medusa sinks from an independent
  personality to an organ of the polyp-colony, becoming a so-called
  _medusoid gonophore_, or bearer of the reproductive organs, and losing
  gradually all organs necessary for an independent existence, namely
  those of sense, locomotion and nutrition.

  In some cases both free medusae and gonophores may be produced from
  the same hydroid colony. This is the case in _Syncoryne mirabilis_
  (Allman [1], p. 278) and in _Campanularia volubilis_; in the latter,
  free medusae are produced in summer, gonophores in winter (Duplessis
  [14]). Again in _Pennaria_, the male medusae are set free in a state
  of maturity, and have ocelli; the female medusae remain attached and
  have no sense organs.

  [Illustration: Modified from Weismann, _Entstehung der Sexualzellen
  bei den Hydromedusen_.

  FIG. 41.--Diagrams of the Structure of the Gonophores of various
  Hydromedusae, based on the figures of G. J. Allman and A. Weismann.

    A,   "Meconidium" of _Gonothyraea_.
    B,   Type of _Tubularia_.
    C,   Type of _Garveia_, &c.
    D,   Type of _Plumularia_, _Agalma_, &c.
    E,   Type of _Coryne_, _Forskalia_, &c.
    F, G, H, Sporosacs.
    F,   With simple spadix.
    G,   With  spadix  prolonged (_Eudendrium_).
    H,   With spadix branched (_Cordylophora_).
    s.c, Sub-umbral cavity.
    t,   Tentacles.
    c.c, Circular canal,
    g,   Gonads.
    sp,  Spadix.
    e.l, Endoderm-lamella.
    ex,  Ex-umbral ectoderm.
    ect, Ectotheca.]

  The gonophores of different hydroids differ greatly in structure from
  one another, and form a series showing degeneration of the
  medusa-individual, which is gradually stripped, as it were, of its
  characteristic features of medusan organization and finally reduced to
  the simplest structure. A very early stage in the degeneration is well
  exemplified by the so-called "meconidium" of _Gonothyraea_ (fig. 41,
  A). Here the medusoid, attached by the centre of its ex-umbral
  surface, has lost its velum and sub-umbral muscles, its sense organs
  and mouth, though still retaining rudimentary tentacles. The gonads
  (g) are produced on the manubrium, which has a hollow endodermal axis,
  termed the spadix (sp.), in open communication with the coenosarc of
  the polyp-colony and serving for the nutrition of the generative
  cells. A very similar condition is seen in _Tubularia_ (fig. 41, B),
  where, however, the tentacles have quite disappeared, and the circular
  rim formed by the margin of the umbrella has nearly closed over the
  manubrium leaving only a small aperture through which the embryos
  emerge. The next step is illustrated by the female gonophores of
  _Cladocoryne_, where the radial and ring-canals have become
  obliterated by coalescence of their walls, so that the entire endoderm
  of the umbrella is in the condition of the endoderm-lamella. Next the
  opening of the umbrella closes up completely and disappears, so that
  the sub-umbral cavity forms a closed space surrounding the manubrium,
  on which the gonads are developed; such a condition is seen in the
  male gonophore of _Cladocoryne_ and in _Garveia_ (fig. 41, C), where,
  however, there is a further complication in the form of an
  adventitious envelope or ectotheca (ect.) split off from the gonophore
  as a protective covering, and not present in _Cladocoryne_. The
  sub-umbral cavity (s.c.) functions as a brood-space for the developing
  embryos, which are set free by rupture of the wall. It is evident that
  the outer envelope of the gonophore represents the ex-umbral ectoderm
  (ex.), and that the inner ectoderm lining the cavity represents the
  sub-umbral ectoderm of the free medusa. The next step is the gradual
  obliteration of the sub-umbral cavity (s.c.) by disappearance of which
  the sub-umbral ectoderm comes into contact with the ectoderm of the
  manubrium. Such a type is found in _Plumularia_ and also in _Agalma_
  (fig. 41, D); centrally is seen the spadix (sp.), bearing the
  generative cells (g), and external to these (1) a layer of ectoderm
  representing the epithelium of the manubrium; (2) the layer of
  sub-umbral ectoderm; (3) the endoderm-lamella (e.l.); (4) the
  ex-umbral ectoderm (ex.); and (5) there may or may not be present also
  an ectotheca. Thus the gonads are covered over by at least four layers
  of epithelium, and since these are unnecessary, presenting merely
  obstacles to the dehiscence of the gonads, they gradually undergo
  reduction. The sub-umbral ectoderm and that covering the manubrium
  undergo concrescence to form a single layer (fig. 41, E), which
  finally disappears altogether, and the endoderm-lamella disappears.
  The gonophore is now reduced to its simplest condition, known as the
  _sporosac_ (fig. 41, F, G, H), and consists of the spadix bearing the
  gonads covered by a single layer of ectoderm (ex.), with or without
  the addition of an ectotheca. It cannot be too strongly emphasized,
  however, that the sporosac should not be compared simply with the
  manubrium of the medusa, as is sometimes done. The endodermal spadix
  (sp) of the sporosac represents the endoderm of the manubrium; the
  ectodermal lining of the sporosac (ex.) represents the ex-umbral
  ectoderm of the medusa; and the intervening layers, together with the
  sub-umbral cavity, have disappeared. The spadix, as the organ of
  nutrition for the gonads, may be developed in various ways, being
  simple (fig. 41, F) or branched (fig. 41, H); in _Eudendrium_ (fig.
  41, G) it curls round the single large ovum.

  [Illustration: After Allman, _Gymnoblastic Hydroids_, by permission of
  the Council of the Ray Society.

  FIG. 42.--Gonophores of _Dicoryne conferta_.

    A, A male gonophore still enclosed in its ectotheca.
    B and C, Two views of a female gonophore after liberation.
    t, Tentacles.
    ov, Ova, two carried on each female gonophore.
    sp, Testis.]

  The hydroid _Dicoryne_ is remarkable for the possession of gonophores,
  which are ciliate and become detached and swim away by means of their
  cilia. Each such sporosac has two long tentacle-like processes thickly
  ciliated.

  It has been maintained that the gonads of _Hydra_ represent sporosacs
  or gonophores greatly reduced, with the last traces of medusoid
  structure completely obliterated. There is, however, no evidence
  whatever for this, the gonads of _Hydra_ being purely ectodermal
  structures, while all medusoid gonophores have an endodermal portion.
  _Hydra_ is, moreover, bisexual, in contrast with what is known of
  hydroid colonies.

  In some Leptomedusae the gonads are formed on the radial canals and
  form protruding masses resembling sporosacs superficially, but not in
  structure. Allman, however, regarded this type of gonad as equivalent
  to a sporosac, and considered the medusa bearing them as a non-sexual
  organism, a "blastocheme" as he termed it, producing by budding
  medusoid gonophores. As medusae are known to bud medusae from the
  radial canals there is nothing impossible in Allman's theory, but it
  cannot be said to have received satisfactory proof.


_Reproduction and Ontogeny of the Hydromedusae._

Nearly every possible method of reproduction occurs amongst the
Hydromedusae. In classifying methods of generation it is usual to make
use of the sexual or non-sexual nature of the reproduction as a primary
difference, but a more scientific classification is afforded by the
distinction between tissue-cells (histocytes) and germinal cells, actual
or potential (archaeocytes), amongst the constituent cells of the animal
body. In this way we may distinguish, first, _vegetative_ reproduction,
the result of discontinuous growth of the tissues and cell-layers of the
body as a whole, leading to (1) _fission_, (2) _autotomy_, or (3)
_vegetative budding_; secondly, _germinal_ reproduction, the result of
the reproductive activity of the archaeocytes or germinal tissue. In
germinal reproduction the proliferating cells may be _undifferentiated_,
so-called primitive germ-cells, or they may be _differentiated_ as
sexual cells, male or female, i.e. spermatozoa and ova. If the
germ-cells are _undifferentiated_, the offspring may arise from many
cells or from a single cell; the first type is (4) _germinal budding_,
the second is (5) _sporogony_. If the germ-cells are _differentiated_,
the offspring arises by _syngamy_ or sexual union of the ordinary type
between an ovum and spermatozoon, so-called fertilization, of the ovum,
or by _parthenogenesis_, i.e. development of an ovum without
fertilization. The only one of these possible modes of reproduction not
known to occur in Hydromedusae is parthenogenesis.

(1) True _fission_ or longitudinal division of an individual into two
equal and similar daughter-individuals is not common but occurs in
_Gastroblasta_, where it has been described in detail by Arnold Lang
[30].

(2) _Autotomy_, sometimes termed transverse fission, is the name given
to a process of unequal fission in which a portion of the body separates
off with subsequent regeneration. In _Tubularia_ by a process of
decapitation the hydranths may separate off and give rise to a separate
individual, while the remainder of the body grows a new hydranth.
Similarly in _Schizocladium_ portions of the hydrocaulus are cut off to
form so-called "spores," which grow into new individuals (see Allman
[1]).

[Illustration: Much modified from C. Chun, "Coelenterata," in Bronn's
_Tierreich_.

FIG. 43.--Direct Budding of _Cunina_.

    A, B, C, E, F, In vertical section.
    D, Sketch of external view.
    st, Stomach.
    m, Manubrium.
    t. Tentacle.
    s.o, Sense organ.
    v, Velum.
    s.c, Sub-umbral cavity.
    n.s, Nervous system.]

(3) _Vegetative budding_ is almost universal in the Hydromedusae. By
budding is understood the formation of a new individual from a fresh
growth of undifferentiated material. It is convenient to distinguish
buds that give rise to polyps from those that form medusae.

  (a) _The Polyp._--The buds that form polyps are very simple in mode of
  formation. Four stages may be distinguished; the first is a simple
  outgrowth of both layers, ectoderm and endoderm, containing a
  prolongation of the coelenteric cavity; in the second stage the
  tentacles grow out as secondary diverticula from the side of the first
  outgrowth; in the third stage the mouth is formed as a perforation of
  the two layers; and, lastly, if the bud is to be separated, it becomes
  nipped off from the parent polyp and begins a free existence.

  (b) _The Medusae._--Two types of budding must be distinguished--the
  direct, so-called, palingenetic type, and the _indirect_, so-called
  coenogenetic type.

  The direct type of budding is rare, but is seen in _Cunina_ and
  _Millepora_. In _Cunina_ there arises, first, a simple outgrowth of
  both layers, as in a polyp-bud (fig. 43, A); in this the mouth is
  formed distally as a perforation (B); next the sides of the tube so
  formed bulge out laterally near the attachment to form the umbrella,
  while the distal undilated portion of the tube represents the
  manubrium (C); the umbrella now grows out into a number of lobes or
  lappets, and the tentacles and tentaculocysts grow out, the former in
  a notch between two lappets, the latter on the apex of each lappet (D,
  E); finally, the velum arises as a growth of the ectoderm alone, the
  whole bud shapes itself, so to speak, and the little medusa is
  separated off by rupture of the thin stalk connecting it with the
  parent (F). The direct method of medusa-budding only differs from the
  polyp-bud by its greater complexity of parts and organs.

  [Illustration: FIG. 44.--Diagrams of Medusa budding with the formation
  of an entocodon. The endoderm is shaded, the ectoderm left clear.

    A, B, C, D, F, Successive stages in vertical section.
    E, Transverse section of a stage similar to D.
    Gc, Entocodon.
    s.c, Cavity of entocodon, forming the  future sub-umbral cavity.
    st, Stomach.
    r.c, Radial canal.
    c.c, Circular canal.
    e.l, Endoderm lamella.
    m, Manubrium.
    v, Velum.
    t, Tentacle.]

  The indirect mode of budding (figs. 44, 45) is the commonest method by
  which medusa-buds are formed. It is marked by the formation in the bud
  of a characteristic structure termed the _entocodon_ (_Knospenkern_,
  _Glockenkern_).

  [Illustration: FIG. 45.--Modifications of the method of budding shown
  in fig. 44, with solid Entocodon (Gc.) and formation of an ectotheca
  (ect.).]

  The first stage is a simple hollow outgrowth of both body-layers (fig.
  44, A); at the tip of this is formed a thickening of the ectoderm,
  arising primitively as a hollow ingrowth (fig. 44, B), but more
  usually as a solid mass of ectoderm-cells (fig. 45, A). The ectodermal
  ingrowth is the entocodon (Gc.); it bulges into, and pushes down, the
  endoderm at the apex of the bud, and if solid it soon acquires a
  cavity (fig. 44, C, s.c.). The cavity of the entocodon increases
  continually in size, while the endoderm pushes up at the sides of it
  to form a cup with hollow walls, enclosing but not quite surrounding
  the entocodon, which remains in contact at its outer side with the
  ectoderm covering the bud (fig. 44, D, v). The next changes that take
  place are chiefly in the endoderm-cup (fig. 44, D, E); the cavity
  between the two walls of the cup becomes reduced by concrescence to
  form the radial canals (r.c.), ring-canal (c.c.), and endoderm-lamella
  (e.l., fig. 44, E), and at the same time the base of the cup is thrust
  upwards to form the manubrium (m), converting the cavity of the
  entocodon into a space which is crescentic or horse-shoe-like in
  section. Next tentacles (t, fig. 44, F) grow out from the ring-canal,
  and the double plate of ectoderm on the distal side of the entocodon
  becomes perforated, leaving a circular rim composed of two layers of
  ectoderm, the velum (v) of the medusa. Finally, a mouth is formed by
  breaking through at the apex of the manubrium, and the now
  fully-formed medusa becomes separated by rupture of the stalk of the
  bud and swims away.

  [Illustration: Fig. 46.--Diagrams to show the significance of the
  Entocodon in Medusa-buds. (Modified from a diagram given by A.
  Weismann.)

    I, Ideally primitive method of budding, in which the mouth is formed
      first (Ia), next the tentacles (Ib), and lastly the umbrella.
    II, Method. of _Cunina_; (a) the mouth arises, next the umbrella
      (b), and lastly the tentacles (c).
    III, Hypothetical transition from II to the indirect method with an
      entocodon; the formation of the manubrium is retarded, that of the
      umbrella hastened (IIIa, b).
    IV, a, b, c, budding with an entocodon (cf. fig. 44).
    V, Budding with a solid entocodon (cf. fig. 45).]

  If the bud, however, is destined to give rise not to a free medusa,
  but to a gonophore, the development is similar but becomes arrested at
  various points, according to the degree to which the gonophore is
  degenerate. The entocodon is usually formed, proving the medusoid
  nature of the bud, but in sporosacs the entocodon may be rudimentary
  or absent altogether. The process of budding as above described may be
  varied or complicated in various ways; thus a secondary, amnion-like,
  ectodermal covering or ectotheca (fig. 45, C, ect.) may be formed over
  all, as in _Garveia_, &c.; or the entocodon may remain solid and
  without cavity until after the formation of the manubrium, or may
  never acquire a cavity at all, as described above for the gonophores.

  _Phylogenetic Significance of the Entocodon._--It is seen from the
  foregoing account of medusa-budding that the entocodon is a very
  important constituent of the bud, furnishing some of the most
  essential portions of the medusa; its cavity becomes the sub-umbral
  cavity, and its lining furnishes the ectodermal epithelium of the
  manubrium and of the sub-umbral cavity as far as the edge of the
  velum. Hence the entocodon represents a precocious formation of the
  sub-umbral surface, equivalent to the peristome of the polyp,
  differentiated in the bud prior to other portions of the organism
  which must be regarded as antecedent to it in phylogeny.

  If the three principal organ-systems of the medusa, namely mouth,
  tentacles and umbrella, be considered in the light of phylogeny, it is
  evident that the manubrium bearing the mouth must be the oldest, as
  representing a common property of all the Coelentera, even of the
  gastrula embryo of all Enterozoa. Next in order come the tentacles,
  common to all Cnidaria. The special property of the medusa is the
  umbrella, distinguishing the medusa at once from other morphological
  types among the Coelentera. If, therefore, the formation of these
  three systems of organs took place according to a strictly
  phylogenetic sequence, we should expect them to appear in the order
  set forth above (fig. 46, Ia, b, c). The nearest approach to the
  phylogenetic sequence is seen in the budding of _Cunina_, where the
  manubrium and mouth appear first, but the umbrella is formed before
  the tentacles (fig. 46, IIa, b, c). In the indirect or coenogenetic
  method of budding, the first two members of the sequence exhibited by
  Cunina change places, and the umbrella is formed first, the manubrium
  next, and then the tentacles; the actual mouth-perforation being
  delayed to the very last (fig. 46, IVa, b, c). Hence the budding of
  medusae exemplifies very clearly a common phenomenon in development, a
  phylogenetic series of events completely dislocated in the ontogenetic
  time-sequence.

  The entocodon is to be regarded, therefore, not as primarily an
  ingrowth of ectoderm, but rather as an upgrowth of both body-layers,
  in the form of a circular rim (IVa), representing the umbrellar
  margin; it is comparable to the bulging that forms the umbrella in the
  direct method of budding, but takes place before a manubrium is
  formed, and is greatly reduced in size, so as to become a little pit.
  By a simple modification, the open pit becomes a solid ectodermal
  ingrowth, just as in Teleostean fishes the hollow medullary tube, or
  the auditory pit of other vertebrate embryos, is formed at first as a
  solid cord of cells, which acquires a cavity secondarily. Moreover,
  the entocodon, however developed, gives rise at first to a closed
  cavity, representing a closing over of the umbrella, temporary in the
  bud destined to be a free medusa, but usually permanent in the sessile
  gonophore. As has been shown above, the closing up of the sub-umbral
  cavity is one of the earliest degenerative changes in the evolution of
  the gonophore, and we may regard it as the umbrellar fold taking on a
  protective function, either temporarily for the bud or permanently for
  the gonophore.

  To sum up, the entocodon is a precocious formation of the umbrella,
  closing over to protect the organs in the umbrellar cavity. The
  possession of an entocodon proves the medusa-nature of the bud, and
  can only be explained on the theory that gonophores are degenerate
  medusae, and is inexplicable on the opposed view that medusae are
  derived from gonophores secondarily set free. In the sporosac,
  however, the medusa-individual has become so degenerate that even the
  documentary proof, so to speak, of its medusoid nature may have been
  destroyed, and only circumstantial evidence of its nature can be
  produced.

4. _Germinal Budding._--This method of budding is commonly described as
budding from a single body-layer, instead of from both layers. The layer
that produces the bud is invariably the ectoderm, i.e. the layer in
which, in Hydromedusae, the generative cells are lodged; and in some
cases the buds are produced in the exact spot in which later the gonads
appear. From these facts, and from those of the sporogony, to be
described below, we may regard budding to this type as taking place from
the germinal epithelium rather than from ordinary ectoderm.

  (a) _The Polyp._--Budding from the ectoderm alone has been described
  by A. Lang [29] in _Hydra_ and other polyps. The tissues of the bud
  become differentiated into ectoderm and endoderm, and the endoderm of
  the bud becomes secondarily continuous with that of the parent, but no
  part of the parental endoderm contributes to the building up of the
  daughter-polyp. Lang regarded this method of budding as universal in
  polyps, a notion disproved by O. Seeliger [52] who went to the
  opposite extreme and regarded the type of budding described by Lang as
  non-existent. In view, however, both of the statements and figures of
  Lang and of the facts to be described presently for medusae
  (_Margellium_), it is at least theoretically possible that both
  germinal and vegetative budding may occur in polyps as well as in
  medusae.

  (b) _The Medusa._--The clearest instance of germinal budding is
  furnished by _Margellium (Rathkea) octopunctatum_, one of the
  _Margelidae_. The budding of this medusa has been worked out in detail
  by Chun (HYDROZOA, [1]), to whom the reader must be referred for the
  interesting laws of budding regulating the sequence and order of
  formation of the buds.

  The buds of _Margellium_ are produced on the manubrium in each of the
  four interradii, and they arise from the ectoderm, that is to say, the
  germinal epithelium, which later gives rise to the gonads. The buds do
  not appear simultaneously but successively on each of the four sides
  of the manubrium, thus:

       1
    3     4
       2

  and secondary buds may be produced on the medusa-buds before the
  latter are set free as medusae. Each bud arises as a thickening of the
  epithelium, which first forms two or three layers (fig. 47, A), and
  becomes separated into a superficial layer, future ectoderm,
  surrounding a central mass, future endoderm (fig. 47, B). The
  ectodermal epithelium on the distal side of the bud becomes thickened,
  grows inwards, and forms a typical entocodon (fig. 37, D, E, F). The
  remaining development of the bud is just as described above for the
  indirect method of medusa-budding (fig. 47, G, H). When the bud is
  nearly complete, the body-wall of the parent immediately below it
  becomes perforated, placing the coelenteric cavity of the parent in
  secondary communication with that of the bud (H), doubtless for the
  better nutrition of the latter.

  Especially noteworthy in the germinal budding of _Margellium_ is the
  formation of the entocodon, as in the vegetative budding of the
  indirect type.

5. _Sporogony._--This method of reproduction has been described by E.
Metchnikoff in _Cunina_ and allied genera. In individuals either of the
male or female sex, germ-cells which are quite undifferentiated and
neutral in character, become amoeboid, and wander into the endoderm.
They divide each into two sister-cells, one of which--the spore--becomes
enveloped by the other. The spore-cell multiplies by division, while the
enveloping cell is nutrient and protective. The spore cell gives rise to
a "spore-larva," which is set free in the coelenteron and grows into a
medusa. Whether sporogony occurs also in the polyp or not remains to be
proved.

6. _Sexual Reproduction and Embryology._--The ovum of Hydromedusae is
usually one of a large number of oögonia, and grows at the expense of
its sister-cells. No regular follicle is formed, but the oöcyte absorbs
nutriment from the remaining oögonia. In _Hydra_ the oöcyte is a large
amoeboid cell, which sends out pseudopodia amongst the oögonia and
absorbs nutriment from them. When the oöcyte is full grown, the residual
oögonia die off and disintegrate.

[Illustration: FIG. 47.--Budding from the Ectoderm (germinal epithelium)
in _Margellium_. (After C. Chun.)

  A, The epithelium becomes two-layered.
  B, The lower layer forms a solid mass of cells, which (C) becomes a
    vesicle, the future endoderm, containing the coelenteric cavity
    (coel), while the outer layer furnishes the future ectoderm.
  D, E, F, a thickening of the ectoderm on the distal side of the bud
    forms an entocodon (Gc).
  G,H, Formation of the medusae.
  s.c, Sub-umbral cavity.
  r.c, Radial canal.
  st, Stomach, which in H acquires a secondary communication with the
    digestive cavity of the mother.
  cc, Circular canal.
  v, Velum.
  t, Tentacle.]

The spermatogenesis and maturation and fertilization of the germ-cells
present nothing out of the common and need not be described here. These
processes have been studied in detail by A. Brauer [2] for _Hydra_.

  The general course of the development is described in the article
  HYDROZOA. We may distinguish the following series of stages: (1) ovum;
  (2) cleavage, leading to formation of a blastula; (3) formation of an
  inner mass or parenchyma, the future endoderm, by immigration or
  delamination, leading to the so-called parenchymula-stage; (4)
  formation of an archenteric cavity, the future coelenteron, by a
  splitting of the internal parenchyma, and of a blastopore, the future
  mouth, by perforation at one pole, leading to the gastrula-stage; (5)
  the outgrowth of tentacles round the mouth (blastopore), leading to
  the actinula-stage; and (6) the actinula becomes the polyp or medusa
  in the manner described elsewhere (see articles HYDROZOA, POLYP and
  MEDUSA). This is the full, ideal development, which is always
  contracted or shortened to a greater or less extent. If the embryo is
  set free as a free-swimming, so-called planula-larva, in the blastula,
  parenchymula, or gastrula stage, then a free actinula stage is not
  found; if, on the other hand, a free actinula occurs, then there is no
  free planula stage.

  The cleavage of the ovum follows two types, both seen in _Tubularia_
  (Brauer [3]). In the first, a cleavage follows each nuclear division;
  in the second, the nuclei multiply by division a number of times, and
  then the ovum divides into as many blastomeres as there are nuclei
  present. The result of cleavage in all cases is a typical blastula,
  which when set free becomes oval and develops a flagellum to each
  cell, but when not set free, it remains spherical in form and has no
  flagella.

  The germ-layer formation is always by immigration or delamination,
  never by invagination. When the blastula is oval and free-swimming the
  inner mass is formed by unipolar immigration from the hinder pole.
  When the blastula is spherical and not set free, the germ-layer
  formation is always multipolar, either by immigration or by
  delamination, i.e. by tangential division of the cells of the
  blastoderm, as in _Geryonia_, or by a mixture of immigration and
  delamination, as in _Hydra_, _Tubularia_, &c. The blastopore is formed
  as a secondary perforation at one spot, in free-swimming forms at the
  hinder pole. Formation of archenteron and blastopore may, however, be
  deferred till a later stage (actinula or after).

  The actinula stage is usually suppressed or not set free, but it is
  seen in _Tubularia_ (fig. 48), where it is ambulatory, in _Gonionemus_
  (Trachomedusae), and in _Cunina_ (Narcomedusae), where it is
  parasitic.

  [Illustration: Modified from a plate by L. Agassiz, _Contributions to
  Nat. Hist. U.S._, iv.

  FIG. 48.--Free Actinula of _Tubularia_.]

  In Leptolinae the embryonic development culminates in a polyp, which
  is usually formed by fixation of a planula (parenchymula), rarely by
  fixation of an actinula. The planula may fix itself (1) by one end,
  and then becomes the hydrocaulus and hydranth, while the hydrorhiza
  grows out from the base; or (2) partly by one side and then gives rise
  to the hydrorhiza as well as to the other parts of the polyp; or (3)
  entirely by its side, and then forms a recumbent hydrorhiza from which
  a polyp appears to be budded as an upgrowth.

  In Trachylinae the development produces always a medusa, and there is
  no polyp-stage. The medusa arises direct from the actinula-stage and
  there is no entocodon formed, as in the budding described above.

  _Life-cycles of the Hydromedusae._--The life-cycle of the Leptolinae
  consists of an alternation of generations in which non-sexual
  individuals, polyps, produce by budding sexual individuals, medusae,
  which give rise by the sexual process to the non-sexual polyps again,
  so completing the cycle. Hence the alternation is of the type termed
  metagenesis. The Leptolinae are chiefly forms belonging to the inshore
  fauna. The Trachylinae, on the other hand, are above all oceanic
  forms, and have no polyp-stage, and hence there is typically no
  alternation in their life-cycle. It is commonly assumed that the
  Trachylinae are forms which have lost the alternation of generations
  possessed by them ancestrally, through secondary simplification of the
  life-cycle. Hence the Trachylinae are termed "hypogenetic" medusae to
  contrast them with the metagenetic Leptolinae. The whole question has,
  however, been argued at length by W. K. Brooks [4], who adduces strong
  evidence for a contrary view, that is to say, for regarding the direct
  type of development seen in Trachylinae as more primitive, and the
  metagenesis seen in Leptolinae as a secondary complication introduced
  into the life-cycle by the acquisition of _larval budding_. The polyp
  is regarded, on this view, as a form phylogenetically older than the
  medusa, in short, as nothing more than a sessile actinula. In
  Trachylinae the polyp-stage is passed over, and is represented only by
  the actinula as a transitory embryonic stage. In Leptolinae the
  actinula becomes the sessile polyp which has acquired the power of
  budding and producing individuals either of its own or of a higher
  rank; it represents a persistent larval stage and remains in a
  sexually immature condition as a neutral individual, sex being an
  attribute only of the final stage in the development, namely the
  medusa. The polyp of the Leptolinae has reached the limit of its
  individual development and is incapable of becoming itself a medusa,
  but only produces medusa-buds; hence a true alternation of generations
  is produced. In Trachylinae also the beginnings of a similar
  metagenesis can be found. Thus in _Cunina octonaria_, the ovum
  develops into an actinula which buds daughter-actinulae; all of them,
  both parent and offspring, develop into medusae, so that there is no
  alternation of generations, but only larval multiplication. In _Cunina
  parasitica_, however, the ovum develops into an actinula, which buds
  actinulae as before, but only the daughter-actinulae develop into
  medusae, while the original, parent-actinula dies off; here,
  therefore, larval budding has led to a true alternation of
  generations. In _Gonionemus_ the actinula becomes fixed and
  polyp-like, and reproduces by budding, so that here also an
  alternation of generations may occur. In the Leptolinae we must first
  substitute polyp for actinula, and then a condition is found which can
  be compared to the case of _Cunina parasitica_ or Gonionemus, if we
  suppose that neither the parent-actinula (i.e. founder-polyp) nor its
  offspring by budding (polyps of the colony) have the power of becoming
  medusae, but only of producing medusae by budding. For further
  arguments and illustrations the reader must be referred to Brooks's
  most interesting memoir. The whole theory is one most intimately
  connected with the question of the relation between polyp and medusa,
  to be discussed presently. It will be seen elsewhere, however, that
  whatever view may be held as to the origin of metagenesis in
  Hydromedusae, in the case of Scyphomedusae (q.v.) no other view is
  possible than that the alternation of generations is the direct result
  of larval proliferation.

  To complete our survey of life-cycles in the Hydromedusae it is
  necessary to add a few words about the position of _Hydra_ and its
  allies. If we accept the view that _Hydra_ is a true sexual polyp, and
  that its gonads are not gonophores (i.e. medusa-buds) in the extreme
  of degeneration, then it follows from Brooks's theory that _Hydra_
  must be descended from an archaic form in which the medusan type of
  organization had not yet been evolved. _Hydra_ must, in short, be a
  living representative of the ancestor of which the actinula-stage is a
  transient reminiscence in the development of higher forms. It may be
  pointed out in this connexion that the fixation of _Hydra_ is only
  temporary, and that the animal is able at all times to detach itself,
  to move to a new situation, and to fix itself again. There is no
  difficulty whatever in regarding _Hydra_ as bearing the same relation
  to the actinula-stage of other Hydromedusae that a Rotifer bears to a
  trochophore-larva or a fish to a tadpole.

_The Relation of Polyp and Medusa._--Many views have been put forward as
to the morphological relationship between the two types of person in the
Hydromedusae. For the most part, polyp and medusa have been regarded as
modifications of a common type, a view supported by the existence, among
Scyphomedusae (q.v.), of sessile polyp-like medusae (_Lucernaria_, &c.).
R. Leuckart in 1848 compared medusae in general terms to flattened
polyps. G. J. Allman [1] put forward a more detailed view, which was as
follows. In some polyps the tentacles are webbed at the base, and it was
supposed that a medusa was a polyp of this kind set free, the umbrella
being a greatly developed web or membrane extending between the
tentacles. A very different theory was enunciated by E. Metchnikoff. In
some hydroids the founder-polyp, developed from a planula after
fixation, throws out numerous outgrowths from the base to form the
hydrorhiza; these outgrowths may be radially arranged so as to form by
contact or coalescence a flat plate. Mechnikov considered the plate thus
formed at the base of the polyp as equivalent to the umbrella, and the
body of the polyp as equivalent to the manubrium, of the medusa; on this
view the marginal tentacles almost invariably present in medusae are new
formations, and the tentacles of the polyp are represented in the medusa
by the oral arms which may occur round the mouth, and which sometimes,
e.g. in _Margelidae_, have the appearance and structure of tentacles.
Apart from the weighty arguments which the development furnishes against
the theories of Allman and Mechnikov, it may be pointed out that neither
hypothesis gives a satisfactory explanation of a structure universally
present in medusae of whatever class, namely the endoderm-lamella,
discovered by the brothers O. and R. Hertwig. It would be necessary to
regard this structure as a secondary extension of the endoderm in the
tentacle-web, on Allman's theory, or between the outgrowths of the
hydrorhiza, on Mechnikov's hypothesis. The development, on the contrary,
shows unequivocally that the endoderm-lamella arises as a local
coalescence of the endodermal linings of a primitively extensive gastral
space.

The question is one intimately connected with the view taken as to the
nature and individuality of polyp, medusa and gonophore respectively. On
this point the following theories have been put forward.

  1. The theory that the medusa is simply an organ, which has become
  detached and has acquired a certain degree of independence, like the
  well-known instance of the hectocotyle of the cuttle-fish. On this
  view, put forward by E. van Beneden and T. H. Huxley, the sporosac is
  the starting-point of an evolution leading up through the various
  types of gonophores to the free medusa as the culminating point of a
  phyletic series. The evidence against this view may be classed under
  two heads: first, comparative evidence; hydroids very different in
  their structural characters and widely separate in the systematic
  classification of these organisms may produce medusae very similar, at
  least so far as the essential features of medusan organization are
  concerned; on the other hydroids closely allied, perhaps almost
  indistinguishable, may produce gonophores in the one case, medusae in
  the other; for example, _Hydractinia_ (gonophores) and _Podocoryne_
  (medusae), _Tubularia_ (gonophores) and _Ectopleura_ (medusae),
  _Coryne_ (gonophores) and _Syncoryne_ (medusae), and so on. If it is
  assumed that all these genera bore gonophores ancestrally, then medusa
  of similar type must have been evolved quite independently in a great
  number of cases. Secondly, there is the evidence from the development,
  namely, the presence of the entocodon in the medusa-bud, a structure
  which, as explained above, can only be accounted for satisfactorily by
  derivation from a medusan type of organization. Hence it may be
  concluded that the gonophores are degenerate medusae, and not that the
  medusae are highly elaborated gonophores, as the organ-theory
  requires.

  2. The theory that the medusa is an independent individual, fully
  equivalent to the polyp in this respect, is now universally accepted
  as being supported by all the facts of comparative morphology and
  development. The question still remains open, however, which of the
  two types of person may be regarded as the most primitive, the most
  ancient in the race-history of the Hydromedusae. F. M. Balfour put
  forward the view that the polyp was the more primitive type, and that
  the medusa is a special modification of the polyp for reproductive
  purposes, the result of division of labour in a polyp-colony, whereby
  special reproductive persons become detached and acquire organs of
  locomotion for spreading the species. W. K. Brooks, on the other hand,
  as stated above, regards the medusa as the older type and looks upon
  both polyp and medusa, in the Hydromedusae, as derived from a
  free-swimming or floating actinula, the polyp being thus merely a
  fixed nutritive stage, possessing secondarily acquired powers of
  multiplication by budding.

  The Hertwigs when they discovered the endoderm-lamella showed on
  morphological grounds that polyp and medusa are independent types,
  each produced by modification in different directions of a more
  primitive type represented in development by the actinula-stage. If a
  polyp, such as _Hydra_, be regarded simply as a sessile actinula, we
  must certainly consider the polyp to be the older type, and it may be
  pointed out that in the Anthozoa only polyp-individuals occur. This
  must not be taken to mean, however, that the medusa is derived from a
  sessile polyp; it must be regarded as a direct modification of the
  more ancient free actinula form, without primitively any intervening
  polyp-stage, such as has been introduced secondarily into the
  development of the Leptolinae and represents a revival, so to speak,
  of an ancestral form or larval stage, which has taken on a special
  role in the economy of the species.


SYSTEMATIC REVIEW OF THE HYDROMEDUSAE

ORDER I. Eleutheroblastea.--Simple polyps which become sexually mature
and which also reproduce non-sexually, but without any medusoid stage in
the life-cycle.

The sub-order includes the family _Hydridae_, containing the common
fresh-water polyps of the genus _Hydra_. Certain other forms of doubtful
affinities have also been referred provisionally to this section.

  _Hydra._--This genus comprises fresh-water polyps of simple structure.
  The body bears tentacles, but shows no division into hydrorhiza,
  hydrocaulus or hydranth; it is temporarily fixed and has no perisarc.
  The polyp is usually hermaphrodite, developing both ovaries and testes
  in the same individual. There is no free-swimming planula larva, but
  the stage corresponding to it is passed over in an enveloping cyst,
  which is secreted round the embryo by its own ectodermal layer,
  shortly after the germ-layer formation is complete, i.e. in the
  parenchymula-stage. The envelope is double, consisting of an external
  chitinous stratified shell, and an internal thin elastic membrane.
  Protected by the double envelope, the embryo is set free as a
  so-called "egg," and in Europe it passes the winter in this condition.
  In the spring the embryo bursts its shell and is set free as a minute
  actinula which becomes a _Hydra_.

  Many species are known, of which three are common in European waters.
  It has been shown by C. F. Jickeli (28) that the species are
  distinguishable by the characters of their nematocysts. They also show
  characteristic differences in the egg (Brauer [2]). In _Hydra viridis_
  the polyp is of a green colour and produces a spherical egg with a
  smooth shell which is dropped into the mud. _H. grisea_ is greyish in
  tint and produces a spherical egg with a spiky shell, which also is
  dropped into the mud. _H. fusca_ (= _H. vulgaris_) is brown in colour,
  and produces a bun-shaped egg, spiky on the convex surface, and
  attached to a water-weed or some object by its flattened side. Brauer
  found a fourth species, similar in appearance to _H. fusca_, but
  differing from the three other species in being of separate sexes, and
  in producing a spherical egg with a knobby shell, which is attached
  like that of _H. fusca_.

  The fact already noted that the species of _Hydra_ can be
  distinguished by the characters of their nematocysts is a point of
  great interest. In each species, two or three kinds of nematocysts
  occur, some large, some small, and for specific identification the
  nematocysts must be studied collectively in each species. It is very
  remarkable that this method of characterizing and diagnozing species
  has never been extended to the marine hydroids. It is quite possible
  that the characters of the nematocysts might afford data as useful to
  the systematist in this group as do the spicules of sponges, for
  instance. It would be particularly interesting to ascertain how the
  nematocysts of a polyp are related to those possessed by the medusa
  budded from it, and it is possible that in this manner obscure
  questions of relationship might be cleared up.

  _Protohydra_ is a marine genus characterized by the absence of
  tentacles, by a great similarity to _Hydra_ in histological structure,
  and by reproduction by transverse fission. It was found originally in
  an oyster-farm at Ostend. The sexual reproduction is unknown. For
  further information see C. Chun (HYDROZOA [1]. Pl. I.).

  [Illustration: FIG. 49.--Diagram showing possible modifications of
  persons of a gymnoblastic _Hydromedusa_. (After Allman.)

    a, Hydrocaulus (stem).
    b, Hydrorhiza (root).
    c, Enteric cavity.
    d, Endoderm.
    e, Ectoderm.
    f, Perisarc, (horny case).
    g, Hydranth (hydriform person) expanded.
    g', Hydranth (hydriform person) contracted.
    h, Hypostome, bearing mouth at its extremity.
    k, Sporosac springing from the hydrocaulus.
    k', Sporosac springing from m, a modified hydriform person
      (blastostyle): the genitalia are seen surrounding the spadix or
      manubrium.
    l, Medusiform person or medusa.
    m, Blastostyle.]

  _Polypodium hydriforme_ Ussow is a fresh-water form parasitic on the
  eggs of the sterlet. A "stolon" of unknown origin produces thirty-two
  buds, which become as many _Polypodia_; each has twenty-four tentacles
  and divides by fission repeated twice into four individuals, each with
  six tentacles. The daughter-individuals grow, form the full number of
  twenty-four tentacles and divide again. The polyps are free and walk
  on their tentacles. See Ussow [54].

  _Tetraplatia volitans_ Viguier is a remarkable floating marine form.
  See C. Viguier [56] and Delage and Hérouard (Hydrozoa [2]).

  _Haleremita_ Schaudinn. See F. Schaudinn [50] and Delage and Hérouard
  (HYDROZOA [2]).

  In all the above-mentioned genera, with the exception of _Hydra_, the
  life-cycle is so imperfectly known that their true position cannot be
  determined in the present state of our knowledge. They may prove
  eventually to belong to other orders. Hence only the genus _Hydra_ can
  be considered as truly representing the order Eleutheroblastea. The
  phylogenetic position of this genus has been discussed above.

ORDER II. Hydroidea seu Leptolinae.--Hydromedusae with alternation of
generations (metagenesis) in which a non-sexual polyp-generation
(trophosome) produces by budding a sexual medusa-generation (gonosome).
The polyp may be solitary, but more usually produces polyps by budding
and forms a polyp-colony. The polyp usually has the body distinctly
divisible into hydranth, hydrocaulus and hydrorhiza, and is usually
clothed in a perisarc. The medusae may be set free or may remain
attached to the polyp-colony and degenerate into a gonophore. When fully
developed the medusa is characterized by the sense organs being composed
entirely of ectoderm, developed independently of the tentacles, and
innervated from the sub-umbral nerve-ring.

  The two kinds of persons present in the typical Hydroidea make the
  classification of the group extremely difficult, for reasons explained
  above. Hence the systematic arrangement that follows must be
  considered purely provisional. A natural classification of the
  Hydroidea has yet to be put forward. Many genera and families are
  separated by purely artificial characters, mere shelf-and-bottle
  groupings devised, for the convenience of the museum curator and the
  collector. Thus many subdivisions are diagnosed by setting free
  medusae in one case, or producing gonophores in another, although it
  is very obvious, as pointed out above, that a genus producing medusae
  may be far more closely allied to one producing gonophores than to
  another producing medusae, or vice versa, and that in some cases the
  production of medusae or gonophores varies with the season or the sex.
  Moreover, P. Hallez [22] has recently shown that hydroids hitherto
  regarded as distinct species are only forms of the same species grown
  under different conditions.

SUB-ORDER 1. HYDROIDEA GYMNOBLASTEA (ANTHOMEDUSAE).--Trophosome without
hydrothecae or gonothecae, with monopodial type of budding. Gonosome
with free medusae or gonophores; medusae usually with ocelli, never with
otocysts. The gymnoblastic polyp usually has a distinct perisarc
investing the hydrorhiza and the hydrocaulus, sometimes also the
hydranth as far as the bases of the tentacles (_Bimeria_); but in such
cases the perisarc forms a closely-fitting investment or cuticule on the
hydranth, never a hydrotheca standing off from it, as in the next
sub-order. The polyps may be solitary, or form colonies, which may be of
the spreading or encrusting type, or arborescent, and then always of
monopodial growth and budding. In some cases, any polyp of the colony
may bud medusae; in other cases, only certain polyps, the blastostyles,
have this power. When blastostyles are present, however, they are never
enclosed in special gonothecae as in the next sub-order. In this
sub-order the characters of the hydranth are very variable, probably
owing to the fact that it is exposed and not protected by a hydrotheca,
as in Calyptoblastea.

[Illustration: FIG. 50.--_Sarsia (Dipurena) gemnifera._ b, The long
manubrium, bearing medusiform buds; a, mouth.]

[Illustration: FIG. 51.--_Sarsia prolifera._ Ocelli are seen at the base
of the tentacles, and also (as an exception) groups of medusiform buds.]

  Speaking generally, three principal types of hydranth can be
  distinguished, each with subordinate varieties of form.

  1. Club-shaped hydranths with numerous tentacles, generally scattered
  irregularly, sometimes with a spiral arrangement, or in whorls
  ("verticillate").

  (a) Tentacles filiform; type of _Clava_ (fig. 5), _Cordylophora_,
    &c.

  (b) Tentacles capitate, simple; type of _Coryne_ and _Syncoryne_;
    _Myriothela_ is an aberrant form with some of the tentacles modified
    as "claspers" to hold the ova.

  (c) Tentacles capitate, branched, wholly or in part; type of
    _Cladocoryne_.

  (d) Tentacles filiform or capitate, tending to be arranged in
    definite whorls; type of _Stauridium_ (fig. 2), _Cladonema_ and
    _Pennaria_.

  2. Hydranth more shortened, daisy-like in form, with two whorls of
  tentacles, oral and aboral.

  (a) Tentacles filiform, simple, radially arranged or scattered
    irregularly; type of _Tubularia_ (fig. 4), _Corymorpha_ (fig. 3),
    _Nemopsis_, _Pelagohydra_, &c.

  (b) Tentacles with a bilateral arrangement, branched tentacles in
    addition to simple filiform ones; type of _Branchiocerianthus_.

  3. Hydranth with a single circlet of tentacles.

  (a) With filiform tentacles; the commonest type, seen in
    _Bougainvillea_ (fig. 13), _Eudendrium_, &c.

  (b) With capitate tentacles; type of _Clavatella_.

  4. Hydranth with tentacles reduced below four; type of _Lar_ (fig.
  11), _Monobrachium_, &c.

The _Anthomedusa_ in form is generally deep, bell-shaped. The sense
organs are typically ocelli, never otocysts. The gonads are borne on the
manubrium, either forming a continuous ring (Codonid type), or four
masses or pairs of masses (Oceanid type). The tentacles may be scattered
singly round the margin of the umbrella ("monerenematous") or arranged
in tufts ("lophonematous"); in form they may be simple or branched
(Cladonemid type); in structure they may be hollow ("coelomerinthous");
or solid ("pycnomerinthous"). When sessile gonophores are produced, they
may show all stages of degeneration.

  _Classification._--Until quite recently the hydroids (Gymnoblastea)
  and the medusae (Anthomedusae) have been classified separately, since
  the connexion between them was insufficiently known. Delage and
  Hérouard (HYDROZOA [2]) were the first to make an heroic attempt to
  unite the two classifications into one, to which Hickson (HYDROZOA
  [4]) has made some additions and slight modifications. The
  classification given here is for the most part that of Delage and
  Hérouard. It is certain, however, that no such classification can be
  considered final at present, but must undergo continual revision in
  the future. With this reservation we may recognize fifteen
  well-characterized families and others of more doubtful nature.
  Certain discrepancies must also be noted.

  1. _Margelidae_ (= medusa-family _Margelidae_ + hydroid families
  _Bougainvillidae_, _Dicorynidae_, _Bimeridae_ and _Eudendridae_).
  Trophosome arborescent, with hydranths of _Bougainvillea_-type;
  gonosome free medusae or gonophores, the medusae with solid tentacles
  in tufts (lophonematous). Common genera are the hydroid
  _Bougainvillea_ (figs. 12, 13), and the medusae _Hippocrene_ (budded
  from _Bougainvillea_), _Margelis_, _Rathkea_ (fig. 24), and
  _Margellium_. Other hydroids are _Garveia_, _Bimeria_, _Eudendrium_
  and _Heterocordyle_, with gonophores, and _Dicoryne_ with peculiar
  sporosacs.

  [Illustration: After Haeckel, _System der Medusen_, by permission of
  Gustav Fischer.

  FIG. 52.--_Tiara pileata_, L. Agassiz.]

  2. _Podocorynidae_ (= medusa-families _Thamnostomidae_ and _Cytaeidae_
  + hydroid families _Podocorynidae_ and _Hydractiniidae_). Trophosome
  encrusting with hydranths of _Bougainvillea_-type, polyps
  differentiated into blastostyles, gastrozoids and dactylozoids;
  gonosome free medusae or gonophores. The typical genus is the
  well-known hydroid _Podocoryne_, budding the medusa known as
  _Dysmorphosa_; _Thamnostylus_, _Cytaeis_, &c., are other medusae with
  unknown hydroids. _Hydractinia_ (figs. 9, 10) is a familiar hydroid
  genus, bearing gonophores.

  3. _Cladonemidae_.--Trophosome, polyps with two whorls of tentacles,
  the lower filiform, the upper capitate; gonosome, free medusae, with
  tentacles solid and branched. The type-genus _Cladonema_ (fig. 20) is
  a common British form.

  4. _Clavatellidae._--Trophosome, polyps with a single whorl of
  capitate tentacles; gonosome, free medusae, with tentacles branched,
  solid. _Clavatella_ (fig. 21), with a peculiar ambulatory medusa is a
  British form.

  5. _Pennariidae_.--Trophosome, polyps with an upper circlet of
  numerous capitate tentacles, and a lower circlet of filiform
  tentacles. _Pennaria_, with a free medusa known as _Globiceps_, is a
  common Mediterranean form. _Stauridium_ (fig. 2) is a British hydroid.

  6. _Tubulariidae._--Trophosome, polyps with two whorls of tentacles,
  both filiform. _Tubularia_ (fig. 4), a well-known British hydroid,
  bears gonophores.

  7. _Corymorphidae_ (including the medusa-family
  _Hybocodonidae_).--Trophosome solitary polyps, with two whorls of
  tentacles; gonosome, free medusae or gonophores. _Corymorpha_ (fig.
  3), a well-known British genus, sets free a medusa known as
  _Steenstrupia_ (fig. 22). Here belong the deep-sea genera _Monocaulus_
  and _Branchiocerianthus_, including the largest hydroid polyps known,
  both genera producing sessile gonophores.

  [Illustration: After Haeckel, _System der Medusen_, by permission of
  Gustav Fischer.

  FIG. 53.--_Pteronema darwinii_. The apex of the stomach is prolonged
  into a brood pouch containing embryos.]

  8. _Dendroclavidae._--Trophosome, polyp with filiform tentacles in
  three or four whorls. _Dendroclava_, a hydroid, produces the medusa
  known as _Turritopsis_.

  9. _Clavidae_ (including the medusa-family _Tiaridae_ (figs. 27 and
  51). Trophosome, polyps with scattered filiform tentacles; gonosome,
  medusae or gonophores, the medusae with hollow tentacles. _Clava_
  (fig. 5), a common British hydroid, produces gonophores; so also does
  _Cordylophora_, a form inhabiting fresh or brackish water. _Turris_
  produces free medusae. _Amphinema_ is a medusan genus of unknown
  hydroid.

  10. _Bythotiaridae._--Trophosome unknown; gonosome, free medusae, with
  deep, bell-shaped umbrella, with interradial gonads on the base of the
  stomach, with branched radial canals, and correspondingly numerous
  hollow tentacles. _Bythotiara_, _Sibogita_.

  11. _Corynidae_ (= hydroid families _Corynidae_, _Syncorynidae_ and
  _Cladocorynidae_ + medusan family _Sarsiidae_).--Trophosome polyps
  with capitate tentacles, simple or branched, scattered or
  verticillate; gonosome, free medusae or gonophores. _Coryne_, a common
  British hydroid, produces gonophores; _Syncoryne_, indistinguishable
  from it, produces medusae known as _Sarsia_ (fig. 51). _Cladocoryne_
  is another hydroid genus; _Codonium_ and _Dipurena_ (fig. 50) are
  medusan genera.

  12. _Myriothelidae._--The genus _Myriothela_ is a solitary polyp with
  scattered capitate tentacles, producing sporosacs.

  13. _Hydrolaridae._--Trophosome (only known in one genus), polyps with
  two tentacles forming a creeping colony; gonosome, free medusae with
  four, six or more radial canals, giving off one or more lateral
  branches which run to the margin of the umbrella, with the stomach
  produced into four, six or more lobes, upon which the gonads are
  developed; the mouth with four lips or with a folded margin; the
  tentacles simple, arranged evenly round the margin of the umbrella.
  The remarkable hydroid _Lar_ (fig. 11) grows upon the tubes of the
  worm _Sabella_ and produces a medusa known as _Willia_. Another
  medusan genus is _Proboscidactyla_.

  14. _Monobrachiidae._--The genus _Monobrachium_ is a colony-forming
  hydroid which grows upon the shells of bivalve molluscs, each polyp
  having but a single tentacle. It buds medusae, which, however, are as
  yet only known in an immature condition (C. Mereschkowsky [41]).

  15. _Ceratellidae._--Trophosome polyps forming branching colonies of
  which the stem and main branches are thick and composed of a network
  of anastomosing coenosarcal tubes covered by a common ectoderm and
  supported by a thick chitinous perisarc; hydranths similar to those of
  _Coryne_; gonosome, sessile gonophores. _Ceratella_, an exotic genus
  from the coast of East Africa, New South Wales and Japan. The genera
  _Dehitella_ Gray and _Dendrocoryne_ Inaba should perhaps be referred
  to this family; the last-named is regarded by S. Goto [16] as the type
  of a distinct family, _Dendrocorynidae_.

  Doubtful families, or forms difficult to classify, are: Pteronemidae,
  Medusae of Cladonemid type, with hydroids for the most part unknown.
  The British genus _Gemmaria_, however, is budded from a hydroid
  referable to the family _Corynidae_. _Pteronema_ (fig. 53).

  _Nemopsidae_, for the floating polyp _Nemopsis_, very similar to
  _Tubularia_ in character; the medusa, on the other hand, is very
  similar to _Hippocrene_ (_Margelidae_). See C. Chun (HYDROZOA [1]).

  _Pelagohydridae_, for the floating polyp _Pelagohydra_, Dendy, from
  New Zealand. The animal is a solitary polyp bearing a great number of
  medusa-buds. The body, representing the hydranth of an ordinary
  hydroid, has the aboral portion modified into a float, from which
  hangs down a proboscis bearing the mouth. The float is covered with
  long tentacles and bears the medusa-buds. The proboscis bears at its
  extremity a circlet of smaller oral tentacles. Thus the affinities of
  the hydranth are clearly, as Dendy points out, with a form such as
  _Corymorpha_, which also is not fixed but only rooted in the mud. The
  medusae, on the other hand, have the tentacles in four tufts of (in
  the buds) five each, and thus resemble the medusae of the family
  _Margelidae_. See A. Dendy [12].

  [Illustration: _Fig. 54._--Diagram showing possible modifications of
  the persons of a Calyptoblastic Hydromedusa. Letters a to h same as in
  fig. 49. i, The horny cup or hydrotheca of the hydriform persons; l,
  medusiform person springing from m, a modified, hydriform person
  (blastostyle); n, the horny case or gonangium enclosing the
  blastostyle and its buds. This and the hydrotheca i give origin to the
  name _Calyptoblastea_. (After Allman.)]

  _Perigonimus._--This common British hydroid belongs by its characters
  to the family _Bougainvillidae_; it produces, however, a medusa of the
  genus _Tiara_ (fig. 52), referable to the family _Clavidae_; a fact
  sufficient to indicate the tentative character of even the most modern
  classifications of this order.

SUB-ORDER II. HYDROIDEA CALYPTOBLASTEA (LEPTOMEDUSAE).--Trophosome with
polyps always differentiated into nutritive and reproductive individuals
(blastostyles) enclosed in hydrothecae and gonothecae respectively; with
sympodial type of budding. Gonosome with free medusae or gonophores; the
medusae typically with otocysts, sometimes with cordyli or ocelli (figs.
54, 55).

[Illustration: FIG. 55.--View of the Oral Surface of one of the
_Leptomedusae_ (_Irene pellucida_, Haeckel), to show the numerous
tentacles and the otocysts.

  ge, Genital glands.
  M, Manubrium.
  ot, Otocysts.
  rc, The four radiating canals.
  Ve, The velum.]

The calyptoblastic polyp of the nutritive type is very uniform in
character, its tendency to variation being limited, as it were, by the
enclosing hydrotheca. The hydranth almost always has a single circlet of
tentacles, like the _Bougainvillea_-type, in the preceding sub-order; an
exception is the curious genus _Clathrozoon_, in which the hydranth has
a single tentacle. The characteristic hydrotheca is formed by the bud at
an early stage (fig. 56); when complete it is an open cup, in which the
hydranth develops and can be protruded from the opening for the capture
of food, or is withdrawn into it for protection. Solitary polyps are
unknown in this sub-order; the colony may be creeping or arborescent in
form; if the latter, the budding of the polyps, as already stated, is of
the sympodial type, and either biserial, forming stems capable of
further branching, or uniserial, forming pinnules not capable of further
branching. In the biserial type the polyps on the two sides of the stem
have primitively an alternating, zigzag arrangement; but, by a process
of differential growth, quickened in the 1st, 3rd, 5th, &c., members of
the stem, and retarded in the 2nd, 4th, 6th, &c., members, the polyps
may assume secondarily positions opposite to one another on the two
sides of the stem. Other variations in the mode of growth or budding
bring about further differences in the building up of the colony, which
are not in all cases properly understood and cannot be described in
detail here. The stem may contain a single coenosarcal tube
("monosiphonic") or several united in a common perisarc
("polysiphonic"). An important variation is seen, in the form of the
hydrotheca itself, which may come off from the main stem by a stalk, as
in _Obelia_, or may be sessile, without a stalk, as in _Sertularia_.

[Illustration: After Allman, _Gymnoblastic Hydroids_, by permission of
the council of the Ray Society.

FIG. 56.--Diagrams to show the mode of formation of the Hydrotheca and
Gonotheca in Calyptoblastic Hydroids. A-D are stages common to both;
from D arises the hydrotheca (E) or the gonotheca (F); th, theca; st,
stomach; t, tentacles; m, mouth; mb, medusa-buds.]

In many Calyptoblastea there occur also reduced defensive polyps or
dactylozoids, which in this sub-order have received the special name of
_sarcostyles_. Such are the "snake-like zoids" of _Ophiodes_ and other
genera, and as such are generally interpreted the "machopolyps" of the
_Plumularidea_. These organs are supported by cuplike structures of the
perisarc, termed nematophores, regarded as modified hydrothecae
supporting the specialized polyp-individuals. They are specially
characteristic of the family _Plumularidae_.

The medusa-buds, as already stated, are always produced from
blastostyles, reduced non-nutritive polyps without mouth or tentacles.
An apparent, but not real, exception is _Halecium halecinum_, in which
the blastostyle is produced from the side of a nutritive polyp, and both
are enclosed in a common theca without a partition between them (Allman
[1] p. 50, fig. 24). The gonotheca is formed in its early stage in the
same way as the hydrotheca, but the remains of the hydranth persists as
an operculum closing the capsule, to be withdrawn when the medusae or
genital products are set free (fig. 56).

  The blastostyles, gonophores and gonothecae furnish a series of
  variations which can best be considered as so many stages of
  evolution.

  Stage 1, seen in _Obelia_. Numerous medusae are budded successively
  within the gonotheca and set free; they swim off and mature in the
  open sea (Allman [1], p. 48, figs. 18, 19).

  Stage 2, seen in _Gonothyraea_. Medusae, so-called "meconidia," are
  budded but not liberated; each in turn, when it reaches sexual
  maturity, is protruded from the gonotheca by elongation of the stalk,
  and sets free the embryos, after which it withers and is replaced by
  another (Allman [1], p. 57, fig. 28).

  Stage 3, seen in _Sertularia_.--The gonophores are reduced in varying
  degree, it may be to sporosacs; they are budded successively from the
  blastostyle, and each in turn, when ripe, protrudes the spadix through
  the gonotheca (fig. 57, A, B). The spadix forms a gelatinous cyst, the
  so-called acrocyst (ac), external to the gonotheca (gth), enclosing
  and protecting the embryos. Then the spadix withers, leaving the
  embryos in the acrocyst, which may be further protected by a so-called
  marsupium, a structure formed by tentacle-like processes growing out
  from the blastostyle to enclose the acrocyst, each such process being
  covered by perisarc like a glove-finger secreted by it (fig. 57, C).
  (Allman [1], pp. 50, 51, figs. 21-24; Weismann [58], p. 170, pl. ix.,
  figs. 7, 8.)

  Stage 4, seen in _Plumularidae_.--The generative elements are produced
  in structures termed corbulae, formed by reduction and modification of
  branches of the colony. Each corbula contains a central row of
  blastostyles enclosed and protected by lateral rows of branches
  representing stunted buds (Allman [1], p. 66, fig. 30).

[Illustration: After Allman, _Gymnoblastic Hydroids_, by permission of
the council of the Ray Society.

Fig. 57.--Diagrams to show the mode of formation of an Acrocyst and a
Marsupium. In A two medusa-buds are seen within the gonotheca (gth), the
upper more advanced than the lower one. In B the spadix of the upper bud
has protruded itself through the top of the gonotheca and the acrocyst
(ac) is secreted round it. In C the marsupium (m) is formed as
finger-like process from the summit of the blastostyle, enclosing the
acrocyst; b, medusa-buds on the blastostyle.]

The _Leptomedusa_ in form is generally shallow, more or less
saucer-like, with velum less developed than in Anthomedusae (fig. 55).
The characteristic sense-organs are ectodermal otocysts, absent,
however, in some genera, in which case cordyli may replace them. When
otocysts are present, they are at least eight in number, situated
adradially, but are often very numerous. The cordyli are scattered on
the ring-canal. Ocelli, if present, are borne on the tentacle-bulbs. The
tentacles are usually hollow, rarely solid (_Obelia_). In number they
are rarely less than four, but in _Dissonema_ there are only two.
Primitively there are four perradial tentacles, to which may be added
four interradial, or they may become very numerous and are then
scattered evenly round the margin, never arranged in tufts or clusters.
In addition to tentacles, there may be marginal cirri (_Laodice_) with a
solid endodermal axis, spirally coiled, very contractile, and bearing a
terminal battery of nematocysts. The gonads are developed typically
beneath the radial canals or below the stomach or its pouches, often
stretching as long bands on to the base of the manubrium. In
_Octorchidae_ (fig. 58) each such band is interrupted, forming one mass
at the base of the manubrium and another below the radial canal in each
radius, in all eight separate gonad-masses, as the name implies. In some
Leptomedusae excretory "marginal tubercles" are developed on the
ring-canal.

  _Classification._---As in the Gymnoblastea, the difficulty of uniting
  the hydroid and medusan systems into one scheme of classification is
  very great in the present state of our knowledge. In a great many
  Leptomedusae the hydroid stage is as yet unknown, and it is by no
  means certain even that they possess one. It is quite possible that
  some of these medusae will be found to be truly hypogenetic, that is
  to say, with a life-cycle secondarily simplified by suppression of
  metagenesis. At present, ten recent and one extinct family of
  Calyptoblastea (Leptomedusae) may be recognized provisionally:

  1. _Eucopidae_ (figs. 55, 59).--Trophosome with stalked hydrothecae;
  gonosome, free medusae with otocysts and four, rarely six or eight,
  unbranched radial canals. Two of the commonest British hydroids belong
  to this family, _Obelia_ and _Clytia_. _Obelia_ forms numerous
  polyserial stems of the characteristic zigzag pattern growing up from
  a creeping basal stolon, and buds the medusa of the same name. In
  _Clytia_ the polyps arise singly from the stolon, and the medusa is
  known as _Phialidium_ (fig. 59).

  2. _Aequoridae._--Trophosome only known in one genus (_Polycanna_),
  and similar to the preceding; gonosome, free medusae with otocysts and
  with at least eight radial canals, often a hundred or more, simple or
  branched. _Aequorea_ is a common medusa.

  3. _Thaumantidae._--Trophosome only known in one genus
  (_Thaumantias_), similar to that of the _Eucopidae_; gonosome, free
  medusae with otocysts inconspicuous or absent, with usually four,
  sometimes eight, rarely more than eight, radial canals, simple and
  unbranched, along which the gonads are developed, with numerous
  tentacles bearing ocelli and with marginal sense-clubs. _Laodice_ and
  _Thaumantias_ are representative genera.

  4. _Berenicidae._--Trophosome unknown; gonosome, free medusae, with
  four or six radial canals, bearing the gonads, with numerous
  tentacles, between which occur sense-clubs, without otocysts.
  _Berenice_, _Staurodiscus_, &c.

  [Illustration: After Haeckel, _System der Medusen_, by permission of
  Gustav Fischer.

  FIG. 58.--_Octorchandra canariensis_, from life.]

  5. _Polyorchidae._--Trophosome unknown; gonosome, free medusae of deep
  form, with radial canals branched in a feathery manner, and bearing
  gonads on the main canal, but not on the branches, with numerous
  hollow tentacles bearing ocelli, and without otocysts. _Polyorchis_,
  _Spirocodon_.

  6. _Campanularidae.-_-Trophosome as in _Eucopidae_; gonosome, sessile
  gonophores. Many common or well-known genera belong here, such as
  _Halecium_, _Campanularia_, _Gonothyraea_, &c.

  7. _Lafoëidae._--Trophosome as in the preceding; gonosome, free
  medusae or gonophores, the medusae with large open otocysts. The
  hydroid genus _Lafoëa_ is remarkable for producing gonothecae on the
  hydrorhiza, each containing a blastostyle which bears a single
  gonophore; this portion of the colony was formerly regarded as an
  independent parasitic hydroid, and was named _Coppinia_. Medusan
  genera are _Mitrocoma_, _Halopsis_, _Tiaropsis_ (fig. 29, &c.).

  (So far as the characters of the trophosome are concerned, the seven
  preceding families are scarcely distinguishable, and they form a
  section apart, contrasting sharply with the families next to be
  mentioned, in none of which are free medusae liberated from the
  colony, so that only the characters of the trophosome need be
  considered.)

  [Illustration: After E. T. Browne, _Proc. Zool. Soc. of London_, 1896.

  FIG. 59.--Three stages in the development of _Phialidium temporarium_.
  a, The youngest stage, is magnified about 22 diam.; b, older, is
  magnified about 8 diam.; c, the adult medusa, is magnified.]

  8. _Sertularidae._--Hydrothecae sessile, biserial, alternating or
  opposite on the stem. _Sertularia_ and _Sertularella_ are two very
  common genera of this family.

  9. _Plumularidae._--Hydrothecae sessile, biserial on the main stem,
  uniserial on the lateral branches or pinnules, which give the colony
  its characteristic feathery form; with nematophores. A very abundant
  and prolific family; well-known British genera are _Plumularia_,
  _Antennularia_ and _Aglaophenia_.

  10. _Hydroceratinidae_.--This family contains the single Australian
  species _Clathrozoon wilsoni_ Spencer, in which a massive hydrorhiza
  bears sessile hydrothecae, containing hydranths each with a single
  tentacle, and numerous nematophores. See W. B. Spencer [53].

  11. _Dendrograptidae_, containing fossil (Silurian) genera, such as
  _Dendrograptus_ and _Thamnograptus_, of doubtful affinities.

[Illustration: FIG. 60.--Portion of the calcareous corallum of
_Millepora nodosa_, showing the cyclical arrangement of the pores
occupied by the "persons" or hydranths. About twice the natural size.
(From Moseley.)]

ORDER III. Hydrocorallinae.--Metagenetic colony-forming Hydromedusae, in
which the polyp-colony forms a massive, calcareous _corallum_ into which
the polyps can be retracted; polyp-individuals always of two kinds,
gastrozoids and dactylozoids; gonosome either free medusae or sessile
gonophores. The trophosome consists of a mass of coenosarcal tubes
anastomosing in all planes. The interspaces between the tubes are filled
up by a solid mass of lime, consisting chiefly of calcium carbonate,
which replaces the chitinous perisarc of ordinary hydroids and forms a
stony corallum or _coenosteum_ (fig. 60). The surface of the coenosteum
is covered by a layer of common ectoderm, containing large nematocysts,
and is perforated by pores of two kinds, gastropores and dactylopores,
giving exit to gastrozoids and dactylozoids respectively, which are
lodged in vertical pore-canals of wider calibre than the coenosarcal
canals of the general network. The coenosteum increases in size by new
growth at the surface; and in the deeper, older portions of massive
forms the tissues die off after a certain time, only the superficial
region retaining its vitality down to a certain depth. The living
tissues at the surface are cut off from the underlying dead portions by
horizontal partitions termed _tabulae_, which are formed successively as
the coenosteum increases in age and size. If the coenosteum of
_Millepora_ be broken across, each pore-canal (perhaps better termed a
polyp-canal) is seen to be interrupted by a series of transverse
partitions, representing successive periods of growth with separation
from the underlying dead portions.

[Illustration: FIG. 61.--Enlarged view of the surface of a living
_Millepora_, showing five dactylozooids surrounding a central
gastrozooid. (From Moseley.)]

Besides the wider vertical pore-canals and the narrower, irregular
coenosarcal canals, the coenosteum may contain, in its superficial
portion, chambers or _ampullae_, in which the reproductive zoids
(medusae or gonophores) are budded from the coenosarc.

The gastropores and dactylopores are arranged in various ways at the
surface, a common pattern being the formation of a cyclosystem (fig.
60), in which a central gastrozoid is surrounded by a ring of
dactylozoids (fig. 61). In such a system the dactylopores may be
confluent with the gastropore, so that the entire cyclosystem presents
itself as a single aperture subdivided by radiating partitions, thus
having a superficial resemblance to a madreporarian coral with its
radiating septa (figs. 62 and 63).

[Illustration: FIG. 62.--Diagrams illustrating the successive stages in
the development of the cyclosystems of the _Stylasteridae_. (After
Moseley.)

  1, _Sporadopora dichotoma_.
  2, 3, _Allopora nobilis_.
  4, _Allopora profunda_.
  5, _Allopora miniacea_.
  6, _Astylus subviridis_.
  7, _Distichopora coccinea_.
  s, Style.
  dp, Dactylopore.
  gp, Gastropore.
  b, In fig. 6, inner horseshoe-shaped mouth of gastropore.]

The gastrozoids usually bear short capitate tentacles, four, six or
twelve in number; but in _Astylus_ (fig. 63) they have no tentacles. The
dactylozoids have no mouth; in _Milleporidae_ they have short capitate
tentacles, but lack tentacles in _Stylasteridae_.

The gonosome consists of free medusae in _Milleporidae_, which are
budded from the apex of a dactylozoid in _Millepora murrayi_, but in
other species from the coenosarcal canals. The medusae are produced by
direct budding, without an entocodon in the bud. They are liberated in a
mature condition, and probably live but a short time, merely sufficient
to spread the species. The manubrium bearing the gonads is mouthless,
and the umbrella is without tentacles, sense-organs, velum or radial
canals. In the _Stylasteridae_ sessile gonophores are formed, always by
budding from the coenosarc. In _Distichopora_ the gonophores have radial
canals, but in other genera they are sporosacs with no trace of medusoid
structure.

[Illustration: FIG. 63.--Portion of the corallum of _Astylus subviridis_
(one of the Stylasteridae), showing cyclosystems placed at intervals on
the branches, each with a central gastropore and zone of slit-like
dactylopores. (After Moseley.)]

  _Classification._---Two families are known:--

  1. _Milleporidae._--Coenosteum massive, irregular in form; pores
  scattered irregularly or in cyclosystems, without styles, with
  transverse tabulae; free medusae. A single genus, _Millepora_ (figs.
  60, 61).

  2. _Stylasteridae._--Coenosteum arborescent, sometimes fanlike, with
  pores only on one face, or on the lateral margins of the branches;
  gastropores with tabulae only in two genera, but with (except in
  _Astylus_) a _style_, i.e. a conical, thorn-like projection from the
  base of the pore, sometimes found also in dactylopores; sessile
  gonophores. _Sporadopora_ has the pores scattered irregularly.
  _Distichopora_ has the pores arranged in rows. _Stylaster_ has
  cyclosystems. In _Allopora_ the cyclostems resemble the calyces of
  Anthozoan corals. In _Cryptohelia_ the cyclosystem is covered by a cap
  or operculum. In _Astylus_ (fig. 63) styles are absent.

  _Affinities of the Hydrocorallinae._--There can be no doubt that the
  forms comprised in this order bear a close relationship to the
  Hydroidea, especially the sub-order Gymnoblastea, with which they
  should perhaps be classed in a natural classification. A
  hydrocoralline may be regarded as a form of hydroid colony in which
  the coenosarc forms a felt-work ramifying in all planes, and in which
  the chitinous perisarc is replaced by a massive calcareous skeleton.
  So far as the trophosome is concerned, the step from an encrusting
  hydroid such as _Hydractinia_ to the hydrocoralline _Millepora_ is not
  great.

  Hickson considers that the families _Milleporidae_ and _Stylasteridae_
  should stand quite apart from one another and should not be united in
  one order. The nearest approach to the _Stylasteridae_ is perhaps to
  be found in _Ceratella_, with its arborescent trophosome formed of
  anastomosing coenosarcal tubes supported by a thick perisarc and
  covered by a common ectoderm. _Ceratella_ stands in much the same
  relation to the _Stylasteridae_ that _Hydractinia_ does to the
  _Milleporidae_, in both cases the chitinous perisarc being replaced by
  the solid coenosteum to which the hydrocorallines owe the second half
  of their name.

ORDER IV. Graptolitoidea (Rhabdophora, Allman).--This order has been
constituted for a peculiar group of palaeozoic fossils, which have been
interpreted as the remains of the skeletons of Hydrozoa of an extinct
type.

A typical graptolite consists of an axis bearing a series of tooth-like
projections, like a saw. Each such projection is regarded as
representing a cup or hydrotheca, similar to those borne by a
calyptoblastic hydroid, such as _Sertularia_. The supposed hydrothecae
may be present on one side of the axis only (monoprionid) or on both
sides (diprionid); the first case may be conjectured to be the result of
uniserial (helicoid) budding, the second to be produced by biserial
(scorpioid) budding. In one division (_Retiolitidae_) the axis is
reticulate. In addition to the stems bearing cups, there are found
vesicles associated with them, which have been interpreted as gonothecae
or as floats, that is to say, air-bladders, acting as hydrostatic organs
for a floating polyp-colony.

Since no graptolites are known living, or, indeed, since palaeozoic
times, the interpretation of their structure and affinities must of
necessity be extremely conjectural, and it is by no means certain that
they are Hydrozoa at all. It can only be said that their organization,
so far as the state of their preservation permits it to be ascertained,
offers closer analogies with the Hydrozoa, especially the
Calyptoblastea, than with any other existing group of the animal
kingdom.

  See the treatise of Delage and Hérouard (HYDROZOA, [4]), and the
  article GRAPTOLITES.

ORDER V. Trachylinea.--Hydromedusae without alternation of generations,
i.e. without a hydroid phase; the medusa develops directly from the
actinula larva, which may, however, multiply by budding. Medusae with
sense-organs represented by otocysts derived from modified tentacles
(tentaculocysts), containing otoliths of endodermal origin, and
innervated from the ex-umbral nerve-ring.

This order, containing the typical oceanic medusae, is divided into two
sub-orders.

SUB-ORDER 1. TRACHOMEDUSAE.--Tentacles given off from the margin of the
umbrella, which is entire, i.e. not lobed or indented; tentaculocysts
usually enclosed in vesicles; gonads on the radial canals. The medusae
of this order are characterized by the tough, rigid consistence of the
umbrella, due partly to the dense nature of the mesogloea, partly to the
presence of a marginal rim of chondral tissue, consisting of thickened
ectoderm containing great numbers of nematocysts, and forming, as it
were, a cushion-tyre supporting the edge of the umbrella. Prolongations
from the rim of chondral tissue may form clasps or _peronia_ supporting
the tentacles. The tentacles are primarily four in number, perradial,
alternating with four interradial tentaculocysts, but both tentacles and
sense-organs may be multiplied and the primary perradii may be six
instead of four (fig. 26). The tentacles are always solid, containing an
axis of endoderm-cells resembling notochordal tissue or
plant-parenchyma, and are but moderately flexible. The sense-organs are
tentaculocysts which are usually enclosed in vesicles and may be sunk
far below the surface. The gonads are on the radial canals or on the
stomach (_Ptychogastridae_), and each gonad may be divided into two by a
longitudinal sub-umbral muscle-tract. The radial canals are four, six,
eight or more, and in some genera blindly-ending centripetal canals are
present (fig. 26). The stomach may be drawn out into the manubrium,
forming a proboscis ("Magenstiel") of considerable length.

The development of the Trachomedusae, so far as it is known, shows an
actinula-stage which is either free (larval) or passed over in the egg
(foetal) as in _Geryonia_; in no case does there appear to be a free
planula-stage. The actinula, when free, may multiply by larval budding,
but in all cases both the original actinula and all its descendants
become converted into medusae, so that there is no alternation of
generations. In _Gonionemus_ the actinula becomes attached and
polyp-like and reproduces by budding.

[Illustration: After Haeckel, _System der Medusen_, by permission of
Gustav Fischer.

FIG. 64. _Olindias mülleri._]

  The Trachomedusae are divided into the following families:

  1. _Petasidae_ (_Petachnidae_).--Four radial canals, four gonads;
  stomach not prolonged into the manubrium, which is relatively short;
  tentaculocysts free. _Petasus_ and other genera make up this family,
  founded by Haeckel, but no other naturalist has ever seen them, and it
  is probable that they are simply immature forms of other genera.

  2. _Olindiadae_, with four radial canals and four gonads; manubrium
  short; ring-canals giving off blind centripetal canals; tentaculocysts
  enclosed. _Olindias mülleri_ (fig. 64) is a common Mediterranean
  species. Other genera are _Aglauropsis_, _Gossea_ and _Gonionemus_;
  the last named bears adhesive suckers on the tentacles. Some doubt
  attaches to the position of this family. It has been asserted that the
  tentaculocysts are entirely ectodermal and that either the family
  should be placed amongst the Leptomedusae, or should form, together
  with certain Leptomedusae, an entirely distinct order. In
  _Gonionemus_, however, the concrement-cells are endodermal.

  3. _Trachynemidae._--Eight radial canals, eight gonads, stomach not
  prolonged into manubrium; tentaculocysts enclosed. _Rhopalonema_,
  _Trachynema_, &c.

  [Illustration: After E. T. Browne, _Proc. Zool. Soc. of London_.

  FIG. 65.--_Aglantha rosea_ (Forbes), a British medusa.]

  4. _Ptychogastridae_ (_Pectyllidae_).--As in the preceding, but with
  suckers on the tentacles. _Ptychogastria_ Allman (=_Pectyllis_), a
  deep-sea form.

  5. _Aglauridae._--Eight radial canals, two, four or eight gonads;
  tentacles numerous; tentaculocysts free; stomach prolonged into
  manubrium. _Aglaura_, _Aglantha_ (fig. 65), &c., with eight gonads;
  _Stauraglaura_ with four; _Persa_ with two. _Amphogona_,
  hermaphrodite, with male and female gonads on alternating radial
  canals.

  6. _Geryonidae._--Four or six radial canals; gonads band-like; stomach
  prolonged into a manubrium of great length; tentaculocysts enclosed.
  _Liriope_, &c., with four radial canals; _Geryonia_, _Carmarina_ (fig.
  26), &c., with six.

  7. _Halicreidae._--Eight very broad radial canals; ex-umbrella often
  provided with lateral outgrowths; tentacles differing in size, but in
  a single row. _Halicreas_.

SUB-ORDER 2. NARCOMEDUSAE.--Margin of the umbrella-lobed, tentacles
arising from the ex-umbrella at some distance from the margin;
tentaculocysts exposed, not enclosed in vesicles; gonads on the
sub-umbral floor of the stomach or of the gastric pouches.

[Illustration: FIG. 66.--_Cunina rhododactyla_, one of the
_Narcomedusae_. (After Haeckel.)

  c, Circular canal.
  h, "Otoporpae" or centripetal process of the marginal cartilaginous
    ring connected with tentaculocyst.
  k, Stomach.
  l, Jelly of the disk.
  r, Radiating canal (pouch of stomach).
  tt, Tentacles.
  tw, Tentacle root.]

The Narcomedusae exhibit peculiarities of form and structure which
distinguish them at once from all other Hydromedusae. The umbrella is
shallow and has the margin supported by a rim of thickened ectoderm, as
in the Trachomedusae, but not so strongly developed. The tentacles are
not inserted on the margin of the umbrella, but arise high up on the
ex-umbral surface, and the umbrella is prolonged into lobes
corresponding to the interspaces between the tentacles. The condition of
things can be imagined by supposing that in a medusa primitively of
normal build, with tentacles at the margin, the umbrella has grown down
past the insertion of the tentacles. As a result of this extension of
the umbrellar margin, all structures belonging to this region, namely,
the ring-canal, the nerve-rings, and the rim of thickened ectoderm, do
not run an even course, but are thrown into festoons, caught up under
the insertion of each tentacle in such a way that the ring-canal and its
accompaniments form in each notch of the umbrellar margin an inverted V,
the apex of which corresponds to the insertion of the tentacle; in some
cases the limbs of the V may run for some distance parallel to one
another, and may be fused into one, giving a figure better compared to
an inverted Y. Thus the ectodermal rim runs round the edge of each lobe
of the umbrella and then passes upwards towards the base of the tentacle
from the re-entering angle between two adjacent lobes, to form with its
fellow of the next lobe a tentacle-clasp or _peronium_, i.e. a streak of
thickened ectoderm supporting the tentacle. Similarly the ring-canal
runs round the edge of the lobe as the so-called festoon-canal, and then
runs upwards under the peronium to the base of the tentacle as one of a
pair of peronial canals, the limbs of the V-like figure already
mentioned. The nerve-rings have a similar course. The tentaculocysts are
implanted round the margins of the lobes of the umbrella and may be
supported by prolongations of the ectodermal rim termed _otoporpae_
(_Gehörspangen_). The radial canals are represented by wide gastric
pouches, and may be absent, so that the tentacles arise directly from
the stomach (_Solmaridae_). The tentacles are always solid, as in
Trachomedusae.

The development of the Narcomedusae is in the main similar to that of
the Trachomedusae, but shows some remarkable features. In _Aeginopsis_ a
planula is formed by multipolar immigration. The two ends of the planula
become greatly lengthened and give rise to the two primary tentacles of
the actinula, of which the mouth arises from one side of the planula.
Hence the principal axis of the future medusa corresponds, not to the
longitudinal axis of the planula, but to a transverse axis. This is in
some degree parallel to the cases described above, in which a planula
gives rise to the hydrorhiza, and buds a polyp laterally.

In _Cunina_ and allied genera the actinula, formed in the manner
described, has a hypostome of great length, quite disproportionate to
the size of the body, and is further endowed with the power of producing
buds from a stolon arising from the aboral side of the body. In these
species the actinula is parasitic upon another medusa; for instance,
_Cunoctantha octonaria_ upon _Turritopsis_, _C. proboscidea_ upon
_Liriope_ or _Geryonia_. The parasite effects a lodgment in the host
either by invading it as a free-swimming planula, or, apparently, in
other cases, as a spore-embryo which is captured and swallowed as food
by the host. The parasitic actinula is found attached to the proboscis
of the medusa; it thrusts its greatly elongated hypostome into the mouth
of the medusa and nourishes itself upon the food in the digestive cavity
of its host. At the same time it produces buds from an aboral stolon.
The buds become medusae by the direct method of budding described above.
In some cases the buds do not become detached at once, but the stolon
continues to grow and to produce more buds, forming a "bud-spike"
(_Knospenähre_), which consists of the axial stolon bearing medusa-buds
in all stages of development. In such cases the original parent-actinula
does not itself become a medusa, but remains arrested in development and
ultimately dies off, so that a true alternation of generations is
brought about. It is in these parasitic forms that we meet with the
method of reproduction by sporogony described above.

In other Narcomedusae, e.g. _Cunoctantha fowleri_ Browne, buds are
formed from the sub-umbrella on the under side of the stomach pouches,
where later the gonads are developed.

  _Classification._--Three families of Narcomedusae are recognized (see
  O. Maas [40]):

  [Illustration: After O. Maas, _Craspedoten Medusen der Siboga
  Expedition_, by permission of E. S. Brill & Co.

  FIG. 67.--_Solmundella bitentaculata_ (Quoy and Gaimard).]

  1. _Cunanthidae._--With broad gastric pouches which are simple, i.e.
  undivided, and "pernemal," i.e. correspond in position with the
  tentacles. _Cunina_ (fig. 66) with more than eight tentacles;
  _Cunoctantha_ with eight tentacles, four perradial, four interradial.

  2. _Aeginidae._--Radii a multiple of four, with radial gastric pouches
  bifurcated or subdivided; the tentacles are implanted in the notch
  between the two subdivisions of each (primary) gastric pouch, hence
  the (secondary) gastric pouches appear to be "internemal" in position,
  i.e. to alternate in position with the tentacles. _Aegina_, with four
  tentacles and eight pouches; _Aeginura_ (fig. 25), with eight
  tentacles and sixteen pouches; _Solmundella_ (fig. 67), with two
  tentacles and eight pouches; _Aeginopsis_ (fig. 23), with two or four
  tentacles and sixteen pouches.

  3. _Solmaridae._--No gastric pouches; the numerous tentacles arise
  direct from the stomach, into which also the peronial canals open, so
  that the ring-canal is cut up into separate festoons. _Solmaris_,
  _Pegantha_, _Polyxenia_, &c. To this family should be referred,
  probably, the genus _Hydroctena_, described by C. Dawydov [11a] and
  regarded by him as intermediate between Hydromedusae and Ctenophora.
  See O. Maas [35].

  _Appendix to the Trachylinae._

  Of doubtful position, but commonly referred to the Trachylinae, are
  the two genera of fresh-water medusae, _Limnocodium_ and _Limnocnida_.

  _Limnocodium sowerbyi_ was first discovered in the _Victoria regia_
  tank in the Botanic Gardens, Regent's Park, London. Since then it has
  been discovered in other botanic gardens in various parts of Europe,
  its two most recent appearances being at Lyons (1901) and Munich
  (1905), occurring always in tanks in which the _Victoria regia_ is
  cultivated, a fact which indicates that tropical South America is its
  original habitat. In the same tanks a small hydroid, very similar to
  _Microhydra_, has been found, which bears medusa-buds and is probably
  the stock from which the medusa is budded. It is a remarkable fact
  that all specimens of _Limnocodium_ hitherto seen have been males; it
  may be inferred from this either that only one polyp-stock has been
  introduced into Europe, from which all the medusae seen hitherto have
  been budded, or perhaps that the female medusa is a sessile gonophore,
  as in _Pennaria_. The male gonads are carried on the radial canals.

  _Limnocnida tanganyicae_ was discovered first in Lake Tanganyika, but
  has since been discovered also in Lake Victoria and in the river
  Niger. It differs from _Limnocodium_ in having practically no
  manubrium but a wide mouth two-thirds the diameter of the umbrella
  across. It buds medusae from the margin of the mouth in May and June,
  and in August and September the gonads are formed in the place where
  the buds arose. The hydroid phase, if any, is not known.

  Both these medusae have sense-organs of a peculiar type, which are
  said to contain an endodermal axis like the sense-organs of
  Trachylinae, but the fact has recently been called in question for
  _Limnocodium_ by S. Goto, who considers the genus to be allied to
  _Olindias_. Allman, on the other hand, referred _Limnocodium_ to the
  Leptomedusae.

  In this connexion must be mentioned, finally, the medusae budded from
  the fresh-water polyp _Microhydra_. The polyp-stages of _Limnocodium_
  and _Microhydra_ are extremely similar in character. In both cases the
  hydranth is extremely reduced and has no tentacles, and the polyp
  forms a colony by budding from the base. In _Limnocodium_ the body
  secretes a gelatinous mucus to which adhere particles of mud, &c.,
  forming a protective covering. In _Microhydra_ no such protecting case
  is formed. In view of the great resemblance between _Microhydra_ and
  the polyp of _Limnocodium_, it might be expected that the medusae to
  which they give origin would also be similar. As yet, however, the
  medusa of _Microhydra_ has only been seen in an immature condition,
  but it shows some well-marked differences from _Limnocodium_,
  especially in the structure of the tentacles, which furnish useful
  characters for distinguishing species amongst medusae. The possession
  of a polyp-stage by _Limnocodium_ and _Microhydra_ furnishes an
  argument against placing them in the Trachylinae. Their sense-organs
  require renewed investigations. (Browne [10] and [10a].)

ORDER VI. Siphonophora.--Pelagic floating Hydrozoa with great
differentiation of parts, each performing a special function; generally
regarded as colonies showing differentiation of individuals in
correspondence with a physiological division of labour.

[Illustration: FIG. 68.--Diagram showing possible modifications of
medusiform and hydriform persons of a colony of _Siphonophora_. The
thick black line represents endoderm, the thinner line ectoderm. (After
Allman.)

  n, Pneumatocyst.
  k, Nectocalyces (swimming bells).
  l, Hydrophyllium (covering-piece).
  i, Generative medusiform person.
  g, Palpon with attached palpacle, h.
  e, Siphon with branched grappling tentacle, f.
  m, Stem.]

A typical Siphonophore is a stock or _cormus_ consisting of a number of
_appendages_ placed in organic connexion with one another by means of a
_coenosarc_. The coenosarc does not differ in structure from that
already described in colonial Hydrozoa. It consists of a hollow tube, or
tubes, of which the wall is made up of the two body-layers, ectoderm and
endoderm, and the cavity is a continuation of the digestive cavities of
the nutritive and other appendages, i.e. of the coelenteron. The
coenosarc may consist of a single elongated tube or stolon, forming the
stem or axis of the cormus on which, usually, the appendages are
arranged in groups termed cormidia; or it may take the form of a compact
mass of ramifying, anastomosing tubes, in which case the cormus as a
whole has a compact form and _cormidia_ are not distinguishable. In the
Disconectae the coenosarc forms a spongy mass, the "_centradenia_,"
which is partly hepatic in function, forming the so-called liver, and
partly excretory.

The appendages show various types of form and structure corresponding to
different functions. The cormus is always differentiated into two parts;
an upper portion termed the _nectosome_, in which the appendages are
locomotor or hydrostatic in function, that is to say, serve for swimming
or floating; and a lower portion termed the _siphosome_, bearing
appendages which are nutritive, reproductive or simply protective in
function.

Divergent views have been held by different authors both as regards the
nature of the cormus as a whole, and as regards the homologies of the
different types of appendages borne by it.

  The general theories of Siphonophoran morphology are discussed below,
  but in enumerating the various types of appendages it is convenient to
  discuss their morphological interpretation at the same time.

  [Illustration: After A. Agassiz, from Lankester's _Treatise on
  Zoology_.

  FIG. 69.--_Porpita_, seen from above, showing the pneumatophore and
  expanded palpons.]

  In the nectosome one or more of the following types of appendage
  occur:--

  1. Swimming-bells, termed _nectocalyces_ or _nectophores_ (fig. 68,
  k), absent in _Chondrophorida_ and _Cystophorida_; they are
  contractile and resemble, both in appearance, structure and function,
  the umbrella of a medusa, with radial canals, ring-canal and velum;
  but they are without manubrium, tentacles or sense-organs, and are
  always bilaterally symmetrical, a peculiarity of form related with the
  fact that they are attached on one side to the stem. A given cormus
  may bear one or several nectocalyces, and by their contractions they
  propel the colony slowly along, like so many medusae harnessed
  together. In cases where the cormus has no pneumatophore the topmost
  swimming bell may contain an oil-reservoir or _oleocyst_.

  2. The pneumatophore or air-bladder (fig. 68, n), for passive
  locomotion, forming a float which keeps the cormus at or near the
  surface of the water. The pneumatophore arises from the ectoderm as a
  pit or invagination, part of which forms a gas-secreting gland, while
  the rest gives rise to an air-sack lined by a chitinous cuticle. The
  orifice of invagination forms a pore which may be closed up or may
  form a protruding duct or funnel. As in the analogous swim-bladder of
  fishes, the gas in the pneumatophore can be secreted or absorbed,
  whereby the specific gravity of the body can be diminished or
  increased, so as to cause it to float nearer the surface or at a
  deeper level. Never more than one pneumatophore is found in a cormus,
  and when present it is always situated at the highest point above the
  swimming bells, if these are present also. In _Velella_ the
  pneumatophore becomes of complex structure and sends air-tubes, lined
  by a chitin and resembling tracheae, down into the compact coenosarc,
  thus evidently serving a respiratory as well as a hydrostatic
  function.

  Divergent views have been held as to the morphological significance of
  the pneumatophore. E. Haeckel regarded the whole structure as a
  glandular ectodermal pit formed on the ex-umbral surface of a
  medusa-person. C. Chun and, more recently, R. Woltereck [59], on the
  other hand, have shown that the ectodermal pit which gives rise to the
  pneumatophore represents an entocodon. Hence the cavity of the
  air-sack is equivalent to a sub-umbral cavity in which no manubrium is
  formed, and the pore or orifice of invagination would represent the
  margin of the umbrella. In the wall of the sack is a double layer of
  endoderm, the space between which is a continuation of the
  coelenteron. By coalescence of the endoderm-layers, the coelenteron
  may be reduced to vessels, usually eight in number, opening into a
  ring-sinus surrounding the pore. Thus the disposition of the
  endoderm-cavities is roughly comparable to the gastrovascular system
  of a medusa.

  The difference between the theories of Haeckel and Chun is connected
  with a further divergence in the interpretation of the stem or axis of
  the cormus. Haeckel regards it as the equivalent of the manubrium, and
  as it is implanted on the blind end of the pneumatophore, such a view
  leads necessarily to the air-sack and gland being a development on the
  ex-umbral surface of the medusa-person. Chun and Woltereck, on the
  other hand, regard the stem as a _stolo prolifer_ arising from the
  aboral pole, that is to say, from the ex-umbrella, similar to that
  which grows out from the ex-umbral surface of the embryo of the
  Narcomedusae and produces buds, a view which is certainly supported by
  the embryological evidence to be adduced shortly.

  In the siphosome the following types of appendages occur:--

  1. _Siphons_ or nutritive appendages, from which the order takes its
  name; never absent and usually present in great numbers (fig. 68, e).
  Each is a tube dilated at or towards the base and containing a mouth
  at its extremity, leading into a stomach placed in the dilatation
  already mentioned. The siphons have been compared to the manubrium of
  a medusa-individual, or to polyps, and hence are sometimes termed
  gastrozoids.

  2. _Palpons_ (fig. 68, g), present in some genera, especially in
  Physonectae; similar to the siphons but without a mouth, and purely
  tactile in function, hence sometimes termed dactylozoids. If a distal
  pore or aperture is present, it is excretory in function; such
  varieties have been termed "cystons" by Haeckel.

  3. _Tentacles_ ("_Fangfäden_"), always present, and implanted one at
  the base of each siphon (fig. 68, f). The tentacles of siphonophores
  may reach a great length and have a complex structure. They may bear
  accessory filaments or _tentilla_ (f'), covered thickly with batteries
  of nematocysts, to which these organisms owe their great powers of
  offence and defence.

  4. _Palpacles_ ("_Tastfäden_"), occurring together with palpons, one
  implanted at the base of each palpon (fig. 68, h). Each palpacle is a
  tactile filament, very extensile, without accessory filaments or
  nematocysts.

  5. _Bracts_ ("_hydrophyllia_"), occur in _Calycophorida_ and some
  _Physophorida_ as scale-like appendages protecting other parts (fig.
  68, l). The mesogloea is greatly developed in them and they are often
  of very tough consistency. By Haeckel they are considered homologous
  with the umbrella of a medusa.

  [Illustration: From G. H. Fowler, after A. Agassiz, Lankester's
  _Treatise on Zoology_.

  FIG. 70.--Diagram of the structure of _Velella_, showing the central
  and peripheral thirds of a half-section of the colony, the middle
  third being omitted. The ectoderm is indicated by close hatching, the
  endoderm by light hatching, the mesogloea by thick black lines, the
  horny skeleton of the pneumatophore and sail by dotting.

    BL, Blastostyle.
    C, Centradenia.
    D, Palpon.
    EC, Edge of colony prolonged beyond the pneumatophore.
    G, Cavity of the large central siphon.
    M, Medusoid gonophores.
    PN, Primary central chamber, and
    PN', concentric chamber of the pneumatophore, showing an opening to
      the exterior and a "trachea."
    S, Sail.]

  6. _Gonostyles_, appendages which produce by budding medusae or
  gonophores, like the blastostyles of a hydroid colony. In their most
  primitive form they are seen in _Velella_ as "gonosiphons," which
  possess mouths like the ordinary sterile siphons and bud free medusae.
  In other forms they have no mouths. They may be branched, so-called
  "gonodendra," and amongst them may occur special forms of palpons,
  "gonopalpons." The gonostyles have been compared to the blastostyles
  of a hydroid colony, or to the manubrium of a medusa which produces
  free or sessile medusa-buds.

  7. _Gonophores_, produced either on the gonostyles already mentioned
  or budded, as in hydrocorallines, from the coenosarc, i.e. the stem
  (fig. 68, i.). They show every transition between free medusae and
  sporosacs, as already described, for hydroid colonies. Thus in
  _Velella_ free medusae are produced, which have been described as an
  independent genus of medusae, _Chrysomitra_. In other types the
  medusae may be set free in a mature condition as the so-called
  "genital swimming bells," comparable to the _Globiceps of Pennaria_.
  The most usual condition, however, is that in which sessile medusoid
  gonophores or sporosacs are produced.

  The various types of appendages described in the foregoing may be
  arranged in groups termed _cormidia_. In forms with a compact
  coenosarc such as _Velella_, _Physalia_, &c., the separate cormidia
  cannot be sharply distinguished, and such a condition is described
  technically as one with "scattered" cormidia. In forms in which, on
  the other hand, the coenosarc forms an elongated, tubular axis or
  stem, the appendages are arranged as regularly recurrent cormidia
  along it, and the cormidia are then said to be "ordinate." In such
  cases the oldest cormidia, that is to say, those furthest from the
  nectosome, may become detached (like the segments or proglottides of a
  tape-worm) and swim off, each such detached cormidium then becoming a
  small free cormus which, in many cases, has been given an independent
  generic name. A cormidium may contain a single nutritive siphon
  ("monogastric") or several siphons ("polygastric"):

  [Illustration: From G. H. Fowler, after G. Cuvier, Lankester's
  _Treatise on Zoology_.

  FIG. 71.--Upper surface of _Velella_, showing pneumatophore and sail.]

  The following are some of the forms of cormidia that occur:--

  1. The _eudoxome_ (Calycophorida), consisting of a bract, siphon,
  tentacle and gonophore; when free it is known as _Eudoxia_.

  2. The _ersaeome_ (Calycophorida), made up of the same appendages as
  the preceding type but with the addition of a nectocalyx; when free
  termed _Ersaea_.

  3. The _rhodalome_ of some _Rhodalidae_, consisting of siphon,
  tentacle and one or more gonophores.

  4. The _athorome_ of _Physophora_, &c., consisting of siphon,
  tentacle, one or more palpons with palpacles, and one or more
  gonophores.

  5. The _crystallome_ of _Anthemodes_, &c., similar to the athorome but
  with the addition of a group of bracts.

  [Illustration: FIG. 72.--A, _Diphyes campanulata_; B, a group of
  appendages (cormidium) of the same _Diphyes_. (After C. Gegenbaur.)

    a, Axis of the colony.
    m, Nectocalyx.
    c, Sub-umbral cavity of nectocalyx.
    v, Radial canals of nectocalyx.
    o, Orifice of nectocalyx.
    t, Bract.
    n, Siphon.
    g, Gonophore.
    i, Tentacle.]

  _Embryology of the Siphonophora._--The fertilized ovum gives rise to a
  parenchymula, with solid endoderm, which is set free as a
  free-swimming planula larva, in the manner already described (see
  HYDROZOA). The planula has its two extremities dissimilar
  (Bipolaria-larva). The subsequent development is slightly different
  according as the future cormus is headed by a pneumatophore
  (Physophorida, Cystophorida) or by a nectocalyx (Calycophorida).

  (i.) Physophorida, for example _Halistemma_ (C. Chun, HYDROZOA [1]).
  The planula becomes elongated and broader towards one pole, at which a
  pit or invagination of the ectoderm arises. Next the pit closes up to
  form a vesicle with a pore, and so gives rise to the pneumatophore.
  From the broader portion of the planula an outgrowth arises which
  becomes the first tentacle of the cormus. The endoderm of the planula
  now acquires a cavity, and at the narrower pole a mouth is formed,
  giving rise to the primary siphon. Thus from the original planula
  three appendages are, as it were, budded off, while the planula itself
  mostly gives rise to coenosarc, just as in some hydroids the planula
  is converted chiefly into hydrorhiza.

  (ii.) Calycophorida, for example, _Muggiaea_. The planula develops, on
  the whole, in a similar manner, but the ectodermal invagination
  arises, not at the pole of the planula, but on the side of its broader
  portion, and gives rise, not to a pneumatophore, but to a nectocalyx,
  the primary swimming bell or _protocodon_ ("_Fallschirm_") which is
  later thrown off and replaced by secondary swimming bells,
  _metacodons_, budded from the coenosarc.

  From a comparison of the two embryological types there can be no doubt
  on two points; first, that the pneumatophore and the protocodon are
  strictly homologous, and, therefore if the nectocalyx is comparable to
  the umbrella of a medusa, as seems obvious, the pneumatophore must be
  so too; secondly, that the coenosarcal axis arises from the
  ex-umbrella of the medusa and cannot be compared to a manubrium, but
  is strictly comparable to the "bud-spike" of a Narcomedusan.

  _Theories of Siphonophore Morphology._--The many theories that have
  been put forward as to the interpretation of the cormus and the
  various parts are set forth and discussed in the treatise of Y. Delage
  and E. Hérouard (HYDROZOA [4]) and more recently by R. Woltereck [59],
  and only a brief analysis can be given here.

  [Illustration: After C. Gegenbaur.

  FIG. 73.--_Physophora hydrostatica._

    a´, Pneumatocyst.
    t,  Palpons.
    a,  Axis of the colony.
    m,  Nectocalyx.
    o,  Orifice of nectocalyx.
    n,  Siphon.
    g,  Gonophore.
    i,  Tentacle.]

  In the first place the cormus has been regarded as a single individual
  and its appendages as _organs_. This is the so-called "polyorgan"
  theory, especially connected with the name of Huxley; but it must be
  borne in mind that Huxley regarded all the forms produced, in any
  animal, between one egg-generation and the next, as constituting in
  the lump one single individual. Huxley, therefore, considered a
  hydroid colony, for example, as a single individual, and each separate
  polyp or medusa budded from it as having the value of an organ and not
  of an individual. Hence Huxley's view is not so different from those
  held by other authors as it seems to be at first sight.

  In more recent years Woltereck [59] has supported Huxley's view of
  individuality, at the same time drawing a fine distinction between
  "individual" and "person." The individual is the product of sexual
  reproduction; a person is an individual of lower rank, which may be
  produced asexually. A Siphonophore is regarded as a single individual
  composed of numerous zoids, budded from the primary zoid (siphon)
  produced from the planula. Any given zoid is a person-zoid if
  equivalent to the primary zoid, an organ-zoid if equivalent only to a
  part of it. Woltereck considers the siphonophores most nearly allied
  to the Narcomedusae, producing like the buds from an aboral stolon,
  the first bud being represented by the pneumatophore or protocodon, in
  different cases.

  Contrasting, in the second place, with the polyorgan theory are the
  various "polyperson" theories which interpret the Siphonophore cormus
  as a colony composed of more or fewer individuals in organic union
  with one another. On this interpretation there is still room for
  considerable divergence of opinion as regards detail. To begin with,
  it is not necessary on the polyperson theory to regard each appendage
  as a distinct individual; it is still possible to compare appendages
  with parts of an individual which have become separated from one
  another by a process of "dislocation of organs." Thus a bract may be
  regarded, with Haeckel, as a modified umbrella of a medusa, a siphon
  as its manubrium, and a tentacle as representing a medusan tentacle
  shifted in attachment from the margin to the sub-umbrella; or a siphon
  may be compared with a polyp, of which the single tentacle has become
  shifted so as to be attached to the coenosarc and so on. Some authors
  prefer, on the other hand, to regard every appendage as a separate
  individual, or at least as a portion of an individual, of which other
  portions have been lost or obliterated.

  A further divergence of opinion arises from differences in the
  interpretation of the persons composing the colony. It is possible to
  regard the cormus (1) as a colony of medusa-persons, (2) as a colony
  of polyp-persons, (3) as composed partly of one, partly of the other.
  It is sufficient here to mention briefly the views put forward on this
  point by C. Chun and R. Haeckel.

  Chun (HYDROZOA [1]) maintains the older views of Leuckart and Claus,
  according to which the cormus is to be compared to a floating hydroid
  colony. It may be regarded as derived from floating polyps similar to
  _Nemopsis_ or _Pelagohydra_, which by budding produce a colony of
  polyps and also form medusa-buds. The polyp-individuals form the
  nutritive siphosome or trophosome. The medusa-buds are either fertile
  or sterile. If fertile they become free medusae or sessile gonophores.
  If sterile they remain attached and locomotor in function, forming the
  nectosome, the pneumatophore and swimming-bells.

  Haeckel, on the other hand, is in accordance with Balfour in regarding
  a Siphonophore as a medusome, that is to say, as a colony composed of
  medusoid persons or organs entirely. Haeckel considers that the
  Siphonophores have two distinct ancestral lines of evolution:

  1. In the _Disconanthae_, i.e. in such forms as _Velella_, _Porpita_,
  &c., the ancestor was an eight-rayed medusa (_Disconula_) which
  acquired a pneumatophore as an ectodermal pit on the ex-umbrella, and
  in which the organs (manubrium, tentacles, &c.) became secondarily
  multiplied, just as they do in _Gastroblasta_ as the result of
  incomplete fission. The nearest living allies of the ancestral
  _Disconula_ are to be sought in the _Pectyllidae_.

  [Illustration: After Haeckel, from Lankester's _Treatise on Zoology_.

  FIG. 74.--_Stephalia corona_, a young colony.

    p, Pneumatophore.
    n, Nectocalyx.
    l, Aurophore.
    lo, Orifice of the aurophore.
    s, Siphon.
    t, Tentacle.]

  2. In the _Siphonanthae_, i.e. in all other Siphonophores, the
  ancestral form was a _Siphonula_, a bilaterally symmetrical
  Anthomedusa with a single long tentacle (cf. _Corymorpha_), which
  became displaced from the margin to the sub-umbrella. The _Siphonula_
  produced buds on the manubrium, as many Anthomedusae are known to do,
  and these by reduction or dislocation of parts gave rise to the
  various appendages of the colony. Thus the umbrella of the _Siphonula_
  became the protocodon, and its manubrium, the axis or stolon, which,
  by a process of dislocation of organs, escaped, as it were, from the
  sub-umbrella through a cleft and became secondarily attached to the
  ex-umbrella. It must be pointed out that, however probable Haeckel's
  theory may be in other respects, there is not the slightest evidence
  for any such cleft in the umbrella having been present at any time,
  and that the embryological evidence, as already pointed out, is all
  against any homology between the stem and a manubrium, since the
  primary siphon does not become the stem, which arises from the
  ex-umbral side of the protocodon and is strictly comparable to a
  stolon.

_Classification._--The Siphonophora may be divided, following Delage and
Hérouard, into four sub-orders:

I. CHONDROPHORIDA (_Disconectae_ Haeckel, _Tracheophysae_ Chun). With an
apical chambered pneumatophore, from which tracheal tubes may take
origin (fig. 70); no nectocalyces or bracts; appendages all on the lower
side of the pneumatophore arising from a compact coenosarc, and
consisting of a central principal siphon, surrounded by gonosiphons, and
these again by tentacles.

  Three families: (1) _Discalidae_, for _Discalia_ and allied genera,
  deep-sea forms not well known; (2) _Porpitidae_ for the familiar genus
  _Porpita_ (fig. 69) and its allies; and (3) _Velellidae_, represented
  by the well-known genus _Velella_ (figs. 70, 71), common in the
  Mediterranean and other seas.

II. CALYCOPHORIDA (_Calyconectae_, Haeckel). Without pneumatophore, with
one, two, rarely more nectocalyces.

  Three families: (1) _Monophyidae_, with a single nectocalyx; examples
  _Muggiaea_, sometimes found in British seas, _Sphaeronectes_, &c.; (2)
  _Diphyidae_, with two nectocalyces; examples _Diphyes_ (fig. 72),
  _Praya_, _Abyla_, &c.; and (3) _Polyphyidae_, with numerous
  nectocalyces; example _Hippopodius_, _Stephanophyes_ and other genera.

[Illustration: From G. H. Fowler, modified after G. Cuvier and E.
Haeckel, Lankester's _Treatise on Zoology_.

FIG. 75.--A. _Physalia_, general view, diagrammatic; B, cormidium of
Physalia; D, palpon; T, palpacle; G, siphon; GP, gonopalpon; M[male],
male gonophore; M[female], female gonophore, ultimately set free.]

III. PHYSOPHORIDA (_Physonectae_ + _Auronectae_, Haeckel). With an
apical pneumatophore, not divided into chambers, followed by a series of
nectocalyces or bracts.

  A great number of families and genera are referred to this group,
  amongst which may be mentioned specially--(1) _Agalmidae_, containing
  the genera _Stephanomia_, _Agalma_, _Anthemodes_, _Halistemma_, &c.;
  (2) _Apolemidae_, with the genus _Apolemia_ and its allies; (3)
  _Forskaliidae_, with _Forskalia_ and allied forms; (4)
  _Physophoridae_, for _Physophora_ (fig. 73) and other genera, (5)
  _Anthophysidae_, for _Anthophysa_, _Athorybia_, &c.; and lastly the
  two families (6) _Rhodalidae_ and (7) _Stephalidae_ (fig. 74),
  constituting the group Auronectae of Haeckel. The Auronectae are
  peculiar deep-sea forms, little known except from Haeckel's
  descriptions, in which the large pneumatophore has a peculiar duct,
  termed the aurophore, placed on its lower side in the midst of a
  circle of swimming-bells.

IV. CYSTOPHORIDA (_Cystonectae_, Haeckel). With a very large
pneumatophore not divided into chambers, but without nectocalyces or
bracts. Two sections can be distinguished, the Rhizophysina, with long
tubular coenosarc-bearing ordinate cormidia, and Physalina, with compact
coenosarc-bearing scattered cormidia.

  A type of the Rhizophysina is the genus _Rhizophysa_. The Physalina
  comprise the families _Physalidae_ and _Epibulidae_, of which the
  types are _Physalia_ (figs. 74, 75) and _Epibulia_, respectively.
  _Physalia_, known commonly as the Portuguese man-of-war, is remarkable
  for its great size, its brilliant colours, and its terrible stinging
  powers.

  BIBLIOGRAPHY.--In addition to the works cited below, see the general
  works cited in the article HYDROZOA, in some of which very full
  bibliographies will be found.

  1. G. J. Allman, "A Monograph of the Gymnoblastic or Tubularian
  Hydroids," Ray Society (1871-1872); 2. A. Brauer, "Über die
  Entwickelung von Hydra," _Zeitschr. f. wiss. Zool._ lii. (1891), pp.
  169-216, pls. ix.-xii.; 3. "Über die Entstehung der
  Geschlechtsprodukte und die Entwickelung von Tubularia
  mesembryanthemum Allm.," _t.c._ pp. 551-579, pls. xxxiii.-xxxv.; 4. W.
  K. Brooks, "The Life-History of the Hydromedusae: a discussion of the
  Origin of the Medusae, and of the significance of Metagenesis," _Mem.
  Boston Soc. Nat. Hist._ iii. (1886), pp. 259-430, pis. xxxvii.-xliv.;
  5. "The Sensory Clubs of Cordyli of _Laodice_," _Journ. Morphology_,
  x. (1895), pp. 287-304, pl. xvii.; 6. E. T. Browne, "On British
  Hydroids and Medusae," _Proc. Zool. Soc._ (1896), pp. 459-500, pls.
  xvi., xvii., (1897), pp. 816-835, pls. xlviii. xlix. 12 text-figs.; 7.
  "Biscayan Medusae," _Trans. Linn. Soc._ x. (1906), pp. 163-187, pl.
  xiii.; 8. "Medusae" in Herdman, _Rep. Pearl Oyster Fisheries, Gulf of
  Manaar_, iv. (1905), pp. 131-166, 4 pls.; 9. "Hydromedusae with a
  Revision of the _Williadae_ and _Petasidae_," _Fauna and Geogr.
  Maldive and Laccadive Archipelagos_, ii. (1904), pp. 722-749, pls.
  liv.-lvii.; 10. "On the Freshwater Medusa liberated by _Microhydra
  ryderi_, Potts, and a Comparison with _Limnocodium_," _Quart. Journ.
  Micr. Sci._ I (1906), pp. 635, 645, pl. xxxvii.; 10a. "On the
  Freshwater Medusa _Limnocnida tanganicae_" _Budgett Memorial Volume_
  (Cambridge, 1908, pp. 471-482, pl. xxviii.; 11. C. Claus, "Über die
  Struktur der Muskelzellen und über den Körperbau von Mnestra parasites
  Krohn," _Verhandl. zool. bot. Ges. Wien_, xxv. (1876), pp. 9-12, pl.
  i.; 11a. C. Dawydov, "Hydroctena salenskii," _Mém. Acad. Imp. St.
  Pétersbourg_ (viii.) xiv. No. 9 (1903), 17 pp., 1 pl.; 12. A. Dendy,
  "On a Free-swimming Hydroid, _Pelagohydra mirabilis_," n. gen. et sp.,
  _Quart. Journ. Micr. Sci._ xlvi. (1903), pp. 1-24, pls. i. ii.; 13. H.
  Driesch, "Tektonische Studien an Hydroidpolypen," (1) _Jen.
  Zeitschr._, xxiv. (1890), pp. 189-226, 12 figs.; (2) _t.c._ pp.
  657-688, 6 figs.; (3) _ibid._ xxv. (1891), pp. 467-479, 3 figs.; 14.
  G. Duplessis, "On _Campanularia volubilis_," _Soc. Vaud. Bull._ 13
  (Lausanne, 1874-1875); 15. J. W. Fewkes, "On _Mnestra_," _Amer.
  Natural._, xviii. (1884), pp. 197-198, 3 figs.; 16. S. Goto,
  "Dendrocoryne Inaba, Vertreterin einer neuen Familie der
  Hydromedusen," _Annot. Zool. Tokyo_, i. (1897), pp. 93-104, pl. vi.,
  figs. 106-113; 17. "The Craspe dote Medusa _Olindias_ and some of its
  Natural Allies," _Mark Anniversary Volume_ (New York, 1903), pp. 1-22,
  3 pls.; 18. H. Grenacher, "Über die Nesselkapseln von Hydra," _Zool.
  Anz._ xviii. (1895), pp. 310-321, 7 figs.; 19. R. T. Günther, "On the
  Structure and Affinities of _Mnestra parasites_ Krohn; with a revision
  of the Classification of the _Cladonemidae_," _Mitt. Stat. Neapel_,
  xvi. (1903), pp. 35-62, pls. ii. iii.; 20. E. Haeckel, "Das System der
  Medusen," _Denkschr. med.-nat.-wiss. Ges._ (Jena, 1879-1881); 21.
  "Deep Sea Medusae," in _Reports of the Challenger Expedition_, Zool.
  iv. pt. 2 (London, 1882); 22. P. Hallez, "Bougainvillia fruticosa
  Allm. est le faciès d'eau agitée du Bougainvillia ramosa Van Ben."
  _C.-R. Acad. Sci. Paris_, cxl. (1905), pp. 457-459; 23. O. & R.
  Hertwig, _Der Organismus der Medusen_ (Jena, 1878), 70 pp., 3 pls.;
  24. _Das Nervensystem und die Sinnesorgane der Medusen_ (Leipzig,
  1878), 186 pp., 10 pls.; 25. S. J. Hickson, "The Medusae of
  _Millepora_," _Proc. Roy. Soc._ lxvi. (1899), pp. 6-10, 10 figs.; 26.
  T. Hincks, _A History of British Hydroid Zoophytes_ (2 vols., London,
  1868); 27. N. Iwanzov, "Über den Bau, die Wirkungsweise und die
  Entwickelung der Nesselkapseln von Coelenteraten," _Bull. Soc. Imp.
  Natural, Moscou_ (1896), pp. 323-355, 4 pls.; 28. C. F. Jickeli, "Der
  Bau der Hydroidpolypen," (1) _Morph. Jahrbuch_, viii. (1883), pp.
  373-416, pls. xvi.-xviii.; (2) t.c., pp. 580-680, pls. xxv.-xxviii.;
  29. Albert Lang, "Über die Knospung bei Hydra und einigen
  Hydropolypen," _Zeitschr. f. wiss. Zool._ liv. (1892), pp. 365-384,
  pl. xvii.; 30. Arnold Lang, "Gastroblasta Raffaelei. Eine durch eine
  Art unvollständiger Theilung entstehende Medusen-Kolonie," _Jena
  Zeitschr._ xix. (1886), pp. 735-762, pls. xx., xxi.; 31. A. Linko,
  "Observations sur les méduses de la mer Blanche," _Trav. Soc. Imp.
  Nat. St Pétersbourg_, xxix. (1899); 32. "Über den Bau der Augen bei
  den Hydromedusen," _Zapiski Imp. Akad. Nauk (Mém. Acad. Imp. Sci.) St
  Pétersbourg_ (8) x. 3 (1900), 23 pp., 2 pls.; 33. O. Maas, "Die
  craspedoten Medusen," in _Ergebn. Plankton Expedition_, ii. (Kiel and
  Leipzig, 1893), 107 pp., 8 pls., 3 figs.; 34. "Die Medusen," _Mem.
  Mus. Comp. Zool. Harvard_, xxiii. (1897), i.; 35. "On _Hydroctena_,"
  _Zool. Centralbl._ xi. (1904), pp. 240-243; 36. "Revision des méduses
  appartenant aux familles des _Cunanthidae_ et des _Aeginidae_, et
  groupement nouveau des genres," _Bull. Mus. Monaco_, v. (1904), 8 pp.;
  37. "Revision der Cannotiden Haeckels," _SB. K. Bayer. Akad._ xxxiv.
  (1904), pp. 421-445; 38. "Meduses," _Result. Camp. Sci. Monaco_,
  xxviii. (1904), 71 pp., 6 pls.; 39. "Die craspedoten Medusen der
  Siboga-Expedition," _Uitkomst. Siboga-Exped._ x. (1905), 84 pp., 14
  pls.; 40. "Die arktischen Medusen (ausschliesslich der
  Polypomedusen)," _Fauna arctica_, iv. (1906), pp. 479-526; 41. C.
  Mereschkowsky, "On a new Genus of Hydroids (_Monobrachium_) from the
  White Sea, with a short description of other new Hydroids," _Ann. Mag.
  Nat. Hist._ (4) xx. (1877), pp. 220-229, pls. v. vi.; 42. E.
  Metchinkoft, "Studien über die Entwickelung der Medusen und
  Siphonophoren," _Zeitschr. f. wiss. Zool._ xxiv. (1874), pp. 15-83,
  pls. i.-xii.; 43. "Vergleichend-embryologische Studien" (_Geryoniden,
  Cunina_), _ibid._ xxxvi. (1882), pp. 433-458, pl. xxviii.; 44.
  _Embryologische Studien an Medusen_ (Vienna, 1886), 150 pp., 12 pls.,
  10 figs.; 45. "Medusologische Mittheilungen," _Arb. zool. Inst. Wien_,
  vi. (1886), pp. 237-266, pls. xxii. xxiii.; 46. L. Murbach, "Beiträge
  zur Kenntnis der Anatomie und Entwickelung der Nesselorgane der
  Hydroiden," _Arch. f. Naturgesch._ lx. i. (1894), pp. 217-254, pl.
  xii.; 47. "Preliminary Note on the Life-History of _Gonionemus_,"
  _Journ. Morph._ xi. (1895), pp. 493-496; 48. L. Murbach and C.
  Shearer, "On Medusae from the Coast of British Columbia and Alaska,"
  _Proc. Zool. Soc._ (1903), ii. pp. 164-191, pls. xvii.-xxii.; 49. H.
  F. Perkins, "The Development of _Gonionema murbachii_," _Proc. Acad.
  Nat. Sci. Philadelphia_ (1902), pp. 750-790, pls. xxxi-xxxiv.; 50. F.
  Schaudinn, "Über Haleremita cumulans, n. g. n. sp., einen marinen
  Hydroidpolypen," _SB. Ges. natforsch. Freunde Berlin_ (1894), pp.
  226-234, 8 figs.; 51. F. E. Schulze, "On the Structure and Arrangement
  of the Soft Parts in _Euplectella aspergillum_" (_Amphibrachium_),
  _Tr. R. Soc. Edinburgh_, xxix. (1880), pp. 661-673, pl. xvii.; 52. O.
  Seeliger, "Über das Verhalten der Keimblätter bei der Knospung der
  Cölenteraten," _Zeitschr. f. wiss. Zool._ lviii. (1894), pp. 152-188,
  pls. vii.-ix.; 53. W. B. Spencer, "A new Family of Hydroidea
  (_Clathrozoon_), together with a description of the Structure of a new
  Species of _Plumularia_," _Trans. Roy. Soc. Victoria_ (1890), pp.
  121-140, 7 pls.; 54. M. Ussow, "A new Form of Fresh-water
  Coelenterate" (_Polypodium_), _Ann. Mag. Nat. Hist._ (5) xviii.
  (1886), pp. 110-124, pl. iv.; 55. E. Vanhöffen, "Versuch einer
  natürlichen Gruppierung der Anthomedusen," _Zool. Anzeiger_, xiv.
  (1891), pp. 439-446; 56. C. Viguier, "Études sur les animaux
  inférieurs de la baie d'Alger" (_Tetraplatia_), _Arch. Zool. Exp.
  Gen._ viii. (1890), pp. 101-142, pls. vii.-ix.; 57. J. Wagner,
  "Recherches sur l'organisation de Monobrachium parasiticum Méréjk,"
  _Arch. biol._ x. (1890), pp. 273-309, pls. viii. ix.; 58. A. Weismann,
  _Die Entstehung der Sexualzellen bei den Hydromedusen_ (Jena, 1883);
  59. R. Woltereck, "Beiträge zur Ontogenie und Ableitung des
  Siphonophorenstocks," _Zeitschr. f. wiss. Zool._ lxxxii. (1905), pp.
  611-637, 21 text-figs.; 60. J. Wulfert, "Die Embryonalentwickelung von
  Gonothyraea loveni Allm.," _Zeitschr. f. wiss. Zool._ lxxi. (1902),
  pp. 296-326, pls. xvi.-xviii.     (E. A. M.)


FOOTNOTES:

  [1] In some cases hydroids have been reared in aquaria from ova of
    medusae, but these hydroids have not yet been found in the sea
    (Browne [10 a]).

  [2] The numbers in square brackets [] refer to the bibliography at
    the end of this article; but when the number is preceded by the word
    Hydrozoa, it refers to the bibliography at the end of the article
    HYDROZOA.



HYDROMETER (Gr. [Greek: hydôr], water, and [Greek: metron], a measure),
an instrument for determining the density of bodies, generally of
fluids, but in some cases of solids. When a body floats in a fluid under
the action of gravity, the weight of the body is equal to that of the
fluid which it displaces (see HYDROMECHANICS). It is upon this principle
that the hydrometer is constructed, and it obviously admits of two modes
of application in the case of fluids: either we may compare the weights
of floating bodies which are capable of displacing the same volume of
different fluids, or we may compare the volumes of the different fluids
which are displaced by the same weight. In the latter case, the
densities of the fluids will be inversely proportional to the volumes
thus displaced.

The hydrometer is said by Synesius Cyreneus in his fifth letter to have
been invented by Hypatia at Alexandria,[1] but appears to have been
neglected until it was reinvented by Robert Boyle, whose "New Essay
Instrument," as described in the _Phil. Trans._ for June 1675, differs
in no essential particular from Nicholson's hydrometer. This instrument
was devised for the purpose of detecting counterfeit coin, especially
guineas and half-guineas. In the first section of the paper (_Phil.
Trans._ No. 115, p. 329) the author refers to a glass instrument
exhibited by himself many years before, and "consisting of a bubble
furnished with a long and slender stem, which was to be put into several
liquors, to compare and estimate their specific gravities." This seems
to be the first reference to the hydrometer in modern times.

In fig. 1 C represents the instrument used for guineas, the circular
plates A representing plates of lead, which are used as ballast when
lighter coins than guineas are examined. B represents "a small glass
instrument for estimating the specific gravities of liquors," an account
of which was promised by Boyle in the following number of the _Phil.
Trans._, but did not appear.

[Illustration: FIG. 1.--Boyle's New Essay Instrument.]

The instrument represented at B (fig. 1), which is copied from Robert
Boyle's sketch in the _Phil. Trans._ for 1675, is generally known as the
common hydrometer. It is usually made of glass, the lower bulb being
loaded with mercury or small shot which serves as ballast, causing the
instrument to float with the stem vertical. The quantity of mercury or
shot inserted depends upon the density of the liquids for which the
hydrometer is to be employed, it being essential that the whole of the
bulb should be immersed in the heaviest liquid for which the instrument
is used, while the length and diameter of the stem must be such that the
hydrometer will float in the lightest liquid for which it is required.
The stem is usually divided into a number of equal parts, the divisions
of the scale being varied in different instruments, according to the
purposes for which they are employed.

  Let V denote the volume of the instrument immersed (i.e. of liquid
  displaced) when the surface of the liquid in which the hydrometer
  floats coincides with the lowest division of the scale, A the area of
  the transverse section of the stem, l the length of a scale division,
  n the number of divisions on the stem, and W the weight of the
  instrument. Suppose the successive divisions of the scale to be
  numbered 0, 1, 2 ... n starting with the lowest, and let w0, W1, w2
  ... w_n be the weights of unit volume of the liquids in which the
  hydrometer sinks to the divisions 0, 1, 2 ... n respectively. Then, by
  the principle of Archimedes,

    W = Vw0; or w0 = W/V. Also

    W = (V + lA)w1; or w1 = W/(V + lA),

    w_p = W/(V + plA), and

    w_n= W/(V + nlA),

  or the densities of the several liquids vary inversely as the
  respective volumes of the instrument immersed in them; and, since the
  divisions of the scale correspond to equal increments of volume
  immersed, it follows that the densities of the several liquids in
  which the instrument sinks to the successive divisions form a harmonic
  series.

  If V = NlA then N expresses the ratio of the volume of the instrument
  up to the zero of the scale to that of one of the scale-divisions. If
  we suppose the lower part of the instrument replaced by a uniform bar
  of the same sectional area as the stem and of volume V, the
  indications of the instrument will be in no respect altered, and the
  bottom of the bar will be at a distance of N scale-divisions below the
  zero of the scale.

  In this case we have w_p = W/(N + p)lA; or the density of the liquid
  varies inversely as N + p, that is, as the whole number of
  scale-divisions between the bottom of the tube and the plane of
  flotation.

  If we wish the successive divisions of the scale to correspond to
  equal increments in the density of the corresponding liquids, then the
  volumes of the instrument, measured up to the successive divisions of
  the scale, must form a series in harmonical progression, the lengths
  of the divisions increasing as we go up the stem.

  The greatest density of the liquid for which the instrument described
  above can be employed is W/V, while the least density is W/(V + nlA),
  or W/(V + v), where v represents the volume of the stem between the
  extreme divisions of the scale. Now, by increasing v, leaving W and V
  unchanged, we may increase the range of the instrument indefinitely.
  But it is clear that if we increase A, the sectional area of the stem,
  we shall diminish l, the length of a scale-division corresponding to a
  given variation of density, and thereby proportionately diminish the
  sensibility of the instrument, while diminishing the section A will
  increase l and proportionately increase the sensibility, but will
  diminish the range over which the instrument can be employed, unless
  we increase the length of the stem in the inverse ratio of the
  sectional area. Hence, to obtain great sensibility along with a
  considerable range, we require very long slender stems, and to these
  two objections apply in addition to the question of portability; for,
  in the first place, an instrument with a very long stem requires a
  very deep vessel of liquid for its complete immersion, and, in the
  second place, when most of the stem is above the plane of flotation,
  the stability of the instrument when floating will be diminished or
  destroyed. The various devices which have been adopted to overcome
  this difficulty will be described in the account given of the several
  hydrometers which have been hitherto generally employed.

  The plan commonly adopted to obviate the necessity of inconveniently
  long stems is to construct a number of hydrometers as nearly alike as
  may be, but to load them differently, so that the scale-divisions at
  the bottom of the stem of one hydrometer just overlap those at the top
  of the stem of the preceding. By this means a set of six hydrometers,
  each having a stem rather more than 5 in. long, will be equivalent to
  a single hydrometer with a stem of 30 in. But, instead of employing a
  number of instruments differing only in the weights with which they
  are loaded, we may employ the same instrument, and alter its weight
  either by adding mercury or shot to the interior (if it can be opened)
  or by attaching weights to the exterior. These two operations are not
  quite equivalent, since a weight added to the interior does not affect
  the volume of liquid displaced when the instrument is immersed up to a
  given division of the scale, while the addition of weights to the
  exterior increases the displacement. This difficulty may be met, as in
  Keene's hydrometer, by having all the weights of precisely the same
  volume but of different masses, and never using the instrument except
  with one of these weights attached.

[Illustration: FIG. 2.--Clarke's Hydrometer.]

The first hydrometer intended for the determination of the densities of
liquids, and furnished with a set of weights to be attached when
necessary, was that constructed by Mr Clarke (instrument-maker) and
described by J. T. Desaguliers in the _Philosophical Transactions_ for
March and April 1730, No. 413, p. 278. The following is Desaguliers's
account of the instrument (fig. 2):--

  "After having made several fruitless trials with ivory, because it
  imbibes spirituous liquors, and thereby alters its gravity, he (Mr
  Clarke) at last made a copper hydrometer, represented in fig. 2,
  having a brass wire of about 1 in. thick going through, and soldered
  into the copper ball Bb. The upper part of this wire is filed flat on
  one side, for the stem of the hydrometer, with a mark at m, to which
  it sinks exactly in proof spirits. There are two other marks, A and B,
  at top and bottom of the stem, to show whether the liquor be (1/10)th
  above proof (as when it sinks to A), or (1/10)th under proof (as when
  it emerges to B), when a brass weight such as C has been screwed on to
  the bottom at c. There are a great many such weights, of different
  sizes, and marked to be screwed on instead of C, for liquors that
  differ more than (1/10)th from proof, so as to serve for the specific
  gravities in all such proportions as relate to the mixture of
  spirituous liquors, in all the variety made use of in trade. There are
  also other balls for showing the specific gravities quite to common
  water, which make the instrument perfect in its kind."

Clarke's hydrometer, as afterwards constructed for the purposes of the
excise, was provided with thirty-two weights to adapt it to spirits of
different specific gravities, and eleven smaller weights, or "weather
weights" as they were called, which were attached to the instrument in
order to correct for variations of temperature. The weights were
adjusted for successive intervals of 5° F., but for degrees intermediate
between these no additional correction was applied. The correction for
temperature thus afforded was not sufficiently accurate for excise
purposes, and William Speer in his essay on the hydrometer (Tilloch's
_Phil. Mag._, 1802, vol. xiv.) mentions cases in which this imperfect
compensation led to the extra duty payable upon spirits which were more
than 10% over proof being demanded on spirits which were purposely
diluted to below 10% over proof in order to avoid the charge. Clarke's
hydrometer, however, remained the standard instrument for excise
purposes from 1787 until it was displaced by that of Sikes.

Desaguliers himself constructed a hydrometer of the ordinary type for
comparing the specific gravities of different kinds of water
(Desaguliers's _Experimental Philosophy_, ii. 234). In order to give
great sensibility to the instrument, the large glass ball was made
nearly 3 in. in diameter, while the stem consisted of a wire 10 in. in
length and only (1/40)in. in diameter. The instrument weighed 4000
grains, and the addition of a grain caused it to sink through an inch.
By altering the quantity of shot in the small balls the instrument could
be adapted for liquids other than water.

To an instrument constructed for the same purpose, but on a still larger
scale than that of Desaguliers, A. Deparcieux added a small dish on the
top of the stem for the reception of the weights necessary to sink the
instrument to a convenient depth. The effect of weights placed in such a
dish or pan is of course the same as if they were placed within the bulb
of the instrument, since they do not alter the volume of that part which
is immersed.

[Illustration: FIG. 3.--Nicholson's Hydrometer.]

The first important improvement in the hydrometer after its reinvention
by Boyle was introduced by G. D. Fahrenheit, who adopted the second mode
of construction above referred to, arranging his instrument so as always
to displace the same volume of liquid, its weight being varied
accordingly. Instead of a scale, only a single mark is placed upon the
stem, which is very slender, and bears at the top a small scale pan into
which weights are placed until the instrument sinks to the mark upon its
stem. The volume of the displaced liquid being then always the same, its
density will be proportional to the whole weight supported, that is, to
the weight of the instrument together with the weights required to be
placed in the scale pan.

Nicholson's hydrometer (fig. 3) combines the characteristics of
Fahrenheit's hydrometer and of Boyle's essay instrument.[2] The
following is the description given of it by W. Nicholson in the
_Manchester Memoirs_, ii. 374:--

  "AA represents a small scale. It may be taken off at D. Diameter 1½
  in., weight 44 grains.

  "B a stem of hardened steel wire. Diameter 1/100 in.

  "E a hollow copper globe. Diameter 2(8/10) in. Weight with stem 369
  grains.

  "FF a stirrup of wire screwed to the globe at C.

  "G a small scale, serving likewise as a counterpoise. Diameter 1½ in.
  Weight with stirrup 1634 grains.

  "The other dimensions may be had from the drawing, which is one-sixth
  of the linear magnitude of the instrument itself.

  "In the construction it is assumed that the upper scale shall
  constantly carry 1000 grains when the lower scale is empty, and the
  instrument sunk in distilled water at the temperature of 60° Fahr. to
  the middle of the wire or stem. The length of the stem is arbitrary,
  as is likewise the distance of the lower scale from the surface of the
  globe. But, the length of the stem being settled, the lower scale may
  be made lighter, and, consequently, the globe less, the greater its
  distance is taken from the surface of the globe; and the contrary."

In comparing the densities of different liquids, it is clear that this
instrument is precisely equivalent to that of Fahrenheit, and must be
employed in the same manner, weights being placed in the top scale only
until the hydrometer sinks to the mark on the wire, when the specific
gravity of the liquid will be proportional to the weight of the
instrument together with the weights in the scale.

In the subsequent portion of the paper above referred to, Nicholson
explains how the instrument may be employed as a thermometer, since,
fluids generally expanding more than the solids of which the instrument
is constructed, the instrument will sink as the temperature rises.

  To determine the density of solids heavier than water with this
  instrument, let the solid be placed in the upper scale pan, and let
  the weight now required to cause the instrument to sink in distilled
  water at standard temperature to the mark B be denoted by w, while W
  denotes the weight required when the solid is not present. Then W - w
  is the weight of the solid. Now let the solid be placed in the lower
  pan, care being taken that no bubbles of air remain attached to it,
  and let w1 be the weight now required in the scale pan. This weight
  will exceed w in consequence of the water displaced by the solid, and
  the weight of the water thus displaced will be W1 - w, which is
  therefore the weight of a volume of water equal to that of the solid.
  Hence, since the weight of the solid itself is W - w, its density must
  be (W - w)/(w1 - w).

The above example illustrates how Nicholson's or Fahrenheit's hydrometer
may be employed as a weighing machine for small weights.

In all hydrometers in which a part only of the instrument is immersed,
there is a liability to error in consequence of the surface tension, or
capillary action, as it is frequently called, along the line of contact
of the instrument and the surface of the liquid (see CAPILLARY ACTION).
This error diminishes as the diameter of the stem is reduced, but is
sensible in the case of the thinnest stem which can be employed, and is
the chief source of error in the employment of Nicholson's hydrometer,
which otherwise would be an instrument of extreme delicacy and
precision. The following is Nicholson's statement on this point:--

  "One of the greatest difficulties which attends hydrostatical
  experiments arises from the attraction or repulsion that obtains at
  the surface of the water. After trying many experiments to obviate the
  irregularities arising from this cause, I find reason to prefer the
  simple one of carefully wiping the whole instrument, and especially
  the stem, with a clean cloth. The weights in the dish must not be
  esteemed accurate while there is either a cumulus or a cavity in the
  water round the stem."

It is possible by applying a little oil to the upper part of the bulb of
a common or of a Sikes's hydrometer, and carefully placing it in pure
water, to cause it to float with the upper part of the bulb and the
whole of the stem emerging as indicated in fig. 4, when it ought
properly to sink almost to the top of the stem, the surface tension of
the water around the circumference of the circle of contact, AA',
providing the additional support required.

[Illustration: FIG. 4.]

  The universal hydrometer of G. Atkins, described in the _Phil. Mag._
  for 1808, xxxi. 254, is merely Nicholson's hydrometer with the screw
  at C projecting through the collar into which it is screwed, and
  terminating in a sharp point above the cup G. To this point soft
  bodies lighter than water (which would float if placed in the cup)
  could be attached, and thus completely immersed. Atkins's instrument
  was constructed so as to weigh 700 grains, and when immersed to the
  mark on the stem in distilled water at 60° F. it carried 300 grains in
  the upper dish. The hydrometer therefore displaced 1000 grains of
  distilled water at 60° F. and hence the specific gravity of any other
  liquid was at once indicated by adding 700 to the number of grains in
  the pan required to make the instrument sink to the mark on the stem.
  The small divisions on the scale corresponded to differences of
  (1/10)th of a grain in the weight of the instrument.

  The "Gravimeter," constructed by Citizen Guyton and described in
  _Nicholson's Journal_, 4to, i. 110, differs from Nicholson's
  instrument in being constructed of glass, and having a cylindrical
  bulb about 21 centimetres in length and 22 millimetres in diameter.
  Its weight is so adjusted that an additional weight of 5 grammes must
  be placed in the upper pan to cause the instrument to sink to the mark
  on the stem in distilled water at the standard temperature. The
  instrument is provided with an additional piece, or "plongeur," the
  weight of which exceeds 5 grammes by the weight of water which it
  displaces; that is to say, it is so constructed as to weigh 5 grammes
  in water, and consists of a glass envelope filled with mercury. It is
  clear that the effect of this "plongeur," when placed in the lower
  pan, is exactly the same as that of the 5 gramme weight in the upper
  pan. Without the extra 5 grammes the instrument weighs about 20
  grammes, and therefore floats in a liquid of specific gravity .8. Thus
  deprived of its additional weight it may be used for spirits. To use
  the instrument for liquids of much greater density than water
  additional weights must be placed in the upper pan, and the "plongeur"
  is then placed in the lower pan for the purpose of giving to the
  instrument the requisite stability.

  Charles's balance areometer is similar to Nicholson's hydrometer,
  except that the lower basin admits of inversion, thus enabling the
  instrument to be employed for solids lighter than water, the inverted
  basin serving the same purpose as the pointed screw in Atkins's
  modification of the instrument.

  Adie's sliding hydrometer is of the ordinary form, but can be adjusted
  for liquids of widely differing specific gravities by drawing out a
  sliding tube, thus changing the volume of the hydrometer while its
  weight remains constant.

  The hydrometer of A. Baumé, which has been extensively used in France,
  consists of a common hydrometer graduated in the following manner.
  Certain fixed points were first determined upon the stem of the
  instrument. The first of these was found by immersing the hydrometer
  in pure water, and marking the stem at the level of the surface. This
  formed the zero of the scale. Fifteen standard solutions of pure
  common salt in water were then prepared, containing respectively 1, 2,
  3, ... 15% (by weight) of dry salt. The hydrometer was plunged in
  these solutions in order, and the stem having been marked at the
  several surfaces, the degrees so obtained were numbered 1, 2, 3, ...
  15. These degrees were, when necessary, repeated along the stem by the
  employment of a pair of compasses till 80 degrees were marked off. The
  instrument thus adapted to the determination of densities exceeding
  that of water was called the hydrometer for salts.

  The hydrometer intended for densities less than that of water, or the
  hydrometer for spirits, is constructed on a similar principle. The
  instrument is so arranged that it floats in pure water with most of
  the stem above the surface. A solution containing 10% of pure salt is
  used to indicate the zero of the scale, and the point at which the
  instrument floats when immersed in distilled water at 10° R. (54½° F.)
  is numbered 10. Equal divisions are then marked off upwards along the
  stem as far as the 50th degree.

  The densities corresponding to the several degrees of Baumé's
  hydrometer are given by Nicholson (_Journal of Philosophy_, i. 89) as
  follows:--

  _Baumé's Hydrometer for Spirits. Temperature 10° R._

    +--------+--------+--------+--------+--------+--------+
    |Degrees.|Density.|Degrees.|Density.|Degrees.|Density.|
    +--------+--------+--------+--------+--------+--------+
    |   10   | 1.000  |   21   |  .922  |   31   |  .861  |
    |   11   |  .990  |   22   |  .915  |   32   |  .856  |
    |   12   |  .985  |   23   |  .909  |   33   |  .852  |
    |   13   |  .977  |   24   |  .903  |   34   |  .847  |
    |   14   |  .970  |   25   |  .897  |   35   |  .842  |
    |   15   |  .963  |   26   |  .892  |   36   |  .837  |
    |   16   |  .955  |   27   |  .886  |   37   |  .832  |
    |   17   |  .949  |   28   |  .880  |   38   |  .827  |
    |   18   |  .943  |   29   |  .874  |   39   |  .822  |
    |   19   |  .935  |   30   |  .867  |   40   |  .817  |
    |   20   |  .928  |        |        |        |        |
    +--------+--------+--------+--------+--------+--------+

  _Baume's Hydrometer for Salts._

    +--------+--------+--------+--------+--------+--------+
    |Degrees.|Density.|Degrees.|Density.|Degrees.|Density.|
    +--------+--------+--------+--------+--------+--------+
    |    0   |  1.000 |   27   |  1.230 |   51   |  1.547 |
    |    3   |  1.020 |   30   |  1.261 |   54   |  1.594 |
    |    6   |  1.040 |   33   |  1.295 |   57   |  1.659 |
    |    9   |  1.064 |   36   |  1.333 |   60   |  1.717 |
    |   12   |  1.089 |   39   |  1.373 |   63   |  1.779 |
    |   15   |  1.114 |   42   |  1.414 |   66   |  1.848 |
    |   18   |  1.140 |   45   |  1.455 |   69   |  1.920 |
    |   21   |  1.170 |   48   |  1.500 |   72   |  2.000 |
    |   24   |  1.200 |        |        |        |        |
    +--------+--------+--------+--------+--------+--------+

  Carrier's hydrometer was very similar to that of Baumé, Cartier having
  been employed by the latter to construct his instruments for the
  French revenue. The point at which the instrument floated in distilled
  water was marked 10° by Cartier, and 30° on Carrier's scale
  corresponded to 32° on Baumé's.

  Perhaps the main object for which hydrometers have been constructed is
  the determination of the value of spirituous liquors, chiefly for
  revenue purposes. To this end an immense variety of hydrometers have
  been devised, differing mainly in the character of their scales.

  In Speer's hydrometer the stem has the form of an octagonal prism, and
  upon each of the eight faces a scale is engraved, indicating the
  percentage strength of the spirit corresponding to the several
  divisions of the scale, the eight scales being adapted respectively to
  the temperature 35°, 40°, 45°, 50°, 55°, 60°, 65° and 70° F. Four
  small pins, which can be inserted into the counterpoise of the
  instrument, serve to adapt the instrument to the temperatures
  intermediate between those for which the scales are constructed.
  William Speer was supervisor and chief assayer of spirits in the port
  of Dublin. For a more complete account of this instrument see
  Tilloch's _Phil. Mag._, xiv. 151.

  [Illustration: FIG. 5.--Jones's Hydrometer.]

  The hydrometer constructed by Jones, of Holborn, consists of a
  spheroidal bulb with a rectangular stem (fig. 5). Between the bulb and
  counterpoise is placed a thermometer, which serves to indicate the
  temperature of the liquid, and the instrument is provided with three
  weights which can be attached to the top of the stem. On the four
  sides of the stem AD are engraved four scales corresponding
  respectively to the unloaded instrument, and to the instrument loaded
  with the respective weights. The instrument when unloaded serves for
  the range from 74 to 47 over proof; when loaded with the first weight
  it indicates from 46 to 13 over proof, with the second weight from 13
  over proof to 29 under proof, and with the third from 29 under proof
  to pure water, the graduation corresponding to which is marked W at
  the bottom of the fourth scale. One side of the stem AD is shown in
  fig. 5, the other three in fig. 6. The thermometer is also provided
  with four scales corresponding to the scales above mentioned. Each
  scale has its zero in the middle corresponding to 60° F. If the
  mercury in the thermometer stand above this zero the spirit must be
  reckoned weaker than the hydrometer indicates by the number on the
  thermometer scale level with the top of the mercury, while if the
  thermometer indicate a temperature lower than the zero of the scale
  (60° F.) the spirit must be reckoned stronger by the scale reading. At
  the side of each of the four scales on the stem of the hydrometer is
  engraved a set of small numbers indicating the contraction in volume
  which would be experienced if the requisite amount of water (or
  spirit) were added to bring the sample tested to the proof strength.

  [Illustration: FIG. 6.]

  The hydrometer constructed by Dicas of Liverpool is provided with a
  sliding scale which can be adjusted for different temperatures, and
  which also indicates the contraction in volume incident on bringing
  the spirit to proof strength. It is provided with thirty-six different
  weights which, with the ten divisions on the stem, form a scale from 0
  to 370. The employment of so many weights renders the instrument
  ill-adapted for practical work where speed is an object.

  [Illustration: FIG. 7.--Atkins's Hydrometer.]

  This instrument was adopted by the United States in 1790, but was
  subsequently discarded by the Internal Revenue Service for another
  type. In this latter form the observations have to be made at the
  standard temperature of 60° F., at which the graduation 100
  corresponds to proof spirit and 200 to absolute alcohol. The need of
  adjustable weights is avoided by employing a set of five instruments,
  graduated respectively 0°-100°, 80°-120°, 100°-140°, 130°-170°,
  160°-200°. The reading gives the volume of proof spirit equivalent to
  the volume of liquor; thus the readings 80° and 120° mean that 100
  volumes of the test liquors contain the same amount of absolute
  alcohol as 80 and 120 volumes of proof spirit respectively. Proof
  spirit is defined in the United States as a mixture of alcohol and
  water which contains equal volumes of alcohol and water at 60° F., the
  alcohol having a specific gravity of 0.7939 at 60° as compared with
  water at its maximum density. The specific gravity of proof spirit is
  0.93353 at 60°; and 100 volumes of the mixture is made from 50 volumes
  of absolute alcohol and 53.71 volumes of water.

  Quin's universal hydrometer is described in the _Transactions of the
  Society of Arts_, viii. 98. It is provided with a sliding rule to
  adapt it to different temperatures, and has four scales, one of which
  is graduated for spirits and the other three serve to show the
  strengths of worts. The peculiarity of the instrument consists in the
  pyramidal form given to the stem, which renders the scale-divisions
  more nearly equal in length than they would be on a prismatic stem.

  Atkins's hydrometer, as originally constructed, is described in
  _Nicholson's Journal_, 8vo, ii. 276. It is made of brass, and is
  provided with a spheroidal bulb the axis of which is 2 in. in length,
  the conjugate diameter being 1½ in. The whole length of the instrument
  is 8 in., the stem square of about 1/8-in. side, and the weight about
  400 grains. It is provided with four weights, marked 1, 2, 3, 4, and
  weighing respectively 20, 40, 61 and 84 grains, which can be attached
  to the shank of the instrument at C (fig. 7) and retained there by the
  fixed weight B. The scale engraved upon one face of the stem contains
  fifty-five divisions, the top and bottom being marked 0 or zero and
  the alternate intermediate divisions (of which there are twenty-six)
  being marked with the letters of the alphabet in order. The four
  weights are so adjusted that, if the instrument floats with the stem
  emerging as far as the lower division 0 with one of the weights
  attached, then replacing the weight by the next heavier causes the
  instrument to sink through the whole length of the scale to the upper
  division 0, and the first weight produces the same effect when applied
  to the naked instrument. The stem is thus virtually extended to five
  times its length, and the number of divisions increased practically to
  272. When no weight is attached the instrument indicates densities
  from .806 to .843; with No. 1 it registers from .843 to .880, with No.
  2 from .880 to .918, with No. 3 from .918 to .958, and with No. 4 from
  .958 to 1.000, the temperature being 55° F. It will thus be seen that
  the whole length of the stem corresponds to a difference of density of
  about .04, and one division to about .00074, indicating a difference
  of little more than 1/3% in the strength of any sample of spirits.

  The instrument is provided with a sliding rule, with scales
  corresponding to the several weights, which indicate the specific
  gravity corresponding to the several divisions of the hydrometer scale
  compared with water at 55° F. The slider upon the rule serves to
  adjust the scale for different temperatures, and then indicates the
  strength of the spirit in percentages over or under proof. The slider
  is also provided with scales, marked respectively Dicas and Clarke,
  which serve to show the readings which would have been obtained had
  the instruments of those makers been employed. The line on the scale
  marked "concentration" indicates the diminution in volume consequent
  upon reducing the sample to proof strength (if it is _over proof_,
  O.P.) or upon reducing proof spirit to the strength of the sample (if
  it is _under proof_, U.P.). By applying the several weights in
  succession in addition to No. 4 the instrument can be employed for
  liquids heavier than water; and graduations on the other three sides
  of the stem, together with an additional slide rule, adapt the
  instrument for the determination of the strength of worts.

  Atkins subsequently modified the instrument (_Nicholson's Journal_,
  8vo, iii. 50) by constructing the different weights of different
  shapes, viz. circular, square, triangular and pentagonal, instead of
  numbering them 1, 2, 3 and 4 respectively, a figure of the weight
  being stamped on the sliding rule opposite to every letter in the
  series to which it belongs, thus diminishing the probability of
  mistakes. He also replaced the letters on the stem by the
  corresponding specific gravities referred to water as unity. Further
  information concerning these instruments and the state of hydrometry
  in 1803 will be found in Atkins's pamphlet _On the Relation between
  the Specific Gravities and the Strength of Spirituous Liquors_ (1803);
  or _Phil. Mag._ xvi. 26-33, 205-212, 305-312; xvii. 204-210 and
  329-341.

  In Gay-Lussac's alcoholometer the scale is divided into 100 parts
  corresponding to the presence of 1, 2, ... % by volume of alcohol at
  15° C., the highest division of the scale corresponding to the purest
  alcohol he could obtain (density .7947) and the lowest division
  corresponding to pure water. A table provides the necessary
  corrections for other temperatures.

  Tralles's hydrometer differs from Gay-Lussac's only in being graduated
  at 4° C. instead of 15° C., and taking alcohol of density .7939 at
  15.5° C. for pure alcohol instead of .7947 as taken by Gay-Lussac
  (Keene's _Handbook of Hydrometry_).

  In Beck's hydrometer the zero of the scale corresponds to density
  1.000 and the division 30 to density .850, and equal divisions on the
  scale are continued as far as is required in both directions.

  [Illustration: FIG. 8.--Sike's Hydrometer.]

  In the centesimal hydrometer of Francoeur the volume of the stem
  between successive divisions of the scale is always (1/100)th of the
  whole volume immersed when the instrument floats in water at 4° C. In
  order to graduate the stem the instrument is first weighed, then
  immersed in distilled water at 4° C., and the line of flotation marked
  zero. The first degree is then found by placing on the top of the stem
  a weight equal to (1/100)th of the weight of the instrument, which
  increases the volume immersed by (1/100)th of the original volume. The
  addition to the top of the stem of successive weights, each (1/100)th
  of the weight of the instrument itself, serves to determine the
  successive degrees. The length of 100 divisions of the scale, or the
  length of the uniform stem the volume of which would be equal to that
  of the hydrometer up to the zero graduation, Francoeur called the
  "modulus" of the hydrometer. He constructed his instruments of glass,
  using different instruments for different portions of the scale
  (Francoeur, _Traité d'aréométrie_, Paris, 1842).

  Dr Boriés of Montpellier constructed a hydrometer which was based upon
  the results of his experiments on mixtures of alcohol and water. The
  interval between the points corresponding to pure alcohol and to pure
  water Boriés divided into 100 equal parts, though the stem was
  prolonged so as to contain only 10 of these divisions, the other 90
  being provided for by the addition of 9 weights to the bottom of the
  instrument as in Clarke's hydrometer.

  The instrument which has now been exclusively used for revenue
  purposes for nearly a century is that associated with the name of
  Bartholomew Sikes, who was correspondent to the Board of Excise from
  1774 to 1783, and for some time collector of excise for Hertfordshire.

  Sikes's hydrometer, on account of its similarity to that of Boriés,
  appears to have been borrowed from that instrument. It is made of
  gilded brass or silver, and consists of a spherical ball A (fig. 8),
  1.5 in. in diameter, below which is a weight B connected with the ball
  by a short conical stem C. The stem D is rectangular in section and
  about 3½ in. in length. This is divided into ten equal parts, each of
  which is subdivided into five. As in Boriés's instrument, a series of
  9 weights, each of the form shown at E, serves to extend the scale to
  100 principal divisions. In the centre of each weight is a hole
  capable of admitting the lowest and thickest end of the conical stem
  C, and a slot is cut into it just wide enough to allow the upper part
  of the cone to pass. Each weight can thus be dropped on to the lower
  stem so as to rest on the counterpoise B. The weights are marked 10,
  20, ... 90; and in using the instrument that weight must be selected
  which will allow it to float in the liquid with a portion only of the
  stem submerged. Then the reading of the scale at the line of
  flotation, added to the number on the weight, gives the reading
  required. A small supernumerary weight F is added, which can be placed
  upon the top of the stem. F is so adjusted that when the 60 weight is
  placed on the lower stem the instrument sinks to the same point in
  distilled water when F is attached as in proof spirit when F is
  removed. The best instruments are now constructed for revenue purposes
  of silver, heavily gilded, because it was found that saccharic acid
  contained in some spirits attacked brass behind the gilding.

  The following table gives the specific gravities corresponding to the
  principal graduations on Sikes's hydrometer at 60° F. and 62° F.,
  together with the corresponding strengths of spirits. The latter are
  based upon the tables of Charles Gilpin, clerk to the Royal Society,
  for which the reader is referred to the _Phil. Trans._ for 1794.
  Gilpin's work is a model for its accuracy and thoroughness of detail,
  and his results have scarcely been improved upon by more recent
  workers. The merit of Sikes's system lies not so much in the
  hydrometer as in the complete system of tables by which the readings
  of the instrument are at once converted into percentage of
  proof-spirit.

  _Table showing the Densities corresponding to the Indications of
  Sike's Hydrometer._

    +------------+------------------+------------------+
    |            |       60° F.     |      62° F.      |
    |            +---------+--------+---------+--------+
    |   Sike's   |  Proof  |        |  Proof  |        |
    |Indications.|  Spirit |Density.|  Spirit |Density.|
    |            |per cent.|        |per cent.|        |
    +------------+---------+--------+---------+--------+
    |      0     | .815297 | 167.0  | .815400 | 166.5  |
    |      1     | .816956 | 166.1  | .817059 | 165.6  |
    |      2     | .818621 | 165.3  | .818725 | 164.8  |
    |      3     | .820294 | 164.5  | .820397 | 163.9  |
    |      4     | .821973 | 163.6  | .822077 | 163.1  |
    |      5     | .823659 | 162.7  | .823763 | 162.3  |
    |      6     | .825352 | 161.8  | .825457 | 161.4  |
    |      7     | .827052 | 160.9  | .827157 | 160.5  |
    |      8     | .828759 | 160.0  | .828864 | 159.6  |
    |      9     | .830473 | 159.1  | .830578 | 158.7  |
    |     10     | .832195 | 158.2  | .832300 | 157.8  |
    |     11     | .833888 | 157.3  | .833993 | 156.8  |
    |     12     | .835587 | 156.4  | .835692 | 155.9  |
    |     13     | .837294 | 155.5  | .837400 | 155.0  |
    |     14     | .839008 | 154.6  | .839114 | 154.0  |
    |     15     | .840729 | 153.7  | .840835 | 153.1  |
    |     16     | .842458 | 152.7  | .842564 | 152.1  |
    |     17     | .844193 | 151.7  | .844299 | 151.1  |
    |     18     | .845936 | 150.7  | .846042 | 150.1  |
    |     19     | .847685 | 149.7  | .847792 | 149.1  |
    |     20     | .849442 | 148.7  | .849549 | 148.1  |
    |     20B    | .849393 | 148.7  | .849500 | 148.1  |
    |     21     | .851122 | 147.6  | .851229 | 147.1  |
    |     22     | .852857 | 146.6  | .852964 | 146.1  |
    |     23     | .854599 | 145.6  | .854707 | 145.1  |
    |     24     | .856348 | 144.6  | .856456 | 144.0  |
    |     25     | .858105 | 143.5  | .858213 | 142.9  |
    |     26     | .859869 | 142.4  | .859978 | 141.8  |
    |     27     | .861640 | 141.3  | .861749 | 140.8  |
    |     28     | .863419 | 140.2  | .863528 | 139.7  |
    |     29     | .865204 | 139.1  | .865313 | 138.5  |
    |     30     | .866998 | 138.0  | .867107 | 137.4  |
    |     30B    | .866991 | 138.0  | .867100 | 137.4  |
    |     31     | .868755 | 136.9  | .868865 | 136.2  |
    |     32     | .870526 | 135.7  | .870636 | 135.1  |
    |     33     | .872305 | 134.5  | .872415 | 133.9  |
    |     34     | .874090 | 133.4  | .874200 | 132.8  |
    |     35     | .875883 | 132.2  | .873994 | 131.6  |
    |     36     | .877684 | 131.0  | .877995 | 130.4  |
    |     37     | .879492 | 129.8  | .879603 | 129.1  |
    |     38     | .881307 | 128.5  | .881419 | 127.9  |
    |     39     | .883129 | 127.3  | .883241 | 126.7  |
    |     40     | .884960 | 126.0  | .885072 | 125.4  |
    |     40B    | .884888 | 126.0  | .885000 | 125.4  |
    |     41     | .886689 | 124.8  | .886801 | 124.2  |
    |     42     | .888497 | 123.5  | .888609 | 122.9  |
    |     43     | .890312 | 122.2  | .890425 | 121.6  |
    |     44     | .892135 | 120.9  | .892248 | 120.3  |
    |     45     | .893965 | 119.6  | .894078 | 119.0  |
    |     46     | .895803 | 118.3  | .895916 | 117.6  |
    |     47     | .897647 | 116.9  | .897761 | 116.3  |
    |     48     | .899509 | 115.6  | .899614 | 114.9  |
    |     49     | .901360 | 114.2  | .901417 | 113.5  |
    |     50     | .903229 | 112.8  | .903343 | 112.1  |
    |     50B    | .903186 | 112.8  | .903300 | 112.1  |
    |     51     | .905024 | 111.4  | .905138 | 110.7  |
    |     52     | .906869 | 110.0  | .906983 | 109.3  |
    |     53     | .908722 | 108.6  | .908837 | 107.9  |
    |     54     | .910582 | 107.1  | .910697 | 106.5  |
    |     55     | .912450 | 105.6  | .912565 | 105.0  |
    |     56     | .914326 | 104.2  | .914441 | 103.5  |
    |     57     | .916209 | 102.7  | .916323 | 102.0  |
    |     58     | .918100 | 101.3  | .918216 | 100.5  |
    |     59     | .919999 |  99.7  | .820115 |  98.9  |
    |     60     | .921906 |  98.1  | .922022 |  97.4  |
    |     60B    | .921884 |  98.1  | .922000 |  97.4  |
    |     61     | .923760 |  96.6  | .923877 |  95.9  |
    |     62     | .925643 |  95.0  | .925760 |  94.2  |
    |     63     | .927534 |  93.3  | .927652 |  92.6  |
    |     64     | .929433 |  91.7  | .929550 |  90.9  |
    |     65     | .931339 |  90.0  | .931457 |  89.2  |
    |     66     | .933254 |  88.3  | .933372 |  87.5  |
    |     67     | .935176 |  86.5  | .935294 |  85.8  |
    |     68     | .937107 |  84.7  | .937225 |  84.0  |
    |     69     | .939045 |  82.9  | .939163 |  82.2  |
    |     70     | .940991 |  81.1  | .941110 |  80.3  |
    |     70B    | .940981 |  81.1  | .941100 |  80.3  |
    |     71     | .942897 |  79.2  | .943016 |  78.4  |
    |     72     | .944819 |  77.3  | .944938 |  76.5  |
    |     73     | .946749 |  75.3  | .946869 |  74.5  |
    |     74     | .948687 |  73.3  | .948807 |  72.5  |
    |     75     | .950634 |  71.2  | .950753 |  70.4  |
    |     76     | .952588 |  69.0  | .952708 |  68.2  |
    |     77     | .954550 |  66.8  | .954670 |  66.0  |
    |     78     | .956520 |  64.4  | .956641 |  63.5  |
    |     79     | .958498 |  61.9  | .958619 |  61.1  |
    |     80     | .960485 |  59.4  | .960606 |  58.5  |
    |     80B    | .960479 |  59.4  | .960600 |  58.5  |
    |     81     | .962433 |  56.7  | .962555 |  55.8  |
    |     82     | .964395 |  53.9  | .964517 |  53.0  |
    |     83     | .966366 |  50.9  | .966488 |  50.0  |
    |     84     | .968344 |  47.8  | .968466 |  47.0  |
    |     85     | .970331 |  44.5  | .970453 |  43.8  |
    |     86     | .972325 |  41.0  | .972448 |  40.4  |
    |     87     | .974328 |  37.5  | .974451 |  36.9  |
    |     88     | .976340 |  34.0  | .976463 |  33.5  |
    |     89     | .978359 |  30.6  | .978482 |  30.1  |
    |     90     | .980386 |  27.2  | .980510 |  26.7  |
    |     90B    | .980376 |  27.2  | .980500 |  26.7  |
    |     91     | .982371 |  23.9  | .982496 |  23.6  |
    |     92     | .984374 |  20.8  | .984498 |  20.5  |
    |     93     | .986385 |  17.7  | .986510 |  17.4  |
    |     94     | .988404 |  14.8  | .988529 |  14.5  |
    |     95     | .990431 |  12.0  | .990557 |  11.7  |
    |     96     | .992468 |   9.3  | .992593 |   9.0  |
    |     97     | .994512 |   6.7  | .994637 |   6.5  |
    |     98     | .996565 |   4.1  | .996691 |   4.0  |
    |     99     | .998626 |   1.8  | .998752 |   1.6  |
    |    100     |1.000696 |   0.0  |1.000822 |   0.0  |
    +------------+---------+--------+---------+--------+

  In the above table for Sikes's hydrometer two densities are given
  corresponding to each of the degrees 20, 30, 40, 50, 60, 70, 80 and
  90, indicating that the successive weights belonging to the particular
  instrument for which the table has been calculated do not quite agree.
  The discrepancy, however, does not produce any sensible error in the
  strength of the corresponding spirit.

  A table which indicates the weight per gallon of spirituous liquors
  for every degree of Sikes's hydrometer is printed in 23 and 24 Vict.
  c. 114, schedule B. This table differs slightly from that given above,
  which has been abridged from the table given in Keene's _Handbook of
  Hydrometry_, apparently on account of the equal divisions on Sikes's
  scale having been taken as corresponding to equal increments of
  density.

  Sikes's hydrometer was established for the purpose of collecting the
  revenue of the United Kingdom by Act of Parliament, 56 Geo. III. c.
  140, by which it was enacted that "all spirits shall be deemed and
  taken to be of the degree of strength which the said hydrometers
  called Sikes's hydrometers shall, upon trial by any officer or
  officers of the customs or excise, denote such spirits to be." This
  act came into force on January 5, 1817, and was to have remained in
  force until August 1, 1818, but was repealed by 58 Geo. III. c. 28,
  which established Sikes's hydrometer on a permanent footing. By 3 and
  4 Will. IV. c. 52, § 123, it was further enacted that the same
  instruments and methods should be employed in determining the duty
  upon imported spirits as should in virtue of any Act of Parliament be
  employed in the determination of the duty upon spirits distilled at
  home. It is the practice of the officers of the inland revenue to
  adjust Sikes's hydrometer at 62° F., that being the temperature at
  which the imperial gallon is defined as containing 10 lb. avoirdupois
  of distilled water. The specific gravity of any sample of spirits thus
  determined, when multiplied by ten, gives the weight in pounds per
  imperial gallon, and the weight of any bulk of spirits divided by this
  number gives its volume at once in imperial gallons.

  Mr (afterwards Colonel) J. B. Keene, of the Hydrometer Office, London,
  has constructed an instrument after the model of Sikes's, but provided
  with twelve weights of different masses but equal volumes, and the
  instrument is never used without having one of these attached. When
  loaded with either of the lightest two weights the instrument is
  specifically lighter than Sikes's hydrometer when unloaded, and it may
  thus be used for specific gravities as low as that of absolute
  alcohol. The volume of each weight being the same, the whole volume
  immersed is always the same when it floats at the same mark whatever
  weight may be attached.

  Besides the above, many hydrometers have been employed for special
  purposes. Twaddell's hydrometer is adapted for densities greater than
  that of water. The scale is so arranged that the reading multiplied by
  5 and added to 1000 gives the specific gravity with reference to water
  as 1000. To avoid an inconveniently long stem, different instruments
  are employed for different parts of the scale as mentioned above.

  The lactometer constructed by Dicas of Liverpool is adapted for the
  determination of the quality of milk. It resembles Sikes's hydrometer
  in other respects, but is provided with eight weights. It is also
  provided with a thermometer and slide rule, to reduce the readings to
  the standard temperature of 55° F. Any determination of density can be
  taken only as affording prima facie evidence of the quality of milk,
  as the removal of cream and the addition of water are operations which
  tend to compensate each other in their influence on the density of the
  liquid, so that the lactometer cannot be regarded as a reliable
  instrument.

  The marine hydrometers, as supplied by the British government to the
  royal navy and the merchant marine, are glass instruments with slender
  stems, and generally serve to indicate specific gravities from 1.000
  to 1.040. Before being issued they are compared with a standard
  instrument, and their errors determined. They are employed for taking
  observations of the density of sea-water.

  The salinometer is a hydrometer originally intended to indicate the
  strength of the brine in marine boilers in which sea-water is
  employed. Saunders's salinometer consists of a hydrometer which floats
  in a chamber through which the water from the boiler is allowed to
  flow in a gentle stream, at a temperature of 200° F. The peculiarity
  of the instrument consists in the stream of water, as it enters the
  hydrometer chamber, being made to impinge against a disk of metal, by
  which it is broken into drops, thus liberating the steam, which would
  otherwise disturb the instrument.

  The use of Sikes's hydrometer necessitates the employment of a
  considerable quantity of spirit. For the testing of spirits in bulk no
  more convenient instrument has been devised, but where very small
  quantities are available more suitable laboratory methods must be
  adopted.

  In England, the Finance Act 1907 (7 Ed. VII. c. 13), section 4,
  provides as follows: (1) The Commissioners of Customs and the
  Commissioners of Inland Revenue may jointly make regulations
  authorizing the use of any means described in the regulations for
  ascertaining for any purpose the strength or weight of spirits. (2)
  Where under any enactment Sykes's (sic) Hydrometer is directed to be
  used or may be used for the purpose of ascertaining the strength or
  weight of spirits, any means so authorized by regulations may be used
  instead of Sykes's Hydrometer and references to Sykes's Hydrometer in
  any enactment shall be construed accordingly. (3) Any regulations made
  under this section shall be published in the London, Edinburgh and
  Dublin Gazette, and shall take effect from the date of publication, or
  such later date as may be mentioned in the regulations for the
  purpose. (4) The expression "spirits" in this section has the same
  meaning as in the Spirits Act 1880.     (W. G.)


FOOTNOTES:

  [1] In _Nicholson's Journal_, iii. 89, Citizen Eusebe Salverte calls
    attention to the poem "De Ponderibus et Mensuris" generally ascribed
    to Rhemnius Fannius Palaemon, and consequently 300 years older than
    Hypatia, in which the hydrometer is described and attributed to
    Archimedes.

  [2] _Nicholson's Journal_, vol. i. p. 111, footnote.



HYDROPATHY, the name given, from the Greek, to the "water-cure," or the
treatment of disease by water, used outwardly and inwardly. Like many
descriptive names, the word "hydropathy" is defective and even
misleading, the active agents in the treatment being heat and cold, of
which water is little more than the vehicle, and not the only one.
Thermotherapeutics (or thermotherapy) is a term less open to objection.

Hydropathy, as a formal system, dates from about 1829, when Vincenz
Priessnitz (1801-1851), a farmer of Gräfenberg in Silesia, Austria,
began his public career in the paternal homestead, extended so as to
accommodate the increasing numbers attracted by the fame of his cures.
Two English works, however, on the medical uses of water had been
translated into German in the century preceding the rise of the movement
under Priessnitz. One of these was by Sir John Floyer (1649-1734), a
physician of Lichfield, who, struck by the remedial use of certain
springs by the neighbouring peasantry, investigated the history of cold
bathing, and published in 1702 his [Greek: "Psychrolousia], _or the
History of Cold Bathing, both Ancient and Modern_." The book ran through
six editions within a few years, and the translation was largely drawn
upon by Dr J. S. Hahn of Silesia, in a work published in 1738, _On the
Healing Virtues of Cold Water, Inwardly and Outwardly applied, as proved
by Experience_. The other work was that of Dr James Currie (1756-1805)
of Liverpool, entitled _Medical Reports on the Effects of Water, Cold
and Warm, as a remedy in Fevers and other Diseases_, published in 1797,
and soon after translated into German by Michaelis (1801) and Hegewisch
(1807). It was highly popular, and first placed the subject on a
scientific basis. Hahn's writings had meanwhile created much enthusiasm
among his countrymen, societies having been everywhere formed to promote
the medicinal and dietetic use of water; and in 1804 Professor Örtel of
Ansbach republished them and quickened the popular movement by
unqualified commendation of water drinking as a remedy for all diseases.
In him the rising Priessnitz found a zealous advocate, and doubtless an
instructor also.

At Gräfenberg, to which the fame of Priessnitz drew people of every rank
and many countries, medical men were conspicuous by their numbers, some
being attracted by curiosity, others by the desire of knowledge, but the
majority by the hope of cure for ailments which had as yet proved
incurable. Many records of experiences at Gräfenberg were published, all
more or less favourable to the claims of Priessnitz, and some
enthusiastic in their estimate of his genius and penetration; Captain
Claridge introduced hydropathy into England in 1840, his writings and
lectures, and later those of Sir W. Erasmus Wilson (1809-1884), James
Manby Gully (1808-1883) and Edward Johnson, making numerous converts,
and filling the establishments opened soon after at Malvern and
elsewhere. In Germany, France and America hydropathic establishments
multiplied with great rapidity. Antagonism ran high between the old
practice and the new. Unsparing condemnation was heaped by each on the
other; and a legal prosecution, leading to a royal commission of
inquiry, served but to make Priessnitz and his system stand higher in
public estimation.

Increasing popularity diminished before long that timidity which had in
great measure prevented trial of the new method from being made on the
weaker and more serious class of cases, and had caused hydropathists to
occupy themselves mainly with a sturdy order of chronic invalids well
able to bear a rigorous regimen and the severities of unrestricted
crisis. The need of a radical adaptation to the former class was first
adequately recognized by John Smedley, a manufacturer of Derbyshire,
who, impressed in his own person with the severities as well as the
benefits of "the cold water cure," practised among his workpeople a
milder form of hydropathy, and began about 1852 a new era in its
history, founding at Matlock a counterpart of the establishment at
Gräfenberg.

Ernst Brand (1826-1897) of Berlin, Räljen and Theodor von Jürgensen of
Kiel, and Karl Liebermeister (1833-1901) of Basel, between 1860 and
1870, employed the cooling bath in abdominal typhus with striking
results, and led to its introduction to England by Dr Wilson Fox. In the
Franco-German war the cooling bath was largely employed, in conjunction
frequently with quinine; and it now holds a recognized position in the
treatment of hyperpyrexia. The wet sheet pack has become part of medical
practice; the Turkish bath, introduced by David Urquhart (1805-1877)
into England on his return from the East, and ardently adopted by Dr
Richard Barter (1802-1870) of Cork, has become a public institution,
and, with the "morning tub" and the general practice of water drinking,
is the most noteworthy of the many contributions by hydropathy to public
health (see BATHS, ad fin.).

  The appliances and arrangements by means of which heat and cold are
  brought to bear on the economy are--(a) Packings, hot and cold,
  general and local, sweating and cooling; (b) hot air and steam baths;
  (c) general baths, of hot water and cold; (d) sitz, spinal, head and
  foot baths; (e) bandages (or compresses), wet and dry; also (f)
  fomentations and poultices, hot and cold, sinapisms, stupes, rubbings
  and water potations, hot and cold.

  (a) Packings.--The full pack consists of a wet sheet enveloping the
  body, with a number of dry blankets packed tightly over it, including
  a macintosh covering or not. In an hour or less these are removed and
  a general bath administered. The pack is a derivative, sedative,
  sudorific and stimulator of cutaneous excretion. There are numerous
  modifications of it, notably the cooling pack, where the wrappings are
  loose and scanty, permitting evaporation, and the application of
  indefinite duration, the sheet being rewetted as it dries; this is of
  great value in protracted febrile conditions. There are also local
  packs, to trunk, limbs or head separately, which are derivative,
  soothing or stimulating, according to circumstance and detail.

  (b) Hot air baths, the chief of which is the Turkish (properly, the
  Roman) bath, consisting of two or more chambers ranging in temperature
  from 120° to 212° or higher, but mainly used at 150° for curative
  purposes. Exposure is from twenty minutes up to two hours according to
  the effect sought, and is followed by a general bath, and occasionally
  by soaping and shampooing. It is stimulating, derivative, depurative,
  sudorific and alterative, powerfully promoting tissue change by
  increase of the natural waste and repair. It determines the blood to
  the surface, reducing internal congestions, is a potent diaphoretic,
  and, through the extremes of heat and cold, is an effective nervous
  and vascular stimulant and tonic. Morbid growths and secretions, as
  also the uraemic, gouty and rheumatic diathesis, are beneficially
  influenced by it. The full pack and Turkish bath have between them
  usurped the place and bettered the function of the once familiar hot
  bath. The Russian or steam bath and the lamp bath are primitive and
  inferior varieties of the modern Turkish bath, the atmosphere of which
  cannot be too dry and pure.

  (c) General baths comprise the rain (or needle), spray (or rose),
  shower, shallow, plunge, douche, wave and common morning sponge baths,
  with the dripping sheet, and hot and cold spongings, and are
  combinations, as a rule, of hot and cold water. They are stimulating,
  tonic, derivative and detergent.

  (d) Local baths comprise the sitz (or sitting), douche (or spouting),
  spinal, foot and head baths, of hot or cold water, singly or in
  combination, successive or alternate. The sitz, head and foot baths
  are used "flowing" on occasion. The application of cold by "Leiter's
  tubes" is effective for reducing inflammation (e.g. in meningitis and
  in sunstroke); in these a network of metal or indiarubber tubing is
  fitted to the part affected, and cold water kept continuously flowing
  through them. Rapid alternations of hot and cold water have a powerful
  effect in vascular stasis and lethargy of the nervous system and
  absorbents, yielding valuable results in local congestions and chronic
  inflammations.

  (e) Bandages (or compresses) are of two kinds,--_cooling_, of wet
  material left exposed for evaporation, used in local inflammations and
  fevers; and _heating_, of the same, covered with waterproof material,
  used in congestion, external or internal, for short or long periods.
  Poultices, warm, of bread, linseed, bran, &c., changed but twice in
  twenty-four hours, are identical in action with the heating bandage,
  and superior only in the greater warmth and consequent vital activity
  their closer application to the skin ensures.

  (f) Fomentations and poultices, hot or cold, sinapisms, stupes,
  rubefacients, irritants, frictions, kneadings, calisthenics,
  gymnastics, electricity, &c., are adjuncts largely employed.

  BIBLIOGRAPHY.--Among the numerous earlier works on hydropathy, the
  following are worth mention: Balbirnie, _Water Cure in Consumption_
  (1847), _Hydropathic Aphorisms_ (1856) and _A Plea for the Turkish
  Bath_ (1862); Beni-Barde, _Traité d'hydrothérapie_ (1874); Claridge,
  _Cold Water Cure, or Hydropathy_ (1841), _Facts and Evidence in
  Support of Hydropathy_ (1843) and _Cold Water, Tepid Water and
  Friction Cure_ (1849); Dunlop, _Philosophy of the Bath_ (1873);
  Floyer, _Psychrolousia, or the History of Cold-Bathing_, &c. (1702);
  J. S. Hahn (Schweidnitz), _Observations on the Healing Virtues of Cold
  Water_ (1738); Hunter, _Hydropathy for Home Use_ (1879); E. W. Lane,
  _Hydropathy, or the Natural System of Medical Treatment_ (1857); R. J.
  Lane, _Life at the Water Cure_ (1851); Shew, _Hydropathic Family
  Physician_ (1857); Smedley, _Practical Hydropathy_ (1879); Smethurst,
  _Hydrotherapia, or the Water Cure_ (1843); Wainwright, _Inquiry into
  the Nature and Use of Baths_ (1737); Weiss, _Handbook of Hydropathy_
  (1844); Wilson _Principles and Practice of the Cold Water Cure_ (1854)
  and _The Water Cure_ (1859). A useful recent work dealing
  comprehensively with the subject is Richard Metcalfe's _Rise and
  Progress of Hydropathy_ (1906).



HYDROPHOBIA (Gr. [Greek: Hydor], water, and [Greek: phobos], fear; so
called from the symptom of dread of water), or RABIES (Lat. for
"madness"), an acute disease, occurring chiefly in certain of the lower
animals, particularly the canine species, and liable to be communicated
by them to other animals and to man.

_In Dogs, &c._--The occurrence of rabies in the fox, wolf, hyaena,
jackal, raccoon, badger and skunk has been asserted; but there is every
probability that it is originally a disease of the dog. It is
communicated by inoculation to nearly all, if not all, warm-blooded
creatures. The transmission from one animal to another only certainly
takes place through inoculation with viruliferous matters. The malady is
generally characterized at a certain stage by an irrepressible desire in
the animal to act offensively with its natural weapons--dogs and other
carnivora attacking with their teeth, herbivora with their hoofs or
horns, and birds with their beaks, when excited ever so slightly. In the
absence of excitement the malady may run its course without any fit of
fury or madness.

  _Symptoms._--The disease has been divided into three stages or
  periods, and has also been described as appearing in at least two
  forms, according to the peculiarities of the symptoms. But, as a rule,
  one period of the disease does not pass suddenly into another, the
  transition being almost imperceptible; and the forms do not differ
  essentially from each other, but appear merely to constitute varieties
  of the same disease, due to the natural disposition of the animal, or
  other modifying circumstances. These forms have been designated _true_
  or _furious rabies_ (Fr. _rage vrai_; Ger. _rasende Wuth_) and _dumb
  rabies_ (Fr. _rage mue_; Ger. _stille Wuth_).

  The malady does not commence with fury and madness, but in a strange
  and anomalous change in the habits of the dog: it becomes dull,
  gloomy, and taciturn, and seeks to isolate itself in out-of-the-way
  places, retiring beneath chairs and to odd corners. But in its
  retirement it cannot rest: it is uneasy and fidgety, and no sooner has
  it lain down than suddenly it jumps up in an agitated manner, walks
  backwards and forwards several times, again lies down and assumes a
  sleeping attitude, but has only maintained it for a few minutes when
  it is once more moving about. Again it retires to its corner, to the
  farthest recess it can find, and huddles itself up into a heap, with
  its head concealed beneath its chest and fore-paws. This state of
  continual agitation and inquietude is in striking contrast with its
  ordinary habits, and should therefore receive attention. Not
  unfrequently there are a few moments when the creature appears more
  lively than usual, and displays an extraordinary amount of affection.
  Sometimes there is a disposition to gather up straw, thread, bits of
  wood, &c., which are industriously carried away; a tendency to lick
  anything cold, as iron, stones, &c., is also observed in many
  instances; and there is also a desire evinced to lick other animals.
  Sexual excitement is also frequently an early symptom. At this period
  no disposition to bite is observed; the animal is docile with its
  master and obeys his voice, though not so readily as before, nor with
  the same pleased countenance. There is something strange in the
  expression of its face, and the voice of its owner is scarcely able to
  make it change from a sudden gloominess to its usual animated aspect.
  These symptoms gradually become more marked; the restlessness and
  agitation increase. If on straw the dog scatters and pulls it about
  with its paws, and if in a room it scratches and tumbles the cushions
  or rugs on which it usually lies. It is incessantly on the move,
  rambling about, scratching the ground, sniffing in corners and at the
  doors, as if on the scent or seeking for something. It indulges in
  strange movements, as if affected by some mental influences or a prey
  to hallucinations. When not excited by any external influence it will
  remain for a brief period perfectly still and attentive, as if
  watching something, or following the movements of some creature on the
  wall; then it will suddenly dart forward and snap at the vacant air,
  as if pursuing an annoying object, or endeavouring to seize a fly. At
  another time it throws itself, yelling and furious, against the wall,
  as if it heard threatening voices on the other side, or was bent on
  attacking an enemy. Nevertheless, the animal is still docile and
  submissive, for its master's voice will bring it out of its frenzy.
  But the saliva is already virulent, and the excessive affection which
  it evinces at intervals, by licking the hands or face of those it
  loves, renders the danger very great should there be a wound or
  abrasion. Until a late period in the disease the master's voice has a
  powerful influence over the animal. When it has escaped from all
  control and wanders erratically abroad, ferocious and restless, and
  haunted by horrid phantoms, the familiar voice yet exerts its
  influence, and it is rare indeed that it attacks its master.

  There is no dread of water in the rabid dog; the animal is generally
  thirsty, and if water be offered will lap it with avidity, and swallow
  it at the commencement of the disease. And when, at a later period,
  the constriction about the throat--symptomatic of the disease--renders
  swallowing difficult, the dog will none the less endeavour to drink,
  and the lappings are as frequent and prolonged when deglutition
  becomes impossible. So little dread has the rabid dog of water that it
  will ford streams and swim rivers; and when in the ferocious stage it
  will even do this in order to attack other creatures on the opposite
  side.

  At the commencement of the disease the dog does not usually refuse to
  eat, and some animals are voracious to an unusual degree. But in a
  short time it becomes fastidious, only eating what it usually has a
  special predilection for. Soon, however, this gives place to a most
  characteristic symptom--either the taste becomes extremely depraved or
  the dog has a fatal and imperious desire to bite and ingest
  everything. The litter of its kennel, wool from cushions, carpets,
  stockings, slippers, wood, grass, earth, stones, glass, horse-dung,
  even its own faeces and urine, or whatever else may come in its way,
  are devoured. On examination of the body of a dog which has died of
  rabies it is so common to find in the stomach a quantity of dissimilar
  and strange matters on which the teeth have been exercised that, if
  there was nothing known of the animal's history, there would be strong
  evidence of its having been affected with the disease. When a dog,
  then, is observed to gnaw and eat suchlike matters, though it exhibits
  no tendency to bite, it should be suspected.

  The mad dog does not usually foam at the mouth to any great extent at
  first. The mucus of the mouth is not much increased in quantity, but
  it soon becomes thicker, viscid, and glutinous, and adheres to the
  angles of the mouth, fauces and teeth. It is at this period that the
  thirst is most ardent, and the dog sometimes furiously attempts to
  detach the saliva with its paws; and if after a while it loses its
  balance in these attempts and tumbles over, there can no longer be any
  doubt as to the nature of the malady. There is another symptom
  connected with the mouth in that form of the disease named "dumb
  madness" which has frequently proved deceptive. The lower jaw drops in
  consequence of paralysis of its muscles, and the mouth remains open.
  The interior is dry from the air passing continually over it, and
  assumes a deep red tint, somewhat masked by patches of dust or earth,
  which more especially adhere to the upper surface of the tongue and to
  the lips. The strange alteration produced in the dog's physiognomy by
  its constantly open mouth and the dark colour of the interior is
  rendered still more characteristic by the dull, sad, or dead
  expression of the animal's eyes. In this condition the creature is not
  very dangerous, because generally it could not bite if it
  tried--indeed there does not appear to be much desire to bite in dumb
  madness; but the saliva is none the less virulent, and accidental
  inoculations with it, through imprudent handling, will prove as fatal
  as in the furious form. The mouth should not be touched,--numerous
  deaths having occurred through people thinking the dog had some
  foreign substance lodged in its throat, and thrusting their fingers
  down to remove it. The sensation of tightness which seems to exist at
  the throat causes the dog to act as if a bone were fixed between its
  teeth or towards the back of its mouth, and to employ its fore-paws as
  if to dislodge it. This is a very deceptive symptom, and may prove
  equally dangerous if caution be not observed. Vomiting of blood or a
  chocolate-coloured fluid is witnessed in some cases, and has been
  supposed to be due to the foreign substances in the stomach, which
  abrade the lining membrane; this, however, is not correct, as it has
  been observed in man.

  The voice of the rabid dog is very peculiar, and so characteristic
  that to those acquainted with it nothing more is needed to prove the
  presence of the disease. Those who have heard it once or twice never
  forget its signification. Owing to the alterations taking place in the
  larynx the voice becomes hoarse, cracked and stridulous, like that of
  a child affected with croup--the "voix du coq," as the French have it.
  A preliminary bark is made in a somewhat elevated tone and with open
  mouth; this is immediately succeeded by five, six or eight decreasing
  howls, emitted when the animal is sitting or standing, and always with
  the nose elevated, which seem to come from the depths of the throat,
  the jaws not coming together and closing the mouth during such
  emission, as in the healthy bark. This alteration in the voice is
  frequently the first observable indication of the malady, and should
  at once attract attention. In dumb madness the voice is frequently
  lost from the very commencement--hence the designation.

  The sensibility of the mad dog appears to be considerably diminished,
  and the animal appears to have lost the faculty of expressing the
  sensations it experiences: it is mute under the infliction of pain,
  though there can be no doubt that it still has peripheral sensation to
  some extent. Burning, beating and wounding produce much less effect
  than in health, and the animal will even mutilate itself with its
  teeth. Suspicion, therefore, should always strongly attach to a dog
  which does not manifest a certain susceptibility to painful
  impressions and receives punishment without any cry or complaint.
  There is also reason for apprehension when a dog bites itself
  persistently in any part of its body. A rabid dog is usually stirred
  to fury at the sight of one of its own species; this test has been
  resorted to by Henrie Marie Bouley (1814-1885) to dissipate doubts as
  to the existence of the disease when the diagnosis is otherwise
  uncertain. As soon as the suspected animal, if it is really rabid,
  finds itself in the presence of another of its species it at once
  assumes the aggressive, and, if allowed, will bite furiously. All
  rabid animals indeed become excited, exasperated, and furious at the
  sight of a dog, and attack it with their natural weapons, even the
  timid sheep when rabid butts furiously at the enemy before which in
  health it would have fled in terror. This inversion of sentiment is
  sometimes valuable in diagnosing the malady; it is so common that it
  may be said to be present in every case of rabies. When, therefore, a
  dog, contrary to its habits and natural inclination, becomes suddenly
  aggressive to other dogs, it is time to take precautions.

  In the large majority of instances the dog is inoffensive in the early
  period of the disease to those to whom it is familiar. It then flies
  from its home and either dies, is killed as "mad," or returns in a
  miserable plight, and in an advanced stage of the malady, when the
  desire to bite is irresistible. It is in the early stage that
  sequestration and suppressive measures are most valuable. The dogs
  which propagate the disease are usually those that have escaped from
  their owners. After two or three days, frequently in about twelve
  hours, more serious and alarming symptoms appear, ferocious instincts
  are developed, and the desire to do injury is irrepressible. The
  animal has an indefinable expression of sombre melancholy and cruelty.
  The eyes have their pupils dilated, and emit flashes of light when
  they are not dull and heavy; they always appear so fierce as to
  produce terror in the beholder; they are red, and their sensibility to
  light is increased; and wrinkles, which sometimes appear on the
  forehead, add to the repulsive aspect of the animal. If caged it flies
  at the spectator, emitting its characteristic howl or bark, and
  seizing the iron bars with its teeth, and if a stick be thrust before
  it this is grasped and gnawed. This fury is soon succeeded by
  lassitude, when the animal remains insensible to every excitement.
  Then all at once it rouses up again, and another paroxysm of fury
  commences. The first paroxysm is usually the most intense, and the
  fits vary in duration from some hours to a day, and even longer; they
  are ordinarily briefer in trained and pet dogs than in those which are
  less domesticated, but in all the remission is so complete after the
  first paroxysm that the animals appear to be almost well, if not in
  perfect health. During the paroxysms respiration is hurried and
  laboured, but tranquil during the remissions. There is an increase of
  temperature, and the pulse is quick and hard. When the animal is kept
  in a dark place and not excited, the fits of fury are not observed.
  Sometimes it is agitated and restless in the manner already described.
  It never becomes really furious or aggressive unless excited by
  external objects--the most potent of these, as has been said, being
  another dog, which, however, if it be admitted to its cage, it may not
  at once attack. The attacked animal rarely retaliates, but usually
  responds to the bites by acute yells, which contrast strangely with
  the silent anger of the aggressor, and tries to hide its head with its
  paws or beneath the straw. These repeated paroxysms hurry the course
  of the disease. The secretion and flowing of a large quantity of
  saliva from the mouth are usually only witnessed in cases in which
  swallowing has become impossible, the mouth being generally dry. At
  times the tongue, nose and whole head appear swollen. Other dogs
  frequently shun one which is rabid, as if aware of their danger.

  The rabid dog, if lodged in a room or kept in a house, is continually
  endeavouring to escape; and when it makes its escape it goes freely
  forward, as if impelled by some irresistible force. It travels
  considerable distances in a short time, perhaps attacking every living
  creature it meets--preferring dogs, however, to other animals, and
  these to mankind; cats, sheep, cattle and horses are particularly
  liable to be injured. It attacks in silence, and never utters a snarl
  or a cry of anger; should it chance to be hurt in return it emits no
  cry or howl of pain. The degree of ferocity appears to be related to
  natural disposition and training. Some dogs, for instance, will only
  snap or give a slight bite in passing, while others will bite
  furiously, tearing the objects presented to them, or which they meet
  in their way, and sometimes with such violence as to injure their
  mouth and break their teeth, or even their jaws. If chained, they will
  in some cases gnaw the chain until their teeth are worn away and the
  bones laid bare. The rabid dog does not continue its progress very
  long. Exhausted by fatigue and the paroxysms of madness excited in it
  by the objects it meets, as well as by hunger, thirst, and also, no
  doubt, by the malady, its limbs soon become feeble; the rate of
  travelling is lessened and the walk is unsteady, while its drooping
  tall, head inclined towards the ground, open mouth, and protruded
  tongue (of a leaden colour or covered with dust) give the distressed
  creature a very striking and characteristic physiognomy. In this
  condition, however, it is much less to be dreaded than in its early
  fits of fury, since it is no longer capable or desirous of altering
  its course or going out of its way to attack an animal or a man not
  immediately in the path. It is very probable that its fast-failing
  vision, deadened scent, and generally diminished perception prevent
  its being so readily impressed or excited by surrounding objects as it
  previously was. To each paroxysm, which is always of short duration,
  there succeeds a degree of exhaustion as great as the fits have been
  violent and oft repeated. This compels the animal to stop; then it
  shelters itself in obscure places--frequently in ditches by the
  roadside--and lies there in a somnolescent state for perhaps hours.
  There is great danger, nevertheless, in disturbing the dog at this
  period; for when roused from its torpor it has sometimes sufficient
  strength to inflict a bite. This period, which may be termed the
  second stage, is as variable in its duration as the first, but it
  rarely exceeds three or four days. The above-described phenomena
  gradually merge into those of the third or last period, when symptoms
  of paralysis appear, which are speedily followed by death. During the
  remission in the paroxysms these paralytic symptoms are more
  particularly manifested in the hind limbs, which appear as if unable
  to support the animal's weight, and cause it to stagger about; or the
  lower jaw becomes more or less drooping, leaving the parched mouth
  partially open. Emaciation rapidly sets in, and the paroxysms diminish
  in intensity, while the remissions become less marked. The physiognomy
  assumes a still more sinister and repulsive aspect; the hair is dull
  and erect; the flanks are retracted; the eyes lose their lustre and
  are buried in the orbits, the pupil being dilated, and the cornea dull
  and semi-opaque; very often, even at an early period, the eyes squint,
  and this adds still more to the terrifying appearance of the poor dog.
  The voice, if at all heard, is husky, the breathing laborious, and the
  pulse hurried and irregular. Gradually the paralysis increases, and
  the posterior extremities are dragged as if the animal's back were
  broken, until at length it becomes general; it is then the prelude to
  death. Or the dog remains lying in a state of stupor, and can only
  raise itself with difficulty on the fore-limbs when greatly excited.
  In this condition it may yet endeavour to bite at objects within its
  reach. At times convulsions of a tetanic character appear in certain
  muscles; at other times these are general. A comatose condition
  ensues, and the rabid dog, if permitted to die naturally, perishes, in
  the great majority of cases, from paralysis and asphyxia.

  In dumb madness there is paralysis of the lower jaw, which imparts a
  curious and very characteristic physiognomy to the dog; the voice is
  also lost, and the animal can neither eat nor drink. In this condition
  the creature remains with its jaw pendent and the mouth consequently
  wide open, showing the flaccid or swollen tongue covered with brownish
  matter, and a stringy gelatinous-looking saliva lying between it and
  the lower lip and coating the fauces, which sometimes appear to be
  inflamed. Though the animal is unable to swallow fluids, the desire to
  drink is nevertheless intense; for the creature will thrust its face
  into the vessel of water in futile attempts to obtain relief, even
  until the approach of death. Water may be poured down its throat
  without inducing a paroxysm. The general physiognomy and demeanour of
  the poor creature inspire the beholder with pity rather than fear. The
  symptoms due to cerebral excitement are less marked than in the
  furious form of the disease; the agitation is not so considerable, and
  the restlessness, tendency to run away, and desire to bite are nearly
  absent; generally the animal is quite passive. Not unfrequently one or
  both eyes squint, and it is only when very much excited that the dog
  may contrive to close its mouth. Sometimes there is swelling about the
  pharynx and the neck; when the tongue shares in this complication it
  hangs out of the mouth. In certain cases there is a catarrhal
  condition of the membrane lining the nasal cavities, larynx, and
  bronchi; sometimes the animal testifies to the existence of abdominal
  pain, and the faeces are then soft or fluid. The other symptoms--such
  as the rapid exhaustion and emaciation, paralysis of the posterior
  limbs towards the termination of the disease, as well as the rapidity
  with which it runs its course--are the same as in the furious form.

  The simultaneous occurrence of furious and dumb madness has frequently
  been observed in packs of fox-hounds. Dumb madness differs, then, from
  the furious type in the paralysis of the lower jaw, which hinders the
  dog from biting, save in very exceptional circumstances; the ferocious
  instincts are also in abeyance; and there is no tendency to
  aggression. It has been calculated that from 15 to 20% of rabid dogs
  have this particular form of the disease. Puppies and young dogs
  chiefly have furious rabies.

  These are the symptoms of rabies in the dog; but it is not likely, nor
  is it necessary, that they will all be present in every case. In other
  species the symptoms differ more or less from those manifested by the
  dog, but they are generally marked by a change in the manner and
  habits of the creatures affected, with strong indications of nervous
  disturbance, in the majority of species amounting to ferociousness and
  a desire to injure, timid creatures becoming bold and aggressive.

_In Human Beings._--The disease of hydrophobia has been known from early
times, and is alluded to in the works of Aristotle, Xenophon, Plutarch,
Virgil, Horace, Ovid and many others, as well as in those of the early
writers on medicine. Celsus gives detailed instructions respecting the
treatment of men who have been bitten by rabid dogs, and dwells on the
dangers attending such wounds. After recommending suction of the bitten
part by means of a dry cupping glass, and thereafter the application of
the actual cautery or of strong caustics, and the employment of baths
and various internal remedies, he says: "Idque cum ita per triduum
factum est, tutus esse homo a periculo videtur. Solet autem ex eo
vulnere, ubi parum occursum est, aquae timor nasci, [Greek:
hydrophobian] Graeci appellant. Miserrimum genus morbi; in quo simul
aeger et siti et aquae metu cruciatur; quo oppressis in angusto spes
est." Subsequently Galen described minutely the phenomena of
hydrophobia, and recommended the excision of the wounded part as a
protection against the disease. Throughout many succeeding centuries
little or nothing was added to the facts which the early physicians had
made known upon the subject. The malady was regarded with universal
horror and dread, and the unfortunate sufferers were generally abandoned
by all around them and left to their terrible fate. In later times the
investigations of Boerhaave, Gerard van Swieten (1700-1772), John
Hunter, François Magendie (1783-1855), Gilbert Breschet (1784-1845),
Virchow, Albert Reder, as also of William Youatt (1776-1847), George
Fleming, Meynell, Karl Hertwig (1798-1881), and others, have furnished
important information; but all these were put into the shade by the
researches of Pasteur.

The disease is communicated by the secretions of the mouth of the
affected animal entering a wound or abrasion of the human skin or mucous
membrane. In the great majority of cases (90%) this is due to the bite
of a rabid dog, but bites of rabid cats, wolves, foxes, jackals, &c. are
occasionally the means of conveying the disease. Numerous popular
fallacies still prevail on the subject of hydrophobia. Thus it is
supposed that the bite of an angry dog may produce the disease, and all
the more if the animal should subsequently develop symptoms of rabies.
The ground for this erroneous notion is the fact, which is
unquestionable, that animals in whom rabies is in the stage of
incubation, during which there are few if any symptoms, may by their
bites convey the disease, though fortunately during this early stage
they are little disposed to bite. The bite of a non-rabid animal,
however enraged, cannot give rise to hydrophobia.

The period of incubation of the disease, or that time which elapses
between the introduction of the virus and the development of the
symptoms, appears to vary in a remarkable degree, being in some cases as
short as a fortnight, and in others as long as several months or even
years. On an average it seems to be from about six weeks to three
months, but it mainly depends on the part bitten; bites on the head are
the most dangerous. The incubation period is also said to be shorter in
children. The rare instances of the appearance of hydrophobia many years
after the introduction of the poison are always more or less open to
question as to subsequent inoculation.

When the disease is about to declare itself it not unfrequently happens
that the wound, which had quickly and entirely healed after the bite,
begins to exhibit evidence of irritation or inflammatory action, or at
least to be the seat of morbid sensations such as numbness, tingling or
itching. The symptoms characterizing the premonitory stage are great
mental depression and disquietude, together with restlessness and a kind
of indefinite fear. There is an unusual tendency to talk, and the
articulation is abrupt and rapid. Although in some instances the
patients will not acknowledge that they have been previously bitten, and
deny it with great obstinacy, yet generally they are well aware of the
nature of their malady, and speak despairingly of its consequences.
There is in this early stage a certain amount of constitutional
disturbance showing itself by feverishness, loss of appetite,
sleeplessness, headache, great nervous excitability, respiration of a
peculiar sighing or sobbing character, and even occasionally a
noticeable aversion to liquids. These symptoms--constituting what is
termed the melancholic stage--continue in general for one or two days,
when they are succeeded by the stage of excitement in which all the
characteristic phenomena of the malady are fully developed. Sometimes
the disease first shows itself in this stage, without antecedent
symptoms.

The agitation of the sufferer now becomes greatly increased, and the
countenance exhibits anxiety and terror. There is noticed a marked
embarrassment of the breathing, but the most striking and terrible
features of this stage are the effects produced by attempts to swallow
fluids. The patient suffers from thirst and desires eagerly to drink,
but on making the effort is seized with a most violent suffocative
paroxysm produced by spasm of the muscles of swallowing and breathing,
which continues for several seconds, and is succeeded by a feeling of
intense alarm and distress. With great caution and determination the
attempt is renewed, but only to be followed with a repetition of the
seizure, until the unhappy sufferer ceases from sheer dread to try to
quench the thirst which torments him. Indeed the very thought of doing
so suffices to bring on a choking paroxysm, as does also the sound of
the running of water. The patient is extremely sensitive to any kind of
external impression; a bright light, a loud noise, a breath of cool air,
contact with any one, are all apt to bring on one of these seizures. But
besides these suffocative attacks there also occur general convulsions
affecting the whole muscular system of the body, and occasionally a
condition of tetanic spasm. These various paroxysms increase in
frequency and severity with the advance of the disease, but alternate
with intervals of comparative quiet, in which, however, there is intense
anxiety and more or less constant difficulty of breathing, accompanied
with a peculiar sonorous expiration, which has suggested the notion that
the patient barks like a dog. In many instances there is great mental
disturbance, with fits of maniacal excitement, in which he strikes at
every one about him, and accuses them of being the cause of his
sufferings--these attacks being succeeded by calm intervals in which he
expresses great regret for his violent behaviour. During all this stage
of the disease the patient is tormented with a viscid secretion
accumulating in his mouth, which from dread of swallowing he is
constantly spitting about him. There may also be noticed snapping
movements of the jaws as if he were attempting to bite, but these are in
reality a manifestation of the spasmodic action which affects the
muscles generally. There is no great amount of fever, but there is
constipation, diminished flow of urine, and often sexual excitement.

After two or three days of suffering of the most terrible description
the patient succumbs, death taking place either in a paroxysm of
choking, or on the other hand in a tranquil manner from exhaustion, all
the symptoms having abated, and the power of swallowing returned before
the end. The duration of the disease from the first declaration of the
symptoms is generally from three to five days.

Apart from the inoculation method (see below), the treatment of most
avail is that which is directed towards preventing the absorption of the
poison into the system. This may be accomplished by excision of the part
involved in the bite of the rabid animal, or, where this from its
locality is impracticable, in the application to the wound of some
chemical agent which will destroy the activity of the virus, such as
potassa fusa, lunar caustic (nitrate of silver), or the actual cautery
in the form of a red-hot wire. The part should be thoroughly acted on by
these agents, no matter what amount of temporary suffering this may
occasion. Such applications should be resorted to immediately after the
bite has been inflicted, or as soon thereafter as possible. Further,
even though many hours or days should elapse, these local remedies
should still be applied; for if, as appears probable, some at least of
the virus remains for long at the injured part, the removal or effectual
destruction of this may prevent the dread consequences of its
absorption. Every effort should be made to tranquillize and reassure the
patient.

Two special points of interest have arisen in recent years in connexion
with this disease. One is the Pasteur treatment by inoculation with
rabic virus (see also PARASITIC DISEASES), and the other was the attempt
of the government to exterminate rabies in the British Isles by muzzling
dogs.


  Pasteur treatment.

The Pasteur treatment was first applied to human beings in 1885 after
prolonged investigation and experimental trial on animals. It is based
on the fact that a virus, capable of giving rabies by inoculation, can
be extracted from the tissues of a rabid animal and then intensified or
attenuated at pleasure. It appears that the strength of the rabic virus,
as determined by inoculation, is constant in the same species of animal,
but is modified by passing through another species. For instance, the
natural virus of dogs is always of the same strength, but when
inoculated into monkeys it becomes weakened, and the process of
attenuation can be carried on by passing the virus through a succession
of monkeys, until it loses the power of causing death. If this weakened
virus is then passed back through guinea-pigs, dogs or rabbits, it
regains its former strength. Again, if it be passed through a succession
of dogs it becomes intensified up to a maximum of strength which is
called the _virus fixe_. Pasteur further discovered that the strength
can be modified by temperature and by keeping the dried tissues of a
rabid animal containing the virus. Thus, if the spinal cord of a rabid
dog be preserved in a dry state, the virus loses strength day by day.
The system of treatment consists in making an emulsion of the cord and
graduating the strength of the dose by using a succession of cords,
which have been kept for a progressively diminishing length of time.
Those which have been kept for fourteen days are used as a
starting-point, yielding virus of a minimum strength. They are followed
by preparations of diminishing age and increasing strength, day by day,
up to the maximum, which is three days old. These are successively
injected into the circulatory system. The principle is the artificial
acquisition by the patient of resistance to the rabic virus, which is
presumed to be already in the system but has not yet become active, by
accustoming him gradually to its toxic effect, beginning with a weak
form and progressively increasing the dose. It is not exactly treatment
of the disease, because it is useless or nearly so when the disease has
commenced, nor is it exactly preventive, for the patient has already
been bitten. It must be regarded as a kind of anticipatory cure. The
cords are cut into sections and preserved dry in sterilized flasks
plugged with cotton-wool. Another method of preparing the inoculatory
virus, which has been devised by Guido Tizzoni and Eugenio Centanni,
consists in subjecting the _virus fixe_ to peptic digestion by diluted
gastric juice for varying periods of time.

The first patient was treated by Pasteur's system in July 1885. He was
successively inoculated with emulsions made from cords that had been
kept fourteen and ten days, then eleven and eight days, then eight,
seven, six days, and so on. Two forms of treatment are now used--(1) the
"simple," in which the course from weak to strong virus is extended over
nine days; (2) the "intensive," in which the maximum is reached in seven
days. The latter is used in cases of very bad bites and those of some
standing, in which it is desirable to lose no time. Two days are
compressed into one at the commencement by making injections morning and
evening instead of once a day, so that the fifth-day cord is reached in
four days instead of six, as in the "simple" treatment. When the
maximum--the third-day cord--is reached the injections are continued
with fifth-, fourth-, and third-day cords. The whole course is fifteen
days in the simple treatment and twenty-one in the intensive. The doses
injected range from 1 to 3 cubic centimetres. Injections are made
alternately into the right and left flanks. The following table shows
the number treated from 1886 to 1905, with the mortality.

  +------+--------+-------+---------+
  | Year.|Patients|Deaths.|Mortality|
  |      |Treated.|       |per cent.|
  +------+--------+-------+---------+
  | 1886 |  2671  |  25   |   .94   |
  | 1887 |  1770  |  14   |   .79   |
  | 1888 |  1622  |   9   |   .55   |
  | 1889 |  1830  |   7   |   .38   |
  | 1890 |  1540  |   5   |   .32   |
  | 1891 |  1559  |   4   |   .25   |
  | 1892 |  1790  |   4   |   .22   |
  | 1893 |  1648  |   6   |   .36   |
  | 1894 |  1387  |   7   |   .50   |
  | 1895 |  1520  |   5   |   .33   |
  | 1896 |  1308  |   4   |   .30   |
  | 1897 |  1521  |   6   |   .39   |
  | 1898 |  1465  |   3   |   .20   |
  | 1899 |  1614  |   4   |   .25   |
  | 1900 |  1419  |  10   |   .70   |
  | 1901 |  1318  |   5   |   .37   |
  | 1902 |  1105  |   2   |   .18   |
  | 1903 |   630  |   4   |   .65   |
  | 1904 |   757  |   5   |   .66   |
  | 1905 |   727  |   4   |   .54   |
  +------+--------+-------+---------+

These figures do not include cases which develop hydrophobia during
treatment or within fifteen days after treatment is completed, for it is
held that persons who die within that period have their nervous centres
invaded by virus before the cure has time to act. The true mortality
should therefore be considerably higher. For instance, in 1898 three
deaths came within this category, which just doubles the mortality; and
in 1899 the additional deaths were six, bringing the mortality up to
two-and-a-half times that indicated in the table. When, however, the
additional deaths are included the results remain sufficiently striking,
if two assumptions are granted--(1) that all the persons treated have
been bitten by rabid animals; (2) that a large proportion of persons so
bitten usually have hydrophobia. Unfortunately, both these assumptions
lack proof, and therefore the evidence of the efficacy of the treatment
cannot be said to satisfy a strictly scientific standard. With regard to
the first point, the patients are divided into three categories--(1)
those bitten by an animal the rabidity of which is proved by the
development of rabies in other animals bitten by it or inoculated from
its spinal cord; (2) those bitten by an animal pronounced rabid on a
veterinary examination; (3) those bitten by an animal suspected of being
rabid. The number of patients in each category in 1898 was (1) 141, (2)
855, (3) 469; and in 1899 it was (1) 152, (2) 1099, (3) 363. As might be
expected, the vast majority came under the second and third heads, in
which the evidence of rabidity is doubtful or altogether lacking. With
regard to the second point, the proportion of persons bitten by rabid
animals who ordinarily develop hydrophobia has only been "estimated"
from very inadequate data. Otto Bollinger from a series of collected
statistics states that before the introduction of the Pasteur treatment,
of patients bitten by dogs undoubtedly rabid 47% died, the rate being
33% in those whose wounds had been cauterized and 83% when there had
been no local treatment. If the number of rabid dogs be compared with
the deaths from hydrophobia in any year or series of years, it can
hardly be very high. For instance, in 1895, 668 dogs, besides other
animals, were killed and certified to be rabid in England, and the
deaths from hydrophobia were twenty. Of course this proves nothing, as
the number of persons bitten is not known, but the difference between
the amount of rabies and of hydrophobia is suggestively great in view of
the marked propensity of rabid dogs to bite, nor is it accounted for by
the fact that some of the persons bitten were treated at the Institut
Pasteur. A comparison of the annual mortality from hydrophobia in France
before and after the introduction of the treatment would afford decisive
evidence as to its efficacy; but unfortunately no such comparison can be
made for lack of vital statistics in that country. The experience of the
Paris hospitals, however, points to a decided diminution of mortality.
On the whole it must be said, in the absence of further data, that the
Pasteur treatment certainly diminishes the danger of hydrophobia from
the bites of rabid animals.

More recently treatment with an anti-rabic serum has been suggested (see
PARASITIC DISEASES). Victor Babes and Lepp and later Guido Tizzoni and
Eugenio Centanni have worked out a method of serum treatment curative
and protective. In this method not the rabic poison itself, as in the
Pasteur treatment, but the protective substance formed is injected into
the tissues. The serum of a vaccinated animal is capable of neutralizing
the power of the virus of rabies not only when mixed with the virus
before injection but even when injected simultaneously or within
twenty-four hours after the introduction of the virus. These authors
showed that the serum of a rabbit protects a rabbit better than does the
serum of a dog, and vice versa. At the end of twenty days' injections
they found they could obtain such a large quantity of anti-rabic
substance in the serum of an animal, that even 1 part of serum to 25,000
of the body weight would protect an animal. This process differs from
that of Pasteur in so far as that in place of promoting the formation of
the antidote within the body of the patient, by a process of vaccination
with progressively stronger and stronger virus, this part of the process
is carried on in an animal, Babes using the dog and Centanni the sheep,
the blood serum of which is injected. This method of vaccination is
useful as a protective to those in charge of kennels.


  Muzzling order in England.

The attempt to stamp out rabies in Great Britain was an experiment
undertaken by the government in the public interest. The principal means
adopted were the muzzling of dogs in infected areas, and prolonged
quarantine for imported animals. The efficacy of dog-muzzling in
checking the spread of rabies and diminishing its prevalence has been
repeatedly proved in various countries. Liable as other animals may be
to the disease, in England at least the dog is pre-eminently the vehicle
of contagion and the great source of danger to human beings. There is a
difference of opinion on the way in which muzzling acts, though there
can be none as to the effect it produces in reducing rabies. Probably it
acts rather by securing the destruction of ownerless and stray--which
generally includes rabid--dogs than by preventing biting; for though it
may prevent snapping, even the wire-cage muzzle does not prevent furious
dogs from biting, and it is healthy, not rabid, dogs that wear the
muzzle. It has therefore been suggested that a collar would have the
same effect, if all collarless dogs were seized; but the evidence goes
to show that it has not, perhaps because rabid dogs are more likely to
stray from home with their collars, which are constantly worn, than with
muzzles which are not, and so escape seizure. Moreover, it is much
easier for the police to see whether a dog is wearing a muzzle or not
than it is to make sure about the collar. However this may be, the
muzzle has proved more efficacious, but it was not applied
systematically in England until a late date. Sometimes the regulations
were in the hands of the government, and sometimes they were left to
local authorities; in either case they were allowed to lapse as soon as
rabies had died down. In April 1897 the Board of Agriculture entered on
a systematic attempt to exterminate rabies by the means indicated. The
plan was to enforce muzzling over large areas in which the disease
existed, and to maintain it for six months after the occurrence of the
last case. In spite of much opposition and criticism, this was
resolutely carried out under Mr Walter Long, the responsible minister,
and met with great success. By the spring of 1899--that is, in two
years--the disease had disappeared in Great Britain, except for one area
in Wales; and, with this exception, muzzling was everywhere relaxed in
October 1899. It was taken off in Wales also in the following May, no
case having occurred since November 1899. Rabies was then pronounced
extinct. During the summer of 1900, however, it reappeared in Wales, and
several counties were again placed under the order. The year 1901 was
the third in succession in which no death from hydrophobia was
registered in the United Kingdom. In the ten years preceding 1899, 104
deaths were registered, the death-rate reaching 30 in 1889 and averaging
29 annually. In 1902 two deaths from hydrophobia were registered. From
that date to June 1909 (the latest available for the purpose of this
article) no death from hydrophobia was notified in the United Kingdom.

  See _Annales de l'Institut Pasteur_, from 1886; _Journal of the Board
  of Agriculture_, 1899; Makins, "Hydrophobia," in Treves's _System of
  Surgery_; Woodhead, "Rabies," in Allbutt's _System of Medicine_.



HYDROSPHERE (Gr. [Greek: hydôr], water, and [Greek: sphaira], sphere),
in physical geography, a name given to the whole mass of the water of
the oceans, which fills the depressions in the earth's crust, and covers
nearly three-quarters of its surface. The name is used in distinction
from the atmosphere, the earth's envelope of air, the lithosphere (Gr.
[Greek: lithos], rock) or solid crust of the earth, and the centrosphere
or interior mass within the crust. To these "spheres" some writers add,
by figurative usage, the terms "biosphere," or life-sphere, to cover all
living things, both animals and plants, and "psychosphere," or
mind-sphere, covering all the products of human intelligence.



HYDROSTATICS (Gr. [Greek: hydôr], water, and the root [Greek: sta]-, to
cause to stand), the branch of hydromechanics which discusses the
equilibrium of fluids (see HYDROMECHANICS).



HYDROXYLAMINE, NH2OH, or hydroxy-ammonia, a compound prepared in 1865 by
W. C. Lossen by the reduction of ethyl nitrate with tin and hydrochloric
acid. In 1870 E. Ludwig and T. H. Hein (_Chem. Centralblatt_, 1870, 1,
p. 340) obtained it by passing nitric oxide through a series of bottles
containing tin and hydrochloric acid, to which a small quantity of
platinum tetrachloride has been added; the acid liquid is poured off
when the operation is completed, and sulphuretted hydrogen is passed in;
the tin sulphide is filtered off and the filtrate evaporated. The
residue is extracted by absolute alcohol, which dissolves the
hydroxylamine hydrochloride and a little ammonium chloride; this last
substance is removed as ammonium platino-chloride, and the residual
hydroxylamine hydrochloride is recrystallized. E. Divers obtains it by
mixing cold saturated solutions containing one molecular proportion of
sodium nitrate, and two molecular proportions of acid sodium sulphite,
and then adding a saturated solution of potassium chloride to the
mixture. After standing for twenty-four hours, hydroxylamine potassium
disulphonate crystallizes out. This is boiled for some hours with water
and the solution cooled, when potassium sulphate separates first, and
then hydroxylamine sulphate. E. Tafel (_Zeit. anorg. Chem._, 1902, 31,
p. 289) patented an electrolytic process, wherein 50% sulphuric acid is
treated in a divided cell provided with a cathode of amalgamated lead,
50% nitric acid being gradually run into the cathode compartment. Pure
anhydrous hydroxylamine has been obtained by C. A. Lobry de Bruyn from
the hydrochloride, by dissolving it in absolute methyl alcohol and then
adding sodium methylate. The precipitated sodium chloride is filtered,
and the solution of hydroxylamine distilled in order to remove methyl
alcohol, and finally fractionated under reduced pressure. The free base
is a colourless, odourless, crystalline solid, melting at about 30° C.,
and boiling at 58° C. (under a pressure of 22 mm.). It deliquesces and
oxidizes on exposure, inflames in dry chlorine and is reduced to ammonia
by zinc dust. Its aqueous solution is strongly alkaline, and with acids
it forms well-defined stable salts. E. Ebler and E. Schott (_J. pr.
Chem._, 1908, 78, p. 289) regard it as acting with the formula NH2·OH
towards bases, and as NH3:O towards acids, the salts in the latter case
being of the oxonium type. It is a strong reducing agent, giving a
precipitate of cuprous oxide from alkaline copper solutions at ordinary
temperature, converting mercuric chloride to mercurous chloride, and
precipitating metallic silver from solutions of silver salts. With
aldehydes and ketones it forms oximes (q.v.). W. R. Dunstan (_Jour.
Chem. Soc._, 1899, 75, p. 792) found that the addition of methyl iodide
to a methyl alcohol solution of hydroxylamine resulted in the formation
of trimethyloxamine, N(CH3)3O.

  Many substituted hydroxylamines are known, substitution taking place
  either in the [alpha] or [beta] position

    [beta]    [alpha]
     (NH2   ·   OH^).

  [beta]-phenylhydroxyl-amine, C6H5NH·OH·, is obtained in the reduction
  of nitrobenzene in neutral solution (e.g. by the action of the
  aluminium-mercury couple and water), but better, according to C.
  Goldschmidt (_Ber._, 1896, 29, p. 2307) by dissolving nitrobenzene in
  ten times its weight of ether containing a few cubic centimetres of
  water, and heating with excess of zinc dust and anhydrous calcium
  chloride for three hours on a water bath. It also appears as an
  intermediate product in the electrolytic reduction of nitrobenzene in
  sulphuric acid solution. By gentle oxidation it yields nitrosobenzene.
  Derivatives of the type R2N·OH result in the action of the Grignard
  reagent on amyl nitrite. Dihydroxy-ammonia or nitroxyl, NH(OH)2, a
  very unstable and highly reactive substance, has been especially
  studied by A. Angeli (see A. W. Stewart, _Recent Advances in Physical
  and Inorganic Chemistry_, 1909).



HYDROZOA, one of the most widely spread and prolific groups of aquatic
animals. They are for the most part marine in habitat, but a familiar
fresh-water form is the common _Hydra_ of ponds and ditches, which gives
origin to the name of the class. The Hydrozoa comprise the hydroids, so
abundant on all shores, most of which resemble vegetable organisms to
the unassisted eye; the hydrocorallines, which, as their name implies,
have a massive stony skeleton and resemble corals; the jelly-fishes so
called; and the Siphonophora, of which the species best known by repute
is the so-called "Portuguese man-of-war" (_Physalia_), dreaded by
sailors on account of its terrible stinging powers.

In external form and appearance the Hydrozoa exhibit such striking
differences that there would seem at first sight to be little in common
between the more divergent members of the group. Nevertheless there is
no other class in the animal kingdom with better marked characteristics,
or with more uniform morphological peculiarities underlying the utmost
diversity of superficial characters.

All Hydrozoa, in the first place, exhibit the three structural features
distinctive of the Coelentera (q.v.). (1) The body is built up of two
layers only, an external protective and sensory layer, the ectoderm, and
an internal digestive layer, the endoderm. (2) The body contains but a
single internal cavity, the coelenteron or gastrovascular space, which
may be greatly ramified, but is not shut off into cavities distinct from
the central digestive space. (3) The generative cells are produced in
either the ectoderm or endoderm, and not in a third layer arising in the
embryo, distinct from the two primary layers; in other words, there is
no mesoderm or coelom.

To these three characters the Hydrozoa add a fourth which is distinctive
of the subdivision of the Coelenterata termed the Cnidaria; that is to
say, they always possess peculiar stinging organs known as nettle-cells,
or _nematocysts_ (_Cnidae_), each produced in a cell forming an integral
part of the animal's tissues. The Hydrozoa are thus shown to belong to
the group of Coelenterata Cnidaria, and it remains to consider more
fully their distinctive features, and in particular those which mark
them off from the other main division of the Cnidaria, the Anthozoa
(q.v.), comprising the corals and sea-anemones.

The great diversity, to which reference has already been made, in the
form and structure of the Hydrozoa is due to two principal causes. In
the first place, we find in this group two distinct types of person or
individual, the polyp and the medusa (qq.v.), each capable of a wide
range of variations; and when both polyp and medusa occur in the
life-cycle of the same species, as is frequently the case, the result is
an alternation of generations of a type peculiarly characteristic of the
class. In the second place, the power of non-sexual reproduction by
budding is practically of universal occurrence among the Hydrozoa, and
by the buds failing to separate from the parent stock, colonies are
produced, more or less complicated in structure and often of great size.
We find that polyps may either bud other polyps or may produce medusae,
and that medusae may bud medusae, though never, apparently, polyps.
Hence we have a primary subdivision of the colonies of Hydrozoa into
those produced by budding of polyps and those produced by budding of
medusae. The former may contain polyp-persons and medusa-persons, either
one kind alone or both kinds combined; the latter will contain only
medusa-persons variously modified.

The morphology of the Hydrozoa reduces itself, therefore, to a
consideration of the morphology of the polyp, of the medusa and of the
colony. Putting aside the last-named, for a detailed account of which
see HYDROMEDUSAE, we can best deal with the peculiarities of the polyp
and medusa from a developmental point of view.

  In the development of the Hydrozoa, and indeed of the Cnidaria
  generally, the egg usually gives rise to an oval larva which swims
  about by means of a coating of cilia on the surface of the body. This
  very characteristic larva is termed a _planula_, but though very
  uniform externally, the planulae of different species, or of the same
  species at different periods, do not always represent the same stage
  of embryonic development internally. On examining more minutely the
  course of the development, it is found that the ovum goes through the
  usual process of cleavage, always total and regular in this group, and
  so gives rise to a hollow sphere or ovoid with the wall composed of a
  single layer of cells, and containing a spacious cavity, the
  blastocoele or segmentation-cavity. This is the _blastula_ stage
  occurring universally in all Metazoa, probably representing an
  ancestral Protozoan colony in phylogeny. Next the blastula gives rise
  to an internal mass of cells (fig. 1, hy) which come from the wall
  either by immigration (fig. 1, A) or by splitting off (delamination).
  The formation of an inner cell-mass converts the single-layered
  blastula (monoblastula) into a double-layered embryo (diblastula)
  which may be termed a parenchymula, since at first the inner cell-mass
  forms an irregular parenchyma which may entirely fill up and
  obliterate the segmentation cavity (fig. 1, B). At a later stage,
  however, the cells of the inner mass arrange themselves in a definite
  layer surrounding an internal cavity (fig. 1, C, al), which soon
  acquires an opening to the exterior at one pole, and so forms the
  characteristic embryonic stage of all Enterozoa known as the
  _gastrula_ (fig. 2). In this stage the body is composed of two layers,
  ectoderm (d) externally, and endoderm (c) internally, surrounding a
  central cavity, the _archenteron_ (b), which communicates with the
  exterior by a pore (a), the _blastopore_.

  Thus a planula larva may be a blastula, or but slightly advanced
  beyond this stage, or it may be (and most usually is) a parenchymula;
  or in some cases (Scyphomedusae) it may be a gastrula. It should be
  added that the process of development, the gastrulation as it is
  termed, may be shortened by the immigration of cells taking place at
  one pole only, and in a connected layer with orderly arrangement, so
  that the gastrula stage is reached at once from the blastula without
  any intervening parenchymula stage. This is a process of gastrulation
  by invagination which is found in all animals above the Coelenterata,
  but which is very rare in the Cnidaria, and is known only in the
  Scyphomedusae amongst the Hydrozoa.

  [Illustration: From Balfour, after Kowalewsky.

  FIG. 1.--Formation of the Diblastula of _Eucope_ (one of the
  Calyptoblastic _Hydromedusae_) by immigration. A, B, C, three
  successive stages. _ep_, Ectoderm; _hy_, endoderm; _al_, enteric
  cavity.]

  After the gastrula stage, which is found as a developmental stage in
  all Enterozoa, the embryo of the Hydrozoa proceeds to develop
  characters which are peculiar to the Coelenterata only. Round the
  blastopore hollow outgrowths, variable in number, arise by the
  evagination of the entire body-wall, both ectoderm and endoderm. Each
  outgrowth contains a prolongation of the archenteric cavity (compare
  figs. 2 and 3, A). In this way is formed a ring of tentacles, the most
  characteristic organs of the Cnidaria. They surround a region which is
  termed the peristome, and which contains in the centre the blastopore,
  which becomes the adult mouth. The archenteron becomes the
  gastrovascular system or coelenteron. Between the ectoderm and
  endoderm a gelatinous supporting layer, termed the mesogloea, makes
  its appearance. The gastrula has now become an _actinula_, which may
  be termed the distinctive larva of the Cnidaria, and doubtless
  represents in a transitory manner the common ancestor of the group. In
  no case known, however, does the actinula become the adult, sexually
  mature individual, but always undergoes further modifications, whereby
  it develops into either a polyp or a medusa.

  [Illustration: From Gegenbaur's _Elements of Comparative Anatomy_.

  FIG. 2.--Diagram of a Diblastula.

    a, Blastopore.
    b, Archenteric cavity.
    c, Endoderm.
    d, Ectoderm.]

  To become a polyp, the actinula (fig. 3, A) becomes attached to some
  firm object by the pole farthest from the mouth, and its growth
  preponderates in the direction of the principal axis, that is to say,
  the axis passing through the mouth (fig. 3, _a-b_). As a result the
  body becomes columnar in form (fig. 3, B), and without further change
  passes into the characteristic polyp-form (see POLYP).

  [Illustration: FIG. 3.--Diagram showing the change of the Actinula (A)
  into a Polyp (B); _a-b_, principal (vertical) axis; _c-d_, horizontal
  axis. The endoderm is shaded, the ectoderm is left clear.]

  It is convenient to distinguish two types of polyp by the names hydro
  polyp and anthopolyp, characteristic of the Hydrozoa and Anthozoa
  respectively. In the hydropolyp the body is typically elongated, the
  height of the column being far greater than the diameter. The
  peristome is relatively small and the mouth is generally raised on a
  projecting spout or _hypostome_. The ectoderm loses entirely the
  ciliation which it had in the planula and actinula stages and commonly
  secretes on its external surface a protective or supporting
  investment, the perisarc. Contrasting with this, the anthopolyp is
  generally of squat form, the diameter often exceeding the height; the
  peristome is wide, a hypostome is lacking, and the ectoderm, or so
  much of it as is exposed, i.e. not covered by secretion of skeletal or
  other investment, retains its ciliation throughout life. The internal
  structural differences are even more characteristic. In the hydropolyp
  the blastopore of the embryo forms the adult mouth situated at the
  extremity of the hypostome, and the ectoderm and endoderm meet at this
  point. In the anthopolyp the blastopore is carried inwards by an
  in-pushing of the body-wall of the region of the peristome, so that
  the adult mouth is an opening leading into a short ectodermal
  oesophagus or stomodaeum, at the bottom of which is the blastopore.
  Further, in the hydropolyp the digestive cavity either remains simple
  and undivided and circular in transverse section, or may show ridges
  projecting internally, which in this case are formed of endoderm
  alone, without any participation of the mesogloea. In the anthopolyp,
  on the other hand, the digestive cavity is always subdivided by
  so-called mesenteries, in-growths of the endoderm containing vertical
  lamellae of mesogloea (see ANTHOZOA). In short, the hydropolyp is
  characterized by a more simple type of organization than the
  anthopolyp, and is in most respects less modified from the actinula
  type of structure.

  [Illustration: FIG. 4.--Diagram showing the change of the Actinula
  into a Medusa. A, Vertical section of the actinula; _a-b_ and _c-d_ as
  in fig. 3, B, transitional stage, showing preponderating growth in the
  horizontal plane. C, C', D, D', two types of medusa organization; C
  and D are composite sections, showing a radius (R) on one side, an
  interradius (IR) on the other; C' and D' are plans; the mouth and
  manubrium are indicated at the centre, leading into the gastral cavity
  subdivided by the four areas of concrescence in each interradius (IR).
  t, tentacle; g.p, gastric pouch; r.c, radial canal not present in C
  and C'; c.c, circular or ring-canal; e.l, endoderm-lamella formed by
  concrescence. For a more detailed diagram of medusa-structure see
  article MEDUSA.]

  Returning now to the actinula, this form may, as already stated,
  develop into a medusa, a type of individual found only in the
  Hydrozoa, as here understood. To become a medusa, the actinula grows
  scarcely at all in the direction of the principal axis, but greatly
  along a plane at right angles to it. Thus the body becomes
  umbrella-shaped, the concave side representing the peristome, and the
  convex side the column, of the polyp. Hence the tentacles are found at
  the edge of the umbrella, and the hypostome forms usually a projecting
  tube, with the mouth at the extremity, forming the _manubrium_ or
  handle of the umbrella. The medusa has a pronounced radial symmetry,
  and the positions of the primary tentacles, usually four in number,
  mark out the so-called _radii_, alternating with which are four
  _interradii_. The ectoderm retains its ciliation only in the sensory
  organs. The mesogloea becomes enormously increased in quantity (hence
  the popular name "jelly-fish"), and in correlation with this the
  endoderm-layer lining the coelenteron becomes pressed together in the
  interradial areas and undergoes concrescence, forming a more or less
  complicated gastrovascular system (see MEDUSA). It is sufficient to
  state here that the medusa is usually a free-swimming animal, floating
  mouth downwards on the open seas, but in some cases it may be attached
  by its aboral pole, like a polyp, to some firm basis, either
  temporarily or permanently.

  Thus the development of the two types of individual seen in the
  Hydrozoa may be summarized as follows:--

                  /      Egg
                 |        |
    Free         |     Blastula
                 |        |
    "Planula"   <   Parenchymula
                 |        |
    Stage        |     Gastrula
                 |        |
                  \    Actinula
                         /  \
                        /    \
                     Polyp  Medusa

  This development, though probably representing the primitive sequence
  of events, is never actually found in its full extent, but is always
  abbreviated by omission or elimination of one or more of the stages.
  We have already seen that the parenchymula stage is passed over when
  the gastrulation is of the invaginate type. On the other hand, the
  parenchymula may develop directly into the actinula or even into the
  polyp, with suppression of the intervening steps. Great apparent
  differences may also be brought about by variations in the period at
  which the embryo is set free as a larva, and since two free-swimming
  stages, planula and actinula, are unnecessary, one or other of them is
  always suppressed. A good example of this is seen in two common genera
  of British hydroids, _Cordylophora_ and _Tabularia_. In _Cordylophora_
  the embryo is set free at the parenchymula stage as a planula which
  fixes itself and develops into a polyp, both gastrula and actinula
  stages being suppressed. In _Tubularia_, on the other hand, the
  parenchymula develops into an actinula within the maternal tissues,
  and is then set free, creeps about for a time, and after fixing
  itself, changes into a polyp; hence in this case the planula-stage, as
  a free larva, is entirely suppressed.

  The Hydrozoa may be defined, therefore, as Cnidaria in which two types
  of individual, the polyp and the medusa, may be present, each type
  developed along divergent lines from the primitive actinula form. The
  polyp (hydropolyp) is of simple structure and never has an ectodernal
  oesophagus or mesenteries.[1] The general ectoderm loses its cilia,
  which persist only in the sensory cells, and it frequently secretes
  external protective or supporting structures. An internal mesogloeal
  skeleton is not found.

  The class is divisible into two main divisions or sub-classes,
  Hydromedusae and Scyphomedusae, of which definitions and detailed
  systematic accounts will be found under these headings.

  GENERAL WORKS ON HYDROZOA.--C. Chun, "Coelenterata (Hohlthiere),"
  _Bronn's Klassen und Ordnungen des Thier-Reichs_ ii. 2 (1889 et seq.);
  Y. Delage, and E. Hérouard, _Traité de zoologie concrète_, ii. part 2,
  _Les Coelentérés_ (1901); G. H. Fowler, "The Hydromedusae and
  Scyphomedusae" in E. R. Lankester's _Treatise on Zoology_, ii.
  chapters iv. and v. (1900); S. J. Hickson, "Coelenterata and
  Ctenophora," _Cambridge Natural History_, i. chapters x.-xv. (1906).
       (E. A. M.)


FOOTNOTE:

  [1] See further under SCYPHOMEDUSAE.



HYENA, a name applicable to all the representatives of the mammalian
family _Hyaenidae_, a group of Carnivora (q.v.) allied to the civets.
From all other large Carnivora except the African hunting-dog, hyenas
are distinguished by having only four toes on each foot, and are further
characterized by the length of the fore-legs as compared with the hind
pair, the non-retractile claws, and the enormous strength of the jaws
and teeth, which enables them to break the hardest bones and to retain
what they have seized with unrelaxing grip.

[Illustration: FIG. 1.--The Striped Hyena (_Hyaena striata_).]

[Illustration: FIG. 2.--The Spotted Hyena (_Hyaena crocuta_).]

The striped hyena (_Hyaena striata_) is the most widely distributed
species, being found throughout India, Persia, Asia Minor, and North and
East Africa, the East African form constituting a distinct race, _H.
striata schillingsi_; while there are also several distinct Asiatic
races. The species resembles a wolf in size, and is greyish-brown In
colour, marked with indistinct longitudinal stripes of a darker hue,
while the legs are transversely striped. The hairs on the body are long,
especially on the ridge of the neck and back, where they form a distinct
mane, which is continued along the tail. Nocturnal in habits, it prefers
by day the gloom of caves and ruins, or of the burrows which it
occasionally forms, and issues forth at sunset, when it commences its
unearthly howling. When the animal is excited, the howl changes into
what has been compared to demoniac laughter, whence the name of
"laughing-hyena." These creatures feed chiefly on carrion, and thus
perform useful service by devouring remains which might otherwise
pollute the air. Even human dead are not safe from their attacks, their
powerful claws enabling them to gain access to newly interred bodies in
cemeteries. Occasionally (writes Dr W. T. Blanford) sheep or goats, and
more often dogs, are carried off, and the latter, at all events, are
often taken alive to the animal's den. This species appears to be
solitary in habits, and it is rare to meet with more than two together.
The cowardice of this hyena is proverbial; despite its powerful teeth,
it rarely attempts to defend itself. A very different animal is the
spotted hyena, _Hyaena (Crocuta) crocuta_, which has the sectorial teeth
of a more cat-like type, and is marked by dark-brown spots on a
yellowish ground, while the mane is much less distinct. At the Cape it
was formerly common, and occasionally committed great havoc among the
cattle, while it did not hesitate to enter the Kaffir dwellings at
night and carry off children sleeping by their mothers. By persistent
trapping and shooting, its numbers have now been considerably reduced,
with the result, however, of making it exceedingly wary, so that it is
not readily caught in any trap with which it has had an opportunity of
becoming acquainted. Its range extends from Abyssinia to the Cape. The
Abyssinian form has been regarded as a distinct species, under the name
of _H. liontiewi_, but this, like various more southern forms, is but
regarded as a local race. The brown hyena (_H. brunnea_) is South
African, ranging to Angola on the west and Kilimanjaro on the east. In
size it resembles the striped hyena, but differs in appearance, owing to
the fringe of long hair covering the neck and fore part of the back. The
general hue is ashy-brown, with the hair lighter on the neck (forming a
collar), chest and belly; while the legs are banded with dark brown.
This species is not often seen, as it remains concealed during the day.
Those frequenting the coast feed on dead fish, crabs and an occasional
stranded whale, though they are also a danger to the sheep and cattle
kraal. Strand-wolf is the local name at the Cape.

Although hyenas are now confined to the warmer regions of the Old World,
fossil remains show that they had a more northerly range during Tertiary
times; the European cave-hyena being a form of the spotted species,
known as _H. crocuta spelaea_. Fossil hyenas occur in the Lower Pliocene
of Greece, China, India, &c.; while remains indistinguishable from those
of the striped species have been found in the Upper Pliocene of England
and Italy.



HYÈRES, a town in the department of the Var in S.E. France, 11 m. by
rail E. of Toulon. In 1906 the population of the commune was 17,790, of
the town 10,464; the population of the former was more than doubled in
the last decade of the 19th century. Hyères is celebrated (as is also
its fashionable suburb, Costebelle, nearer the seashore) as a winter
health resort. The town proper is situated about 2½ m. from the
seashore, and on the south-western slope of a steep hill (669 ft.,
belonging to the Maurettes chain, 961 ft.), which is one of the
westernmost spurs of the thickly wooded Montagnes des Maures. It is
sheltered from the north-east and east winds, but is exposed to the cold
north-west wind or _mistral_. Towards the south and south-east a fertile
plain, once famous for its orange groves, but now mainly covered by
vineyards and farms, stretches to the sea, while to the south-west,
across a narrow valley, rises a cluster of low hills, on which is the
suburb of Costebelle. The older portion of the town is still surrounded,
on the north and east, by its ancient, though dilapidated medieval
walls, and is a labyrinth of steep and dirty streets. The more modern
quarter which has grown up at the southern foot of the hill has handsome
broad boulevards and villas, many of them with beautiful gardens, filled
with semi-tropical plants. Among the objects of interest in the old town
are: the house (Rue Rabaton, 7) where J. B. Massillon (1663-1742), the
famous pulpit orator, was born; the parish church of St Louis, built
originally in the 13th century by the Cordelier or Franciscan friars,
but completely restored in the earlier part of the 19th century; and the
site of the old château, on the summit of the hill, now occupied by a
villa. The plain between the new town and the sea is occupied by large
nurseries, an excellent _jardin d'acclimatation_, and many market
gardens, which supply Paris and London with early fruits and vegetables,
especially artichokes, as well as with roses in winter. There are
extensive salt beds (_salines_) both on the peninsula of Giens, S. of
the town, and also E. of the town. To the east of the Giens peninsula is
the fine natural harbour of Hyères, as well as three thinly populated
islands (the Stoechades of the ancients), Porquerolles, Port Cros and Le
Levant, which are grouped together under the common name of Îles
d'Hyères.

The town of Hyères seems to have been founded in the 10th century, as a
place of defence against pirates, and takes its name from the aires
(_hierbo_ in the Provençal dialect), or threshing-floors for corn, which
then occupied its site. It passed from the possession of the viscounts
of Marseilles to Charles of Anjou, count of Provence, and brother of St
Louis (the latter landed here in 1254, on his return from Egypt). The
château was dismantled by Henri IV., but thanks to its walls, the town
resisted in 1707 an attack made by the duke of Savoy.

  See Ch. Lenthéric, _La Provence Maritime ancienne et moderne_ (chap.
  5) (Paris, 1880).     (W. A. B. C.)



HYGIEIA, in Greek mythology, the goddess of health. It seems probable
that she was originally an abstraction, subsequently personified, rather
than an independent divinity of very ancient date. The question of the
original home of her worship has been much discussed. The oldest traces
of it, so far as is known at present, are to be found at Titane in the
territory of Sicyon, where she was worshipped together with Asclepius,
to whom she appears completely assimilated, not an independent
personality. Her cult was not introduced at Epidaurus till a late date,
and therefore, when in 420 B.C. the worship of Asclepius was introduced
at Athens coupled with that of Hygieia, it is not to be inferred that
she accompanied him from Epidaurus, or that she is a Peloponnesian
importation at all. It is most probable that she was invented at the
time of the introduction of Asclepius, after the sufferings caused by
the plague had directed special attention to sanitary matters. The
already existing worship of Athena Hygieia had nothing to do with
Hygieia the goddess of health, but merely denoted the recognition of the
power of healing as one of the attributes of Athena, which gradually
became crystallized into a concrete personality. At first no special
relationship existed between Asclepius and Hygieia, but gradually she
came to be regarded as his daughter, the place of his wife being already
secured by Epione. Later Orphic hymns, however, and Herodas iv. 1-9,
make her the wife of Asclepius. The cult of Hygieia then spread
concurrently with that of Asclepius, and was introduced at Rome from
Epidaurus in 293, by which time she may have been admitted (which was
not the case before) into the Epidaurian family of the god. Her proper
name as a Romanized Greek importation was Valetudo, but she was
gradually identified with Salus, an older genuine Italian divinity, to
whom a temple had already been erected in 302. While in classical times
Asclepius and Hygieia are simply the god and goddess of health, in the
declining years of paganism they are protecting divinities generally,
who preserve mankind not only from sickness but from all dangers on land
and sea. In works of art Hygieia is represented, together with
Asclepius, as a maiden of benevolent appearance, wearing the chiton and
giving food or drink to a serpent out of a dish.

  See the article by H. Lechat in Daremberg and Saglio's _Dictionnaire
  des antiquités_, with full references to authorities; and E. Thrämer
  in Roscher's _Lexikon der Mythologie_, with a special section on the
  modern theories of Hygieia.



HYGIENE (Fr. _hygiène_, from Gr. [Greek: hygiainein], to be healthy),
the science of preserving health, its practical aim being to render
"growth more perfect, decay less rapid, life more vigorous, death more
remote." The subject is thus a very wide one, embracing all the agencies
which affect the physical and mental well-being of man, and it requires
acquaintance with such diverse sciences as physics, chemistry, geology,
engineering, architecture, meteorology, epidemiology, bacteriology and
statistics. On the personal or individual side it involves consideration
of the character and quality of food and of water and other beverages;
of clothing; of work, exercise and sleep; of personal cleanliness, of
special habits, such as the use of tobacco, narcotics, &c.; and of
control of sexual and other passions. In its more general and public
aspects it must take cognizance of meteorological conditions, roughly
included under the term climate; of the site or soil on which dwellings
are placed; of the character, materials and arrangement of dwellings,
whether regarded individually or in relation to other houses among which
they stand; of their heating and ventilation; of the removal of excreta
and other effete matters; of medical knowledge relating to the incidence
and prevention of disease; and of the disposal of the dead.

  These topics will be found treated in such articles as DIETETICS,
  FOOD, FOOD-PRESERVATION, ADULTERATION, WATER, HEATING, VENTILATION,
  SEWERAGE, BACTERIOLOGY, HOUSING, CREMATION, &c. For legal enactments
  which concern the sanitary well-being of the community, see PUBLIC
  HEALTH.



HYGINUS, eighth pope. It was during his pontificate (c. 137-140) that
the gnostic heresies began to manifest themselves at Rome.



HYGINUS (surnamed GROMATICUS, from _gruma_, a surveyor's measuring-rod),
Latin writer on land-surveying, flourished in the reign of Trajan (A.D.
98-117). Fragments of a work on legal boundaries attributed to him will
be found in C. F. Lachmann, _Gromatici Veteres_, i. (1848).

  A treatise on Castrametation (_De Munitionibus Castrorum_), also
  attributed to him, is probably of later date, about the 3rd century
  A.D. (ed. W. Gemoll, 1879; A. von Domaszewski, 1887).



HYGINUS, GAIUS JULIUS, Latin author, a native of Spain (or Alexandria),
was a pupil of the famous Cornelius Alexander Polyhistor and a freedman
of Augustus, by whom he was made superintendent of the Palatine library
(Suetonius, _De Grammaticis_, 20). He is said to have fallen into great
poverty in his old age, and to have been supported by the historian
Clodius Licinus. He was a voluminous author, and his works included
topographical and biographical treatises, commentaries on Helvius Cinna
and the poems of Virgil, and disquisitions on agriculture and
bee-keeping. All these are lost.

  Under the name of Hyginus two school treatises on mythology are
  extant: (1) _Fabularum Liber_, some 300 mythological legends and
  celestial genealogies, valuable for the use made by the author of the
  works of Greek tragedians now lost; (2) _De Astronomia_, usually
  called _Poetica Astronomica_, containing an elementary treatise on
  astronomy and the myths connected with the stars, chiefly based on the
  [Greek: Katasterismoi] of Eratosthenes. Both are abridgments and both
  are by the same hand; but the style and Latinity and the elementary
  mistakes (especially in the rendering of the Greek originals) are held
  to prove that they cannot have been the work of so distinguished a
  scholar as C. Julius Hyginus. It is suggested that these treatises are
  an abridgment (made in the latter half of the 2nd century) of the
  _Genealogiae_ of Hyginus by an unknown grammarian, who added a
  complete treatise on mythology.

  EDITIONS.--_Fabulae_, by M. Schmidt (1872); _De Astronomia_, by B.
  Bunte (1875); see also Bunte, _De C. Julii Hygini, Augusti Liberti,
  Vita et Scriptis_ (1846).



HYGROMETER (Gr. [Greek: hygros], moist, [Greek: metron], a measure), an
instrument for measuring the absolute or relative amount of moisture in
the atmosphere; an instrument which only qualitatively determines
changes in the humidity is termed a "hygroscope." The earlier
instruments generally depended for their action on the contraction or
extension of substances when exposed to varying degrees of moisture;
catgut, hair, twisted cords and wooden laths, all of which contract with
an increase in the humidity and vice versa, being the most favoured
materials. The familiar "weather house" exemplifies this property. This
toy consists of a house provided with two doors, through which either a
man or woman appears according as the weather is about to be wet or
fine. This action is effected by fixing a catgut thread to the base on
which the figures are mounted, in such a manner that contraction of the
thread rotates the figures so that the man appears and extension so that
the woman appears.

  Many of the early forms are described in C. Hutton, _Math. and Phil.
  Dictionary_ (1815). The modern instruments, which utilize other
  principles, are described in METEOROLOGY: II. _Methods and Apparatus_.



HYKSOS, or "SHEPHERD KINGS," the name of the earliest invaders of Egypt
of whom we have definite evidence in tradition. Josephus (c. _Apion._ i.
14), who identifies the Hyksos with the Israelites, preserves a passage
from the second book of Manetho giving an account of them. (It may be
that Josephus had it, not direct from Manetho's writings, but through
the garbled version of some Alexandrine compiler.) In outline it is as
follows. In the days of a king of Egypt named Timaeus the land was
suddenly invaded from the east by men of ignoble race, who conquered it
without a struggle, destroyed cities and temples, and slew or enslaved
the inhabitants. At length they elected a king named Salatis, who,
residing at Memphis, made all Egypt tributary, and established garrisons
in different parts, especially eastwards, fearing the Assyrians. He
built also a great fortress at Avaris, in the Sethroite nome, east of
the Bubastite branch of the Nile. Salatis was followed in succession by
Beon, Apachnas, Apophis, Jannas and Asses. These six kings reigned 198
years and 10 months, and all aimed at extirpating the Egyptians. Their
whole race was named Hyksos, i.e. "shepherd kings," and some say they
were Arabs (another explanation found by Josephus is "captive
shepherds"). When they and their successors had held Egypt for 511
years, the kings of the Thebais and other parts of Egypt rebelled, and a
long and mighty war began. Misphragmuthosis worsted the "Shepherds" and
shut them up in Avaris; and his son Thutmosis, failing to capture the
stronghold, allowed them to depart; whereupon they went forth, 240,000
in number, established themselves in Judea and built Jerusalem.

In Manetho's list of kings, the six above named (with many variations in
detail) form the XVth dynasty, and are called "six foreign Phoenician
kings." The XVIth dynasty is of thirty-two "Hellenic (_sic?_) shepherd
kings," the seventeenth is of "shepherds and Theban kings" (reigning
simultaneously). The lists vary greatly in different versions, but the
above seems the most reasonable selection of readings to be made. For
"Hellenic" see below. The supposed connexion with the Israelites has
made the problem of the Hyksos attractive, but light is coming upon it
very slowly. In 1847 E. de Rougé proved from a fragment of a story in
the papyri of the British Museum, that Apopi was one of the latest of
the Hyksos kings, corresponding to Aphobis; he was king of the "pest"
and suppressed the worship of the Egyptian gods, and endeavoured to make
the Egyptians worship his god Setekh or Seti; at the same time an
Egyptian named Seqenenre reigned in Thebes, more or less subject to
Aphobis. The city of Hawari (Avaris) was also mentioned in the fragment.

In 1850 a record of the capture of this city from the Hyksos by Ahmosi,
the founder of the eighteenth dynasty, was discovered by the same
scholar. A large class of monuments was afterwards attributed to the
Hyksos, probably in error. Some statues and sphinxes, found in 1861 by
Mariette at Tanis (in the north-east of the Delta), which had been
usurped by later kings, had peculiar "un-Egyptian" features. One of
these bore the name of Apopi engraved lightly on the shoulder; this was
evidently a usurper's mark, but from the whole circumstances it was
concluded that these, and others of the same type of features found
elsewhere, must have belonged to the Hyksos. This view held the field
until 1893, when Golénischeff produced an inferior example bearing its
original name, which showed that in this case it represented Amenemhe
III. In consequence it is now generally believed that they all belong to
the twelfth dynasty. Meanwhile a headless statue of a king named Khyan,
found at Bubastis, was attributed on various grounds to the Hyksos, the
soundest arguments being his foreign name and the boastful un-Egyptian
epithet "beloved of his _ka_," where "beloved of Ptah" or some other god
was to be expected. His name was immediately afterwards recognized on a
lion found as far away from Egypt as Bagdad. Flinders Petrie then
pointed out a group of kings named on scarabs of peculiar type, which,
including Khyan, he attributed to the period between the Old Kingdom and
the New, while others were in favour of assigning them all to the
Hyksos, whose appellation seemed to be recognizable in the title
Hek-khos, "ruler of the barbarians," borne by Khyan. The extraordinary
importance of Khyan was further shown by the discovery of his name on a
jar-lid at Cnossus in Crete. Semitic features were pointed out in the
supposed Hyksos names, and Petrie was convinced of their date by his
excavations of 1905-1906 in the eastern Delta. Avaris is generally
assigned to the region towards Pelusium on the strength of its being
located in the Sethroite nome by Josephus, but Petrie thinks it was at
Tell el-Yahudiyeh (Yehudia), where Hyksos scarabs are common. From the
remains of fortifications there he argues that the Hyksos were
uncivilized desert people, skilled in the use of the bow, and must thus
have destroyed by their archery the Egyptian armies trained to fight
hand-to-hand; further, that their hordes were centered in Syria, but
were driven thence by a superior force in the East to take refuge in the
islands and became a sea-power--whence the strange description
"Hellenic" in Manetho, which most editors have corrected to [Greek:
alloi], "others." Besides the statue of Khyan, blocks of granite with
the name of Apopi have been found in Upper Egypt at Gebelen and in
Lower Egypt at Bubastis. The celebrated Rhind mathematical papyrus was
copied in the reign of an Apopi from an original of the time of Amenemhe
III. Large numbers of Hyksos scarabs are found in Upper and Lower Egypt,
and they are not unknown in Palestine. Khyan's monuments, inconspicuous
as they are, actually extend over a wider area--from Bagdad to
Cnossus--than those of any other Egyptian king.

It is certain that this mysterious people were Asiatic, for they are
called so by the Egyptians. Though Seth was an Egyptian god, as god of
the Hyksos he represents some Asiatic deity. The possibility of a
connexion between the Hyksos and the Israelites is still admitted in
some quarters. Hatred of these impious foreigners, of which there is
some trace in more than one text, aroused amongst the Egyptians (as
nothing ever did before or since) that martial spirit which carried the
armies of Tethmosis to the Euphrates.

  Besides the histories of Egypt, see J. H. Breasted, _Ancient Records
  of Egypt_; Historical Documents ii. 4, 125; G. Maspero, _Contes
  populaires_, 3me éd. p. 236; W. M. F. Petrie, _Hyksos and Israelite
  Cities_, p. 67; Golénischeff in _Recueil de travaux_, xv. p. 131.
       (F. Ll. G.)



HYLAS, In Greek legend, son of Theiodamas, king of the Dryopians in
Thessaly, the favourite of Heracles and his companion on the Argonautic
expedition. Having gone ashore at Kios in Mysia to fetch water, he was
carried off by the nymphs of the spring in which he dipped his pitcher.
Heracles sought him in vain, and the answer of Hylas to his
thrice-repeated cry was lost in the depths of the water. Ever
afterwards, in memory of the threat of Heracles to ravage the land if
Hylas were not found, the inhabitants of Kios every year on a stated day
roamed the mountains, shouting aloud for Hylas (Apollonius Rhodius i.
1207; Theocritus xiii.; Strabo xii. 564; Propertius i. 20; Virgil,
_Ecl._ vi. 43). But, although the legend is first told in Alexandrian
times, the "cry of Hylas" occurs long before as the "Mysian cry" in
Aeschylus (_Persae_, 1054), and in Aristophanes (_Plutus_, 1127) "to cry
Hylas" is used proverbially of seeking something in vain. Hylas, like
Adonis and Hyacinthus, represents the fresh vegetation of spring, or the
water of a fountain, which dries up under the heat of summer. It is
suggested that Hylas was a harvest deity and that the ceremony gone
through by the Kians was a harvest festival, at which the figure of a
boy was thrown into the water, signifying the dying vegetation-spirit of
the year.

  See G. Türk in _Breslauer Philologische Abhandlungen_, vii. (1895); W.
  Mannhardt, _Mythologische Forschungen_ (1884).



HYLOZOISM (Gr. [Greek: hylê], matter, [Greek: zôê], life), in
philosophy, a term applied to any system which explains all life,
whether physical or mental, as ultimately derived from matter ("cosmic
matter," _Weldstoff_). Such a view of existence has been common
throughout the history of thought, and especially among physical
scientists. Thus the Ionian school of philosophy, which began with
Thales, sought for the beginning of all things in various material
substances, water, air, fire (see IONIAN SCHOOL). These substances were
regarded as being in some sense alive, and taking some active part in
the development of being. This primitive hylozoism reappeared in
modified forms in medieval and Renaissance thought, and in modern times
the doctrine of materialistic monism is its representative. Between
modern materialism and hylozoism proper there is, however, the
distinction that the ancients, however vaguely, conceived the elemental
matter as being in some sense animate if not actually conscious and
conative.



HYMEN, or HYMENAEUS, originally the name of the song sung at marriages
among the Greeks. As usual the name gradually produced the idea of an
actual person whose adventures gave rise to the custom of this song. He
occurs often in association with Linus and Ialemus, who represent
similar personifications, and is generally called a son of Apollo and a
Muse. As the son of Dionysus and Aphrodite, he was regarded as a god of
fruitfulness. In Attic legend he was a beautiful youth who, being in
love with a girl, followed her in a procession to Eleusis disguised as a
woman, and saved the whole band from pirates. As reward he obtained the
girl in marriage, and his happy married life caused him ever afterwards
to be invoked in marriage songs (Servius on Virgil, _Aen._ i. 651).
According to another story, he was a youth who was killed by the fall of
his house on his wedding day; hence he was invoked, to propitiate him
and avert a similar fate from others (Servius, loc. cit.). He is
represented in works of art as an effeminate-looking, winged youth,
carrying a bridal torch and wearing a nuptial veil. The marriage song
was sung, with musical accompaniment, during the procession of the bride
from her parents' house to that of the bridegroom, Hymenaeus being
invoked at the end of each portion.

  See R. Schmidt, _De Hymenaeo el Talasio_ (1886), and J. A. Hild in
  Daremberg and Saglis's _Dictionnaire des antiquités_.



HYMENOPTERA (Gr. [Greek: hymên], a membrane, and [Greek: pteron], a
wing), a term used in zoological classification for one of the most
important orders of the class _Hexapoda_ (q.v.). The order was founded
by Linnaeus (_Systema Naturae_, 1735), and is still recognized by all
naturalists in the sense proposed by him, to include the saw-flies,
gall-flies, ichneumon-flies and their allies, ants, wasps and bees. The
relationship of the Hymenoptera to other orders of insects is discussed
in the article HEXAPODA, but it may be mentioned here that in structure
the highest members of the order are remarkably specialized, and that in
the perfection of their instincts they stand at the head of all insects
and indeed of all invertebrate animals. About 30,000 species of
Hymenoptera are now known.

[Illustration: After C. L. Marlatt, _Bur. Ent. Bull. 3, N.S., U.S. Dept.
Agric._

FIG. 1.--A, Front of head of Saw-fly (_Pachynematus_); a, labrum; b,
clypeus; c, vertex; d, d, antennal cavities. C and D, Mandibles. E,
First maxilla; a, cardo; b, stipes; c, galea; d, lacinia; e, palp. B,
Second maxillae (Labium); a, mentum; b, ligula (between the two galeae);
c, c, palps. Magnified.]

[Illustration: FIG. 2.--Jaws of Hive-bee (_Apis mellifica_). Magnified
about 6½ times. a, mandible; b, c, palp and lacinia of first maxilla; d,
e, g, h, mentum, palp, fused laciniae (ligula or "tongue") and galea of
2nd maxillae.]

[Illustration: After C. Janet, _Mem. Soc. Zool. France_ (1898).

FIG. 3.--Median section through mid-body of female Red Ant (_Myrmica
rubra_). H, Head; 1, 2, 3, the thoracic segments; i., ii., the first and
second abdominal segments; i., being the propodeum.]

  _Characters._--In all Hymenoptera the mandibles (fig. 1, C, D) are
  well developed, being adapted, as in the more lowly winged insects,
  such as the Orthoptera, for biting. The more generalized Hymenoptera
  have the second maxillae but slightly modified, their inner lobes
  being fused to form a _ligula_ (fig. 1, B, b). In the higher families
  this structure becomes elongated (fig. 2, g) so as to form an
  elaborate sucking-organ or "tongue." These insects are able,
  therefore, to bite as well as to suck, whereas most insects which have
  acquired the power of suction have lost that of biting. Both fore- and
  hind-wings are usually present, both pairs being membranous, the
  hind-wings small and not folded when at rest, each provided along the
  costa with a row of curved hooks which catch on to a fold along the
  dorsum of the adjacent fore-wing during flight. A large number of
  Hymenoptera are, however, entirely wingless--at least as regards one
  sex or form of the species. One of the most remarkable features is the
  close union of the foremost abdominal segment (fig. 3, i.) with the
  metathorax, of which it often seems to form a part, the apparent first
  abdominal segment being, in such case, really the second (fig. 3,
  ii.). The true first segment, which undergoes a more or less complete
  fusion with the thorax is known as the "median segment" or
  _propodeum_. In female Hymenoptera the typical insectan ovipositor
  with its three pairs of processes is well developed, and in the higher
  families this organ becomes functional as a sting (fig. 5),--used for
  offence and defence. As regards their life history, all Hymenoptera
  undergo a "complete" metamorphosis. The larva is soft-skinned
  (eruciform), being either a caterpillar (fig. 6, b) or a legless grub
  (fig. 7, a), and the pupa is free (fig. 7, c), i.e. with the
  appendages not fixed to the body, as is the case in the pupa of most
  moths.

  [Illustration: FIG. 4.--Fore-Wings of Hymenoptera.

    1. Tenthredinidae (_Hylotoma_)-- 1, marginal; 2, appendicular; 3, 4,
      5, 6, radial or submarginal; 7, 8, 9, median or discoidal; 10,
      sub-costal; 11, 12, cubital or branchial; and 13, anal or lanceolate
      cellules; a, b, c, submarginal nervures; d, basal nervures; e, f,
      recurrent nervures; st, stigma; co, costa.
    2. Cynipidae (_Cynips_).
    3. Chalcididae (_Perilampus_).
    4. Proctotrypidae (_Codrus_).
    5. Mymaridae (_Mymar_).
    6. Braconidae (_Bracon_).
    7. Ichneumonidae (_Trogus_).
    8. Chrysididae (_Cleptes_).
    9. Formicidae (_Formica_).
    10. Vespidae (_Vespa_).
    11. Apidae (_Apathus_).]

  _Structure._--The head of a hymenopterous insect bears three simple
  eyes (ocelli) on the front and vertex in addition to the large
  compound eyes. The feelers are generally simple in type, rarely
  showing serrations or prominent appendages; but one or two basal
  segments are frequently differentiated to form an elongate "scape,"
  the remaining segments--carried at an elbowed angle to the
  scape--making up the "flagellum"; the segments of the flagellum often
  bear complex sensory organs. The general characters of the jaws have
  been mentioned above, and in detail there is great variation in these
  organs among the different families. The sucking tongue of the
  Hymenoptera has often been compared with the hypopharynx of other
  insects. According to D. Sharp, however, the hypopharynx is present in
  all Hymenoptera as a distinct structure at the base of the "tongue,"
  which must be regarded as representing the fused laciniae of the
  second maxillae. In the thorax the pronotum and prosternum are closely
  associated with the mesothorax, but the pleura of the prothorax are
  usually shifted far forwards, so that the fore-legs are inserted just
  behind the head. A pair of small plates--the tegulae--are very
  generally present at the bases of the fore-wings. The union of the
  first abdominal segment with the metathorax has been already
  mentioned. The second (so-called "first") abdominal segment is often
  very constricted, forming the "waist" so characteristic of wasps and
  ants for example. The constriction of this segment and its very
  perfect articulation with the propodeum give great mobility to the
  abdomen, so that the ovipositor or sting can be used with the greatest
  possible accuracy and effect.

  Mention has already been made of the series of curved hooks along the
  costa of the hind-wing; by means of this arrangement the two wings of
  a side are firmly joined together during flight, which thus becomes
  particularly accurate. The wings in the Hymenoptera show a marked
  reduction in the number of nervures as compared with more primitive
  insects. The main median nervure, and usually also the sub-costal
  become united with the radial, while the branches of radial, median
  and cubital nervures pursuing a transverse or recurrent course across
  the wing, divide its area into a number of areolets or "cells," that
  are of importance in classification. Among many of the smaller
  Hymenoptera we find that the wings are almost destitute of nervures.
  In the hind-wings--on account of their reduced size--the nervures are
  even more reduced than in the fore-wings.

  The legs of Hymenoptera are of the typical insectan form, and the foot
  is usually composed of five segments. In many families the trochanter
  appears to be represented by two small segments, there being thus an
  extra joint in the leg. It is almost certain that the distal of these
  two segments really belongs to the thigh, but the ordinary
  nomenclature will be used in the present article, as this character is
  of great importance in discriminating families, and the two segments
  in question are referred to the trochanter by most systematic writers.

  [Illustration: After C. Janet, _Aiguillon de la Myrmica rubra_ (Paris,
  1898).

  FIG. 5.--Ovipositor or Sting of Red Ant (_Myrmica rubra_) Queen.
  Magnified. The right sheath C (outer process of the ninth abdominal
  segment--9) is shown in connexion with the guide B formed by the inner
  processes of the 9th segment. The stylet A (process of the 8th
  abdominal segment--8) is turned over to show its groove a, which works
  along the tongue or rail b.]

  The typical insectan ovipositor, so well developed among the
  Hymenoptera, consists of three pairs of processes (gonapophyses) two
  of which belong to the ninth abdominal segment and one to the eighth.
  The latter are the cutting or piercing stylets (fig. 5, A) of the
  ovipositor, while the two outer processes of the ninth segment are
  modified into sheaths or feelers (fig. 5, C) and the two inner
  processes form a guide (fig. 5, B) on which the stylets work, tongues
  or rails on the "guide" fitting accurately into longitudinal grooves
  on the stylet. In the different families of the Hymenoptera, there are
  various modifications of the ovipositor, in accord with the habits of
  the insects and the purposes to which the organ is put. The sting of
  wasps, ants and bees is a modified ovipositor and is used for
  egg-laying by the fertile females, as well as for defence. Most male
  Hymenoptera have processes which form claspers or genital armature.
  These processes are not altogether homologous with those of the
  ovipositor, being formed by inner and outer lobes of a pair of
  structures on the ninth abdominal segment.

  Many points of interest are to be noted in the internal structure of
  the Hymenoptera. The gullet leads into a moderate-sized crop, and
  several pairs of salivary glands open into the mouth. The crop is
  followed by a proventriculus which, in the higher Hymenoptera, forms
  the so-called "honey stomach," by the contraction of whose wails the
  solid and liquid food can be separated, passed on into the digestive
  stomach, or held in the crop ready for regurgitation into the mouth.
  Behind the digestive stomach are situated, as usual, intestine and
  rectum, and the number of kidney (Malpighian) tubes varies from only
  six to over a hundred, being usually great.

  In the female, each ovary consists of a large number of ovarian tubes,
  in which swollen chambers containing the egg-cells alternate with
  smaller chambers enclosing nutrient material. In connexion with the
  ovipositor are two poison-glands, one acid and the other alkaline in
  its secretion. The acid gland consists of one, two or more tubes, with
  a cellular coat of several layers, opening into a reservoir whence
  the duct leads to the exterior. The alkaline gland is an irregular
  tube with a single cellular layer, its duct opening alongside that of
  the acid reservoir. These glands are most strongly developed when the
  ovipositor is modified into a sting.

  _Development._--Parthenogenesis is of normal occurrence in the
  life-cycle of many Hymenoptera. There are species of gall-fly in which
  males are unknown, the unfertilized eggs always developing into
  females. On the other hand, in certain saw-flies and among the higher
  families, the unfertilized eggs, capable of development, usually give
  rise to male insects (see BEE). The larvae of most saw-flies feeding
  on the leaves of plants are caterpillars (fig. 6, b) with numerous
  abdominal pro-legs, but in most families of Hymenoptera the egg is
  laid in such a situation that an abundant food-supply is assured
  without exertion on the part of the larva, which is consequently a
  legless grub, usually white in colour, and with soft flexible cuticle
  (fig. 7, a). The organs and instincts for egg-laying and
  food-providing are perhaps the most remarkable features in the economy
  of the Hymenoptera. Gall-fly grubs are provided with vegetable food
  through the eggs being laid by the mother insect within plant tissues.
  The ichneumon pierces the body of a caterpillar and lays her eggs
  where the grubs will find abundant animal food. A digging-wasp hunts
  for insect prey and buries it with the egg, while a true wasp feeds
  her brood with captured insects, as a bird her fledglings. Bees store
  honey and pollen to serve as food for their young. Thus we find
  throughout the order a degree of care for offspring unreached by other
  insects, and this family-life has, in the best known of the
  Hymenoptera--ants, wasps and bees--developed into an elaborate social
  organization.

_Social Life._--The development of a true insect society among the
Hymenoptera is dependent on a differentiation among the females between
individuals with well-developed ovaries ("queens") whose special
function is reproduction; and individuals with reduced or aborted
ovaries ("workers") whose duty is to build the nest, to gather food and
to tend and feed the larvae. Among the wasps the workers may only differ
from the queens in size, and individuals intermediate between the two
forms of female may be met with. Further, the queen wasp, and also the
queen humble-bee, commences unaided the work of building and founding a
new nest, being afterwards helped by her daughters (the workers) when
these have been developed. In the hive-bee and among ants, on the other
hand, there are constant structural distinctions between queen and
worker, and the function of the queen bee in a hive is confined to
egg-laying, the labour of the community being entirely done by the
workers. Many ants possess several different forms of worker, adapted
for special duties. Details of this fascinating subject are given in the
special articles ANT, BEE and WASP (q.v.).

_Habits and Distribution._--Reference has been already made to the
various methods of feeding practised by Hymenoptera in the larval stage,
and the care taken of or for the young throughout the order leads in
many cases to the gathering of such food by the mother or nurse. Thus,
wasps catch flies; worker ants make raids and carry off weak insects of
many kinds; bees gather nectar from flowers and transform it into honey
within their stomachs--largely for the sake of feeding the larvae in the
nest. The feeding habits of the adult may agree with that of the larva,
or differ, as in the ease of wasps which feed their grubs on flies, but
eat principally vegetable food themselves. The nest-building habit is
similarly variable. Digging wasps make simple holes in the ground; many
burrowing bees form branching tunnels; other bees excavate timber or
make their brood-chambers in hollow plant-stems; wasps work up with
their saliva vegetable fibres bitten off tree-bark to make paper; social
bees produce from glands in their own bodies the wax whence their
nest-chambers are built. The inquiline habit ("cuckoo-parasitism"), when
one species makes use of the labour of another by invading the nest and
laying her eggs there, is of frequent occurrence among Hymenoptera; and
in some cases the larva of the intruder is not content with taking the
store of food provided, but attacks and devours the larva of the host.

Most Hymenoptera are of moderate or small size, the giants of the
order--certain saw-flies and tropical digging-wasps--never reach the bulk
attained by the largest beetles, while the wing-spread is narrow compared
with that of many dragon-flies and moths. On the other hand, there are
thousands of very small species, and the tiny "fairy-flies"
(_Mymaridae_), whose larvae live as parasites in the eggs of various
insects, are excessively minute for creatures of such complex
organization. Hymenoptera are probably less widely distributed than
Aptera, Coleoptera or Diptera, but they are to be found in all except the
most inhospitable regions of the globe. The order is, with few
exceptions, terrestrial or aerial in habit. Comparatively only a few
species are, for part of their lives, denizens of fresh water; these, as
larvae, are parasitic on the eggs or larvae of other aquatic insects, the
little hymenopteron, _Polynema natans_, one of the "fairy-flies"--swims
through the water by strokes of her delicate wings in search of a
dragon-fly's egg in which to lay her own egg, while the rare _Agriotypus_
dives after the case of a caddis-worm. It is of interest that the waters
have been invaded by the parasitic group of the Hymenoptera, since in
number of species this is by far the largest of the order. No group of
terrestrial insects escapes their attacks--even larvae boring in wood are
detected by ichneumon flies with excessively long ovipositors. Not a few
cases are known in which a parasitic larva is itself pierced by the
ovipositor of a "hyperparasite," and even the offspring of the latter may
itself fall a victim to the attack of a "tertiary parasite."

  _Fossil History._--Very little is known of the history of the
  Hymenoptera previous to the Tertiary epoch, early in which, as we know
  from the evidence of many Oligocene and Miocene fossils, all the more
  important families had been differentiated. Fragments of wings from
  the Lias and Oolitic beds have been referred to ants and bees, but the
  true nature of these remains is doubtful.

_Classification._--Linnaeus divided the Hymenoptera into two
sections--the Terebrantia, whose females possess a cutting or piercing
ovipositor, and the Aculeata, in which the female organ is modified into
a sting. This nomenclature was adopted by P. A. Latreille and has been
in general use until the present day. A closely similar division of the
order results from T. Hartig's character drawn from the
trochanter--whether of two segments or undivided--the groups being
termed respectively Ditrocha and Monotrocha. But the most natural
division is obtained by the separation of the saw-flies as a primitive
sub-order, characterized by the imperfect union of the first abdominal
segment with the thorax, and by the broad base of the abdomen, so that
there is no median constriction or "waist," and by the presence of
thoracic legs--usually also of abdominal pro-legs--in the larva. All the
other families of Hymenoptera, including the gall-flies, ichneumons and
aculeates, have the first abdominal segment closely united with the
thorax, the second abdominal segment constricted so as to form a narrow
stalk or "waist," and legless larvae without a hinder outlet to the
food-canal. These two sub-orders are usually known as the
_Sessiliventra_ and _Petioliventra_ respectively, but the names
_Symphyta_ and _Apocrita_ proposed in 1867 by C. Gerstaecker have
priority, and should not be replaced.


  _Symphyta._

  This sub-order, characterized by the "sessile," broad-based abdomen,
  whose first segment is imperfectly united with the thorax, and by the
  usually caterpillar-like larvae with legs, includes the various groups
  of saw-flies. Three leading families may be mentioned. The _Cephidae_,
  or stem saw-flies, have an elongate pronotum, a compressed abdomen,
  and a single spine on the shin of the fore-leg. The soft, white larvae
  have the thoracic legs very small and feed in the stems of various
  plants. _Cephus pygmaeus_ is a well-known enemy of corn crops. The
  _Siricidae_ ("wood-wasps") are large elongate insects also with one
  spine on each fore-shin, but with the pronotum closely joined to the
  mesothorax. The ovipositor is long and prominent, enabling the female
  insect to lay her eggs in the wood of trees, where the white larvae,
  whose legs are excessively short, tunnel and feed. These insects are
  adorned with bands of black and yellow, or with bright metallic
  colours, and on account of their large size and formidable ovipositors
  they often cause needless alarm to persons unfamiliar with their
  habits. The _Tenthredinidae_, or true saw-flies, are distinguished by
  two spines on each fore-shin, while the larvae are usually
  caterpillars, with three pairs of thoracic legs, and from six to eight
  pairs of abdominal pro-legs the latter not possessing the hooks found
  on the pro-legs of lepidopterous caterpillars. Most saw-fly larvae
  devour leaves, and the beautifully serrate processes of the ovipositor
  are well adapted for egg-laying in plant tissues. Some saw-fly larvae
  are protected by a slimy secretion (fig. 6, c) and a few live
  concealed in galls. In the form of the feelers, the wing-neuration and
  minor structural details there is much diversity among the saw-flies.
  They have been usually regarded as a single family, but W. H. Ashmead
  has lately differentiated eleven families of them.


  _Apocrita._

  This sub-order includes the vast majority of the Hymenoptera,
  characterized by the narrowly constricted waist in the adult and by
  the legless condition of the larva. The trochanter is simple in some
  genera and divided in others. With regard to the minor divisions of
  this group, great difference of opinion has prevailed among students.
  In his recent classification Ashmead (1901) recognizes seventy-nine
  families arranged under eight "super-families." The number of species
  included in this division is enormous, and the multiplication of
  families is, to some extent, a natural result of increasingly close
  study. But the distinctions between many of these rest on
  comparatively slight characters, and it is likely that the future
  discovery of new genera may abolish many among such distinctions as
  may now be drawn. It seems advisable, therefore, in the present
  article to retain the wider conception of the family that has hitherto
  contented most writers on the Hymenoptera. Ashmead's "super-families"
  have, however, been adopted as--founded on definite structural
  characters--they probably indicate relationship more nearly than the
  older divisions founded mostly on habit. The Cynipoidea include the
  gall-flies and their parasitic relations. In the Chalcidoidea,
  Ichneumonoidea and Proctotrypoidea will be found nearly all the
  "parasitic Hymenoptera" of older classifications. The Formicoidea are
  the ants. The group of Fossores, or "digging-wasps," is divided by
  Ashmead, one section forming the Sphecoidea, while the other, together
  with the Chrysidae and the true wasps, make up the Vespoidea. The
  Apoidea consists of the bees only.

  [Illustration: After Marlatt, _Ent. Circ._ 26, U.S. Dept. Agric.

  FIG. 6.--a, Pear Saw-fly (_Eriocampoides limacina_); b, larva without,
  and c, with its slimy protective coat; e, cocoon; f, larva before
  pupation; g, pupa, magnified; d, leaves with larvae.]

  [Illustration: After Howard, _Ent. Tech. Bull._ 5 U.S. Dept. Agric.

  FIG. 7.--Chalcid (_Dibrachys boucheanus_), a hyper-parasite.

    a, Larva.
    d, Its head more highly magnified.
    b, Female fly.
    c, Pupa of male.
    e, Feeler.]

  _Cynipoidea._--In this division the ovipositor issues from the ventral
  surface of the abdomen; the pronotum reaches back to the tegulae; the
  trochanter has two segments; the fore-wing (fig. 4, 2) has no stigma,
  but one or two areolets. The feelers with twelve to fifteen segments
  are thread-like and straight. All the insects included in this group
  are small and form two families--the Cynipidae and the Figitidae. They
  are the "gall-flies," many of the species laying eggs in various
  plant-tissues where the presence of the larva causes the formation of
  a pathological growth or gall, always of a definite form and
  characteristic of the species; the "oak-apple" and the bedeguar of
  the rose are familiar examples. Other flies of this group have the
  inquiline habit, laying their eggs in the galls of other species,
  while others again pierce the cuticle of maggots or aphids, in whose
  bodies their larvae live as parasites.

  _Chalcidoidea._--This division resembles the Cynipoidea in the
  position of the ovipositor, and in the two segmented trochanters. The
  fore-wing also has no stigma, and the whole wing is almost destitute
  of nervures and areolets, while the pronotum does not reach back to
  the tegulae, and the feelers are elbowed (fig. 7). The vast majority
  of this group, including nearly 5000 known species, are usually
  reckoned as a single family, the _Chalcididae_, comprising small
  insects, often of bright metallic colours, whose larvae are parasitic
  in insects of various orders. The "fig-insects," whose presence in
  ripening figs is believed essential to the proper development of the
  fruit, belong to _Blastophaga_ and other genera of this family. They
  are remarkable in having wingless males and winged females. The
  "polyembryonic" development of an _Encyrtus_, as studied by P.
  Marchal, is highly remarkable. The female lays her egg in the egg of a
  small ermine moth (_Hyponomeuta_) and the egg gives rise not to a
  single embryo but to a hundred, which develop as the host-caterpillar
  develops, being found at a later stage within the latter enveloped in
  a flexible tube.

  The _Mymaridae_ or "fairy-flies" are distinguished from the
  _Chalcididae_ by their narrow fringed wings (figs. 4, 5) and by the
  situation of the ovipositor just in front of the tip of the abdomen.
  They are among the most minute of all insects and their larvae are
  probably all parasitic in insects' eggs.

  [Illustration: After Riley and Howard, _Insect Life_, vol. i.

  FIG. 8.--Ichneumon Fly (_Rhyssa per-suasoria_) ovipositing.]

  _Ichneumonoidea._--The ten thousand known species included in this
  group agree with the Cynipoidea and Chalcidoidea in the position of
  the ovipositor and in the jointed trochanters, but are distinguished
  by the fore-wing possessing a distinct stigma and usually a typical
  series of nervures and areolets (figs. 4, 8). Many of the species are
  of fair size. They lay their eggs (fig. 8) in the bodies of insects
  and their larvae belonging to various orders. A few small families
  such as the _Evaniidae_ and the _Stephanidae_ are included here, but
  the vast majority of the group fall into two large families, the
  _Ichneumonidae_ and the _Braconidae_, the former distinguished by the
  presence of two median (or discoidal) cells in the fore-wing (figs. 4,
  7), while the latter has only one (figs. 4, 6). Not a few of these
  insects, however, are entirely wingless. On account of their work in
  destroying plant-eating insects, the ichneumon-flies are of great
  economic importance.

  _Proctotrypoidea._--This group may be distinguished from the preceding
  by the position of the ovipositor at the extreme apex of the abdomen,
  and from the groups that follow (with very few exceptions) by the
  jointed trochanters of the legs. The pronotum reaches back to the
  tegulae. The _Pelecinidae_--included here by Ashmead--are large
  insects with remarkably elongate abdomens and undivided trochanters.
  All the other members of the group may be regarded as forming a single
  family--the _Proctotrypidae_, including an immense number of small
  parasitic Hymenoptera, not a few of which are wingless. Of special
  interest are the transformations of _Platygaster_, belonging to this
  family, discovered by M. Ganin, and familiarized to English readers
  through the writings of Sir J. Lubbock (Lord Avebury). The first larva
  is broad in front and tapers behind to a "tail" provided with two
  divergent processes, so that it resembles a small crustacean. It lives
  in the grub of a gall-midge and it ultimately becomes changed into the
  usual white and fleshy hymenopterous larva. The four succeeding
  sections, in which the ovipositor is modified into a sting (always
  exserted from the tip of the abdomen) and the trochanters are with few
  exceptions simple, form the _Aculeata_ of Linnaeus.

  _Formicoidea._--The ants which form this group are readily
  distinguished by the differentiation of the females into winged
  "queens" and wingless "workers." The pronotum extends back to the
  wing-bases, and the "waist" is greatly constricted and marked by one
  or two "nodes." The differentiation of the females leads to a complex
  social life, the nesting habits of ants and the various industries
  that they pursue being of surpassing interest (see ANT).

  _Vespoidea._--This section includes a number of families characterized
  by the backward extension of the prothorax to the tegulae and
  distinguished from the ants by the absence of "nodes" at the base of
  the abdomen. The true wasps have the fore-wings folded lengthwise when
  at rest and the fore-legs of normal build--not specialized for
  digging. The _Vespidae_ or social wasps have "queens" and "workers"
  like the ants, but both these forms of female are winged; the claws on
  their fret are simple. In the _Eumenidae_ or solitary wasps the female
  sex is undifferentiated, and the foot claws are toothed. (For the
  habits of these insects see WASP.) The _Chrysididae_ or ruby wasps are
  small insects with a very hard cuticle exhibiting brilliant metallic
  colours--blue, green and crimson. Only three or four abdominal
  segments are visible, the hinder segments being slender and retracted
  to form a telescope-like tube in which the ovipositor lies. When the
  ovipositor is brought into use this tube is thrust out. The eggs are
  laid in the nests of various bees and wasps, the chrysid larva living
  as a "cuckoo" parasite. The _Trigonalidae_, a small family whose
  larvae are parasitic in wasps' nests, also probably belong here.

  The other families of the _Vespoidea_ belong to the series of
  "Fossores" or digging-wasps. In two of the families--the _Mutillidae_
  and _Thynnidae_--the females are wingless and the larvae live as
  parasites in the larvae of other insects; the female _Mutilla_ enters
  bumble-bees' nests and lays her eggs in the bee-grubs. In the other
  families both sexes are winged, and the instinct and industry of the
  females are among the most wonderful in the Hymenoptera. They make
  burrows wherein they place insects or spiders which they have caught
  and stung, laying their eggs beside the victim so that the young
  larvae find themselves in presence of an abundant and appropriate
  food-supply. Valuable observations on the habits of these insects are
  due to J. H. Fabre and G. W. and E. Peckham. The prey is sometimes
  stung in the neighbourhood of the nerve ganglia, so that it is
  paralysed but not killed, the grub of the fossorial wasp devouring its
  victim alive; but this instinct varies in perfection, and in many
  cases the larva flourishes equally whether its prey be killed or not.
  The females have a wonderful power of finding their burrows on
  returning from their hunting expeditions. Among the Vespoid families
  of fossorial wasps, the _Pompilidae_ are the most important. They are
  recognizable by their slender and elongate hind-legs; many of them
  provision their burrows with spiders. The _Sapygidae_ are parasitic on
  bees, while the _Scoliidae_ are large, robust and hairy insects, many
  of which prey upon the grubs of chafers.

  _Sphecoidea._--In this division are included the rest of the
  "digging-wasps," distinguished from the _Vespoidea_ by the short
  pronotum not reaching backward to the tegulae. They have usually been
  reckoned as forming a single, very large family--the _Sphegidae_--but
  ten or twelve subdivisions of the group are regarded as distinct
  families by Ashmead and others. Great diversity is shown in the
  details of structure, habits and nature of the prey. Species of
  _Sphex_, studied by Fabre, provisioned their brood-chambers with
  crickets. _Pelopoeus_ hunts spiders, while _Ammophila_ catches
  caterpillars for the benefit of her young. Fabre states that the
  last-named insect uses a stone for the temporary closing of her
  burrow, and the Peckhams have seen a female _Ammophila_ take a stone
  between her mandibles and use it as a hammer for pounding down the
  earth over her finished nest. The habits of _Bembex_ are of especial
  interest. The female, instead of provisioning her burrow with a supply
  of food that will suffice the larva for its whole life, brings fresh
  flies with which she regularly feeds her young. In this instinct we
  have a correspondence with the habits of social wasps and bees. Yet it
  may be thought that the usual instinct of the "digging-wasps" to
  capture and store up food in an underground burrow for the benefit of
  offspring which they will never see is even more surprising. The habit
  of some genera is to catch the prey before making their tunnel, but
  more frequently the insect digs her nest, and then hunts for prey to
  put into it.

  _Apoidea._--The bees which make up this group agree with the
  Sphecoidea in the short pronotum, but may be distinguished from all
  other Hymenoptera by the widened first tarsal segment and the plumose
  hairs on head and body. They are usually regarded as forming a single
  family--the _Apidae_--but there is very great diversity in structural
  details, and Ashmead divides them into fourteen families. The
  "tongue," for example, is short and obtuse or emarginate in _Colletes_
  and _Prosopis_, while in all other bees it is pointed at the tip. But
  in _Andrena_ and its allies it is comparatively short, while in the
  higher genera, such as _Apis_ and _Bombus_, it is elongate and
  flexible, forming a most elaborate and perfect organ for taking liquid
  food. Bees feed on honey and pollen. Most of the genera are "solitary"
  in habit, the female sex being undifferentiated; but among the
  humble-bees and hive-bees we find, as in social wasps and ants, the
  occurrence of workers, and the consequent elaboration of a wonderful
  insect-society. (See BEE.)

  BIBLIOGRAPHY.--The literature of several special families of the
  Hymenoptera will be found under the articles ANT, BEE, ICHNEUMON-FLY,
  WASP, &c., referred to above. Among earlier students on structure may
  be mentioned P. A. Latreille, _Familles naturelles du règne animal_
  (Paris, 1825), who recognized the nature of the "median segment." C.
  Gerstaecker (_Arch. f. Naturg._ xx., 1867) and F. Brauer (_Sitzb. K.
  Akad. Wiss. Wien._ lxxxv., 1883) should also be consulted on this
  subject. For internal anatomy, specially the digestive organs, see L.
  Dufour, _Mém. savants étrangers_, vii. (1841), and _Ann. Sci. Nat.
  Zool._ (4), i. 1854. For nervous system H. Viallanes, _Ann. Sci. Nat.
  Zool._ (7), ii. iv. 1886-1887, and F. C. Kenyon, _Journ. Comp.
  Neurol._ vi., 1896. For poison and other glands, see L. Bordas, _Ann.
  Sci. Nat. Zool._ (7) xix., 1895. For the sting and ovipositor H.
  Dewitz, _Zeits. wiss. Zool._ xxv., 1874, xxviii., 1877, and F. Zander,
  _ib._ lxvi., 1899. For male genital armature S. A. Peytoureau,
  _Morphologie de l'armure génitale des insectes_ (Bordeaux, 1895),
  and E. Zander, Zeits. wiss. Zool. lxvii., 1900. The systematic student
  of Hymenoptera is greatly helped by C. G. de Dalla Torre's _Catalogus
  Hymenopterorum_ (10 vols., Leipzig, 1893-1902). For general
  classifications see F. W. Konow, _Entom. Nachtr._ (1897), and W. H.
  Ashmead, _Proc. U.S. Nat. Mus._ xxiii., 1901; the latter paper deals
  also especially with the Ichneumonoidea of the globe. For habits and
  life histories of Hymenoptera see J. Lubbock (Lord Avebury), _Ants,
  Bees and Wasps_ (9th ed., London, 1889); C. Janet, _Études sur les
  fourmis, les guêpes et les abeilles_ (Paris, &c., 1893 and onwards);
  and G. W. and E. G. Peckham, _Instincts and Habits of Solitary Wasps_
  (Madison, Wis. U.S.A., 1898). Monographs of most of the families of
  British Hymenoptera have now been published. For saw-flies and
  gall-flies, see P. Cameron's _British Phytophagous Hymenoptera_ (4
  vols., London, _Roy. Soc._, 1882-1893). For Ichneumonoidea, C.
  Morley's _Ichneumons of Great Britain_ (Plymouth, 1903, &c.), and T.
  A. Marshall's "British Braconidae," _Trans. Entom. Soc._, 1885-1899.
  The smaller parasitic Hymenoptera have been neglected in this country
  since A. H. Haliday's classical papers _Entom. Mag._ i.-v.,
  (1833-1838) but Ashmead's "North American Proctotrypidae" (_Bull. U.S.
  Nat. Mus._ xlv., 1893) is valuable for the European student. For the
  Fossores, wasps, ants and bees see E. Saunders, _Hymenoptera Aculeata
  of the British Islands_ (London, 1896). Exhaustive references to
  general systematic works will be found in de Dalla Torre's _Catalogue_
  mentioned above. Of special value to English students are C. T.
  Bingham's _Fauna of British India_, "Hymenoptera" (London, 1897 and
  onwards), and P. Cameron's volumes on Hymenoptera in the _Biologia
  Centrali-Americana_. F. Smith's _Catalogues of Hymenoptera in the
  British Museum_ (London, 1853-1859) are well worthy of study.
       (G. H. C.)



HYMETTUS (Ital. Monte Matto, hence the modern name Trello Vouni), a
mountain in Attica, bounding the Athenian plain on the S.E. Height, 3370
ft. It was famous in ancient times for its bees, which gathered honey of
peculiar flavour from its aromatic herbs; their fame still persists. The
spring mentioned by Ovid (_Ars Amat._ iii. 687) is probably to be
recognized near the monastery of Syriani or Kaesariani on the western
slope. This may be identical with that known as [Greek: Kyllon Pêra],
said to be a remedy for barrenness in women. The marble of Hymettus,
which often has a bluish tinge, was used extensively for building in
ancient Athens, and also, in early times, for sculpture; but the white
marble of Pentelicus was preferred for both purposes.

  See E. Dodwell, _Classical and Topographical Tour_ (1819), i. 483.



HYMNS.--1. _Classical Hymnody._--The word "hymn" ([Greek: hymnos]) was
employed by the ancient Greeks[1] to signify a song or poem composed in
honour of gods, heroes or famous men, or to be recited on some joyful,
mournful or solemn occasion. Polymnia was the name of their lyric muse.
Homer makes Alcinous entertain Odysseus with a "hymn" of the minstrel
Demodocus, on the capture of Troy by the wooden horse. The _Works and
Days_ of Hesiod begins with an invocation to the Muses to address hymns
to Zeus, and in his _Theogonia_ he speaks of them as singing or
inspiring "hymns" to all the divinities, and of the bard as "their
servant, hymning the glories of men of old, and of the gods of Olympus."
Pindar calls by this name odes, like his own, in praise of conquerors at
the public games of Greece. The Athenian dramatists (Euripides most
frequently) use the word and its cognate verbs in a similar manner; they
also describe by them metrical oracles and apophthegms, martial, festal
and hymeneal songs, dirges and lamentations or incantations of woe.

Hellenic hymns, according to this conception of them, have come down to
us, some from a very early and others from a late period of Greek
classical literature. Those which passed by the name of Homer[2] were
already old in the time of Thucydides. They are mythological poems
(several of them long), in hexameter verse--some very interesting. That
to Apollo contains a traditionary history of the origin and progress of
the Delphic worship; those on Hermes and on Dionysus are marked by much
liveliness and poetical fancy. Hymns of a like general character, but of
less interest (though these also embody some fine poetical traditions of
the Greek mythology, such as the story of Teiresias, and that of the
wanderings of Leto), were written in the 3rd century before Christ, by
Callimachus of Cyrene. Cleanthes, the successor of Zeno, composed (also
in hexameters) an "excellent and devout hymn" (as it is justly called by
Cudworth, in his _Intellectual System_) to Zeus, which is preserved in
the _Eclogae_ of Stobaeus, and from which Aratus borrowed the words,
"For we are also His offspring," quoted by St Paul at Athens. The
so-called Orphic hymns, in hexameter verse, styled [Greek: teletai], or
hymns of initiation into the "mysteries" of the Hellenic religion, are
productions of the Alexandrian school,--as to which learned men are not
agreed whether they are earlier or later than the Christian era.

The Romans did not adopt the word "hymn"; nor have we many Latin poems
of the classical age to which it can properly be applied. There are,
however, a few--such as the simple and graceful "Dianae sumus in fide"
("Dian's votaries are we") of Catullus, and "Dianam tenerae dicite
virgines" ("Sing to Dian, gentle maidens") of Horace--which approach
much more nearly than anything Hellenic to the form and character of
modern hymnody.

2. _Hebrew Hymnody._--For the origin and idea of Christian hymnody we
must look, not to Gentile, but to Hebrew sources. St Augustine's
definition of a hymn, generally accepted by Christian antiquity, may be
summed up in the words, "praise to God with song" ("cum cantico"); Bede
understood the "canticum" as properly requiring metre; though he thought
that what in its original language was a true hymn might retain that
character in an unmetrical translation. Modern use has enlarged the
definition; Roman Catholic writers extend it to the praises of saints;
and the word now comprehends rhythmical prose as well as verse, and
prayer and spiritual meditation as well as praise.

The modern distinction between psalms and hymns is arbitrary (see
PSALMS). The former word was used by the LXX. as a generic designation,
probably because it implied an accompaniment by the psaltery (said by
Eusebius to have been of very ancient use in the East) or other
instruments. The cognate verb "psallere" has been constantly applied to
hymns, both in the Eastern and in the Western Church; and the same
compositions which they described generically as "psalms" were also
called by the LXX. "odes" (i.e. songs) and "hymns." The latter word
occurs, e.g. in Ps. lxxii. 20 ("the hymns of David the son of Jesse"),
in Ps. lxv. 1, and also in the Greek titles of the 6th, 54th, 55th, 67th
and 76th (this numbering of the psalms being that of the English
version, not of the LXX.). The 44th chapter of Ecclesiasticus, "Let us
now praise famous men," &c., is entitled in the Greek [Greek: paterôn
hymnos], "The Fathers' Hymn." Bede speaks of the whole book of Psalms as
called "liber hymnorum," by the universal consent of Hebrews, Greeks and
Latins.

In the New Testament we find our Lord and His apostles singing a hymn
([Greek: hymnêsantes exêlthon]), after the institution of the Lord's
Supper; St Paul and Silas doing the same ([Greek: hymnoun ton theon]) in
their prison at Philippi; St James recommending psalm-singing ([Greek:
psalletô]), and St Paul "psalms and hymns and spiritual songs" ([Greek:
psalmois kai hymnois kai ôdais pneumatikais]) St Paul also, in the 14th
chapter of the first epistle to the Corinthians, speaks of singing
([Greek: psalô]) and of every man's psalm ([Greek: hekastos hymôn
psalmon echei]). In a context which plainly has reference to the
assemblies of the Corinthian Christians for common worship. All the
words thus used were applied by the LXX. to the Davidical psalms; it is
therefore possible that these only may be intended, in the different
places to which we have referred. But there are in St Paul's epistles
several passages (Eph. v. 14; 1 Tim. iii. 16; 1 Tim. vi. 15, 16; 2 Tim.
ii. 11, 12) which have so much of the form and character of later
Oriental hymnody as to have been supposed by Michaelis and others to be
extracts from original hymns of the Apostolic age. Two of them are
apparently introduced as quotations, though not found elsewhere in the
Scriptures. A third has not only rhythm, but rhyme. The thanksgiving
prayer of the assembled disciples, recorded in Acts iv., is both in
substance and in manner poetical; and in the canticles, "Magnificat,"
"Benedictus," &c., which manifestly followed the form and style of
Hebrew poetry, hymns or songs, proper for liturgical use, have always
been recognized by the church.

3. _Eastern Church Hymnody._--The hymn of our Lord, the precepts of the
apostles, the angelic song at the nativity, and "Benedicite omnia opera"
are referred to in a curious metrical prologue to the hymnary of the
Mozarabic Breviary as precedents for the practice of the Western Church.
In this respect, however, the Western Church followed the Eastern, in
which hymnody prevailed from the earliest times.


  Therapeutae.

Philo describes the Theraputae (q.v.) of the neighbourhood of Alexandria
as composers of original hymns, which (as well as old) were sung at
their great religious festivals--the people listening in silence till
they came to the closing strains, or refrains, at the end of a hymn or
stanza (the "acroteleutia" and "ephymnia"), in which all, women as well
as men, heartily joined. These songs, he says, were in various metres
(for which he uses a number of technical terms); some were choral, some
not; and they were divided into variously constructed strophes or
stanzas. Eusebius, who thought that the Theraputae were communities of
Christians, says that the Christian practice of his own day was in exact
accordance with this description.


  Antiphonal singing.

The practice, not only of singing hymns, but of singing them
antiphonally, appears, from the well-known letter of Pliny to Trajan, to
have been established in the Bithynian churches at the beginning of the
2nd century. They were accustomed "stato die ante lucem convenire,
carmenque Christo, quasi Deo, dicere _secum invicem_." This agrees well,
in point of time, with the tradition recorded by the historian Socrates,
that Ignatius (who suffered martyrdom about A.D. 107) was led by a
vision or dream of angels singing hymns in that manner to the Holy
Trinity to introduce antiphonal singing into the church of Antioch, from
which it quickly spread to other churches. There seems to be an allusion
to choral singing in the epistle of Ignatius himself to the Romans,
where he exhorts them, "[Greek: choros genomenoi]" ("having formed
themselves into a choir"), to "sing praise to the Father in Christ
Jesus." A statement of Theodoret has sometimes been supposed to refer
the origin of antiphonal singing to a much later date; but this seems to
relate only to the singing of Old Testament Psalms ([Greek: tên
Dauidikên melôdian]), the alternate chanting of which, by a choir
divided into two parts, was (according to that statement) first
introduced into the church of Antioch by two monks famous in the history
of their time, Flavianus and Diodorus, under the emperor Constantius II.


  2nd century.

  3rd century.

Other evidence of the use of hymns in the 2nd century is contained in a
fragment of Caius, preserved by Eusebius, which refers to "all the
psalms and odes written by faithful brethren from the beginning," as
"hymning Christ, the Word of God, as God." Tertullian also, in his
description of the "Agapae," or love-feasts, of his day, says that,
after washing hands and bringing in lights, each man was invited to come
forward and sing to God's praise something either taken from the
Scriptures or of his own composition ("ut quisque de Sacris Scripturis
vel proprio ingenio potest"). George Bull, bishop of St David's,
believed one of those primitive compositions to be the hymn appended by
Clement of Alexandria to his _Paedagogus_; and Archbishop Ussher
considered the ancient morning and evening hymns, of which the use was
enjoined by the _Apostolical Constitutions_, and which are also
mentioned in the "Tract on Virginity" printed with the works of St
Athanasius, and in St Basil's treatise upon the Holy Spirit, to belong
to the same family. Clement's hymn, in a short anapaestic metre,
beginning [Greek: stomion pôlôn adaôn] (or, according to some editions,
[Greek: basileu hagiôn, loge pandamatôr]--translated by the Rev. A.
Chatfield, "O Thou, the King of Saints, all-conquering Word"), is rapid,
spirited and well-adapted for singing. The Greek "Morning Hymn" (which,
as divided into verses by Archbishop Ussher in his treatise _De
Symbolis_, has a majestic rhythm, resembling a choric or dithyrambic
strophe) is the original form of "Gloria in Excelsis," still said or
sung, with some variations, in all branches of the church which have not
relinquished the use of liturgies. The Latin form of this hymn (of which
that in the English communion office is an exact translation) is said,
by Bede and other ancient writers, to have been brought into use at Rome
by Pope Telesphorus, as early as the time of the emperor Hadrian. A
third, the Vesper or "Lamp-lighting" hymn ("[Greek: phôs hilaron hagias
doxês]"--translated by Canon Bright "Light of Gladness, Beam Divine"),
holds its place to this day in the services of the Greek rite. In the
3rd century Origen seems to have had in his mind the words of some other
hymns or hymn of like character, when he says (in his treatise _Against
Celsus_): "We glorify in hymns God and His only begotten Son; as do also
the Sun, the Moon, the Stars and all the host of heaven. All these, in
one Divine chorus, with the just among men, glorify in hymns God who is
over all, and His only begotten Son." So highly were these compositions
esteemed in the Syrian churches that the council which deposed Paul of
Samosata from the see of Antioch in the time of Aurelian justified that
act, in its synodical letter to the bishops of Rome and Alexandria, on
this ground (among others) that he had prohibited the use of hymns of
that kind, by uninspired writers, addressed to Christ.

After the conversion of Constantine, the progress of hymnody became
closely connected with church controversies. There had been in Edessa,
at the end of the 2nd or early in the 3rd century, a Gnostic writer of
conspicuous ability, named Bardesanes, who was succeeded, as the head of
his sect or school, by his son Harmonius. Both father and son wrote
hymns, and set them to agreeable melodies, which acquired, and in the
4th century still retained, much local popularity. Ephraem Syrus, the
first voluminous hymn-writer whose works remain to us, thinking that the
same melodies might be made useful to the faith, if adapted to more
orthodox words, composed to them a large number of hymns in the Syriac
language, principally in tetrasyllabic, pentasyllable and heptasyllabic
metres, divided into strophes of from 4 to 12, 16 and even 20 lines
each. When a strophe contained five lines, the fifth was generally an
"ephymnium," detached in sense, and consisting of a prayer, invocation,
doxology or the like, to be sung antiphonally, either in full chorus or
by a separate part of the choir. The _Syriac Chrestomathy_ of August
Hahn (Leipzig, 1825), and the third volume of H. A. Daniel's _Thesaurus
Hymnologicus_ (Leipzig, 1841-1856), contain specimens of these hymns.
Some of them have been translated into (unmetrical) English by the Rev.
Henry Burgess (_Select Metrical Hymns of Ephrem Syrus_, &c., 1853). A
considerable number of those so translated are on subjects connected
with death, resurrection, judgment, &c., and display not only Christian
faith and hope, but much simplicity and tenderness of natural feeling.
Theodoret speaks of the spiritual songs of Ephraem as very sweet and
profitable, and as adding much, in his (Theodoret's) time, to the
brightness of the commemorations of martyrs in the Syrian Church.

The Greek hymnody contemporary with Ephraem followed, with some licence,
classical models. One of its favourite metres was the Anacreontic; but
it also made use of the short anapaestic, Ionic, iambic and other
lyrical measures, as well as the hexameter and pentameter. Its principal
authors were Methodius, bishop of Olympus, who died about A.D. 311,
Synesius, who became bishop of Ptolemais in Cyrenaica in 410, and
Gregory Nazianzen, for a short time (380-381) patriarch of
Constantinople. The merits of these writers have been perhaps too much
depreciated by the admirers of the later Greek "Melodists." They have
found an able English translator in the Rev. Allen Chatfield (_Songs and
Hymns of Earliest Greek Christian Poets_, London, 1876). Among the most
striking of their works are [Greek: mnôeo Christe] ("Lord Jesus, think
of me"), by Synesius; [Greek: se ton aphthiton monarchên] ("O Thou, the
One Supreme") and [Greek: ti soi theleis genesthai] ("O soul of mine,
repining"), by Gregory; also [Greek: anôthen parthenoi] ("The Bridegroom
cometh"), by Methodius. There continued to be Greek metrical
hymn-writers, in a similar style, till a much later date. Sophronius,
patriarch of Jerusalem in the 7th century, wrote seven Anacreontic
hymns; and St John Damascene, one of the most copious of the second
school of "Melodists," was also the author of some long compositions in
trimeter iambics.


  Period of Arian controversy.

An important development of hymnody at Constantinople arose out of the
Arian controversy. Early in the 4th century Athanasius had rebuked, not
only the doctrine of Arius, but the light character of certain hymns by
which he endeavoured to make that doctrine popular. When, towards the
close of that century (398), St John Chrysostom was raised to the
metropolitan see, the Arians, who were still numerous at Constantinople,
had no places of worship within the walls; but they were in the habit of
coming into the city at sunset on Saturdays, Sundays and the greater
festivals, and congregating in the porticoes and other places of public
resort, where they sung, all night through, antiphonal songs, with
"acroteleutia" (closing strains, or refrains), expressive of Arian
doctrine, often accompanied by taunts and insults to the orthodox.
Chrysostom was apprehensive that this music might draw some of the
simpler church people to the Arian side; he therefore organized, in
opposition to it, under the patronage and at the cost of Eudoxia, the
empress of Arcadius (then his friend), a system of nightly processional
hymn-singing, with silver crosses, wax-lights and other circumstances of
ceremonial pomp. Riots followed, with bloodshed on both sides, and with
some personal injury to the empress's chief eunuch, who seems to have
officiated as conductor or director of the church musicians. This led to
the suppression, by an imperial edict, of all public Arian singing;
while in the church the practice of nocturnal hymn-singing on certain
solemn occasions, thus first introduced, remained an established
institution.


  Greek system of hymnody.

It is not improbable that some rudiments of the peculiar system of
hymnody which now prevails throughout the Greek communion, and whose
affinities are rather to the Hebrew and Syriac than to the classical
forms, may have existed in the church of Constantinople, even at that
time. Anatolius, patriarch of Constantinople in the middle of the 5th
century, was the precursor of that system; but the reputation of being
its proper founder belongs to Romanos, of whom little more is known than
that he wrote hymns still extant, and lived towards the end of that
century. The importance of that system in the services of the Greek
church may be understood from the fact that Dr J. M. Neale computed
four-fifths of the whole space (about 5000 pages) contained in the
different service-books of that church to be occupied by hymnody, all in
a language or dialect which has ceased to be anywhere spoken.

  The system has a peculiar technical terminology, in which the words
  "troparion," "ode," "canon" and "hirmus" ([Greek: eirmos]) chiefly
  require explanation.

  The _troparion_ is the unit of the system, being a strophe or stanza,
  seen, when analysed, to be divisible into verses or clauses, with
  regulated caesuras, but printed in the books as a single prose
  sentence, without marking any divisions. The following (turned into
  English, from a "canon" by John Mauropus) may be taken as an example:
  "The never-sleeping Guardian, | the patron of my soul, | the guide of
  my life, | allotted me by God, | I hymn thee, Divine Angel | of
  Almighty God." Dr Neale and most other writers regard all these
  "troparia" as rhythmical or modulated prose. Cardinal J. B. Pitra, on
  the other hand, who in 1867 and 1876 published two learned works on
  this subject, maintains that they are really metrical, and governed by
  definite rules of prosody, of which he lays down sixteen. According to
  him, each "troparion" contains from three to thirty-three verses; each
  verse varies from two to thirteen syllables, often in a continuous
  series, uniform, alternate or reciprocal, the metre being always
  syllabic, and depending, not on the quantity of vowels or the position
  of consonants, but on an harmonic series of accents.

  In various parts of the services solitary troparia are sung, under
  various names, "contacion," "oecos," "cathisma," &c., which mark
  distinctions either in their character or in their use.

  An _ode_ is a song or hymn compounded of several similar
  "troparia,"--usually three, four or five. To these is always prefixed
  a typical or standard "troparion," called the _hirmus_, by which the
  syllabic measure, the periodic series of accents, and in fact the
  whole structure and rhythm of the stanzas which follow it are
  regulated. Each succeeding "troparion" in the same "ode" contains the
  same number of verses, and of syllables in each verse, and similar
  accents on the same or equivalent syllables. The "hirmus" may either
  form the first stanza of the "ode" itself, or (as is more frequently
  the case) may be taken from some other piece; and, when so taken, it
  is often indicated by initial words only, without being printed at
  length. It is generally printed within commas, after the proper rubric
  of the "ode." A hymn in irregular "stichera" or stanzas, without a
  "hirmus," is called "idiomelon." A system of three or four odes is
  "triodion" or "tetraodion."

  A _canon_ is a system of eight (theoretically nine) connected odes,
  the second being always suppressed. Various pauses, relieved by the
  interposition of other short chants or readings, occur during the
  singing of a whole "canon." The final "troparion" in each ode of the
  series is not unfrequently detached in sense (like the "ephymnia" of
  Ephraem Syrus), particularly when it is in the (very common) form of a
  "theotokion," or ascription of praise to the mother of our Lord, and
  when it is a recurring refrain or burden.

There were two principal periods of Greek hymnography constructed on
these principles--the first that of Romanos and his followers, extending
over the 6th and 7th centuries, the second that of the schools which
arose during the Iconoclastic controversy in the 8th century, and which
continued for some centuries afterwards, until the art itself died out.


  School of Romanos.

The works of the writers of the former period were collected in
_Tropologia_, or church hymn-books, which were held in high esteem till
the 10th century, when they ceased to be regarded as church-books, and
so fell into neglect. They are now preserved only in a very small number
of manuscripts. From three of these, belonging to public libraries at
Moscow, Turin and Rome, Cardinal Pitra has printed, in his _Analecta_, a
number of interesting examples, the existence of which appears to have
been unknown to Dr Neale, and which, in the cardinal's estimation, are
in many respects superior to the "canons," &c., of the modern Greek
service-books, from which all Neale's translations (except some from
Anatolius) are taken. Cardinal Pitra's selections include twenty-nine
works by Romanos, and some by Sergius, and nine other known, as well as
some unknown, authors. He describes them as having generally a more
dramatic character than the "melodies" of the later period, and a much
more animated style; and he supposes that they may have been originally
sung with dramatic accompaniments, by way of substitution for the
theatrical performances of Pagan times. As an instance of their peculiar
character, he mentions a Christmas or Epiphany hymn by Romanos, in
twenty-five long strophes, in which there is, first, an account of the
Nativity and its accompanying wonders, and then a dialogue between the
wise men, the Virgin mother and Joseph. The magi arrive, are admitted,
describe the moral and religious condition of Persia and the East, and
the cause and adventures of their journey, and then offer their gifts.
The Virgin intercedes for them with her Son, instructs them in some
parts of Jewish history, and ends with a prayer for the salvation of the
world.


  Melodists.

The controversies and persecutions of the 8th and succeeding centuries
turned the thoughts of the "melodists" of the great monasteries of the
Studium at Constantinople and St Saba in Palestine and their followers,
and those of the adherents of the Greek rite in Sicily and South Italy
(who suffered much from the Saracens and the Normans), into a less
picturesque but more strictly theological course; and the influence of
those controversies, in which the final success of the cause of "Icons"
was largely due to the hymns, as well as to the courage and sufferings,
of these confessors, was probably the cause of their supplanting, as
they did, the works of the older school. Cardinal Pitra gives them the
praise of having discovered a graver and more solemn style of chant, and
of having done much to fix the dogmatic theology of their church upon
its present lines of near approach to the Roman.

Among the "melodists" of this latter Greek school there were many saints
of the Greek church, several patriarchs and two emperors--Leo the
Philosopher, and Constantine Porphyrogenitus, his son. Their greatest
poets were Theodore and Joseph of the Studium, and Cosmas and John
(called Damascene) of St Saba. Neale translated into English verse
several selected portions, or centoes, from the works of these and
others, together with four selections from earlier works by Anatolius.
Some of his translations--particularly "The day is past and over," from
Anatolius, and "Christian, dost thou see them," from Andrew of
Crete--have been adopted into hymn-books used in many English churches;
and the hymn "Art thou weary," which is rather founded upon than
translated from one by Stephen the Sabaite, has obtained still more
general popularity.

4. _Western Church Hymnody._--It was not till the 4th century that Greek
hymnody was imitated in the West, where its introduction was due to two
great lights of the Latin Church--St Hilary of Poitiers and St Ambrose
of Milan.

Hilary was banished from his see of Poitiers in 356, and was absent from
it for about four years, which he spent in Asia Minor, taking part
during that time in one of the councils of the Eastern Church. He thus
had full opportunity of becoming acquainted with the Greek church music
of that day; and he wrote (as St Jerome, who was thirty years old when
Hilary died, and who was well acquainted with his acts and writings, and
spent some time in or near his diocese, informs us) a "book of hymns,"
to one of which Jerome particularly refers, in the preface to the second
book of his own commentary on the epistle to the Galatians. Isidore,
archbishop of Seville, who presided over the fourth council of Toledo,
in his book on the offices of the church, speaks of Hilary as the first
Latin hymn-writer; that council itself, in its 13th canon, and the
prologue to the Mozarabic hymnary (which is little more than a
versification of the canon), associate his name, in this respect, with
that of Ambrose. A tradition, ancient and widely spread, ascribed to him
the authorship of the remarkable "Hymnum dicat turba fratrum, hymnum
cantus personet" ("Band of brethren, raise the hymn, let your song the
hymn resound"), which is a succinct narrative, in hymnal form, of the
whole gospel history; and is perhaps the earliest example of a strictly
didactic hymn. Both Bede and Hincmar much admired this composition,
though the former does not mention, in connexion with it, the name of
Hilary. The private use of hymns of such a character by Christians in
the West may probably have preceded their ecclesiastical use; for Jerome
says that in his day those who went into the fields might hear "the
ploughman at his hallelujahs, the mower at his hymns, and the
vine-dresser singing David's psalms." Besides this, seven shorter
metrical hymns attributed to Hilary are still extant.


  Ambrose.

Of the part taken by Ambrose, not long after Hilary's death, in bringing
the use of hymns into the church of Milan, we have a contemporary
account from his convert, St Augustine. Justina, mother of the emperor
Valentinian, favoured the Arians, and desired to remove Ambrose from his
see. The "devout people," of whom Augustine's mother, Monica, was one,
combined to protect him, and kept guard in the church. "Then," says
Augustine, "it was first appointed that, after the manner of the Eastern
churches, hymns and psalms should be sung, lest the people should grow
weary and faint through sorrow; which custom has ever since been
retained, and has been followed by almost all congregations in other
parts of the world." He describes himself as moved to tears by the
sweetness of these "hymns and canticles":--"The voices flowed into my
ears; the truth distilled into my heart; I overflowed with devout
affections, and was happy." To this time, according to an uncertain but
not improbable tradition which ascribed the composition of the "Te Deum"
to Ambrose, and connected it with the conversion of Augustine, is to be
referred the commencement of the use in the church of that sublime
unmetrical hymn.

It is not, however, to be assumed that the hymnody thus introduced by
Ambrose was from the first used according to the precise order and
method of the later Western ritual. To bring it into (substantially)
that order and method appears to have been the work of St Benedict.
Walafrid Strabo, the earliest ecclesiastical writer on this subject (who
lived at the beginning of the 9th century), says that Benedict, on the
constitution of the religious order known by his name (about 530),
appointed the Ambrosian hymns to be regularly sung in his offices for
the canonical hours. Hence probably originated the practice of the
Italian churches, and of others which followed their example, to sing
certain hymns (Ambrosian, or by the early successors of the Ambrosian
school) daily throughout the week, at "Vespers," "Lauds" and "Nocturns,"
and on some days at "Compline" also--varying them with the different
ecclesiastical seasons and festivals, commemorations of saints and
martyrs and other special offices. Different dioceses and religious
houses had their own peculiarities of ritual, including such hymns as
were approved by their several bishops or ecclesiastical superiors,
varying in detail, but all following the same general method. The
national rituals, which were first reduced into a form substantially
like that which has since prevailed, were probably those of Lombardy and
of Spain, now known as the "Ambrosian" and the "Mozarabic." The age and
origin of the Spanish ritual are uncertain, but it is mentioned in the
7th century by Isidore, bishop of Seville. It contained a copious
hymnary, the original form of which may be regarded as canonically
approved by the fourth council of Toledo (633). By the 13th canon of
that council, an opinion (which even then found advocates) against the
use in churches of any hymns not taken from the Scriptures--apparently
the same opinion which had been held by Paul of Samosata--was censured;
and it was ordered that such hymns should be used in the Spanish as well
as in the Gallican churches, the penalty of excommunication being
denounced against all who might presume to reject them.

The hymns of which the use was thus established and authorized were
those which entered into the daily and other offices of the church,
afterwards collected in the "Breviaries"; in which the hymns "proper"
for "the week," and for "the season," continued for many centuries, with
very few exceptions, to be derived from the earliest epoch of Latin
Church poetry--reckoning that epoch as extending from Hilary and Ambrose
to the end of the pontificate of Gregory the Great. The "Ambrosian"
music, to which those hymns were generally sung down to the time of
Gregory, was more popular and congregational than the "Gregorian," which
then came into use, and afterwards prevailed. In the service of the mass
it was not the general practice, before the invention of sequences in
the 9th century, to sing any hymns, except some from the Scriptures
esteemed canonical, such as the "Song of the Three Children"
("Benedicite omnia opera"). But to this rule there were, according to
Walafrid Strabo, some occasional exceptions; particularly in the case of
Paulinus, patriarch of Aquileia under Charlemagne, himself a
hymn-writer, who frequently used hymns, composed by himself or others,
in the eucharistic office, especially in private masses.

Some of the hymns called "Ambrosian" (nearly 100 in number) are beyond
all question by Ambrose himself, and the rest probably belong to his
time or to the following century. Four, those beginning "Aeterne rerum
conditor" ("Dread Framer of the earth and sky"), "Deus Creator omnium"
("Maker of all things, glorious God"), "Veni Redemptor Gentium"
("Redeemer of the nations, come") and "Jam surgit hora tertia" ("Christ
at this hour was crucified"), are quoted as works of Ambrose by
Augustine. These, and others by the hand of the same master, have the
qualities most valuable in hymns intended for congregational use. They
are short and complete in themselves; easy, and at the same time
elevated in their expression and rhythm; terse and masculine in thought
and language; and (though sometimes criticized as deficient in
theological precision) simple, pure and not technical in their rendering
of the great facts and doctrines of Christianity, which they present in
an objective and not a subjective manner. They have exercised a powerful
influence, direct or indirect, upon many of the best works of the same
kind in all succeeding generations. With the Ambrosian hymns are
properly classed those of Hilary, and the contemporary works of Pope
Damasus I. (who wrote two hymns in commemoration of saints), and of
Prudentius, from whose _Cathemerina_ ("Daily Devotions") and
_Peristephana_ ("Crown-songs for Martyrs"), all poems of considerable,
some of great length--about twenty-eight hymns, found in various
Breviaries, were derived. Prudentius was a layman, a native of
Saragossa, and it was in the Spanish ritual that his hymns were most
largely used. In the Mozarabic Breviary almost the whole of one of his
finest poems (from which most churches took one part only, beginning
"Corde natus ex parentis") was appointed to be sung between Easter and
Ascension-Day, being divided into eight or nine hymns; and on some of
the commemorations of Spanish saints long poems from his _Peristephana_
were recited or sung at large. He is entitled to a high rank among
Christian poets, many of the hymns taken from his works being full of
fervour and sweetness, and by no means deficient in dignity or strength.


  5th and 6th centuries.

These writers were followed in the 5th and early in the 6th century by
the priest Sedulius, whose reputation perhaps exceeded his merit; Elpis,
a noble Roman lady (considered, by an erroneous tradition, to have been
the wife of the philosophic statesman Boetius); Pope Gelasius I.; and
Ennodius, bishop of Pavia. Sedulius and Elpis wrote very little from
which hymns could be extracted; but the small number taken from their
compositions obtained wide popularity, and have since held their ground.
Gelasius was of no great account as a hymn-writer; and the works of
Ennodius appear to have been known only in Italy and Spain. The latter
part of the 6th century produced Pope Gregory the Great and Venantius
Fortunatus, an Italian poet, the friend of Gregory, and the favourite of
Radegunda, queen of the Franks, who died (609) bishop of Poitiers.
Eleven hymns of Gregory, and twelve or thirteen (mostly taken from
longer poems) by Fortunatus, came into general use in the Italian,
Gallican and British churches. Those of Gregory are in a style hardly
distinguishable from the Ambrosian; those of Fortunatus are graceful,
and sometimes vigorous. He does not, however, deserve the praise given
to him by Dr Neale, of having struck out a new path in Latin hymnody. On
the contrary, he may more justly be described as a disciple of the
school of Prudentius, and as having affected the classical style, at
least as much as any of his predecessors.

  The poets of this primitive epoch, which closed with the 6th century,
  wrote in the old classical metres, and made use of a considerable
  variety of them--anapaestic, anacreontic, hendecasyllabic, asclepiad,
  hexameters and pentameters and others. Gregory and some of the
  Ambrosian authors occasionally wrote in sapphics; but the most
  frequent measure was the iambic dimeter, and, next to that, the
  trochaic. The full alcaic stanza does not appear to have been used for
  church purposes before the 16th century, though some of its elements
  were. In the greater number of these works, a general intention to
  conform to the rules of Roman prosody is manifest; but even those
  writers (like Prudentius) in whom that conformity was most decided
  allowed themselves much liberty of deviation from it. Other works,
  including some of the very earliest, and some of conspicuous merit,
  were of the kind described by Bede as not metrical but
  "rhythmical"--i.e. (as he explains the term "rhythm"), "modulated to
  the ear in imitation of different metres." It would be more correct to
  call them metrical--(e.g. still trochaic or iambic, &c., but,
  according to new laws of syllabic quantity, depending entirely on
  accent, and not on the power of vowels or the position of
  consonants)--laws by which the future prosody of all modern European
  nations was to be governed. There are also, in the hymns of the
  primitive period (even in those of Ambrose), anticipations--irregular
  indeed and inconstant, but certainly not accidental--of another great
  innovation, destined to receive important developments, that of
  assonance or rhyme, in the final letters or syllables of verses.
  Archbishop Trench, in the introduction to his _Sacred Latin Poetry_,
  has traced the whole course of the transition from the ancient to the
  modern forms of versification, ascribing it to natural and necessary
  causes, which made such changes needful for the due development of the
  new forms of spiritual and intellectual life, consequent upon the
  conversion of the Latin-speaking nations to Christianity.


  6th century downwards.

From the 6th century downwards we see this transformation making
continual progress, each nation of Western Christendom adding, from time
to time, to the earlier hymns in its service-books others of more recent
and frequently of local origin. For these additions, the commemorations
of saints, &c., as to which the devotion of one place often differed
from that of another, offered especial opportunities. This process,
while it promoted the development of a medieval as distinct from the
primitive style, led also to much deterioration in the quality of
hymns, of which, perhaps, some of the strongest examples may be found in
a volume published in 1865 by the Irish Archaeological Society from a
manuscript in the library of Trinity College, Dublin. It contains a
number of hymns by Irish saints of the 6th, 7th and 8th centuries--in
several instances fully rhymed, and in one mixing Erse and Latin
barbarously together, as was not uncommon, at a much later date, in
semi-vernacular hymns of other countries. The Mozarabic Breviary, and
the collection of hymns used in the Anglo-Saxon churches, published in
1851 by the Surtees Society (chiefly from a Benedictine MS. In the
college library of Durham, supplemented by other MSS. in the British
Museum), supply many further illustrations of the same decline of
taste:--such Sapphics, e.g., as the "Festum insigne prodiit coruscum" of
Isidore, and the "O veneranda Trinitas laudanda" of the Anglo-Saxon
books. The early medieval period, however, from the time of Gregory the
Great to that of Hildebrand, was far from deficient in the production of
good hymns, wherever learning flourished. Bede in England, and Paul "the
Deacon"--the author of a fairly classical sapphic ode on St John the
Baptist--in Italy, were successful followers of the Ambrosian and
Gregorian styles. Eleven metrical hymns are attributed to Bede by
Cassander; and there are also in one of Bede's works (_Collectanea et
flores_) two rhythmical hymns of considerable length on the Day of
Judgment, with the refrains "In tremendo die" and "Attende homo," both
irregularly rhymed, and, in parts, not unworthy of comparison with the
"Dies Irae." Paulinus, patriarch of Aquileia, contemporary with Paul,
wrote rhythmical trimeter iambics in a manner peculiar to himself.
Theodulph, bishop of Orleans (793-835), author of the famous
processional hymn for Palm Sunday in hexameters and pentameters,
"Gloria, laus, et honor tibi sit, Rex Christe Redemptor" ("Glory and
honour and laud be to Thee, King Christ the Redeemer"), and Hrabanus
Maurus, archbishop of Mainz, the pupil of Alcuin, and the most learned
theologian of his day, enriched the church with some excellent works.
Among the anonymous hymns of the same period there are three of great
beauty, of which the influence may be traced in most, if not all, of the
"New Jerusalem" hymns of later generations, including those of Germany
and Great Britain:--"Urbs beata Hierusalem" ("Blessed city, heavenly
Salem"); "Alleluia piis edite laudibus" ("Alleluias sound ye in strains
of holy praise"--called, from its burden, "Alleluia perenne"); and
"Alleluia dulce carmen" ("Alleluia, song of sweetness"), which, being
found in Anglo-Saxon hymnaries certainly older than the Conquest, cannot
be of the late date assigned to it, in his _Mediaeval Hymns and
Sequences_, by Neale. These were followed by the "Chorus novae
Hierusalem" ("Ye Choirs of New Jerusalem") of Fulbert, bishop of
Chartres. This group of hymns is remarkable for an attractive union of
melody, imagination, poetical colouring and faith. It represents,
perhaps, the best and highest type of the middle school, between the
severe Ambrosian simplicity and the florid luxuriance of later times.


  Veni Creator.

  Notker.

Another celebrated hymn, which belongs to the first medieval period, is
the "Veni Creator Spiritus" ("Come, Holy Ghost, our souls inspire"). The
earliest recorded occasion of its use is that of a translation (898) of
the relics of St Marcellus, mentioned in the _Annals_ of the Benedictine
order. It has since been constantly sung throughout Western Christendom
(as versions of it still are in the Church of England), as part of the
appointed offices for the coronation of kings, the consecration and
ordination of bishops and priests, the assembling of synods and other
great ecclesiastical solemnities. It has been attributed--probably in
consequence of certain corruptions in the text of Ekkehard's _Life of
Notker_ (a work of the 13th century)--to Charlemagne. Ekkehard wrote in
the Benedictine monastery of St Gall, to which Notker belonged, with
full access to its records; and an ignorant interpolator, regardless of
chronology, added, at some later date, the word "Great" to the name of
"the emperor Charles," wherever it was mentioned in that work. The
biographer relates that Notker--a man of a gentle, contemplative nature,
observant of all around him, and accustomed to find spiritual and
poetical suggestions in common sights and sounds--was moved by the
sound of a mill-wheel to compose his "sequence" on the Holy Spirit,
"Sancti Spiritus adsit nobis gratia" ("Present with us ever be the Holy
Spirit's grace"); and that, when finished, he sent it as a present to
"the emperor Charles," who in return sent him back, "by the same
messenger," the hymn "Veni Creator," which (says Ekkehard) the same
"Spirit had inspired him to write" ("Sibi idem Spiritus inspiraverat").
If this story is to be credited--and, from its circumstantial and almost
dramatic character, it has an air of truth--the author of "Veni Creator"
was not Charlemagne, but his grandson the emperor Charles the Bald.
Notker himself long survived that emperor, and died in 912.


  Sequences.

The invention of "sequences" by Notker may be regarded as the beginning
of the later medieval epoch of Latin hymnody. In the eucharistic
service, in which (as has been stated) hymns were not generally used, it
had been the practice, except at certain seasons, to sing "laud," or
"Alleluia," between the epistle and the gospel, and to fill up what
would otherwise have been a long pause, by extending the cadence upon
the two final vowels of the "Alleluia" into a protracted strain of
music. It occurred to Notker that, while preserving the spirit of that
part of the service, the monotony of the interval might be relieved by
introducing at that point a chant of praise specially composed for the
purpose. With that view he produced the peculiar species of rhythmical
composition which obtained the name of "sequentia" (probably from
following after the close of the "Alleluia"), and also that of "prosa,"
because its structure was originally irregular and unmetrical,
resembling in this respect the Greek "troparia," and the "Te Deum,"
"Benedicite" and canticles. That it was in some measure suggested by the
forms of the later Greek hymnody seems probable, both from the
intercourse (at that time frequent) between the Eastern and Western
churches, and from the application by Ekkehard, in his biography and
elsewhere (e.g. in Lyndwood's _Provinciale_), of some technical terms,
borrowed from the Greek terminology, to works of Notker and his school
and to books containing them.

  Dr Neale, in a learned dissertation prefixed to his collection of
  sequences from medieval Missals, and enlarged in a Latin letter to H.
  A. Daniel (printed in the fifth volume of Daniel's _Thesaurus
  hymnologicus_), investigated the laws of caesura and modulation which
  are discoverable in these works. Those first brought into use were
  sent by their author to Pope Nicholas I., who authorized their use,
  and that of others composed after the same model by other brethren of
  St Gall, in all churches of the West.

  Although the sequences of Notker and his school, which then rapidly
  passed into most German, French and British Missals, were not
  metrical, the art of "assonance" was much practised in them. Many of
  those in the Sarum and French Missals have every verse, and even every
  clause or division of a verse, ending with the same vowel "a"--perhaps
  with some reference to the terminal letter of "Alleluia." Artifices
  such as these naturally led the way to the adaptation of the same kind
  of composition to regular metre and fully developed rhyme. Neale's
  full and large collection, and the second volume of Daniel's
  _Thesaurus_, contain numerous examples, both of the "proses," properly
  so called, of the Notkerian type, and of those of the later school,
  which (from the religious house to which its chief writer belonged)
  has been called "Victorine." Most Missals appear to have contained
  some of both kinds. In the majority of those from which Neale's
  specimens are taken, the metrical kind largely prevailed; but in some
  (e.g. those of Sarum and Liége) the greater number were Notkerian.

Of the sequence on the Holy Ghost, sent by Notker (according to
Ekkehard) to Charles the Bald, Neale says that it "was in use all over
Europe, even in those countries, like Italy and Spain, which usually
rejected sequences"; and that, "in the Missal of Palencia, the priest
was ordered to hold a white dove in his hands, while intoning the first
syllables, and then to let it go." Another of the most remarkable of
Notker's sequences, beginning "Media in vita" ("In the midst of life we
are in death"), is said to have been suggested to him while observing
some workmen engaged in the construction of a bridge over a torrent near
his monastery. Catherine Winkworth (_Christian Singers of Germany_,
1869) states that this was long used as a battle-song, until the custom
was forbidden, on account of its being supposed to exercise a magical
influence. A translation of it ("Mitten wir im Leben sind") is one of
Luther's funeral hymns; and all but the opening sentence of that part of
the burial service of the Church of England which is directed to be
"said or sung" at the grave, "while the corpse is made ready to be laid
into the earth," is taken from it.

The "Golden Sequence," "Veni, sancte Spiritus" ("Holy Spirit, Lord of
Light"), is an early example of the transition of sequences from a
simply rhythmical to a metrical form. Archbishop Trench, who esteemed it
"the loveliest of all the hymns in the whole circle of Latin sacred
poetry," inclined to give credit to a tradition which ascribes its
authorship to Robert II., king of France, son of Hugh Capet. Others have
assigned to it a later date--some attributing it to Pope Innocent III.,
and some to Stephen Langton, archbishop of Canterbury. Many
translations, in German, English and other languages, attest its merit.
Berengarius of Tours, St Bernard of Clairvaux and Abelard, in the 11th
century and early in the 12th, followed in the same track; and the art
of the Victorine school was carried to its greatest perfection by Adam
of St Victor (who died between 1173 and 1194)--"the most fertile, and"
(in the concurrent judgment of Archbishop Trench and Neale) "the
greatest of the Latin hymnographers of the Middle Ages." The
archbishop's selection contains many excellent specimens of his works.


  Dies Irae.

  Stabat Mater.

  Aquinas.

But the two most widely celebrated of all this class of
compositions--works which have exercised the talents of the greatest
musical composers, and of innumerable translators in almost all
languages--are the "Dies Irae" ("That day of wrath, that dreadful day"),
by Thomas of Celano, the companion and biographer of St Francis of
Assisi, and the "Stabat Mater dolorosa" ("By the cross sad vigil
keeping") of Jacopone, or Jacobus de Benedictis, a Franciscan humorist
and reformer, who was persecuted by Pope Boniface VIII. for his satires
on the prelacy of the time, and died in 1306. Besides these, the 13th
century produced the famous sequence "Lauda Sion salvatorem" ("Sion,
lift thy voice and sing"), and the four other well-known sacramental
hymns of St Thomas Aquinas, viz. "Pange lingua gloriosi corporis
mysterium" ("Sing, my tongue, the Saviour's glory"), "Verbum supernum
prodiens" ("The Word, descending from above"--not to be confounded with
the Ambrosian hymn from which it borrowed the first line), "Sacris
solemniis juncta sint gaudia" ("Let us with hearts renewed our grateful
homage pay"), and "Adoro Te devote, latens Deitas" ("O Godhead hid,
devoutly I adore Thee")--a group of remarkable compositions, written by
him for the then new festival of Corpus Christi, of which he induced
Pope Urban IV. (1261-1265) to decree the observance. In these (of which
all but "Adoro Te devote" passed rapidly into breviaries and missals)
the doctrine of transubstantiation is set forth with a wonderful degree
of scholastic precision; and they exercised, probably, a not unimportant
influence upon the general reception of that dogma. They are undoubtedly
works of genius, powerful in thought, feeling and expression.


  Medieval hymns.

These and other medieval hymn-writers of the 12th and 13th centuries may
be described, generally, as poet-schoolmen. Their tone is contemplative,
didactic, theological; they are especially fertile and ingenious in the
field of mystical interpretation. Two great monasteries in the East had,
in the 8th and 9th centuries, been the principal centres of Greek
hymnology; and, in the West, three monasteries--St Gall, near Constance
(which was long the especial seat of German religious literature), Cluny
in Burgundy and St Victor, near Paris--obtained a similar distinction.
St Gall produced, besides Notker, several distinguished sequence
writers, probably his pupils--Hartmann, Hermann and Gottschalk--to the
last of whom Neale ascribes the "Alleluiatic Sequence" ("Cantemus cuncti
melodum nunc Alleluia"), well known in England through his translation,
"The strain upraise of joy and praise." The chief poets of Cluny were
two of its abbots, Odo and Peter the Venerable (1122-1156), and one of
Peter's monks, Bernard of Morlaix, who wrote the remarkable poem on
"Contempt of the World" in about 3000 long rolling "leonine-dactylic"
verses, from parts of which Neale's popular hymns, "Jerusalem the
golden," &c., are taken. The abbey of St Victor, besides Adam and his
follower Pistor, was destined afterwards to produce the most popular
church poet of the 17th century.


  Bernard of Clairvaux.

There were other distinguished Latin hymn-writers of the later medieval
period besides those already mentioned. The name of St Bernard of
Clairvaux cannot be passed over with the mere mention of the fact that
he was the author of some metrical sequences. He was, in truth, the
father, in Latin hymnody, of that warm and passionate form of devotion
which some may consider to apply too freely to Divine Objects the
language of human affection, but which has, nevertheless, been popular
with many devout persons, in Protestant as well as Roman Catholic
churches. F. von Spee, "Angelus Silesius," Madame Guyon, Bishop Ken,
Count Zinzendorf and Frederick William Faber may be regarded as
disciples in this school. Many hymns, in various languages, have been
founded upon St Bernard's "Jesu dulcis memoria" ("Jesu, the very thought
of Thee"), "Jesu dulcedo cordium" ("Jesu, Thou joy of loving hearts")
and "Jesu Rex admirabilis" ("O Jesu, King most wonderful")--three
portions of one poem, nearly 200 lines long. Pietro Damiani, the friend
of Pope Gregory VII, Marbode, bishop of Rennes, in the 11th, Hildebert,
archbishop of Tours, in the 12th, and St Bonaventura in the 13th
centuries, are other eminent men who added poetical fame as
hymnographers to high public distinction.

Before the time of the Reformation, the multiplication of sequences
(often as unedifying in matter as unpoetical in style) had done much to
degrade the common conception of hymnody. In some parts of France,
Portugal, Sardinia and Bohemia, their use in the vernacular language had
been allowed. In Germany also there were vernacular sequences as early
as the 12th century, specimens of which may be seen in the third chapter
of C. Winkworth's _Christian Singers of Germany_. Scoffing parodies upon
sequences are said to have been among the means used in Scotland to
discredit the old church services. After the 15th century they were
discouraged at Rome. They retained for a time some of their old
popularity among German Protestants, and were only gradually
relinquished in France. A new "prose," in honour of St Maxentia, is
among the compositions of Jean Baptiste Santeul; and Dr Daniel's second
volume closes with one written in 1855 upon the dogma of the Immaculate
Conception.


    Roman revision of hymns.

  The taste of the Renaissance was offended by all deviations from
  classical prosody and Latinity. Pope Leo X. directed the whole body of
  the hymns in use at Rome to be reformed; and the _Hymni novi
  ecclesiastici juxta veram metri et Latinitatis normam_, prepared by
  Zacharie Ferreri (1479-1530), a Benedictine of Monte Cassino,
  afterwards a Carthusian and bishop of Guardia, to whom Leo had
  committed that task, appeared at Rome in 1525, with the sanction of a
  later pope, Clement VII. The next step was to revise the whole Roman
  Breviary. That undertaking, after passing through several stages under
  different popes (particularly Pius V. and Clement VIII.), was at last
  brought to a conclusion by Urban VIII., in 1631. From this revised
  Breviary a large number of medieval hymns, both of the earlier and the
  later periods, were excluded; and in their places many new hymns,
  including some by Pope Urban himself, and some by Cardinal Bellarmine
  and another cardinal (Silvius Antonianus) were introduced. The hymns
  of the primitive epoch, from Hilary to Gregory the Great, for the most
  part retained their places (especially in the offices for every day of
  the week); and there remained altogether from seventy to eighty of
  earlier date than the 11th century. Those, however, which were so
  retained were freely altered, and by no means generally improved. The
  revisers appointed by Pope Urban (three learned Jesuits--Strada,
  Gallucci and Petrucci) professed to have made "as few changes as
  possible" in the works of Ambrose, Gregory, Prudentius, Sedulius,
  Fortunatus and other "poets of great name." But some changes, even in
  those works, were made with considerable boldness; and the pope, in
  the "constitution" by which his new book was promulgated, boasted
  that, "with the exception of a very small number ('perpaucis'), which
  were either prose or merely rhythmical, all the hymns had been made
  conformable to the laws of prosody and Latinity, those which could not
  be corrected by any milder method being entirely rewritten." The
  latter fate befel, among others, the beautiful "Urbs beata
  Hierusalem," which now assumed the form (to many, perhaps, better
  known), of "Caelestis urbs Jerusalem." Of the "very few" which were
  spared, the chief were "Ave maris stella" ("Gentle star of ocean"),
  "Dies Irae," "Stabat Mater dolorosa," the hymns of Thomas Aquinas,
  two of St Bernard and one Ambrosian hymn, "Jesu nostra Redemptio" ("O
  Jesu, our Redemption"), which approaches nearer than others to the
  tone of St Bernard. A then recent hymn of St Francis Xavier, with
  scarcely enough merit of any kind to atone for its neglect of prosody,
  "O Deus, ego amo Te" ("O God, I love Thee, not because"), was at the
  same time introduced without change. This hymnary of Pope Urban VIII.
  is now in general use throughout the Roman Communion.


    Parisian revisions.

  The Parisian hymnary underwent three revisions--the first in 1527,
  when a new "Psaltery with hymns" was issued. In this such changes only
  were made as the revisers thought justifiable upon the principle of
  correcting supposed corruptions of the original text. Of these, the
  transposition, "Urbs Jerusalem beata," instead of "Urbs beata
  Hierusalem," may be taken as a typical example. The next revision was
  in 1670-1680, under Cardinal Péréfixe, preceptor of Louis XIV., and
  Francis Harlay, successively archbishops of Paris, who employed for
  this purpose Claude Santeul, of the monastery of St Magloire, and,
  through him, obtained the assistance of other French scholars,
  including his more celebrated brother, Jean Baptiste Santeul, of the
  abbey of St Victor--better known as "Santolius Victorinus." The third
  and final revision was completed in 1735, under the primacy of
  Cardinal Archbishop de Vintimille, who engaged for it the services of
  Charles Coffin, then rector of the university of Paris. Many old hymns
  were omitted in Archbishop Harlay's Breviary, and a large number of
  new compositions, by the Santeuls and others, was introduced. It
  still, however, retained in their old places (without further changes
  than had been made in 1527) about seventy of earlier date than the
  11th century--including thirty-one Ambrosian, one by Hilary, eight by
  Prudentius, seven by Fortunatus, three by Paul the Deacon, two each by
  Sedulius, Elpis, Gregory and Hrabanus Maurus, "Veni Creator" and "Urbs
  Jerusalem beata." Most of these disappeared in 1735, although Cardinal
  Vintimille, in his preface, professed to have still admitted the old
  hymns, except when the new were better--("veteribus hymnis locus datus
  est, nisi quibus, ob sententiarum vim, elegantiam verborum, et
  teneriores pietatis sensus, recentiores anteponi satius visum est").
  The number of the new was, at the same time, very largely increased.
  Only twenty-one more ancient than the 16th century remained, of which
  those belonging to the primitive epoch were but eight, viz. four
  Ambrosian, two by Fortunatus and one each by Prudentius and Gregory.
  The number of Jean Baptiste Santeul's hymns rose to eighty-nine; those
  by Coffin--including some old hymns, e.g. "Jam lucis orto sidere"
  ("Once more the sun is beaming bright"), which he substantially
  re-wrote--were eighty-three; those of other modern French writers,
  ninety-seven. Whatever opinion may be entertained of the principles on
  which these Roman and Parisian revisions proceeded, it would be unjust
  to deny very high praise as hymn-writers to several of their poets,
  especially to Coffin and Jean Baptiste Santeul. The noble hymn by
  Coffin, beginning--

    "O luce qui mortalibus        "O Thou who in the light dost dwell,
     Lates inaccessa, Deus,        To mortals unapproachable,
     Praesente quo sancti tremunt  Where angels veil them from Thy rays,
     Nubuntque vultus angeli,"     And tremble as they gaze,"

  and several others of his works, breathe the true Ambrosian spirit;
  and though Santeul (generally esteemed the better poet of the two)
  delighted in alcaics, and did not greatly affect the primitive manner,
  there can be no question as to the excellence of such hymns as his
  "Fumant Sabaeis templa vaporibus" ("Sweet incense breathes around"),
  "Stupete gentes, fit Deus hostia" ("Tremble, ye Gentile lands"),
  "Hymnis dum resonat curia caelitum" ("Ye in the house of heavenly
  morn"), and "Templi sacratas pande, Sion, fores" ("O Sion, open wide
  thy gates"). It is a striking testimony to the merits of those writers
  that such accomplished translators as the Rev. Isaac Williams and the
  Rev. John Chandler appear (from the title-page of the latter, and the
  prefaces of both) to have supposed their hymns to be "ancient" and
  "primitive." Among the other authors associated with them, perhaps the
  first place is due to the Abbé Besnault, of Sens, who contributed to
  the book of 1735 the "Urbs beata vera pacis Visio Jerusalem," in the
  opinion of Neale "much superior" to the "Caelestis urbs Jerusalem" of
  the Roman Breviary. This stood side by side with the "Urbs Jerusalem
  beata" of 1527 (in the office for the dedication of churches) till
  1822, when the older form was at last finally excluded by Archbishop
  de Quelen.

  The Parisian Breviary of 1735 remained in use till the national French
  service-books were superseded (as they have lately been, generally, if
  not universally) by the Roman. Almost all French dioceses followed,
  not indeed the Breviary, but the example, of Paris; and before the end
  of the 18th century the ancient Latin hymnody was all but banished
  from France.


    Modern Latin hymns.

  In some parts of Germany, after the Reformation, Latin hymns continued
  to be used even by Protestants. This was the case at Halberstadt until
  quite a recent date. In England, a few are still occasionally used in
  the older universities and colleges. Some, also, have been composed in
  both countries since the Reformation. The "Carmina lyrica" of Johann
  Jakob Balde, a native of Alsace, and a Jesuit priest in Bavaria, have
  received high commendation from very eminent German critics,
  particularly Herder and Augustus Schlegel. Some of the Latin hymns of
  William Alard (1572-1645), a Protestant refugee from Belgium, and
  pastor in Holstein, have been thought worthy of a place in Archbishop
  Trench's selection. Two by W. Petersen (printed at the end of
  Haberkorn's supplement to Jacobi's _Psalmodia Germanica_) are good in
  different ways--one, "Jesu dulcis amor meus" ("Jesus, Thee my soul
  doth love"), being a gentle melody of spiritual devotion, and the
  other, entitled _Spes Sionis_, violently controversial against Rome.
  An English hymn of the 17th century, in the Ambrosian style, "Te Deum
  Patrem colimus" ("Almighty Father, just and good"), is sung on every
  May-Day morning by the choristers of Magdalen College, Oxford, from
  the top of the tower of their chapel; and another in the style of the
  Renaissance, of about the same date, "Te de profundis, summe Rex"
  ("Thee from the depths, Almighty King"), long formed part of a grace
  formerly sung by the scholars of Winchester College.


  Luther.

5. _German Hymnody._--Luther was a proficient in and a lover of music.
He desired (as he says in the preface to his hymn-book of 1545) that
this "beautiful ornament" might "in a right manner serve the great
Creator and His Christian people." The persecuted Bohemian or Hussite
Church, then settled on the borders of Moravia under the name of "United
Brethren," had sent to him, on a mission in 1522, Michael Weiss, who not
long afterwards published a number of German translations from old
Bohemian hymns (known as those of the "Bohemian Brethren"), with some of
his own. These Luther highly approved and recommended. He himself, in
1522, published a small volume of eight hymns, which was enlarged to 63
in 1527, and to 125 in 1545. He had formed what he called a "house
choir" of musical friends, to select such old and popular tunes (whether
secular or ecclesiastical) as might be found suitable, and to compose
new melodies, for church use. His fellow labourers in this field
(besides Weiss) were Justus Jonas, his own especial colleague; Paul
Eber, the disciple and friend of Melanchthon; John Walther, choirmaster
successively to several German princes, and professor of arts, &c., at
Wittenberg; Nicholas Decius, who from a monk became a Protestant teacher
in Brunswick, and translated the "Gloria in Excelsis," &c.; and Paul
Speratus, chaplain to Duke Albert of Prussia in 1525. Some of their
works are still popular in Germany. Weiss's "Funeral Hymn," "Nun lasst
uns den Leib begraben" ("Now lay we calmly in the grave"); Eber's "Herr
Jesu Christ, wahr Mensch und Gott" ("Lord Jesus Christ, true Man and
God"), and "Wenn wir in höchsten Nöthen sein" ("When in the hour of
utmost need"); Walther's "New Heavens and new Earth" ("Now fain my
joyous heart would sing"); Decius's "To God on high be thanks and
praise"; and Speratus's "Salvation now has come for all," are among
those which at the time produced the greatest effect, and are still best
remembered.

Luther's own hymns, thirty-seven in number (of which about twelve are
translations or adaptations from Latin originals), are for the principal
Christian seasons; on the sacraments, the church, grace, death, &c.; and
paraphrases of seven psalms, of a passage in Isaiah, and of the Lord's
Prayer, Ten Commandments, Creed, Litany and "Te Deum." There is also a
very touching and stirring song on the martyrdom of two youths by fire
at Brussels, in 1523-1524. Homely and sometimes rugged in form, and for
the most part objective in tone, they are full of fire, manly simplicity
and strong faith. Three rise above the rest. One for Christmas, "Vom
Himmel hoch da komm ich her" ("From Heaven above to earth I come"), has
a reverent tenderness, the influence of which may be traced in many
later productions on the same subject. That on salvation through Christ,
of a didactic character, "Nun freuet euch, lieben Christen g'mein"
("Dear Christian people, now rejoice"), is said to have made many
conversions, and to have been once taken up by a large congregation to
silence a Roman Catholic preacher in the cathedral of Frankfort.
Pre-eminent above all is the celebrated paraphrase of the 46th Psalm:
"Ein' feste Burg ist unser Gott" ("A sure stronghold our God is
He")--"the production" (as Ranke says) "of the moment in which Luther,
engaged in a conflict with a world of foes, sought strength in the
consciousness that he was defending a divine cause which could never
perish." Carlyle compares it to "a sound of Alpine avalanches, or the
first murmur of earthquakes." Heine called it "the Marseillaise of the
Reformation."

Luther spent several years in teaching his people at Wittenberg to sing
these hymns, which soon spread over Germany. Without adopting the
hyperbolical saying of Coleridge, that "Luther did as much for the
Reformation by his hymns as by his translation of the Bible," it may
truly be affirmed, that, among the secondary means by which the success
of the Reformation was promoted, none was more powerful. They were sung
everywhere--in the streets and fields as well as the churches, in the
workshop and the palace, "by children in the cottage and by martyrs on
the scaffold." It was by them that a congregational character was given
to the new Protestant worship. This success they owed partly to their
metrical structure, which, though sometimes complex, was recommended to
the people by its ease and variety; and partly to the tunes and melodies
(many of them already well known and popular) to which they were set.
They were used as direct instruments of teaching, and were therefore, in
a large measure, didactic and theological; and it may be partly owing to
this cause that German hymnody came to deviate, so soon and so generally
as it did, from the simple idea expressed in the ancient Augustinian
definition, and to comprehend large classes of compositions which, in
most other countries, would be thought hardly suitable for church use.


  Followers of Luther

The principal hymn-writers of the Lutheran school, in the latter part of
the 16th century, were Nikolaus Selnecker, Herman and Hans Sachs, the
shoemaker of Nuremberg, also known in other branches of literature. All
these wrote some good hymns. They were succeeded by men of another sort,
to whom F. A. Cunz gives the name of "master-singers," as having raised
both the poetical and the musical standard of German
hymnody:--Bartholomäus Ringwaldt, Ludwig Helmbold, Johannes Pappus, Martin
Schalling, Rutilius and Sigismund Weingartner. The principal topics of
their hymns (as if with some foretaste of the calamities which were soon
to follow) were the vanity of earthly things, resignation to the Divine
will, and preparation for death and judgment. The well-known English hymn,
"Great God, what do I see and hear," is founded upon one by Ringwaldt. Of
a quite different character were two of great beauty and universal
popularity, composed by Philip Nicolai, a Westphalian pastor, during a
pestilence in 1597, and published by him, with fine chorales, two years
afterwards. One of these (the "Sleepers wake! a voice is calling," of
Mendelssohn's oratorio, _St Paul_) belongs to the family of Advent or New
Jerusalem hymns. The other, a "Song of the believing soul concerning the
Heavenly Bridegroom" ("Wie schön leucht't uns der Morgenstern"--"O morning
Star, how fair and bright"), became the favourite marriage hymn of
Germany.


  Period of Thirty Years' War.

The hymns produced during the Thirty Years' War are characteristic of
that unhappy time, which (as Miss Winkworth says) "caused religious men
to look away from this world," and made their songs more and more
expressive of personal feelings. In point of refinement and graces of
style, the hymn-writers of this period excelled their predecessors.
Their taste was chiefly formed by the influence of Martin Opitz, the
founder of what has been called the "first Silesian school" of German
poetry, who died comparatively young in 1639, and who, though not of any
great original genius, exercised much power as a critic. Some of the
best of these works were by men who wrote little. In the famous
battle-song of Gustavus Adolphus, published (1631) after the victory of
Breitenfeld, for the use of his army, "Verzage nicht du Häuflein klein"
("Fear not, O little flock, the foe"), we have almost certainly a
composition of the hero-king himself, the versification corrected by his
chaplain Jakob Fabricius (1593-1654) and the music composed by Michael
Altenburg, whose name has been given to the hymn. This, with Luther's
paraphrase of the 67th Psalm, was sung by Gustavus and his soldiers
before the battle of Lützen in 1632. Two very fine hymns, one of prayer
for deliverance and peace, the other of trust in God under calamities,
were written about the same time by Matthäus Löwenstern, a saddler's
son, poet, musician and statesman, who was ennobled after the peace by
the emperor Ferdinand III. Martin Rinckhart, in 1636, wrote the "Chorus
of God's faithful children" ("Nun danket alle Gott"--"Now thank we all
our God"), introduced by Mendelssohn in his "Lobgesang," which has been
called the "Te Deum" of Germany, being usually sung on occasions of
public thanksgiving. Weissel, in 1635, composed a beautiful Advent hymn
("Lift up your heads, ye mighty gates"), and J. M. Meyfart, professor of
theology at Erfurt, in 1642, a fine adaptation of the ancient "Urbs
beata Hierusalem." The hymn of trust in Providence by George Neumark,
librarian to that duke of Weimar ("Wer nur den lieben Gott lässt
walten"--"Leave God to order all thy ways"), is scarcely, if at all,
inferior to that of Paul Gerhardt on the same theme. Paul Flemming, a
great traveller and lover of nature, who died in 1639, also wrote
excellent compositions, coloured by the same tone of feeling; and some,
of great merit, were composed, soon after the close of the war, by
Louisa Henrietta, electress of Brandenburg, granddaughter of the famous
admiral Coligny, and mother of the first king of Prussia. With these may
be classed (though of later date) a few striking hymns of faith and
prayer under mental anxiety, by Anton Ulrich, duke of Brunswick.


  Rist.

  Dach.

The most copious, and in their day most esteemed, hymn-writers of the
first half of the 17th century, were Johann Heermann and Johann Rist.
Heermann, a pastor in Silesia, the theatre (in a peculiar degree) of war
and persecution, experienced in his own person a very large share of the
miseries of the time, and several times narrowly escaped a violent
death. His _Devoti musica cordis_, published in 1630, reflects the
feelings natural under such circumstances. With a correct style and good
versification, his tone is subjective, and the burden of his hymns is
not praise, but prayer. Among his works (which enter largely into most
German hymn-books), two of the best are the "Song of Tears" and the
"Song of Comfort," translated by Miss Winkworth in her _Christian
Singers of Germany_. Rist published about 600 hymns, "pressed out of
him," as he said, "by the cross." He was a pastor, and son of a pastor,
in Holstein, and lived after the peace to enjoy many years of
prosperity, being appointed poet-laureate to the emperor and finally
ennobled. The bulk of his hymns, like those of other copious writers,
are of inferior quality; but some, particularly those for Advent,
Epiphany, Easter Eve and on Angels, are very good. They are more
objective than those of Heermann, and written, upon the whole, in a more
manly spirit. Next to Heermann and Rist in fertility of production, and
above them in poetical genius, was Simon Dach, professor of poetry at
Königsberg, who died in 1659. Miss Winkworth ranks him high among German
poets, "for the sweetness of form and depth of tender contemplative
emotion to be found in his verses."


  Gerhardt.

  Franck.

  Scheffler.

The fame of all these writers was eclipsed in the latter part of the
same century by three of the greatest hymnographers whom Germany has
produced--Paul Gerhardt (1604-1676), Johann Franck (1618-1677) and
Johann Scheffler (1624-1677), the founder of the "second Silesian
school," who assumed the name of "Angelus Silesius." Gerhardt is by
universal consent the prince of Lutheran poets. His compositions, which
may be compared, in many respects, to those of the _Christian Year_, are
lyric poems, of considerable length, rather than hymns, though many
hymns have been taken from them. They are, with few exceptions,
subjective, and speak the language of individual experience. They occupy
a middle ground between the masculine simplicity of the old Lutheran
style and the highly wrought religious emotion of the later pietists,
towards whom they on the whole incline. Being nearly all excellent, it
is not easy to distinguish among the 123 those which are entitled to the
highest praise. Two, which were written one during the war and the other
after the conclusion of peace, "Zeuch ein zu deinen Thoren" ("Come to
Thy temple here on earth"), and "Gottlob, nun ist erschollen" ("Thank
God, it hath resounded"), are historically interesting. Of the rest, one
is well known and highly appreciated in English through Wesley's
translation, "Commit thou all thy ways"; and the evening and
spring-tide hymns ("Now all the woods are sleeping" and "Go forth, my
heart, and seek delight") show an exquisite feeling for nature; while
nothing can be more tender and pathetic than "Du bist zwar mein und
bleibest mein" ("Thou'rt mine, yes, still thou art mine own"), on the
death of his son. Franck, who was burgomaster of Guben in Lusatia, has
been considered by some second only to Gerhardt. If so, it is with a
great distance between them. His approach to the later pietists is
closer than that of Gerhardt. His hymns were published, under the title
of _Geistliche und weltliche Gedichte_, in 1674, some of them being
founded on Ambrosian and other Latin originals. Miss Winkworth gives
them the praise of a condensed and polished style and fervid and
impassioned thought. It was after his conversion to Roman Catholicism
that Scheffler adopted the name of "Angelus Silesius," and published in
1657 his hymns, under a fantastic title, and with a still more fantastic
preface. Their keynote is divine love; they are enthusiastic, intense,
exuberant in their sweetness, like those of St Bernard among medieval
poets. An adaptation of one of them, by Wesley, "Thee will I love, my
Strength, my Tower," is familiar to English readers. Those for the first
Sunday after Epiphany, for Sexagesima Sunday and for Trinity Sunday, in
_Lyra Germanica_, are good examples of his excellences, with few of his
defects. His hymns are generally so free from the expression, or even
the indirect suggestion, of Roman Catholic doctrine, that it has been
supposed they were written before his conversion, though published
afterwards. The evangelical churches of Germany found no difficulty in
admitting them to that prominent place in their services which they have
ever since retained.


  Pietists.

Towards the end of the 17th century, a new religious school arose, to
which the name of "Pietists" was given, and of which Philipp Jakob
Spener was esteemed the founder. He and his pupils and successors,
August Hermann Francke and Anastasius Freylinghausen, all wrote hymns.
Spener's hymns are not remarkable, and Francke's are not numerous.
Freylinghausen was their chief singer; his rhythm is lively, his music
florid; but, though his book attained extraordinary popularity, he was
surpassed in solid merit by other less fertile writers of the same
school. The "Auf hinauf zu deiner Freude" ("Up, yes, upward to thy
gladness") of Schade may recall to an English reader a hymn by Seagrave,
and more than one by Lyte; the "Malabarian hymn" (as it was called by
Jacobi) of Johann Schütz, "All glory to the Sovereign Good," has been
popular in England as well as Germany; and one of the most exquisite
strains of pious resignation ever written is "Whate'er my God ordains is
right," by Samuel Rodigast.


  Neander.

Joachim Neander, a schoolmaster at Düsseldorf, and a friend of Spener
and Schütz (who died before the full development of the "Pietistic"
school), was the first man of eminence in the "Reformed" or Calvinistic
Church who imitated Lutheran hymnody. This he did, while suffering
persecution from the elders of his own church for some other religious
practices, which he had also learnt from Spener's example. As a poet, he
is sometimes deficient in art; but there is feeling, warmth and
sweetness in many of his "Bundeslieder" or "Songs of the Covenant," and
they obtained general favour, both in the Reformed and in Lutheran
congregations. The Summer Hymn ("O Thou true God alone") and that on the
glory of God in creation ("Lo, heaven and earth and sea and air") are
instances of his best style.


  Schmolke.

  Dessler.

  Hiller.

  Arnold.

  Tersteegen.

  Zinzendorf.

With the "Pietists" may be classed Benjamin Schmolke and Dessler,
representatives of the "Orthodox" division of Spener's school; Philipp
Friedrich Hiller, their leading poet in South Germany; Gottfried Arnold
and Gerhard Tersteegen, who were practically independent of
ecclesiastical organization, though connected, one with the "Orthodox"
and the other with the "Reformed" churches; and Nikolaus Ludwig, Graf
von Zinzendorf. Schmolke, a pastor in Silesia, called the Silesian Rist
(1672-1737), was perhaps the most voluminous of all German hymn-writers.
He wrote 1188 religious poems and hymns, a large proportion of which do
not rise above mediocrity. His style, if less refined, is also less
subjective and more simple than that of most of his contemporaries.
Among his best and most attractive works, which indeed, it would be
difficult to praise too highly, are the "Hosianna David's Sohn," for
Palm Sunday--much resembling a shorter hymn by Jeremy Taylor; and the
Ascension, Whitsuntide and Sabbath hymns--"Heavenward doth our journey
tend," "Come deck our feast to-day," and "Light of light, enlighten me."
Dessler was a greater poet than Schmolke. Few hymns, of the subjective
kind, are better than his "I will not let Thee go, Thou Help in time of
need," "O Friend of souls, how well is me," and "Now, the pearly gates
unfold." Hiller (1699-1769), was a pastor in Württemberg who, falling
into ill-health during the latter part of his ministry, published a
_Geistliche Liederhöstlein_ in a didactic vein, with more taste than
power, but (as Miss Winkworth says) in a tone of "deep, thoughtful,
practical piety." They were so well adapted to the wants of his people
that to this day Hiller's Casket is prized, next to their Bibles, by the
peasantry of Württemberg; and the numerous emigrants from that part of
Germany to America and other foreign countries generally take it with
them wherever they go. Arnold, a professor at Giessen, and afterwards a
pastor in Brandenburg, was a man of strong will, uncompromising
character and austere views of life, intolerant and controversial
towards those whose doctrine or practice he disapproved, and more
indifferent to separatism and sectarianism than the "orthodox" generally
thought right. His hymns, like those of Augustus M. Toplady, whom in
these respects he resembled, unite with considerable strength more
gentleness and breadth of sympathy than might be expected from a man of
such a character. Tersteegen (1697-1769), who never formally separated
himself from the "Reformed" communion, in which he was brought up, but
whose sympathies were with the Moravians and with Zinzendorf, was, of
all the more copious German hymn-writers after Luther, perhaps the most
remarkable man. Pietist, mystic and missionary, he was also a great
religious poet. His 111 hymns were published In 1731, in a volume called
_Geistlicher Blumengärtlein inniger_ Seelen. They are intensely
individual, meditative and subjective. Wesley's adaptations of two--"Lo!
God is here; let us adore," and "Thou hidden Love of God, whose
source"--are well known. Among those translated by Miss Winkworth, "O
God, O Spirit, Light of all that live," and "Come, brethren, let us go,"
are specimens which exhibit favourably his manner and power. Miss Cox
speaks of him as "a gentle heaven-inspired soul, whose hymns are the
reflection of a heavenly, happy life, his mind being full of a
child-like simplicity"; and his own poem on the child-character, which
Miss Winkworth has appropriately connected with Innocents' day ("Dear
Soul, couldst thou become a child")--one of his best compositions,
exquisitely conceived and expressed--shows that this was in truth the
ideal which he sought to realize. The hymns of Zinzendorf are often
disfigured by excess in the application of the language and imagery of
human affections to divine objects; and this blemish is also found in
many later Moravian hymns. But one hymn, at least, of Zinzendorf may be
mentioned with unqualified praise, as uniting the merits of force,
simplicity and brevity--"Jesu, geh voran" ("Jesus, lead the way"), which
is taught to most children of religious parents in Germany. Wesley's
"Jesus, Thy blood and righteousness" is a translation from Zinzendorf.


  Gellert.

The transition from Tersteegen and Zinzendorf to Gellert and Klopstock
marks strongly the reaction against Pietism which took place towards the
middle of the 18th century. The _Geistlichen Oden und Lieder_ of
Christian F. Gellert were published in 1757, and are said to have been
received with an enthusiasm almost like that which "greeted Luther's
hymns on their first appearance." It is a proof of the moderation both
of the author and of his times that they were largely used, not only by
Protestant congregations, but in those German Roman Catholic churches in
which vernacular services had been established through the influence of
the emperor Joseph II. They became the model which was followed by most
succeeding hymn-writers, and exceeded all others in popularity till the
close of the century, when a new wave of thought was generated by the
movement which produced the French Revolution. Since that time they have
been, perhaps, too much depreciated. They are, indeed, cold and
didactic, as compared with Scheffler or Tersteegen; but there is
nevertheless in them a spirit of genuine practical piety; and, if not
marked by genius, they are pure in taste, and often terse, vigorous and
graceful.


  Klopstock.

Klopstock, the author of the _Messiah_, cannot be considered great as a
hymn-writer, though his "Sabbath Hymn" (of which there is a version in
_Hymns from the Land of Luther_) is simple and good. Generally his hymns
(ten of which are translated in Sheppard's _Foreign Sacred Lyre_) are
artificial and much too elaborate.


  Fouqué.

Of the "romantic" school, which came in with the French Revolution, the
two leading writers are Friedrich Leopold von Hardenberg, called
"Novalis," and Friedrich de la Motte Fouqué, the celebrated author of
_Undine_ and _Sintram_--both romance-writers, as well as poets. The
genius of Novalis was early lost to the world; he died in 1801, not
thirty years old. Some of his hymns are very beautiful; but even in such
works as "Though all to Thee were faithless," and "If only He is mine,"
there is a feeling of insulation and of despondency as to good in the
actual world, which was perhaps inseparable from his ecclesiastical
idealism. Fouqué survived till 1843. In his hymns there is the same deep
flow of feeling, richness of imagery and charm of expression which
distinguishes his prose works. The two missionary hymns--"Thou, solemn
Ocean, rollest to the strand," and "In our sails all soft and
sweetly"--and the exquisite composition which finds its motive in the
gospel narrative of blind Bartimeus, "Was du vor tausend Jahren" (finely
translated both by Miss Winkworth and by Miss Cox), are among the best
examples.


  Spitta.

The later German hymn-writers of the 19th century belong, generally, to
the revived "Pietistic" school. Some of the best, Johann Baptist von
Albertini, Friedrich Adolf Krummacher, and especially Karl Johann
Philipp Spitta (1801-1859) have produced works not unworthy of the fame
of their nation. Mr Massie, the able translator of Spitta's _Psalter und
Harfe_ (Leipzig, 1833), speaks of it as having "obtained for him in
Germany a popularity only second to that of Paul Gerhardt." In Spitta's
poems (for such they generally are, rather than hymns) the subjective
and meditative tone is tempered, not ungracefully, with a didactic
element; and they are not disfigured by exaggerated sentiment, or by a
too florid and rhetorical style.

6. _British Hymnody._--After the Reformation, the development of hymnody
was retarded, in both parts of Great Britain, by the example and
influence of Geneva. Archbishop Cranmer appears at one time to have been
disposed to follow Luther's course, and to present to the people, in an
English dress, some at least of the hymns of the ancient church. In a
letter to King Henry VIII. (October 7, 1544), among some new
"processions" which he had himself translated, into English, he mentions
the Easter hymn, "Salve, festa dies, toto memorabilis aevo" ("Hail, glad
day, to be joyfully kept through all generations"), of Fortunatus. In
the "Primer" of 1535 (by Marshall) and the one of 1539 (by Bishop Hilsey
of Rochester, published by order of the vicar-general Cromwell) there
had been several rude English hymns, none of them taken from ancient
sources. King Henry's "Primer" of 1545 (commanded by his injunction of
the 6th of May 1545 to be used throughout his dominions) was formed on
the model of the daily offices of the Breviary; and it contains English
metrical translations from some of the best-known Ambrosian and other
early hymns. But in the succeeding reign different views prevailed. A
new direction had been given to the taste of the "Reformed"
congregations in France and Switzerland by the French metrical
translation of the Old Testament Psalms, which appeared about 1540. This
was the joint work of Clement Marot, valet or groom of the chamber to
Francis I., and Theodore Beza, then a mere youth, fresh from his studies
at Orleans.


  Marot's Psalms.

Marot's psalms were dedicated to the French king and the ladies of
France, and, being set to popular airs, became fashionable. They were
sung by Francis himself, the queen, the princesses and the courtiers,
upon all sorts of secular occasions, and also, more seriously and
religiously, by the citizens and the common people. They were soon
perceived to be a power on the side of the Reformation. Calvin, who had
settled at Geneva in the year of Marot's return to Paris, was then
organizing his ecclesiastical system. He rejected the hymnody of the
breviaries and missals, and fell back upon the idea, anciently held by
Paul of Samosata, and condemned by the fourth council of Toledo, that
whatever was sung in churches ought to be taken out of the Scriptures.
Marot's Psalter, appearing thus opportunely, was introduced into his new
system of worship, and appended to his catechism. On the other hand, it
was interdicted by the Roman Catholic priesthood. Thus it became a badge
to the one party of the "reformed" profession, and to the other of
heresy.


  Sternhold and Hopkins.

The example thus set produced in England the translation commonly known
as the "Old Version" of the Psalms. It was begun by Thomas Sternhold,
whose position in the household of Henry VIII., and afterwards of Edward
VI., was similar to that of Marot with Francis I., and whose services to
the former of those kings were rewarded by a substantial legacy under
his will. Sternhold published versions of nineteen Psalms, with a
dedication to King Edward, and died soon afterwards. A second edition
appeared in 1551, with eighteen more Psalms added, of Sternhold's
translating, and seven others by John Hopkins, a Suffolk clergyman. The
work was continued during Queen Mary's reign by British refugees at
Geneva, the chief of whom were William Whittingham, afterwards dean of
Durham, who succeeded John Knox as minister of the English congregation
there, and William Kethe or Keith, said by Strype to have been a
Scotsman. They published at Geneva in 1556 a service-book, containing
fifty-one English metrical psalms, which number was increased, in later
editions, to eighty-seven. On the accession of Queen Elizabeth, this
Genevan Psalmody was at once brought into use in England--first
(according to a letter of Bishop Jewell to Peter Martyr, dated 5th March
1560) in one London church, from which it quickly spread to others both
in London and in other cities. Jewell describes the effect produced by
large congregations, of as many as 6000 persons, young and old, women
and children, singing it after the sermons at St Paul's Cross--adding,
"Id sacrificos et diabolum aegre habet; vident enim sacras conciones hoc
pacto profundius descendere in hominum animos." The first edition of the
completed "Old Version" (containing forty Psalms by Sternhold,
sixty-seven by Hopkins, fifteen by Whittingham, six by Kethe and the
rest by Thomas Norton the dramatist, Robert Wisdom, John Marckant and
Thomas Churchyard) appeared in 1562.

  In the meantime, the Books of Common Prayer, of 1549, 1552 and 1559,
  had been successively established as law by the acts of uniformity of
  Edward VI. and Queen Elizabeth. In these no provision was made for the
  use of any metrical psalm or hymn on any occasion whatever, except at
  the consecration of bishops and the ordination of priests, in which
  offices (first added in 1552) an English version of "Veni Creator"
  (the longer of the two now in use) was appointed to be "said or sung."
  The canticles, "Te Deum," "Benedicite," the Nicene and Athanasian
  Creeds, the "Gloria in Excelsis," and some other parts of the
  communion and other special offices were also directed to be "said or
  sung"; and, by general rubrics, the chanting of the whole service was
  allowed.

  The silence, however, of the rubrics in these books as to any other
  singing was not meant to exclude the use of psalms not expressly
  appointed, when they could be used without interfering with the
  prescribed order of any service. It was expressly provided by King
  Edward's first act of uniformity (by later acts made applicable to the
  later books) that it should be lawful "for all men, as well in
  churches, chapels, oratories or other places, to use openly any psalms
  or prayers taken out of the Bible, at any due time, not letting or
  omitting thereby the service, or any part thereof, mentioned in the
  book." And Queen Elizabeth, by one of the injunctions issued in the
  first year of her reign, declared her desire that the provision made,
  "in divers collegiate and also some parish churches, for singing in
  the church, so as to promote the laudable service of music," should
  continue. After allowing the use of "a modest and distinct song in all
  parts of the common prayers of the church, so that the same may be as
  plainly understanded as if it were read without singing," the
  injunction proceeded thus--"And yet, nevertheless, for the comforting
  of such that delight in music, it may be permitted that in the
  beginning or in the end of the Common Prayer, either at morning or
  evening, there may be sung an hymn, or such like song to the praise of
  Almighty God, in the best sort of melody and music that may be
  conveniently devised, having respect that the sentence" (i.e. sense)
  "of hymn may be understanded and perceived."

  The "Old Version," when published (by John Daye, for the Stationers'
  Company, "cum gratia et privilegio Regiae Majestatis"), bore upon the
  face of it that it was "newly set forth, and allowed to be sung of the
  people in churches, before and after morning and evening prayer, as
  also before and after the sermon." The question of its authority has
  been at different times much debated, chiefly by Peter Heylyn and
  Thomas Warton on one side (both of whom disliked and disparaged it),
  and by William Beveridge, bishop of St Asaph, and the Rev. H. J. Todd
  on the other. Heylyn says, it was "permitted rather than allowed,"
  which seems to be a distinction without much difference. "Allowance,"
  which is all that the book claimed for itself, is authorization by way
  of permission, not of commandment. Its publication in that form could
  hardly have been licensed, nor could it have passed into use as it did
  without question, throughout the churches of England, unless it had
  been "allowed" by some authority then esteemed to be sufficient.
  Whether that authority was royal or ecclesiastical does not appear,
  nor (considering the proviso in King Edward's act of uniformity, and
  Queen Elizabeth's injunctions) is it very important. No inference can
  justly be drawn from the inability of inquirers, in Heylyn's time or
  since, to discover any public record bearing upon this subject, many
  public documents of that period having been lost.

In this book, as published in 1562, and for many years afterwards, there
were (besides the versified Psalms) eleven metrical versions of the "Te
Deum," canticles, Lord's Prayer (the best of which is that of the
"Benedicite"); and also "Da pacem, Domine," a hymn suitable to the
times, rendered into English from Luther; two original hymns of praise,
to be sung before morning and evening prayer; two penitential hymns (one
of them the "humble lamentation of a sinner"); and a hymn of faith,
beginning, "Lord, in Thee is all my trust." In these respects, and also
in the tunes which accompanied the words (stated by Dr Charles Burney,
in his _History of Music_, to be German, and not French), there was a
departure from the Genevan platform. Some of these hymns, and some of
the psalms also (e.g. those by Robert Wisdom, being alternative
versions), were omitted at a later period; and many alterations and
supposed amendments were from time to time made by unknown hands in the
psalms which remained, so that the text, as now printed, is in many
places different from that of 1562.


  Scotch Psalms.

In Scotland, the General Assembly of the kirk caused to be printed at
Edinburgh in 1564, and enjoined the use of, a book entitled _The Form of
Prayers and Ministry of the Sacraments used in the English Church at
Geneva, approved and received by the Church of Scotland; whereto,
besides that was in the former books, are also added sundry other
prayers, with the whole Psalms of David in English metre_. This
contained, from the "Old Version," translations of forty Psalms by
Sternhold, fifteen by Whittingham, twenty-six by Kethe and thirty-five
by Hopkins. Of the remainder two were by John Pulleyn (one of the
Genevan refugees, who became archdeacon of Colchester); six by Robert
Pont, Knox's son-in-law, who was a minister of the kirk, and also a lord
of session; and fourteen signed with the initials I. C., supposed to be
John Craig; one was anonymous, eight were attributed to N., two to M.
and one to T. N. respectively.

So matters continued in both churches until the Civil War. During the
interval, King James I. conceived the project of himself making a new
version of the Psalms, and appears to have translated thirty-one of
them--the correction of which, together with the translation of the
rest, he entrusted to Sir William Alexander, afterwards earl of
Stirling. Sir William having completed his task, King Charles I. had it
examined and approved by several archbishops and bishops of England,
Scotland and Ireland, and caused it to be printed in 1631 at the Oxford
University Press, as the work of King James; and, by an order under the
royal sign manual, recommended its use in all churches of his dominions.
In 1634 he enjoined the Privy Council of Scotland not to suffer any
other psalms, "of any edition whatever," to be printed in or imported
into that kingdom. In 1636 it was republished, and was attached to the
famous Scottish service-book, with which the troubles began in 1637. It
need hardly be added that the king did not succeed in bringing this
Psalter into use in either kingdom.

When the Long Parliament undertook, in 1642, the task of altering the
liturgy, its attention was at the same time directed to psalmody. It had
to judge between two rival translations of the Psalms--one by Francis
Rouse, a member of the House of Commons, afterwards one of Cromwell's
councillors and finally provost of Eton; the other by William Barton, a
clergyman of Leicester. The House of Lords favoured Barton, the House of
Commons Rouse, who had made much use of the labours of Sir William
Alexander. Both versions were printed by order of parliament, and were
referred for consideration to the Westminster Assembly. They decided in
favour of Rouse. His version, as finally amended, was published in 1646,
under an order of the House of Commons dated 14th November 1645. In the
following year it was recommended by the parliament to the General
Assembly at Edinburgh, who appointed a committee, with large powers, to
prepare a revised Psalter, recommending to their consideration not only
Rouse's book but that of 1564, and two other versions (by Zachary Boyd
and Sir William Mure of Rowallan), then lately executed in Scotland. The
result of the labours of this committee was the "Paraphrase" of the
Psalms, which, in 1649-1650, by the concurrent authority of the General
Assembly and the committee of estates, was ordered to be exclusively
used throughout the church of Scotland. Some use was made in the
preparation of this book of the versions to which the attention of the
revisers had been directed, and also of Barton's; but its basis was that
of Rouse. It was received in Scotland with great favour, which it has
ever since retained; and it is fairly entitled to the praise of striking
a tolerable medium between the rude homeliness of the "Old," and the
artificial modernism of the "New" English versions--perhaps as great a
success as was possible for such an undertaking. Sir Walter Scott is
said to have dissuaded any attempt to alter it, and to have pronounced
it, "with all its acknowledged occasional harshness, so beautiful, that
any alterations must eventually prove only so many blemishes." No
further step towards any authorized hymnody was taken by the kirk of
Scotland till the following century.

In England, two changes bearing on church hymnody were made upon the
revision of the prayer-book after the Restoration, in 1661-1662. One was
the addition, in the offices for consecrating bishops and ordaining
priests, of the shorter version of "Veni Creator" ("Come, Holy Ghost,
our souls inspire"), as an alternative form. The other, and more
important, was the insertion of the rubric after the third collect, at
morning and evening prayer: "In quires and places where they sing, here
followeth the anthem." By this rubric synodical and parliamentary
authority was given for the interruption, at that point, of the
prescribed order of the service by singing an anthem, the choice of
which was left to the discretion of the minister. Those actually used,
under this authority, were for some time only unmetrical passages of
scripture, set to music by Blow, Purcell and other composers, of the
same kind with the anthems still generally sung in cathedral and
collegiate churches. But the word "anthem" had no technical
signification which could be an obstacle to the use under this rubric of
metrical hymns.


  Tate and Brady.

The "New Version" of the Psalms, by Dr Nicholas Brady and the
poet-laureate Nahum Tate (both Irishmen), appeared in 1696, under the
sanction of an order in council of William III., "allowing and
permitting" its use "in all such churches, chapels and congregations as
should think fit to receive it." Dr Compton, bishop of London,
recommended it to his diocese. No hymns were then appended to it; but
the authors added a "supplement" in 1703, which received an exactly
similar sanction from an order in council of Queen Anne. In that
supplement there were several new versions of the canticles, and of the
"Veni Creator"; a variation of the old "humble lamentation of a sinner";
six hymns for Christmas, Easter and Holy Communion (all versions or
paraphrases of scripture), which are still usually printed at the end of
the prayer-books containing the new version; and a hymn "on the divine
use of music"--all accompanied by tunes. The authors also reprinted,
with very good taste, the excellent version of the "Benedicite" which
appeared in the book of 1562. Of the hymns in this "supplement," one
("While shepherds watched their flocks by night") greatly exceeded the
rest in merit. It has been ascribed to Tate, but it has a character of
simplicity unlike the rest of his works.


  Old and new versions compared.

The relative merits of the "Old" and "New" versions have been very
variously estimated. Competent judges have given the old the praise, which
certainly cannot be accorded to the new, of fidelity to the Hebrew. In
both, it must be admitted, that those parts which have poetical merit are
few and far between; but a reverent taste is likely to be more offended by
the frequent sacrifice, in the new, of depth of tone and accuracy of sense
to a fluent commonplace correctness of versification and diction, than by
any excessive homeliness in the old. In both, however, some psalms, or
portions of psalms, are well enough rendered to entitle them to a
permanent place in the hymn-books--especially the 8th, and parts of the
18th Psalm, by Sternhold; the 57th, 84th and 100th, by Hopkins; the 23rd,
34th and 36th, and part of the 148th, by Tate and Brady.

The judgment which a fastidious critic might be disposed to pass upon
both these books may perhaps be considerably mitigated by comparing them
with the works of other labourers in the same field, of whom Holland, in
his interesting volumes entitled _Psalmists of Great Britain_,
enumerates above 150. Some of them have been real poets--the celebrated
earl of Surrey, Sir Philip Sidney and his sister the countess of
Pembroke, George Sandys, George Wither, John Milton and John Keble. In
their versions, as might be expected, there are occasional gleams of
power and beauty, exceeding anything to be found in Sternhold and
Hopkins, or Tate and Brady; but even in the best these are rare, and
chiefly occur where the strict idea of translation has been most widely
departed from. In all of them, as a rule, the life and spirit, which in
prose versions of the psalms are so wonderfully preserved, have
disappeared. The conclusion practically suggested by so many failures is
that the difficulties of metrical translation, always great, are in this
case insuperable; and that, while the psalms like other parts of
scripture are abundantly suggestive of motive and material for
hymnographers, it is by assimilation and adaptation, and not by any
attempt to transform their exact sense into modern poetry, that they may
be best used for this purpose.

  The order in council of 1703 is the latest act of any public authority
  by which an express sanction has been given to the use of psalms or
  hymns in the Church of England. At the end, indeed, of many
  Prayer-books, till about the middle of the 19th century, there were
  commonly found, besides some of the hymns sanctioned by that order in
  council, or of those contained in the book of 1562, a sacramental and
  a Christmas hymn by Doddridge; a Christmas hymn (varied by Martin
  Madan) from Charles Wesley; an Easter hymn of the 18th century,
  beginning "Jesus Christ has risen to-day"; and abridgments Bishop
  Ken's Morning and Evening Hymns. These additions first began to be
  made in or about 1791, in London editions of the Prayer-book and
  Psalter, at the mere will and pleasure (so far as appears) of the
  printers. They had no sort of authority.


  English congregational hymnody.

In the state of authority, opinion and practice disclosed by the
preceding narrative may be found the true explanation of the fact that,
in the country of Chaucer, Spenser, Shakespeare and Milton, and
notwithstanding the example of Germany, no native congregational hymnody
worthy of the name arose till after the commencement of the 18th
century. Yet there was no want of appreciation of the power and value
of congregational church music. Milton could write, before 1645:--

  "There let the pealing organ blow
   To the full-voiced quire below
   In service high, and anthems clear,
   As may with sweetness through mine ear
   Dissolve me into ecstasies,
   And bring all Heaven before mine eyes."

Thomas Mace, in his _Music's Monument_ (1676), thus described the effect
of psalm-singing before sermons by the congregation in York Minster on
Sundays, during the siege of 1644: "When that vast concording unity of
the whole congregational chorus came thundering in, even so as it made
the very ground shake under us, oh, the unutterable ravishing soul's
delight! in the which I was so transported and wrapt up in high
contemplations that there was no room left in my whole man, body, soul
and spirit, for anything below divine and heavenly raptures; nor could
there possibly be anything to which that very singing might be truly
compared, except the right apprehension or conceiving of that glorious
and miraculous quire, recorded in the scriptures at the dedication of
the temple." Nor was there any want of men well qualified, and by the
turn of their minds predisposed, to shine in this branch of literature.
Some (like Sandys, Boyd and Barton) devoted themselves altogether to
paraphrases of other scriptures as well as the psalms. Others (like
George Herbert, and Francis and John Quarles) moralized, meditated,
soliloquized and allegorized in verse. Without reckoning these, there
were a few, even before the Restoration, who came very near to the ideal
of hymnody.


  Wedderburn.

First in time is the Scottish poet John Wedderburn, who translated
several of Luther's hymns, and in his _Compendious Book of Godly and
Spiritual Songs_ added others of his own (or his brothers') composition.
Some of these poems, published before 1560, are of uncommon excellence,
uniting ease and melody of rhythm, and structural skill, with grace of
expression, and simplicity, warmth and reality of religious feeling.
Those entitled "Give me thy heart," "Go, heart," and "Leave me not,"
which will be found in a collection of 1860 called _Sacred Songs of
Scotland_, require little, beyond the change of some archaisms of
language, to adapt them for church or domestic use at the present day.


  Dickson.

Next come the two hymns of "The new Jerusalem," by an English Roman
Catholic priest signing himself F. B. P. (supposed to be "Francis Baker,
Presbyter"), and by another Scottish poet, David Dickson, of which the
history is given by Dr Bonar in his edition of Dickson's work. This
(Dickson's), which begins "O mother dear, Jerusalem," and has long been
popular in Scotland, is a variation and amplification by the addition of
a large number of new stanzas of the English original, beginning
"Jerusalem, my happy home," written in Queen Elizabeth's time, and
printed (as appears by a copy in the British Museum) about 1616, when
Dickson was still young. Both have an easy natural flow, and a simple
happy rendering of the beautiful scriptural imagery upon the subject,
with a spirit of primitive devotion uncorrupted by medieval
peculiarities. The English hymn of which some stanzas are now often sung
in churches is the true parent of the several shorter forms,--all of
more than common merit,--which, in modern hymn-books, begin with the
same first line, but afterwards deviate from the original. Kindred to
these is the very fine and faithful translation, by Dickson's
contemporary Drummond of Hawthornden of the ancient "Urbs beata
Hierusalem" ("Jerusalem, that place divine"). Other ancient hymns (two
of Thomas Aquinas, and the "Dies Irae") were also well translated, in
1646, by Richard Crashaw, after he had become a Roman Catholic and had
been deprived by the parliament of his fellowship at Cambridge.


  Wither.

Conspicuous among the sacred poets of the first two Stuart reigns in
England was George Wither. His _Hymnes and Songs of the Church_ appeared
in 1622-1623, under a patent of King James I., by which they were
declared "worthy and profitable to be inserted, in convenient manner and
due place, into every English Psalm-book to metre." His _Hallelujah_
(in which some of the former _Hymnes and Songs_ were repeated) followed
in 1641. Some of the _Hymnes and Songs_ were set to music by Orlando
Gibbons, and those in both books were written to be sung, though there
is no evidence that the author contemplated the use of any of them in
churches. They included hymns for every day in the week (founded, as
those contributed nearly a century afterwards by Charles Coffin to the
Parisian Breviary also were, upon the successive works of the days of
creation); hymns for all the church seasons and festivals, including
saints' days; hymns for various public occasions; and hymns of prayer,
meditation and instruction, for all sorts and conditions of men, under a
great variety of circumstances--being at once a "Christian Year" and a
manual of practical piety. Many of them rise to a very high point of
excellence,--particularly the "general invitation to praise God" ("Come,
O come, in pious lays"), with which _Hallelujah_ opens; the
thanksgivings for peace and for victory, the Coronation Hymn, a
Christmas, an Epiphany, and an Easter Hymn, and one for St Bartholomew's
day (Hymns 1, 74, 75, and 84 in part i., and 26, 29, 36 and 54 in part
ii. of _Hallelujah_).


  Cosin.

John Cosin, afterwards bishop of Durham, published in 1627 a volume of
"Private Devotions," for the canonical hours and other occasions. In
this there are seven or eight hymns of considerable merit,--among them a
very good version of the Ambrosian "Jam lucis orto sidere," and the
shorter version of the "Veni Creator," which was introduced after the
Restoration into the consecration and ordination services of the Church
of England.


  Milton.

The hymns of Milton (on the Nativity, Passion, Circumcision and "at a
Solemn Music"), written about 1629, in his early manhood, were probably
not intended for singing; but they are odes full of characteristic
beauty and power.


  Jeremy Taylor.

During the Commonwealth, in 1654, Jeremy Taylor published at the end of
his _Golden Grove_, twenty-one hymns, described by himself as
"celebrating the mysteries and chief festivals of the year, according to
the manner of the ancient church, fitted to the fancy and devotion of
the younger and pious persons, apt for memory, and to be joined, to
their other prayers." Of these, his accomplished editor, Bishop Heber,
justly says:--

  "They are in themselves, and on their own account, very interesting
  compositions. Their metre, indeed, which is that species of spurious
  Pindaric which was fashionable with his contemporaries, is an
  obstacle, and must always have been one, to their introduction into
  public or private psalmody; and the mixture of that alloy of conceits
  and quibbles which was an equally frequent and still greater
  defilement of some of the finest poetry of the 17th century will
  materially diminish their effect as devotional or descriptive odes.
  Yet, with all these faults, they are powerful, affecting, and often
  harmonious; there are many passages of which Cowley need not have been
  ashamed, and some which remind us, not disadvantageously, of the
  corresponding productions of Milton."

He mentions particularly the advent hymn ("Lord, come away"), part of
the hymn "On heaven," and (as "more regular in metre, and in words more
applicable to public devotion") the "Prayer for Charity" ("Full of
mercy, full of love").


  Restoration period.

The epoch of the Restoration produced in 1664 Samuel Crossman's _Young
Man's Calling_, with a few "Divine Meditations" in verse attached to it;
in 1668 John Austin's _Devotions in the ancient way of offices, with
psalms, hymns and prayers for every day in the week and every holyday in
the year_; and in 1681 Richard Baxter's _Poetical Fragments_. In these
books there are altogether seven or eight hymns, the whole or parts of
which are extremely good: Crossman's "New Jerusalem" ("Sweet place,
sweet place alone"), one of the best of that class, and "My life's a
shade, my days"; Austin's "Hark, my soul, how everything," "Fain would
my thoughts fly up to Thee," "Lord, now the time returns," "Wake all my
hopes, lift up your eyes"; and Baxter's "My whole, though broken heart,
O Lord," and "Ye holy angels bright." Austin's _Offices_ (he was a Roman
Catholic) seem to have attracted much attention. Theophilus Dorrington,
in 1686, published variations of them under the title of _Reformed_
_Devotions_; George Hickes, the non-juror, wrote one of his numerous
recommendatory prefaces to S. Hopton's edition; and the Wesleys, in
their earliest hymn-book, adopted hymns from them, with little
alteration. These writers were followed by John Mason in 1683, and
Thomas Shepherd in 1692,--the former, a country clergyman, much esteemed
by Baxter and other Nonconformists; the latter himself a Nonconformist,
who finally emigrated to America. Between these two men there was a
close alliance, Shepherd's _Penitential Cries_ being published as an
addition to the _Spiritual Songs_ of Mason. Their hymns came into early
use in several Nonconformist congregations; but, with the exception of
one by Mason ("There is a stream which issues forth"), they are not
suitable for public singing. In those of Mason there is often a very
fine vein of poetry; and later authors have, by extracts or centoes from
different parts of his works (where they were not disfigured by his
general quaintness), constructed several hymns of more than average
excellence.

Three other eminent names of the 17th century remain to be mentioned,
John Dryden, Bishop Ken and Bishop Simon Patrick; with which may be
associated that of Addison, though he wrote in the 18th century.


  Dryden, Ken.

  Patrick

  Addison.

Dryden's translation of "Veni Creator" a cold and laboured performance,
is to be met with in many hymn-books. Abridgments of Ken's morning and
evening hymns are in all. These, with the midnight hymn, which is not
inferior to them, first appeared In 1697, appended to the third edition
of the author's _Manual of Prayers for Winchester Scholars_. Between
these and a large number of other hymns (on the attributes of God, and
for the festivals of the church) published by Bishop Ken after 1703 the
contrast is remarkable. The universal acceptance of the morning and
evening hymns is due to their transparent simplicity, warm but not
overstrained devotion, and extremely popular style. Those afterwards
published have no such qualities. They are mystical, florid, stiff,
didactic and seldom poetical, and deserve the neglect into which they
have fallen. Bishop Patrick's hymns were chiefly translations from the
Latin, most of them from Prudentius. The best is a version of "Alleluia
dulce carmen." Of the five attributed to Addison, not more than three
are adapted to public singing; one ("The spacious firmament on high") is
a very perfect and finished composition, taking rank among the best
hymns in the English language.[3]

From the preface to Simon Browne's hymns, published in 1720, we learn
that down to the time of Dr Watts the only hymns known to be "in common
use, either in private families or in Christian assemblies," were those
of Barton, Mason and Shepherd, together with "an attempt to turn some of
George Herbert's poems into common metre," and a few sacramental hymns
by authors now forgotten, named Joseph Boyse (1660-1728) and Joseph
Stennett. Of the 1410 authors of original British hymns enumerated in
Daniel Sedgwick's catalogue, published in 1863, 1213 are of later date
than 1707; and, if any correct enumeration could be made of the total
number of hymns of all kinds published in Great Britain before and after
that date, the proportion subsequent to 1707 would be very much larger.


The English Independents, as represented by Dr Isaac Watts, have a just
claim to be considered the real founders of modern English hymnody.
Watts was the first to understand the nature of the want, and, by the
publication of his _Hymns_ in 1707-1709, and _Psalms_ (not translations,
but hymns founded on psalms) in 1709, he led the way in providing for
it. His immediate followers were Simon Browne and Philip Doddridge.
Later in the 18th century, Joseph Hart, Thomas Gibbons, Miss Anne
Steele, Samuel Medley, Samuel Stennett, John Ryland, Benjamin Beddome
and Joseph Swain succeeded to them.


  Watts.

Among these writers, most of whom produced some hymns of merit, and
several are extremely voluminous, Isaac Watts and Philip Doddridge are
pre-eminent. It has been the fashion with some to disparage Watts, as if
he had never risen above the level of his _Hymns for Little Children_.
No doubt his taste is often faulty, and his style very unequal, but,
looking to the good, and disregarding the large quantity of inferior
matter, it is probable that more hymns which approach to a very high
standard of excellence, and are at the same time suitable for
congregational use, may be found in his works than in those of any other
English writer. Such are "When I survey the wondrous cross," "Jesus
shall reign where'er the sun" (and also another adaptation of the same
72nd Psalm), "Before Jehovah's awful throne" (first line of which,
however, is not his, but Wesley's), "Joy to the world, the Lord is
come," "My soul, repeat His praise," "Why do we mourn departing
friends," "There is a land of pure delight," "Our God, our help in ages
past," "Up to the hills I lift mine eyes," and many more. It is true
that in some of these cases dross is found in the original poems mixed
with gold; but the process of separation, by selection without change,
is not difficult. As long as pure nervous English, unaffected fervour,
strong simplicity and liquid yet manly sweetness are admitted to be
characteristics of a good hymn, works such as these must command
admiration.


  Doddridge.

Doddridge is, generally, much more laboured and artificial; but his
place also as a hymn-writer ought to be determined, not by his failures,
but by his successes, of which the number is not inconsiderable. In his
better works he is distinguished by a graceful and pointed, sometimes
even a noble style. His "Hark, the glad sound, the Saviour comes" (which
is, indeed, his masterpiece), is as sweet, vigorous and perfect a
composition as can anywhere be found. Two other hymns, "How gentle God's
commands," and that which, in a form slightly varied, became the "O God
of Bethel, by whose hand," of the Scottish "Paraphrases," well represent
his softer manner.

Of the other followers in the school of Watts, Miss Anne Steele
(1717-1778) is the most popular and perhaps the best. Her hymn beginning
"Far from these narrow scenes of night" deserves high praise, even by
the side of other good performances on the same subject.

The influence of Watts was felt in Scotland, and among the first whom it
reached there was Ralph Erskine. This seems to have been after the
publication of Erskine's _Gospel Sonnets_, which appeared in 1732, five
years before he joined his brother Ebenezer in the Secession Church. The
_Gospel Sonnets_ became, as some have said, a "people's classic"; but
there is in them very little which belongs to the category of hymnody.
More than nineteen-twentieths of this very curious book are occupied
with what are, in fact, theological treatises and catechisms, mystical
meditations on Christ as a bridegroom or husband, and spiritual enigmas,
paradoxes, and antithetical conceits, versified, it is true, but of a
quality of which such lines as--

  "Faith's certain by fiducial arts,
   Sense by its evidential facts,"

may be taken as a sample. The grains of poetry scattered through this
large mass of Calvinistic divinity are very few; yet in one short
passage of seven stanzas ("O send me down a draught of love"), the fire
burns with a brightness so remarkable as to justify a strong feeling of
regret that the gift which this writer evidently had in him was not more
often cultivated. Another passage, not so well sustained, but of
considerable beauty (part of the last piece under the title "The
believer's soliloquy"), became afterwards, in the hands of John
Berridge, the foundation of a very striking hymn ("O happy saints, who
walk in light").

After his secession, Ralph Erskine published two paraphrases of the
"Song of Solomon," and a number of other "Scripture songs," paraphrased,
in like manner, from the Old and New Testaments. In these the influence
of Watts became very apparent, not only by a change in the writer's
general style, but by the direct appropriation of no small quantity of
matter from Dr Watts's hymns, with variations which were not always
improvements. His paraphrases of I Cor. i. 24; Gal. vi. 14; Heb. vi.
17-19; Rev. v. 11, 12, vii. 10-17, and xii. 7-12 are little else than
Watts transformed. One of these (Rev. vii. 10-17) is interesting as a
variation and improvement, intermediate between the original and the
form which it ultimately assumed as the 66th "Paraphrase" of the Church
of Scotland, of Watts's "What happy men or angels these," and "These
glorious minds, how bright they shine." No one can compare it with its
ultimate product, "How bright these glorious spirits shine," without
perceiving that William Cameron followed Erskine, and only added finish
and grace to his work,--both excelling Watts, in this instance, in
simplicity as well as in conciseness.


  Scottish paraphrases.

Of the contributions to the authorized "Paraphrases" (with the
settlement of which committees of the General Assembly of the Church of
Scotland were occupied from 1745, or earlier, till 1781), the most
noteworthy, besides the two already mentioned, were those of John
Morrison and those claimed for Michael Bruce. The obligations of these
"Paraphrases" to English hymnody, already traced in some instances (to
which may be added the adoption from Addison of three out of the five
"hymns" appended to them), are perceptible in the vividness and force
with which these writers, while adhering with a severe simplicity to the
sense of the passages of Scripture which they undertook to render,
fulfilled the conception of a good original hymn. Morrison's "The race
that long in darkness pined" and "Come, let us to the Lord our God," and
Bruce's "Where high the heavenly temple stands" (if this was really
his), are well entitled to that praise. The advocates of Bruce in the
controversy, not yet closed, as to the poems said to have been entrusted
by him to John Logan, and published by Logan in his own name, also claim
for him the credit of having varied the paraphrase "Behold, the mountain
of the Lord," from its original form, as printed by the committee of the
General Assembly in 1745, by some excellent touches.


  Methodist hymns.

Attention must now be directed to the hymns produced by the "Methodist"
movement, which began about 1738, and which afterwards became divided,
between those esteemed Arminian, under John Wesley, those who adhered to
the Moravians, when the original alliance between that body and the
founders of Methodism was dissolved, and the Calvinists, of whom
Whitfield was the leader, and Selina, countess of Huntingdon, the
patroness. Each of these sections had its own hymn-writers, some of whom
did, and others did not, secede from the Church of England. The
Wesleyans had Charles Wesley, Robert Seagrave and Thomas Olivers; the
Moravians, John Cennick, with whom, perhaps, may be classed John Byrom,
who imbibed the mystical ideas of some of the German schools; the
Calvinists, Augustus Montague Toplady, John Berridge, William Williams,
Martin Madan, Thomas Haweis, Rowland Hill, John Newton and William
Cowper.


  Charles Wesley.

Among all these writers, the palm undoubtedly belongs to Charles Wesley.
In the first volume of hymns published by the two brothers are several
good translations from the German, believed to be by John Wesley, who,
although he translated and adapted, is not supposed to have written any
original hymns; and the influence of German hymnody, particularly of the
works of Paul Gerhardt, Scheffler, Tersteegen and Zinzendorf, may be
traced in a large proportion of Charles Wesley's works. He is more
subjective and meditative than Watts and his school; there is a didactic
turn, even in his most objective pieces, as, for example, in his
Christmas and Easter hymns; most of his works are supplicatory, and his
faults are connected with the same habit of mind. He is apt to repeat
the same thoughts, and to lose force by redundancy--he runs sometimes
even to a tedious length; his hymns are not always symmetrically
constructed, or well balanced and finished off. But he has great truth,
depth and variety of feeling; his diction is manly and always to the
point; never florid, though sometimes passionate and not free from
exaggeration; often vivid and picturesque. Of his spirited style there
are few better examples than "O for a thousand tongues to sing," "Blow
ye the trumpet, blow," "Rejoice, the Lord is King" and "Come, let us
join our friends above"; of his more tender vein, "Happy soul, thy days
are ended"; and of his fervid contemplative style (without going beyond
hymns fit for general use), "O Thou who earnest from above," "Forth in
Thy name, O Lord, I go" and "Eternal beam of light divine." With those
whose taste is for hymns in which warm religious feelings are warmly and
demonstratively expressed, "Jesus, lover of my soul," is as popular as
any of these.


  Olivers.

Of the other Wesleyan hymn-writers, Olivers, originally a Welsh
shoemaker and afterwards a preacher, is the most remarkable. He is the
author of only two works, both odes, in a stately metre, and from their
length unfit for congregational singing, but one of them, "The God of
Abraham praise," an ode of singular power and beauty.


  Cennick, Hammond, Byrom.

The Moravian Methodists produced few hymns now available for general
use. The best are Cennick's "Children of the heavenly King" and
Hammond's "Awake and sing the song of Moses and the Lamb," the former of
which (abridged), and the latter as varied by Madan, are found in many
hymn-books, and are deservedly esteemed. John Byrom, whose name we have
thought it convenient to connect with these, though he did not belong to
the Moravian community, was the author of a Christmas hymn ("Christians
awake, salute the happy morn") which enjoys great popularity; and also
of a short subjective hymn, very fine both in feeling and in expression,
"My spirit longeth for Thee within my troubled breast."


  Toplady.

The contributions of the Calvinistic Methodists to English hymnody are
of greater extent and value. Few writers of hymns had higher gifts than
Toplady, author of "Rock of ages," by some esteemed the finest in the
English language. He was a man of ardent temperament, enthusiastic zeal,
strong convictions and great energy of character. "He had," says one of
his biographers, "the courage of a lion, but his frame was brittle as
glass." Between him and John Wesley there was a violent opposition of
opinion, and much acrimonious controversy; but the same fervour and zeal
which made him an intemperate theologian gave warmth, richness and
spirituality to his hymns. In some of them, particularly those which,
like "Deathless principle, arise," are meditations after the German
manner, and not without direct obligation to German originals, the
setting is somewhat too artificial; but his art is never inconsistent
with a genuine flow of real feeling. Others (e.g. "When languor and
disease invade" and "Your harps, ye trembling saints") fail to sustain
to the end the beauty with which they began, and would have been better
for abridgment. But in all these, and in most of his other works, there
is great force and sweetness, both of thought and language, and an easy
and harmonious versification.


  Berridge, Williams and R. Hill.

Berridge, William Williams (1717-1791) and Rowland Hill, all men
remarkable for eccentricity, activity and the devotion of their lives to
the special work of missionary preaching, though not the authors of many
good hymns, composed, or adapted from earlier compositions, some of
great merit. One of Berridge, adapted from Erskine, has been already
mentioned; another, adapted from Watts, is "Jesus, cast a look on me."
Williams, a Welshman, who wrote "Guide me, O Thou great Jehovah," was
especially an apostle of Calvinistic Methodism in his own country, and
his hymns are still much used in the principality. Rowland Hill wrote
the popular hymn beginning "Exalted high at God's right hand."


  Cowper and Newton.

If, however, the number as well as the quality of good hymns available
for general use is to be regarded, the authors of the _Olney Hymns_ are
entitled to be placed at the head of all the writers of this Calvinistic
school. The greater number of the _Olney Hymns_ are, no doubt, homely
and didactic; but to the best of them, and they are no inconsiderable
proportion, the tenderness of Cowper and the manliness of John Newton
(1725-1807) give the interest of contrast, as well as that of sustained
reality. If Newton carried to some excess the sound principle laid down
by him, that "perspicuity, simplicity and ease should be chiefly
attended to, and the imagery and colouring of poetry, if admitted at
all, should be indulged very sparingly and with great judgment," if he
is often dry and colloquial, he rises at other times into
"soul-animating strains," such as "Glorious things of thee are spoken,
Zion, city of our God"; and sometimes (as in "Approach, my soul, the
mercy seat") rivals Cowper himself in depth of feeling. Cowper's hymns
in this book are, almost without exception, worthy of his name. Among
them are "Hark, my soul, it is the Lord," "There is a fountain filled
with blood," "Far from the world, O Lord, I flee," "God moves in a
mysterious way" and "Sometimes a light surprises." Some, perhaps, even
of these, and others of equal excellence (such as "O for a closer walk
with God"), speak the language of a special experience, which, in
Cowper's case, was only too real, but which could not, without a degree
of unreality not desirable in exercises of public worship, be applied to
themselves by all ordinary Christians.


  19th-century hymns.

  R. Grant.

  Bowdler.

During the first quarter of the 19th century there were not many
indications of the tendency, which afterwards became manifest, to
enlarge the boundaries of British hymnody. _The Remains of Henry Kirke
White_, published by Southey in 1807, contained a series of hymns, some
of which are still in use; and a few of Bishop Heber's hymns and those
of Sir Robert Grant, which, though offending rather too much against
John Newton's canon, are well known and popular, appeared between 1811
and 1816, in the _Christian Observer_. In John Bowdler's Remains,
published soon after his death in 1815, there are a few more of the
same, perhaps too scholarlike, character. But the chief hymn-writers of
that period were two clergymen of the Established Church--one in
Ireland, Thomas Kelly, and the other in England, William Hurn--who both
became Nonconformists, and the Moravian poet, James Montgomery
(1771-1854), a native of Scotland.


  Kelly.

Kelly was the son of an Irish judge, and in 1804 published a small
volume of ninety-six hymns, which grew in successive editions till, in
the last before his death in 1854, they amounted to 765. There is, as
might be expected, in this great number a large preponderance of the
didactic and commonplace. But not a few very excellent hymns may be
gathered from them. Simple and natural, without the vivacity and
terseness of Watts or the severity of Newton, Kelly has some points in
common with both those writers, and he is less subjective than most of
the "Methodist" school. His hymns beginning "Lo! He comes, let all adore
Him," and "Through the day Thy love hath spared us," have a rich,
melodious movement; and another, "We sing the praise of Him who died,"
is distinguished by a calm, subdued power, rising gradually from a
rather low to a very high key.


  Hurn.

Hurn published in 1813 a volume of 370 hymns, which were afterwards
increased to 420. There is little in them which deserves to be saved
from oblivion; but one at least, "There is a river deep and broad," may
bear comparison with the best of those which have been produced upon the
same, and it is rather a favourite, theme.


  Montgomery.

The _Psalms and Hymns_ of James Montgomery were published in 1822 and
1825, though written earlier. More cultivated and artistic than Kelly,
he is less simple and natural. His "Hail to the Lord's Anointed," "Songs
of praise the angels sang" and "Mercy alone can meet my case" are among
his most successful efforts.


  Collections of hymns.

During this period, the collections of miscellaneous hymns for
congregational use, of which the example was set by the Wesleys,
Whitfield, Toplady and Lady Huntingdon, had greatly multiplied; and with
them the practice (for which, indeed, too many precedents existed in the
history of Latin and German hymnody) of every collector altering the
compositions of other men without scruple, to suit his own doctrine or
taste; with the effect, too generally, of patching and disfiguring,
spoiling and emasculating the works so altered, substituting neutral
tints for natural colouring, and a dead for a living sense. In the
Church of England the use of these collections had become frequent in
churches and chapels, principally in cities and towns, where the
sentiments of the clergy approximated to those of the Nonconformists. In
rural parishes, when the clergy were not of the "Evangelical" school,
they were generally held in disfavour; for which, even if doctrinal
prepossessions had not entered into the question, the great want of
taste and judgment often manifested in their compilation, and perhaps
also the prevailing mediocrity of the bulk of the original compositions
from which most of them were derived, would be enough to account. In
addition to this, the idea that no hymns ought to be used in any
services of the Church of England, except prose anthems after the third
collect, without express royal or ecclesiastical authority, continued
down to that time largely to prevail among high churchmen.


  Heber, Milman, Keble.

  Mant.

  Newman.

Two publications, which appeared almost simultaneously in 1827--Bishop
Heber's _Hymns_, with a few added by Dean Milman, and John Keble's
_Christian Year_ (not a hymn-book, but one from which several admirable
hymns have been taken, and the well-spring of many streams of thought
and feeling by which good hymns have since been produced)--introduced a
new epoch, breaking down the barrier as to hymnody which had till then
existed between the different theological schools of the Church of
England. In this movement Richard Mant, bishop of Down, was also one of
the first to co-operate. It soon received a great additional impulse
from the increased attention which, about the same time, began to be
paid to ancient hymnody, and from the publication in 1833 of Bunsen's
_Gesangbuch_. Among its earliest fruits was the _Lyra apostolica_,
containing hymns, sonnets and other devotional poems, most of them
originally contributed by some of the leading authors of the _Tracts for
the Times_ to the _British Magazine_; the finest of which is the
pathetic "Lead, kindly Light, amid th' encircling gloom," by Cardinal
Newman--well known, and universally admired. From that time hymns and
hymn-writers rapidly multiplied in the Church of England, and in
Scotland also. Nearly 600 authors whose publications were later than
1827 are enumerated in Sedgwick's catalogue of 1863, and about half a
million hymns are now in existence. Works, critical and historical, upon
the subject of hymns, have also multiplied; and collections for church
use have become innumerable--several of the various religious
denominations, and many of the leading ecclesiastical and religious
societies, having issued hymn-books of their own, in addition to those
compiled for particular dioceses, churches and chapels, and to books
(like _Hymns Ancient and Modern_, published 1861, supplemented 1889,
revised edition, 1905) which have become popular without any sanction
from authority. To mention all the authors of good hymns since the
commencement of this new epoch would be impossible; but probably no
names could be chosen more fairly representative of its characteristic
merits, and perhaps also of some of its defects, than those of Josiah
Conder and James Edmeston among English Nonconformists; Henry Francis
Lyte and Charlotte Elliott among evangelicals in the Church of England;
John Mason Neale and Christopher Wordsworth, bishop of Lincoln, among
English churchmen of the higher school; Arthur Penrhyn Stanley, Edward
H. Plumptre, Frances Ridley Havergal; and in Scotland, Dr Horatius
Bonar, Dr Norman Macleod and Dr George Matheson. American hymn-writers
belong to the same schools, and have been affected by the same
influences. Some of them have enjoyed a just reputation on both sides
of the Atlantic. Among those best known are John Greenleaf Whittier,
Bishop Doane, Dr W. A. Muhlenberg and Thomas Hastings; and it is
difficult to praise too highly such works as the Christmas hymn, "It
came upon the midnight clear," by Edmund H. Sears; the Ascension hymn,
"Thou, who didst stoop below," by Mrs S. E. Miles; two by Dr Ray Palmer,
"My faith looks up to Thee, Thou Lamb of Calvary," and "Jesus, Thou joy
of loving hearts," the latter of which is the best among several good
English versions of "Jesu, dulcedo, cordium"; and "Lord of all being,
throned afar," by Oliver Wendell Holmes.

The more modern "Moody and Sankey" hymns (see Moody, D. L.) popularized
a new Evangelical type, and the Salvation Army has carried this still
farther.

7. _Conclusion._--The object aimed at in this article has been to trace
the general history of the principal schools of ancient and modern
hymnody, and especially the history of its use in the Christian church.
For this purpose it has not been thought necessary to give any account
of the hymns of Racine, Madame Guyon and others, who can hardly be
classed with any school, nor of the works of Caesar Malan of Geneva
(1787-1864) and other quite modern hymn-writers of the Reformed churches
in Switzerland and France.

On a general view of the whole subject, hymnody is seen to have been a
not inconsiderable factor in religious worship. It has been sometimes
employed to disseminate and popularize particular views, but its spirit
and influence has been, on the whole, catholic. It has embodied the
faith, trust and hope, and no small part of the inward experience, of
generation after generation of men, in many different countries and
climates, of many different nations, and in many varieties of
circumstances and condition. Coloured, indeed, by these differences, and
also by the various modes in which the same truths have been apprehended
by different minds and sometimes reflecting partial and imperfect
conceptions of them, and errors with which they have been associated in
particular churches, times and places, its testimony is, nevertheless,
generally the same. It has upon it a stamp of genuineness which cannot
be mistaken. It bears witness to the force of a central attraction more
powerful than all causes of difference, which binds together times
ancient and modern, nations of various race and language, churchmen and
nonconformists, churches reformed and unreformed; to a true fundamental
unity among good Christians; and to a substantial identity in their
moral and spiritual experience. (S.)

  The regular practice of hymnody in English musical history dates from
  the beginning of the 16th century. Luther's verses were adapted
  sometimes to ancient church melodies, sometimes to tunes of secular
  songs, and sometimes had music composed for them by himself and
  others. Many rhyming Latin hymns are of earlier date whose tunes are
  identified with them, some of which tunes, with the subject of their
  Latin text, are among the Reformer's appropriations; but it was he who
  put the words of praise and prayer into the popular mouth, associated
  with rhythmical music which aided to imprint the words upon the memory
  and to enforce their enunciation. In conjunction with his friend
  Johann Walther, Luther issued a collection of poems for choral singing
  in 1524, which was followed by many others in North Germany. The
  English versions of the Psalms by Sternhold and Hopkins and their
  predecessors, and the French version by Clement Marot and Theodore
  Beza, were written with the same purpose of fitting sacred minstrelsy
  to the voice of the multitude. Goudimel in 1566 and Claudin le Jeune
  in 1607 printed harmonizations of tunes that had then become standard
  for the Psalms, and in England several such publications appeared,
  culminating in Thomas Ravenscroft's famous collection, _The Whole Book
  of Psalms_ (1621); in all of these the arrangements of the tunes were
  by various masters. The English practice of hymn-singing was much
  strengthened on the return of the exiled reformers from Frankfort and
  Geneva, when it became so general that, according to Bishop Jewell,
  thousands of the populace who assembled at Paul's Cross to hear the
  preaching would join in the singing of psalms before and after the
  sermon.

  The placing of the choral song of the church within the lips of the
  people had great religious and moral influence; it has had also its
  great effect upon art, shown in the productions of the North German
  musicians ever since the first days of the Reformation, which abound
  in exercises of scholarship and imagination wrought upon the tunes of
  established acceptance. Some of these are accompaniments to the tunes
  with interludes between the several strains, and some are
  compositions for the organ or for orchestral instruments that consist
  of such elaboration of the themes as is displayed in accompaniments to
  voices, but of far more complicated and extended character. A special
  art-form that was developed to a very high degree, but has passed into
  comparative disuse, was the structure of all varieties of counterpoint
  extemporaneously upon the known hymn-tunes (chorals), and several
  masters acquired great fame by success in its practice, of whom J. A.
  Reinken (1623-1722), Johann Pachelbel (1653-1706), Georg Boehm and the
  great J. S. Bach are specially memorable. The hymnody of North Germany
  has for artistic treatment a strong advantage which is unpossessed by
  that of England, in that for the most part the same verses are
  associated with the same tunes, so that, whenever the text or the
  music is heard, either prompts recollection of the other, whereas in
  England tunes were always and are now often composed to metres and not
  to poems; any tune in a given metre is available for every poem in the
  same, and hence there are various tunes to one poem, and various poems
  to one tune.[4] In England a tune is named generally after some
  place--as "York," "Windsor," "Dundee,"--or by some other unsignifying
  word; in North Germany a tune is mostly named by the initial words of
  the verses to which it is allied, and consequently, whenever it is
  heard, whether with words or without, it necessarily suggests to the
  hearer the whole subject of that hymn of which it is the musical
  moiety undivorceable from the literary half. Manifold as they are,
  knowledge of the choral tunes is included in the earliest schooling of
  every Lutheran and every Calvinist in Germany, which thus enables all
  to take part in performance of the tunes, and hence expressly the
  definition of "choral." Compositions grounded on the standard tune are
  then not merely school exercises, but works of art which link the
  sympathies of the writer and the listener, and aim at expressing the
  feeling prompted by the hymn under treatment.

  BIBLIOGRAPHY: I. Ancient.--George Cassander, _Hymni ecclesiastici_
  (Cologne, 1556); Georgius Fabricius, _Poëtarum veterum
  ecclesiasticorum_ (Frankfort, 1578); Cardinal J. M. Thomasius,
  _Hymnarium in Opera_, ii. 351 seq. (Rome, 1747); A. J. Rambach,
  _Anthologie christlicher Gesänge_ (Altona, 1817); H. A. Daniel,
  _Thesaurus hymnologicus_ (Leipzig, 5 vols., 1841-1856); J. M. Neale,
  _Hymni ecclesiae et sequentiae_ (London, 1851-1852); and _Hymns of the
  Eastern Church_ (1863). The dissertation prefixed to the second volume
  of the _Acta sanctorum_ of the Bollandists; Cardinal J. B. Pitra,
  _Hymnographie de l'église grecque_ (1867), _Analecta sacra_ (1876); W.
  Christ and M. Paranikas, _Anthologia Graeca carminum Christianorum_
  (Leipzig, 1871); F. A. March, _Latin Hymns with English Notes_ (New
  York, 1875); R. C. Trench, _Sacred Latin Poetry_ (London, 4th ed.,
  1874); J. Pauly, _Hymni breviarii Romani_ (Aix-la-Chapelle, 3 vols.,
  1868-1870); Pimont, _Les Hymnes du bréviaire romain_ (vols. 1-3,
  1874-1884, unfinished); A. W. F. Fischer, _Kirchenlieder-Lexicon_
  (Gotha, 1878-1879); J. Kayser, _Beiträge zur Geschichte der ältesten
  Kirchenhymnen_ (1881); M. Manitius, _Geschichte der christlichen
  lateinischen Poesie_ (Stuttgart, 1891); John Julian, _Dictionary of
  Hymnology_ (1892, new ed. 1907). For criticisms of metre, see also
  Huemer, _Untersuchungen über die ältesten christlichen Rhythmen_
  (1879); E. Bouvy, _Poètes et mélodes_ (Nîmes, 1886); C. Krumbacher,
  _Geschichte der byzantinischen Literatur_ (Munich, 1897, p. 700 seq.);
  J. M. Neale, Latin dissertation prefixed to Daniel's _Thesaurus_, vol.
  5; and D. J. Donahoe, _Early Christian Hymns_ (London, 1909).

  II. Medieval.--Walafrid Strabo's treatise, ch. 25, _De hymnis, &c._;
  Radulph of Tongres, _De psaltario observando_ (14th century);
  Clichtavaens, _Elucidatorium ecclesiasticum_ (Paris, 1556); Faustinus
  Arevalus, _Hymnodia Hispanica_ (Rome, 1786); E. du Méril, _Poésies
  populaires latines antérieures au XIII^e siècle_ (Paris, 1843); J.
  Stevenson, _Latin Hymns of the Anglo-Saxon Church_ (Surtees Society,
  Durham, 1851); Norman, _Hymnarium Sarisburiense_ (London, 1851); J. D.
  Chambers, _Psalter, &c._, according to the Sarum use (1852); F. J.
  Mone, _Lateinische Hymnen des Mittelalters_ (Freiburg, 3 vols.,
  1853-1855); Ph. Wackernagel, _Das deutsche Kirchenlied von der
  ältesten Zeit bis zum Anfang des 17. Jahrhunderts_, vol. i. (Leipzig,
  1864); E. Dümmler, _Poëtae latini aevi Carolini_ (1881-1890); the
  _Hymnologische Beiträge: Quellen und Forschungen zur Geschichte der
  lateinischen Hymnendichtung_, edited by C. Blume and G. M. Dreves
  (Leipzig, 1897); G. C. F. Mohnike, _Hymnologische Forschungen_;
  Klemming, _Hymni et sequentiae in regno Sueciae_ (Stockholm, 4 vols.,
  1885-1887); _Das katholische deutsche Kirchenlied_ (vol. i. by K.
  Severin Meister, 1862, vol. ii. by W. Baumker, 1883); the "Hymnodia
  Hiberica," _Spanische Hymnen des Mittelalters_, vol. xvi. (1894); the
  "Hymnodia Gotica," _Mozarabische Hymnen des altspanischen Ritus_, vol.
  xxvii. (1897); J. Dankó, _Vetus hymnarium ecclesiasticae Hungariae_
  (Budapest, 1893); J. H. Bernard and R. Atkinson, _The Irish Liber
  Hymnorum_ (2 vols., London, 1898); C. A. J. Chevalier, _Poésie
  liturgique du moyen âge_ (Paris, 1893).

  III. Modern.--J. C. Jacobi, _Psalmodia Germanica_ (1722-1725 and 1732,
  with supplement added by J. Haberkorn, 1765); F. A. Cunz, _Geschichte
  des deutschen Kirchenliedes_ (Leipzig, 1855); Baron von Bunsen,
  _Versuch eines allgemeinen Gesang- und Gebetbuches_ (1833) and
  _Allgemeines evangelisches Gesang- und Gebetbuch_ (1846); Catherine
  Winkworth, _Christian Singers of Germany_ (1869) and _Lyra Germanica_
  (1855); Catherine H. Dunn, _Hymns from the German_ (1857); Frances E.
  Cox, _Sacred Hymns from the German_ (London, 1841); Massie, _Lyra
  domestica_ (1860); _Appendix on Scottish Psalmody_ in D. Laing's
  edition of Baillie's _Letters and Journals_ (1841-1842); J. and C.
  Wesley, _Collection of Psalms and Hymns_ (1741); Josiah Miller, _Our
  Hymns, their Authors and Origin_ (1866); John Gadsby, _Memoirs of the
  Principal Hymn-writers_ (3rd ed., 1861); L. C. Biggs, Annotations to
  _Hymns Ancient and Modern_ (1867); Daniel Sedgwick, _Comprehensive
  Index of Names of Original Authors of Hymns_ (2nd ed., 1863); R. E.
  Prothero, _The Psalms in Human Life_ (1907); C. J. Brandt and L.
  Helweg, _Den danske Psalmedigtning_ (Copenhagen, 1846-1847); J. N.
  Skaar, _Norsk Salmehistorie_ (Bergen, 1879-1880); H. Schück, _Svensk
  Literaturhistoria_ (Stockholm, 1890); Rudolf Wolkan, _Geschichte der
  deutschen Literatur in Böhmen_, 246-256, and _Das deutsche Kirchenlied
  der böhm. Brüder_ (Prague, 1891); Zahn, _Die geistlichen Lieder der
  Brüder in Böhmen, Mähren u. Polen_ (Nuremberg, 1875); and J. Müller,
  "Bohemian Brethren's Hymnody," in J. Julian's _Dictionary of
  Hymnology_.

  For account of hymn-tunes, &c., see W. Cowan and James Love, _Music of
  the Church Hymnody and the Psalter in Metre_ (London, 1901); and
  Dickinson, _Music in the History of the Western Church_ (New York,
  1902); S. Kümmerle, _Encyklopädie der evangelischen Kirchenmusik_ (4
  vols., 1888-1895); Chr. Palmer, _Evangelische Hymnologie_ (Stuttgart,
  1865); and P. Urto Kornmüller, _Lexikon der kirchlichen Tonkunst_
  (1891).


FOOTNOTES:

  [1] The history of the "hymn" naturally begins with Greece, but it
    may be found in some form much earlier; Assyria and Egypt have left
    specimens, while India has the Vedic hymns, and Confucius collected
    "praise songs" in China.

  [2] See GREEK LITERATURE.

  [3] The authorship of this and of one other, "When all thy mercies, O
    my God," has been made a subject of controversy,--being claimed for
    Andrew Marvell (who died in 1678), in the preface to Captain E.
    Thompson's edition (1776) of Marvell's _Works_. But this claim does
    not appear to be substantiated. The editor did not give his readers
    the means of judging as to the real age, character or value of a
    manuscript to which he referred; he did not say that these portions
    of it were in Marvell's handwriting; he did not even himself include
    them among Marvell's poems, as published in the body of his edition;
    and he advanced a like claim on like grounds to two other poems, in
    very different styles, which had been published as their own by
    Tickell and Mallet. It is certain that all the five hymns were first
    made public in 1712, in papers contributed by Addison to the
    _Spectator_ (Nos. 441, 453, 465, 489, 513), in which they were
    introduced in a way which might have been expected if they were by
    the hand which wrote those papers, but which would have been
    improbable, and unworthy of Addison, if they were unpublished works
    of a writer of so much genius, and such note in his day, as Marvell.
    They are all printed as Addison's in Dr Johnson's _British Poets_.

  [4] The old tune for the 100th Psalm and Croft's tune for the 104th
    are almost the only exceptions, unless "God save the King" may be
    classed under "hymnody." In Scotland also the tune for the 124th
    Psalm is associated with its proper text.



HYPAETHROS (Gr. [Greek: hypaithros], beneath the sky, in the open air,
[Greek: hypo], beneath, and [Greek: aithêr], air), the Greek term quoted
by Vitruvius (iii. 2) for the opening in the middle of the roof of
decastyle temples, of which "there was no example in Rome, but one in
Athens in the temple of Jupiter Olympius, which is octastyle." But at
the time he wrote (c. 25 B.C.) the cella of this temple was unroofed,
because the columns which had been provided to carry, at all events,
part of the ceiling and roof had been taken away by Sulla in 80 B.C. The
decastyle temple of Apollo Didymaeus near Miletus was, according to
Strabo (c. 50 B.C.), unroofed, on account of the vastness of its cella,
in which precious groves of laurel bushes were planted. Apart from these
two examples, the references in various writers to an opening of some
kind in the roofs of temples dedicated to particular deities, and the
statement of Vitruvius, which was doubtless based on the writings of
Greek authors, that in decastyle or large temples the centre was open to
the sky and without a roof (_medium autem sub divo est sine tecto_),
render the existence of the hypaethros probable in some cases; and
therefore C. R. Cockerell's discovery in the temple at Aegina of two
fragments of a coping-stone, in which there were sinkings on one side to
receive the tiles and covering tiles, has been of great importance in
the discussion of this subject. In the conjectural restoration of the
opaion or opening in the roof shown in Cockerell's drawing, it has been
made needlessly large, having an area of about one quarter of the
superficial area of the cella between the columns, and since in the
Pantheon at Rome the relative proportions of the central opening in the
dome and the area of the Rotunda are 1: 22, and the light there is
ample, in the clearer atmosphere of Greece it might have been less. The
larger the opening the more conspicuous would be the notch in the roof
which is so greatly objected to; in this respect T. J. Hittorff would
seem to be nearer the truth when, in his conjectural restoration of
Temple R. at Selinus, he shows an opaion about half the relative size
shown in Cockerell's of that at Aegina, the coping on the side elevation
being much less noticeable. The problem was apparently solved in another
way at Bassae, where, in the excavations of the temple of Apollo by
Cockerell and Baron Haller von Hallerstein, three marble tiles were
found with pierced openings in them about 18 in. by 10 in.; five of
these pierced tiles on either side would have amply lighted the interior
of the cella, and the amount of rain passing through (a serious element
to be considered in a country where torrential rains occasionally fall)
would not be very great or more than could be retained to dry up in the
cella sunk pavement. In favour of both these methods of lighting the
interior of the cella, the sarcophagus tomb at Cyrene, about 20 ft.
long, carved in imitation of a temple, has been adduced, because, on the
top of the roof and in its centre, there is a raised coping, and a
similar feature is found on a tomb found near Delos; an example from
Crete now in the British Museum shows a pierced tile on each side of
the roof, and a large number of pierced tiles have been found in
Pompeii, some of them surrounded with a rim identical with that of the
marble tiles at Bassae. On the other hand, there are many authorities,
among them Dr W. Dörpfeld, who have adhered to their original opinion
that it was only through the open doorway that light was ever admitted
into the cella, and with the clear atmosphere of Greece and the
reflections from the marble pavement such lighting would be quite
sufficient. There remains still another source of light to be
considered, that passing through the Parian marble tiles of the roof;
the superior translucency of Parian to any other marble may have
suggested its employment for the roofs of temples, and if, in the framed
ceilings carried over the cella, openings were left, some light from the
Parian tile roof might have been obtained. It is possibly to this that
Plutarch refers when describing the ceiling and roof of the temple of
Demeter at Eleusis, where the columns in the interior of the temple
carried a ceiling, probably constructed of timbers crossing one another
at right angles, and one or more of the spaces was left open, which
Xenocles surmounted by a roof formed of tiles.

  James Fergusson put forward many years ago a conjectural restoration
  in which he adopted a clerestory above the superimposed columns inside
  the cella; in order to provide the light for these windows he
  indicated two trenches in the roof, one on each side, and pointed out
  that the great Hall of Columns at Karnak was lighted in this way with
  clerestory windows; but in the first place the light in the latter was
  obtained over the flat roofs covering lower portions of the hall, and
  in the second place, as it rarely rains in Thebes, there could be no
  difficulty about the drainage, while in Greece, with the torrential
  rains and snow, these trenches would be deluged with water, and with
  all the appliances of the present day it would be impossible to keep
  these clerestory windows watertight. There is, however, still another
  objection to Fergusson's theory; the water collecting in these
  trenches on the roof would have to be discharged, for which
  Fergusson's suggestions are quite inadequate, and the gargoyles shown
  in the cella wall would make the peristyle insupportable just at the
  time when it was required for shelter. No drainage otherwise of any
  kind has ever been found in any Greek temple, which is fatal to
  Fergusson's view. Nor is it in accordance with the definition "open to
  the sky." English cathedrals and churches are all lighted by
  clerestory windows, but no one has described them as open to the sky,
  and although Vitruvius's statements are sometimes confusing, his
  description is far too clear to leave any misunderstanding as to the
  lighting of temples (where it was necessary on account of great
  length) through an opening in the roof.

  There is one other theory which has been put forward, but which can
  only apply to non-peristylar temples,--that light and air was admitted
  through the metopes, the apertures between the beams crossing the
  cella,--and it has been assumed that because Orestes was advised in
  one of the Greek plays to climb up and look through the metopes of the
  temple, these were left open; but if Orestes could look in, so could
  the birds, and the statue of the god would be defiled. The metopes
  were probably filled in with shutters of some kind which Orestes knew
  how to open.     (R. P. S.)



HYPALLAGE (Gr. [Greek: hypallagê], interchange or exchange), a
rhetorical figure, in which the proper relation between two words
according to the rules of syntax are inverted. The stock instance is
that in Virgil, _Aen._ iii. 61, where _dare classibus austros_, to give
winds to the fleet, is put for _dare classes austris_, to give the fleet
to the winds. The term is also loosely applied to figures of speech
properly known as "metonymy" and, generally, to any striking turn of
expression.



HYPATIA ([Greek: Hypatia]) (c. A.D. 370-415) mathematician and
philosopher, born in Alexandria, was the daughter of Theon, also a
mathematician and philosopher, author of scholia on Euclid and a
commentary on the _Almagest_, in which it is suggested that he was
assisted by Hypatia (on the 3rd book). After lecturing in her native
city, Hypatia ultimately became the recognized head of the Neoplatonic
school there (c. 400). Her great eloquence and rare modesty and beauty,
combined with her remarkable intellectual gifts, attracted to her
class-room a large number of pupils. Among these was Synesius,
afterwards (c. 410) bishop of Ptolemaïs, several of whose letters to
her, full of chivalrous admiration and reverence, are still extant.
Suidas, misled by an incomplete excerpt in Photius from the life of
Isidorus (the Neoplatonist) by Damascius, states that Hypatia was the
wife of Isidorus; but this is chronologically impossible, since Isidorus
could not have been born before 434 (see Hoche in _Philologus_). Shortly
after the accession of Cyril to the patriarchate of Alexandria in 412,
owing to her intimacy with Orestes, the pagan prefect of the city,
Hypatia was barbarously murdered by the Nitrian monks and the fanatical
Christian mob (March 415). Socrates has related how she was torn from
her chariot, dragged to the Caesareum (then a Christian church),
stripped naked, done to death with oyster-shells ([Greek: ostrakois
aneilon,] perhaps "cut her throat") and finally burnt piecemeal. Most
prominent among the actual perpetrators of the crime was one Peter, a
reader; but there seems little reason to doubt Cyril's complicity (see
CYRIL OF ALEXANDRIA).

Hypatia, according to Suidas, was the author of commentaries on the
_Arithmetica_ of Diophantus of Alexandria, on the Conics of Apollonius
of Perga and on the astronomical canon (of Ptolemy). These works are
lost; but their titles, combined with expressions in the letters of
Synesius, who consulted her about the construction of an astrolabe and a
hydroscope, indicate that she devoted herself specially to astronomy and
mathematics. Little is known of her philosophical opinions, but she
appears to have embraced the intellectual rather than the mystical side
of Neoplatonism, and to have been a follower of Plotinus rather than of
Porphyry and Iamblichus. Zeller, however, in his _Outlines of Greek
Philosophy_ (1886, Eng. trans. p. 347), states that "she appears to have
taught the Neoplatonic doctrine in the form in which Iamblichus had
stated it." A Latin letter to Cyril on behalf of Nestorius, printed in
the _Collectio nova conciliorum_, i. (1623), by Stephanus Baluzius
(Étienne Baluze, q.v.), and sometimes attributed to her, is undoubtedly
spurious. The story of Hypatia appears in a considerably disguised yet
still recognizable form in the legend of St Catherine as recorded in the
Roman _Breviary_ (November 25), and still more fully in the
_Martyrologies_ (see A. B. Jameson, _Sacred and Legendary Art_ (1867)
ii. 467.)

  The chief source for the little we know about Hypatia is the account
  given by Socrates (_Hist. ecclesiastica_, vii. 15). She is the subject
  of an epigram by Palladas in the Greek Anthology (ix. 400). See
  Fabricius, _Bibliotheca Graeca_ (ed. Harles), ix. 187; John Toland,
  _Tetradymus_ (1720); R. Hoche in _Philologus_ (1860), xv. 435;
  monographs by Stephan Wolf (Czernowitz, 1879), H. Ligier (Dijon, 1880)
  and W. A. Meyer (Heidelberg, 1885), who devotes attention to the
  relation of Hypatia to the chief representatives of Neoplatonism; J.
  B. Bury, _Hist. of the Later Roman Empire_ (1889), i. 208,317; A.
  Güldenpenning, _Geschichte des oströmischen Reiches unter Arcadius und
  Theodosius II._ (Halle, 1885), p. 230; Wetzer and Welte,
  _Kirchenlexikon_, vi. (1889), from a Catholic standpoint. The story of
  Hypatia also forms the basis of the well-known historical romance by
  Charles Kingsley (1853).



HYPERBATON (Gr. [Greek: huperbaton], a stepping over), the name of a
figure of speech, consisting of a transposition of words from their
natural order, such as the placing of the object before instead of after
the verb. It is a common method of securing emphasis.



HYPERBOLA, a conic section, consisting of two open branches, each
extending to infinity. It may be defined in several ways. The _in
solido_ definition as the section of a cone by a plane at a less
inclination to the axis than the generator brings out the existence of
the two infinite branches if we imagine the cone to be double and to
extend to infinity. The _in plano_ definition, i.e. as the conic having
an eccentricity greater than unity, is a convenient starting-point for
the Euclidian investigation. In projective geometry it may be defined as
the conic which intersects the line at infinity in two real points, or
to which it is possible to draw two real tangents from the centre.
Analytically, it is defined by an equation of the second degree, of
which the highest terms have real roots (see CONIC SECTION).

  While resembling the parabola in extending to infinity, the curve has
  closest affinities to the ellipse. Thus it has a real centre, two
  foci, two directrices and two vertices; the transverse axis, joining
  the vertices, corresponds to the major axis of the ellipse, and the
  line through the centre and perpendicular to this axis is called the
  conjugate axis, and corresponds to the minor axis of the ellipse;
  about these axes the curve is symmetrical. The curve does not appear
  to intersect the conjugate axis, but the introduction of imaginaries
  permits us to regard it as cutting this axis in two unreal points.
  Calling the foci S, S´, the real vertices A, A´, the extremities of
  the conjugate axis B, B' and the centre C, the positions of B, B´ are
  given by AB = AB´ = CS. If a rectangle be constructed about AA´ and
  BB´, the diagonals of this figure are the "asymptotes" of the curve;
  they are the tangents from the centre, and hence touch the curve at
  infinity. These two lines may be pictured in the _in solido_
  definition as the section of a cone by a plane through its vertex and
  parallel to the plane generating the hyperbola. If the asymptotes be
  perpendicular, or, in other words, the principal axes be equal, the
  curve is called the rectangular hyperbola. The hyperbola which has for
  its transverse and conjugate axes the transverse and conjugate axes of
  another hyperbola is said to be the conjugate hyperbola.

  Some properties of the curve will be briefly stated: If PN be the
  ordinate of the point P on the curve, AA' the vertices, X the meet of
  the directrix and axis and C the centre, then PN²: AN·NA´: : SX²:
  AX·A´X, i.e. PN² is to AN·NA´ in a constant ratio. The circle on AA'
  as diameter is called the auxiliarly circle; obviously AN·NA' equals
  the square of the tangent to this circle from N, and hence the ratio
  of PN to the tangent to the auxiliarly circle from N equals the ratio
  of the conjugate axis to the transverse. We may observe that the
  asymptotes intersect this circle in the same points as the
  directrices. An important property is: the difference of the focal
  distances of any point on the curve equals the transverse axis. The
  tangent at any point bisects the angle between the focal distances of
  the point, and the normal is equally inclined to the focal distances.
  Also the auxiliarly circle is the locus of the feet of the
  perpendiculars from the foci on any tangent. Two tangents from any
  point are equally inclined to the focal distance of the point. If the
  tangent at P meet the conjugate axis in t, and the transverse in N,
  then Ct. PN = BC²; similarly if g and G be the corresponding
  intersections of the normal, PG : Pg : : BC² : AC². A diameter is a
  line through the centre and terminated by the curve: it bisects all
  chords parallel to the tangents at its extremities; the diameter
  parallel to these chords is its conjugate diameter. Any diameter is a
  mean proportional between the transverse axis and the focal chord
  parallel to the diameter. Any line cuts off equal distances between
  the curve and the asymptotes. If the tangent at P meets the asymptotes
  in R, R', then CR·CR´ = CS². The geometry of the rectangular hyperbola
  is simplified by the fact that its principal axes are equal.

  Analytically the hyperbola is given by ax² + 2hxy + by² + 2gx + 2fy +
  c = 0 wherein ab > h². Referred to the centre this becomes Ax² + 2Hxy
  + By² + C = 0; and if the axes of coordinates be the principal axes of
  the curve, the equation is further simplified to Ax² - By² = C, or if
  the semi-transverse axis be a, and the semi-conjugate b, x²/a² - y²/b²
  = 1. This is the most commonly used form. In the rectangular hyperbola
  a = b; hence its equation is x² - y² = 0. The equations to the
  asymptotes are x/a = ±y/b and x = ±y respectively. Referred to the
  asymptotes as axes the general equation becomes xy = k²; obviously the
  axes are oblique in the general hyperbola and rectangular in the
  rectangular hyperbola. The values of the constant k² are ½(a² + b²)
  and ½a² respectively. (See GEOMETRY: _Analytical_; _Projective_.)



HYPERBOLE (from Gr. [Greek: hyperballein], to throw beyond), a figure of
rhetoric whereby the speaker expresses more than the truth, in order to
produce a vivid impression; hence, an exaggeration.



HYPERBOREANS ([Greek: Hyperboreoi, Hyperboreioi]), a mythical people
intimately connected with the worship of Apollo. Their name does not
occur in the _Iliad_ or the _Odyssey_, but Herodotus (iv. 32) states
that they were mentioned in Hesiod and in the _Epigoni_, an epic of the
Theban cycle. According to Herodotus, two maidens, Opis and Arge, and
later two others, Hyperoche and Laodice, escorted by five men, called by
the Delians Perphereës, were sent by the Hyperboreans with certain
offerings to Delos. Finding that their messengers did not return, the
Hyperboreans adopted the plan of wrapping the offerings in wheat-straw
and requested their neighbours to hand them on to the next nation, and
so on, till they finally reached Delos. The theory of H. L. Ahrens, that
Hyperboreans and Perphereës are identical, is now widely accepted. In
some of the dialects of northern Greece (especially Macedonia and
Delphi) [phi] had a tendency to become [beta]. The original form of
[Greek: Perpherees] was [Greek: hyperpheretai] or [Greek: hyperphoroi]
("those who carry over"), which becoming [Greek: hyperboroi] gave rise
to the popular derivation from [Greek: boreas] ("dwellers beyond the
north wind"). The Hyperboreans were thus the bearers of the sacrificial
gifts to Apollo over land and sea, irrespective of their home, the name
being given to Delphians, Thessalians, Athenians and Delians. It is
objected by O. Schröder that the form [Greek: Perpherees] requires a
passive meaning, "those who are carried round the altar," perhaps
dancers like the whirling dervishes; distinguishing them from the
Hyperboreans, he explains the latter as those who live "above the
mountains," that is, in heaven. Under the influence of the derivation
from [Greek: boreas], the home of the Hyperboreans was placed in a
region beyond the north wind, a paradise like the Elysian plains,
inaccessible by land or sea, whither Apollo could remove those mortals
who had lived a life of piety. It was a land of perpetual sunshine and
great fertility; its inhabitants were free from disease and war. The
duration of their life was 1000 years, but if any desired to shorten it,
he decked himself with garlands and threw himself from a rock into the
sea. The close connexion of the Hyperboreans with the cult of Apollo may
be seen by comparing the Hyperborean myths, the characters of which by
their names mostly recall Apollo or Artemis (Agyieus, Opis, Hecaergos,
Loxo), with the ceremonial of the Apolline worship. No meat was eaten at
the Pyanepsia; the Hyperboreans were vegetarians. At the festival of
Apollo at Leucas a victim flung himself from a rock into the sea, like
the Hyperborean who was tired of life. According to an Athenian decree
(380 B.C.) asses were sacrificed to Apollo at Delphi, and Pindar
(_Pythia_, x. 33) speaks of "hecatombs of asses" being offered to him by
the Hyperboreans. As the latter conveyed sacrificial gifts to Delos
hidden in wheat-straw, so at the Thargelia a sheaf of corn was carried
round in procession, concealing a symbol of the god (for other
resemblances see Crusius's article). Although the Hyperborean legends
are mainly connected with Delphi and Delos, traces of them are found in
Argos (the stories of Heracles, Perseus, Io), Attica, Macedonia, Thrace,
Sicily and Italy (which Niebuhr indeed considers their original home).
In modern times the name has been applied to a group of races, which
includes the Chukchis, Koryaks, Yukaghirs, Ainus, Gilyaks and
Kamchadales, inhabiting the arctic regions of Asia and America. But if
ever ethnically one, the Asiatic and American branches are now as far
apart from each other as they both are from the Mongolo-Tatar stock.

  See O. Crusius in Roscher's _Lexikon der Mythologie_; O. Schröder in
  _Archiv für Religionswissenschaft_ (1904), viii. 69; W. Mannhardt,
  _Wald- und Feldkulte_ (1905); L. R. Farnell, _Cults of the Greek
  States_ (1907), iv. 100.



HYPEREIDES (c. 390-322 B.C.), one of the ten Attic orators, was the son
of Glaucippus, of the deme of Collytus. Having studied under Isocrates,
he began life as a writer of speeches for the courts, and in 360 he
prosecuted Autocles, a general charged with treason in Thrace (frags.
55-65, Blass). At the time of the so-called "Social War" (358-355) he
accused Aristophon, then one of the most influential men at Athens, of
malpractices (frags. 40-44, Blass), and impeached Philocrates (343) for
high treason. From the peace of 346 to 324 Hypereides supported
Demosthenes in the struggle against Macedon; but in the affair of
Harpalus he was one of the ten public prosecutors of Demosthenes, and on
the exile of his former leader he became the head of the patriotic party
(324). After the death of Alexander, he was the chief promoter of the
Lamian war against Antipater and Craterus. After the decisive defeat at
Crannon (322), Hypereides and the other orators, whose surrender was
demanded by Antipater, were condemned to death by the Athenian partisans
of Macedonia. Hypereides fled to Aegina, but Antipater's emissaries
dragged him from the temple of Aeacus, where he had taken refuge, and
put him to death; according to others, he was taken before Antipater at
Athens or Cleonae. His body was afterwards removed to Athens for burial.

Hypereides was an ardent pursuer of "the beautiful," which in his time
generally meant pleasure and luxury. His temper was easy-going and
humorous; and hence, though in his development of the periodic sentence
he followed Isocrates, the essential tendencies of his style are those
of Lysias, whom he surpassed, however, in the richness of his vocabulary
and in the variety of his powers. His diction was plain and forcible,
though he occasionally indulged in long compound words probably borrowed
from the Middle Comedy, with which, and with the everyday life of his
time, he was in full sympathy. His composition was simple. He was
specially distinguished for subtlety of expression, grace and wit, as
well as for tact in approaching his case and handling his subject
matter. Sir R. C. Jebb sums up the criticism of pseudo-Longinus (_De
sublimitate_, 34) in the phrase--"Hypereides was the Sheridan of
Athens."

  Seventy-seven speeches were attributed to Hypereides, of which
  twenty-five were regarded as spurious even by ancient critics. It is
  said that a MS. of most of the speeches was in existence in the 16th
  century in the library of Matthias Corvinus, king of Hungary, at Ofen,
  but was destroyed at the capture of the city by the Turks in 1526.
  Only a few fragments were known until comparatively recent times. In
  1847 large fragments of his speeches Against _Demosthenes_ (see above)
  and _For Lycophron_ (incidentally interesting as elucidating the order
  of marriage processions and other details of Athenian life, and the
  Athenian government of Lemnos), and the whole of the _For Euxenippus_
  (c. 330, a _locus classicus_ on [Greek: eisangeliai] or state
  prosecutions), were found in a tomb at Thebes in Egypt, and in 1856 a
  considerable portion of a [Greek: logos epitaphios], a _Funeral
  Oration_ over Leosthenes and his comrades who had fallen in the Lamian
  war, the best extant specimen of epideictic oratory (see BABINGTON,
  CHURCHILL). Towards the end of the century further discoveries were
  made of the conclusion of the speech _Against Philippides_ (dealing
  with a [Greek: graphê paranomôn], or indictment for the proposal of an
  unconstitutional measure, arising out of the disputes of the
  Macedonian and anti-Macedonian parties at Athens), and of the whole of
  the _Against Athenogenes_ (a perfumer accused of fraud in the sale of
  his business). These have been edited by F. G. Kenyon (1893). An
  important speech that is lost is the _Deliacus_ (frags. 67-75, Blass)
  on the presidency of the Delian temple claimed by both Athens and
  Delos, which was adjudged by the Amphictyons to Athens.

  On Hypereides generally see pseudo-Plutarch, _Decem oratorum vitae_;
  F. Blass, _Attische Beredsamkeit_, iii.; R. C. Jebb, _Attic Orators_,
  ii. 381. A full list of editions and articles is given in F. Blass,
  _Hyperidis orationes sex cum ceterarum fragmentis_ (1894, Teubner
  series), to which may be added I. Bassi, _Le Quattro Orazioni di
  Iperide_ (introduction and notes, 1888), and J. E. Sandys in
  _Classical Review_ (January 1895) (a review of the editions of Kenyon
  and Blass). For the discourse against Athenogenes see H. Weil, _Études
  sur l'antiquité grecque_ (1900).



HYPERION, in Greek mythology, one of the Titans, son of Uranus and Gaea
and father of Helios, the sun-god (Hesiod, _Theog._ 134, 371;
Apollodorus i. 1. 2). In the well-known passage in Shakespeare
(_Hamlet_, i. 2: "Hyperion to a satyr," where as in other poets the
vowel -_i_- though really long, is shortened for metrical reasons)
Hyperion is used for Apollo as expressive of the idea of beauty. The
name is often used as an epithet of Helios, who is himself sometimes
called simply Hyperion. It is explained as (1) he who moves above
([Greek: hyper-iôn]), but the quantity of the vowel is against this; (2)
he who is above ([Greek: hyperi-ôn]). Others take it to be a patronymic
in form, like [Greek: Kroniôn, Moliôn].



HYPERSTHENE, a rock-forming mineral belonging to the group of
orthorhombic pyroxenes. It differs from the other members (enstatite
[q.v.] and bronzite) of this group in containing a considerable amount
of iron replacing magnesium: the chemical formula is (Mg, Fe)SiO3.
Distinctly developed crystals are rare, the mineral being usually found
as foliated masses embedded in those igneous rocks--norite,
hypersthene-andesite, &c.--of which it forms an essential constituent.
The coarsely grained labradorite-hypersthene-rock (norite) of the island
of St Paul off the coast of Labrador has furnished the most typical
material; and for this reason the mineral has been known as "Labrador
hornblende" or paulite. The colour is brownish-black, and the pleochrism
strong; the hardness is 6, and the specific gravity 3.4-3.5. On certain
surfaces it displays a brilliant copper-red metallic sheen or schiller,
which has the same origin as the bronzy sheen of bronzite (q.v.), but is
even more pronounced. Like bronzite, it is sometimes cut and polished
for ornamental purposes.     (L. J. S.)



HYPERTROPHY (Gr. [Greek: hyper], over, and [Greek: trophê],
nourishment), a term in medicine employed to designate an abnormal
increase in bulk of one or more of the organs or component tissues of
the body (see PATHOLOGY). In its strict sense this term can only be
applied where the increase affects the natural textures of a part, and
is not applicable where the enlargement is due to the presence of some
extraneous morbid formation. Hypertrophy of a part may manifest itself
either by simply an increase in the size of its constituents, or by this
combined with an increase in their number (hyperplasia). In many
instances both are associated.

The conditions giving rise to hypertrophy are the reverse of those
described as producing Atrophy (q.v.). They are concisely stated by Sir
James Paget as being chiefly or only three, namely: (1) the increased
exercise of a part in its healthy functions; (2) an increased
accumulation in the blood of the particular materials which a part
appropriates to its nutrition or in secretion; and (3) an increased
afflux of healthy blood.

Illustrations are furnished of the first of these conditions by the high
development of muscular tissue under habitual active exercise; of the
second in the case of obesity, which is an hypertrophy of the fatty
tissues, the elements of which are furnished by the blood; and of the
third in the occasional overgrowth of hair in the neighbourhood of parts
which are the seat of inflammation. Obviously therefore, in many
instances, hypertrophy cannot be regarded as a deviation from health,
but rather on the contrary as indicative of a high degree of nutrition
and physical power. Even in those cases where it is found associated
with disease, it is often produced as a salutary effort of nature to
compensate for obstructions or other difficulties which have arisen in
the system, and thus to ward off evil consequences. No better example of
this can be seen than in the case of certain forms of heart disease,
where from defect at some of the natural orifices of that organ the
onward flow of the blood is interfered with, and would soon give rise to
serious embarrassment to the circulation, were it not that behind the
seat of obstruction the heart gradually becomes hypertrophied, and thus
acquires greater propelling power to overcome the resistance in front.
Again, it has been noticed, in the case of certain double organs such as
the kidneys, that when one has been destroyed by disease the other has
become hypertrophied to such a degree as enables it to discharge the
functions of both.

Hypertrophy may, however, in certain circumstances constitute a disease,
as in goitre and elephantiasis (q.v.), and also in the case of certain
tumours and growths (such as cutaneous excrescences, fatty tumours,
mucous polypi, &c.), which are simply enlargements of normal textures.
Hypertrophy does not in all cases involve an increase in bulk; for, just
as in atrophy there may be no diminution in the size of the affected
organ, so in hypertrophy there may be no increase. This is apt to be the
case where certain only of the elements of an organ undergo increase,
while the others remain unaffected or are actually atrophied by the
pressure of the hypertrophied tissue, as is seen in the disease known as
cirrhosis of the liver.

A spurious hypertrophy is observed in the rare disease to which G. B.
Duchenne applied the name of _pseudo-hypertrophic paralysis_. This
ailment, which appears to be confined to children, consists essentially
of a progressive loss of power accompanied with a remarkable enlargement
of certain muscles or groups of muscles, more rarely of the whole
muscular system. This increase of bulk is, however, not a true
hypertrophy, but rather an excessive development of connective tissue in
the substance of the muscles, the proper texture of which tends in
consequence to undergo atrophy or degeneration. The appearance presented
by a child suffering from this disease is striking. The attitude and
gait are remarkably altered, the child standing with shoulders thrown
back, small of the back deeply curved inwards, and legs wide apart,
while walking is accompanied with a peculiar swinging or rocking
movement. The calves of the legs, the buttocks, the muscles of the back,
and occasionally other muscles, are seen to be unduly enlarged, and
contrast strangely with the general feebleness. The progress of the
disease is marked by increasing failure of locomotory power, and
ultimately by complete paralysis of the limbs. The malady is little
amenable to treatment, and, although often prolonged for years,
generally proves fatal before the period of maturity.



HYPNOTISM, a term now in general use as covering all that pertains to
the art of inducing the hypnotic state, or hypnosis, and to the study of
that state, its conditions, peculiarities and effects. Hypnosis is a
condition, allied to normal sleep (Gr. [Greek: hypnos]), which can be
induced in a large majority of normal persons. Its most characteristic
and constant symptom is the increased suggestibility of the subject (see
SUGGESTION). Other symptoms are very varied and differ widely in
different subjects and in the same subject at different times. There can
be no doubt that the increased suggestibility and all the other symptoms
of hypnosis imply some abnormal condition of the brain of a temporary
and harmless nature. It would seem that in all ages and in almost all
countries individuals have occasionally fallen into abnormal states of
mind more or less closely resembling the hypnotic state, and have
thereby excited the superstitious wonder of their fellows. In some cases
the state has been deliberately induced, in others it has appeared
spontaneously, generally under the influence of some emotional
excitement. The most familiar of these allied states is the somnambulism
or sleep-walking to which some persons seem to be hereditarily disposed.
Of a rather different type are the states of ecstasy into which
religious enthusiasts have occasionally fallen and which were especially
frequent among the peoples of Europe during the middle ages. While in
this condition individuals have appeared to be insensitive to all
impressions made on their sense-organs, even to such as would excite
acute pain in normal persons, have been capable of maintaining rigid
postures for long periods of time, have experienced vivid
hallucinations, and have produced, through the power of the imagination,
extraordinary organic changes in the body, such as the bloody stigmata
on the hands and feet in several well-attested instances. It has been
proved in recent years that effects of all these kinds may be produced
by hypnotic suggestion. Different again, but closely paralleled by some
subjects in hypnosis, is the state of _latah_ into which a certain
proportion of persons of the Malay race are liable to fall. These
persons, if their attention is suddenly and forcibly drawn to any other
person, will begin to imitate his every action and attitude, and may do
so in spite of their best efforts to restrain their imitative movements.
Among the half-bred French-Canadians of the forest regions of Canada
occur individuals, known as "jumpers," who are liable to fall suddenly
into a similar state of abject imitativeness, and the same peculiar
behaviour has been observed among some of the remote tribes of Siberia.

The deliberate induction of states identical with, or closely allied to,
hypnosis is practised by many barbarous and savage peoples, generally
for ceremonial purposes. Thus, certain dervishes of Algiers are said to
induce in themselves, by the aid of the sound of drums, monotonous songs
and movements, a state in which they are insensitive to pain, and a
similar practice of religious devotees is reported from Tibet. Perhaps
the most marvellous achievement among well-attested cases of this sort
is that of certain _yogis_ of Hindustan; by long training and practice
they seem to acquire the power of arresting almost completely all their
vital functions. An intense effort of abstraction from the impressions
of the outer world, a prolonged fixation of the eyes upon the nose or in
some other strained position and a power of greatly slowing the
respiration, these seem to be important features of their procedure for
the attainment of their abnormal states.

In spite of the wide distribution in time and space, and the not very
infrequent occurrence, of these instances of states identical with or
allied to hypnosis, some three centuries of enthusiastic investigation
and of bitter controversy were required to establish the occurrence of
the hypnotic state among the facts accepted by the world of European
science. Scientific interest in them may be traced back at least as far
as the end of the 16th century. Paracelsus had founded the "sympathetic
system" of medicine, according to which the stars and other bodies,
especially magnets, influence men by means of a subtle emanation or
fluid that pervades all space. J. B. van Helmont, a distinguished man of
science of the latter part of the 16th century, extended this doctrine
by teaching that a similar magnetic fluid radiates from men, and that it
can be guided by their wills to influence directly the minds and bodies
of others. In the middle of the 17th century there appeared in England
several persons who claimed to have the power of curing diseases by
stroking with the hand. Notable amongst these was Valentine Greatrakes,
of Affane, in the county of Waterford, Ireland, who was born in
February 1628, and who attracted great attention in England by his
supposed power of curing the king's evil, or scrofula. Many of the most
distinguished scientific and theological men of the day, such as Robert
Boyle and R. Cudworth, witnessed and attested the cures supposed to be
effected by Greatrakes, and thousands of sufferers crowded to him from
all parts of the kingdom. About the middle of the 18th century John
Joseph Gassner, a Roman Catholic priest in Swabia, took up the notion
that the majority of diseases arose from demoniacal possession, and
could only be cured by exorcism. His method was undoubtedly similar to
that afterwards followed by Mesmer and others, and he had an
extraordinary influence over the nervous systems of his patients.
Gassner, however, believed his power to be altogether supernatural.

But it was not until the latter part of the 18th century that the
doctrine of a magnetic fluid excited great popular interest and became
the subject of fierce controversy in the scientific world. F. A. Mesmer
(q.v.), a physician of Vienna, was largely instrumental in bringing the
doctrine into prominence. He developed it by postulating a specialized
variety of magnetic fluid which he called _animal magnetism_; and he
claimed to be able to cure many diseases by means of this animal
magnetism, teaching, also, that it may be imparted to and stored up in
inert objects, which are thereby rendered potent to cure disease.

It would seem that Mesmer himself was not acquainted with the artificial
somnambulism which for nearly a century was called mesmeric or magnetic
sleep, and which is now familiar as hypnosis of a well-marked degree. It
was observed and described about the year 1780 by the marquis de
Puységur, a disciple of Mesmer, who showed that, while subjects were in
this state, not only could some of their diseases be cured, but also
their movements could be controlled by the "magnetizer," and that they
usually remembered nothing of the events of the period of sleep when
restored to normal consciousness. These are three of the most important
features of hypnosis, and the modern study of hypnotism may therefore be
said to have been initiated at this date by Puységur. For, though it is
probable that this state had often been induced by the earlier
magnetists, they had not recognized that the peculiar behaviour of their
patients resulted from their being plunged into this artificial sleep,
but had attributed all the symptoms they observed to the direct physical
action of external agents upon the patients.

The success of Mesmer and his disciples, especially great in the
fashionable world, led to the appointment in Paris of a royal commission
for the investigation of their claims. The commission, which included
men of great eminence, notably A. L. Lavoisier and Benjamin Franklin,
reported in the year 1784 that it could not accept the evidence for the
existence of the magnetic fluid; but it did not express an opinion as to
the reality of the cures said to be effected by its means, nor as to the
nature of the magnetic sleep. This report and the social upheavals of
the following years seem to have abolished the public interest in
"animal magnetism" for the space of one generation; after which
Alexandre Bertrand, a Parisian physician, revived it by his acute
investigations and interpretations of the phenomena. Bertrand was the
first to give an explanation of the facts of the kind that is now
generally accepted. He exhibited the affinity of the "magnetic sleep" to
ordinary somnambulism, and he taught that the peculiar effects are to be
regarded as due to the suggestions of the operator working themselves
out in the mind and body of the "magnetized" subject, i.e. he regarded
the influence of the magnetizer as exerted in the first instance on the
mind of the subject and only indirectly through the mind upon the body.
Shortly after this revival of public interest, namely in the year 1831,
a committee of the Academy of Medicine of Paris reported favourably upon
"magnetism" as a therapeutic agency, and before many years had elapsed
it was extensively practised by the physicians of all European
countries, with few exceptions, of which England was the most notable.
Most of the practitioners of this period adhered to the doctrine of the
magnetic fluid emanating from the operator to his patient, and the
acceptance of this doctrine was commonly combined with belief in
phrenology, astrology and the influence of metals and magnets,
externally applied, in curing disease and in producing a variety of
strange sensations and other affections of the mind. These beliefs,
claiming to rest upon carefully observed facts, were given a new
elaboration and a more imposing claim to be scientifically established
by the doctrine of _odylic force_ propounded by Baron Karl von
Reichenbach. In this mass of ill-based assertion and belief the valuable
truths of "animal magnetism" and the psychological explanations of them
given by Bertrand were swamped and well-nigh lost sight of. For it was
this seemingly inseparable association between the facts of hypnotism
and these bizarre practices and baseless beliefs that blinded the larger
and more sober part of the scientific world, and led them persistently
to assert that all this group of alleged phenomena was a mass of
quackery, fraud and superstition. And the fact that magnetism was
practised for pecuniary gain, often in a shameless manner, by exponents
who claimed to cure by its means every conceivable ill, rendered this
attitude on the part of the medical profession inevitable and perhaps
excusable, though not justifiable. It was owing to this baleful
association that John Elliotson, one of the leading London physicians of
that time, who became an ardent advocate of "magnetism" and who founded
and edited the _Zoist_ in the interests of the subject, was driven out
of the profession. This association may perhaps be held, also, to excuse
the hostile attitude of the medical profession towards James Esdaile, a
surgeon, who, practising in a government hospital in Calcutta among the
natives of India, performed many major operations, such as the
amputation of limbs, painlessly and with the most excellent results by
aid of the "magnetic" sleep. For both Elliotson and Esdaile, though
honourable practitioners, accepted the doctrine of the "magnetic" fluid
and many of the erroneous beliefs that commonly were bound up with it.

In 1841 James Braid, a surgeon of Manchester, rediscovered independently
Bertrand's physiological and psychological explanations of the facts,
carried them further, and placed "hypnotism," as he named the study, on
a sound basis. Braid showed that subjects in "magnetic" sleep, far from
being in a profoundly insensitive condition, are often abnormally
susceptible to impressions on the senses, and showed that many of the
peculiarities of their behaviour were due to suggestions, made verbally
or otherwise, but unintentionally, by the operator or by onlookers.

It seems, on looking back on the history of hypnotism, that at this time
it was in a fair way to secure general recognition as a most interesting
subject of psychological study and a valuable addition to the resources
of the physician. But it was destined once more to be denied its rights
by official science and to fall back into disrepute. This was due to the
coincidence about the year 1848 of two events of some importance,
namely--the discovery of the anaesthetic properties of chloroform and
the sudden rise of modern spiritualism. The former afforded a very
convenient substitute for the most obvious practical application of
hypnotism, the production of anaesthesia during surgical operations; the
latter involved it once more in a mass of fraud and superstition, and,
for the popular mind, drove it back to the region of the marvellous, the
supernatural and the dangerous, made it, in fact, once more a branch of
the black art.

From this time onward there took place a gradual differentiation of the
"animal magnetism" of the 18th century into two diverging branches,
hypnotism and spiritualism, two branches which, however, are not yet
entirely separated and, perhaps, never will be. At the same time the
original system of "animal magnetism" has lived on in an enfeebled
condition and is now very nearly, though not quite, extinct.

In the development of hypnotism since the time of Braid we may
distinguish three lines, the physiological, the psychological and the
pathological. The last may be dismissed in a few words. Its principal
representative was J. M. Charcot, who taught at the Salpêtrière in Paris
that hypnosis is essentially a symptom of a morbid condition of hysteria
or hystero-epilepsy. This doctrine, which, owing to the great repute
enjoyed by Charcot, has done much to retard the application of
hypnotism, is now completely discredited. The workers of the
physiological party attached special importance to the fixation of the
eyes, or to other forms of long continued and monotonous, or violent,
sensory stimulation in the induction of hypnosis. They believed that by
acting on the senses in these ways they induced a peculiar condition of
the nervous system, which consisted in the temporary abolition of the
cerebral functions and the consequent reduction of the subject to
machine-like unconscious automatism. The leading exponent of this view
was R. Heidenhain, professor of physiology at Breslau, whose
experimental investigations played a large part in convincing the
scientific world of the genuineness of the leading symptoms of hypnosis.
The purely psychological doctrine of hypnosis puts aside all physical
and physiological influences and effects as of but little or no
importance, and seeks a psychological explanation of the induction of
hypnosis and of all the phenomena. This dates from 1884, when H.
Bernheim, professor of medicine at Nancy, published his work _De la
Suggestion_ (republished in 1887 with a second part on the therapeutics
of hypnotism). Bernheim was led to the study of hypnotism by A. A.
Liébeault, who for twenty years had used it very largely and
successfully in his general practice among the poor of Nancy. Liébeault
rediscovered independently, and Bernheim made known to the world the
truths, twice previously discovered and twice lost sight of, that
expectation is a most important factor in the induction of hypnosis,
that increased suggestibility is its essential symptom, and that in
general the operator works upon his patient by mental influences.
Although they went too far in the direction of ignoring the peculiarity
of the state of the brain in hypnosis and the predisposing effect of
monotonous sensory stimulation, and in seeking to identify hypnosis with
normal sleep, the views of the Nancy investigators have prevailed, and
are now in the main generally accepted. Their methods of verbal
suggestion have been adopted by leading physicians in almost all
civilized countries and have been proved to be efficacious in the relief
of many disorders; and as a method of psychological investigation
hypnotism has proved, especially in the hands of the late Ed. Gurney, of
Dr Pierre Janet and of other investigators, capable of throwing much
light on the constitution of the mind, has opened up a number of
problems of the deepest interest, and has done more than any other of
the many branches of modern psychology to show the limitations and
comparative barrenness of the old psychology that relied on
introspection alone and figured as a department of general philosophy.
In England, "always the last to enter into the general movement of the
European mind," the prejudice, incredulity and ignorant
misrepresentation with which hypnotism has everywhere been received have
resisted its progress more stubbornly than elsewhere; but even in
England its reality and its value as a therapeutic agent have at last
been officially recognized. In 1892, just fifty years after Braid
clearly demonstrated the facts and published explanations of them almost
identical with those now accepted, a committee of the British Medical
Association reported favourably upon hypnotism after a searching
investigation; it is now regularly employed by a number of physicians of
high standing, and the formation in 1907 of "The Medical Society for the
Study of Suggestive Therapeutics" shows that the footing it has gained
is likely to be made good.

_Induction of Hypnosis._--It has now been abundantly proved that
hypnosis can be induced in the great majority of normal persons,
provided that they willingly submit themselves to the process. Several
of the most experienced operators have succeeded in hypnotizing more
than 90% of the cases they have attempted, and most of them are agreed
that failure to induce hypnosis in any case is due either to lack of
skill and tact on the part of the operator, or to some unfavourable
mental condition of the subject. It has often been said that some races
or peoples are by nature more readily hypnotizable than others; of the
French people especially this has been maintained. But there is no
sufficient ground for this statement. The differences that undoubtedly
obtain between populations of different regions in respect to the ease
or difficulty with which a large proportion of all persons can be
hypnotized are sufficiently explained by the differences of the attitude
of the public towards hypnotism; in France, e.g., and especially in
Nancy, hypnotism has been made known to the public chiefly as a
recognized auxiliary to the better known methods of medical treatment,
whereas in England the medical profession has allowed the public to make
acquaintance with hypnotism through the medium of disgusting
stage-performances whose only object was to raise a laugh, and has, with
few exceptions, joined in the general chorus of condemnation and
mistrust. Hence in France patients submit themselves with confidence and
goodwill to hypnotic treatment, whereas in England it is still necessary
in most cases to remove an ill-based prejudice before the treatment can
be undertaken with hope of success. For the confidence and goodwill of
the patient are almost essential to success, and even after hypnosis has
been induced on several occasions a patient may be so influenced by
injudicious friends that he cannot again be hypnotized or, if
hypnotized, is much less amenable to the power of suggestion. Various
methods of hypnotization are current, but most practitioners combine the
methods of Braid and of Bernheim. After asking the patient to resign
himself passively into their hands, and after seating him in a
comfortable arm-chair, they direct him to fix his eyes upon some small
object held generally in such a position that some slight muscular
strain is involved in maintaining the fixation; they then suggest to him
verbally the idea or expectation of sleep and the sensations that
normally accompany the oncoming of sleep, the heaviness of the eyes, the
slackness of the limbs and so forth; and when the eyes show signs of
fatigue, they either close them by gentle pressure or tell the subject
to close them. Many also pass their hands slowly and regularly over the
face, with or without contact. The old magnetizers attached great
importance to such "passes," believing that by them the "magnetic fluid"
was imparted to the patient; but it seems clear that, in so far as they
contribute to induce hypnosis, it is in their character merely of
gentle, monotonous, sensory stimulations. A well-disposed subject soon
falls into a drowsy state and tends to pass into natural sleep; but by
speech, by passes, or by manipulating his limbs the operator keeps in
touch with him, keeps his waning attention open to the impressions he
himself makes. Most subjects then find it difficult or impossible to
open their eyes or to make any other movement which is forbidden or said
to be impossible by the operator, although they may be fully conscious
of all that goes on about them and may have the conviction that if they
did but make an effort they could break the spell. This is a light stage
of hypnosis beyond which some subjects can hardly be induced to pass and
beyond which few pass at the first attempt. But on successive occasions,
or even on the first occasion, a favourable subject passes into deeper
stages of hypnosis. Many attempts have been made to distinguish clearly
marked and constantly occurring stages. But it seems now clear that the
complex of symptoms displayed varies in all cases with the
idiosyncrasies of the subject and with the methods adopted by the
operator. In many subjects a waxy rigidity of the limbs appears
spontaneously or can be induced by suggestion; the limbs then retain for
long periods without fatigue any position given them by the operator.
The most susceptible subjects pass into the stage known as artificial
somnambulism. In this condition they continue to respond to all
suggestions made by the operator, but seem as insensitive to all other
impressions as a person in profound sleep or in coma; and on awaking
from this condition they are usually oblivious of all that they have
heard, said or done during the somnambulistic period. When in this last
condition patients are usually more profoundly influenced by
suggestions, especially post-hypnotic suggestions, than when in the
lighter stages; but the lighter stages suffice for the production of
many therapeutic effects. When a patient is completely hypnotized, his
movements, his senses, his ideas and, to some extent, even the organic
processes over which he has no voluntary control become more or less
completely subject to the suggestions of the operator; and usually he is
responsive to the operator alone (_rapport_) unless he is instructed by
the latter to respond also to the suggestions of other persons. If left
to himself the hypnotized subject will usually awake to his normal state
after a period which is longer in proportion to the depth of hypnosis;
and the deeper stages seem to pass over into normal sleep. The subject
can in almost every case be brought quickly back to the normal state by
the verbal command of the operator.

_The Principal Effects produced by Suggestion during Hypnosis._--The
subject may not only be rendered incapable of contracting any of the
muscles of the voluntary system, but may also be made to use them with
extraordinarily great or sustained force (though by no means in all
cases). He can with difficulty refrain from performing any action
commanded by the operator, and usually carries out any simple command
without hesitation. Any one of the sense-organs, or any sensory region
such as the skin or deep tissues of one limb may be rendered anaesthetic
by verbal suggestion, aided perhaps by some gentle manipulation of the
part. On this fact depends the surgical application of hypnotism.
Sceptical observers are always inclined to doubt the genuineness of the
anaesthesia produced by a mere word of command, but the number of
surgical operations performed under hypnotic anaesthesia suffices to put
its reality beyond all question. A convincing experiment may, however,
be made on almost any good subject. Anaesthesia of one eye may be
suggested and its reality tested in the following way. Anaesthesia of
the left eye may be suggested, and the subject be instructed to fix his
gaze on a distant point and to give some signal as soon as he sees the
operator's finger in the peripheral field of view. The operator then
brings his finger slowly from behind and to the right forwards towards
the subject's line of sight. The subject signals as soon as it crosses
the normal temporal boundary of the field of view of the right eye. The
operator then brings his finger forward from a point behind and to the
left of the subject's head. The subject allows it to cross the monocular
field of the left eye and signals only when the finger enters the field
of vision of the right eye across its nasal boundary. Since few persons,
other than physiologists or medical men, are aware of the relations of
the boundaries of the monocular and binocular fields of vision, the
success of this experiment affords proof that the finger remains
invisible to the subject during its passage across the monocular field
of the left eye. The abolition of pain, especially of neuralgias, the
pain of rheumatic and other inflammations, which is one of the most
valuable applications of hypnotism, is an effect closely allied to the
production of such anaesthesia.

It has often been stated that in hypnosis the senses may be rendered
extraordinarily acute or hyperaesthetic, so that impressions too faint
to affect the senses of the normal person may be perceived by the
hypnotized subject; but in view of the fact that most observers are
ignorant of the normal limits of sensitivity and discrimination, all
such statements must be received with caution, until we have more
convincing evidence than has yet been brought forward.

_Positive and Negative Hallucinations_ are among the most striking
effects of hypnotic suggestion. A good subject may be made to experience
an hallucinatory perception of almost any object, the more easily the
less unusual and out of harmony with the surroundings is the suggested
object. He may, e.g., be given a blank card and asked if he thinks it a
good photograph of himself. He may then assent and describe the
photograph in some detail, and, what is more astonishing, he may pick
out the card as the one bearing the photograph, after it has been mixed
with other similar blank cards. This seems to be due to the part played
by _points de repère_, insignificant details of surface or texture,
which serve as an objective basis around which the hallucinatory image
is constructed by the pictorial imagination of the subject. A negative
hallucination may be induced by telling the subject that a certain
object or person is no longer present, when he ignores in every way that
object or person. This is more puzzling than the positive hallucination
and will be referred to again in discussing the theory of hypnosis. Both
kinds of hallucination tend to be systematically and logically
developed; if, e.g., the subject is told that a certain person is no
longer visible, he may become insensitive to impressions made on any
sense by that person.

_Delusions_, or false beliefs as to their present situation or past
experiences may be induced in many subjects. On being assured that he is
some other person, or that he is in some strange situation, the subject
may accept the suggestion and adapt his behaviour with great histrionic
skill to the induced delusion. It is probable that many, perhaps all,
subjects are vaguely aware, as we sometimes are in dreams, that the
delusions and hallucinations they experience are of an unreal nature. In
the lighter stages of hypnosis a subject usually remembers the events of
his waking life, but in the deeper stages he is apt, while remembering
the events of previous hypnotic periods, to be incapable of recalling
his normal life; but in this respect, as also in respect to the extent
to which on awaking he remembers the events of the hypnotic period, the
suggestions of the operator usually play a determining part.

Among the organic changes that have been produced by hypnotic suggestion
are slowing or acceleration of the cardiac and respiratory rhythms; rise
and fall of body-temperature through two or three degrees; local
erythema and even inflammation of the skin with vesication or exudation
of small drops of blood; evacuation of the bowel and vomiting;
modifications of the secretory activity of glands, especially of the
sweat-glands.

_Post-hypnotic Effects._--Most subjects in whom any appreciable degree
of hypnosis can be induced show some susceptibility to post-hypnotic
suggestion, i.e. they may continue to be influenced, when restored to
the fully waking state, by suggestions made during hypnosis, more
especially if the operator suggests that this shall be the case; as a
rule, the deeper the stage of hypnosis reached, the more effective are
post-hypnotic suggestions. The therapeutic applications of hypnotism
depend in the main upon this post-hypnotic continuance of the working of
suggestions. If a subject is told that on awaking, or on a certain
signal, or after the lapse of a given interval of time from the moment
of awaking, he will perform a certain action, he usually feels some
inclination to carry out the suggestion at the appropriate moment. If he
remembers that the action has been suggested to him he may refuse to
perform it, and if it is one repugnant to his moral nature, or merely
one that would make him appear ridiculous, he may persist in his
refusal. But if the action is of a simple and ordinary nature he will
usually perform it, remarking that he cannot be comfortable till it is
done. If the subject was deeply hypnotized and remembers nothing of the
hypnotic period, he will carry out the post-hypnotic suggestion in
almost every case, no matter how complicated or absurd it may be, so
long as it is not one from which his normal self would be extremely
averse; and he will respond appropriately to the suggested signals,
although he is not conscious of their having been named; he will often
perform the action in a very natural way, and will, if questioned, give
some more or less adequate reason for it. Such actions, determined by
post-hypnotic suggestions of which no conscious memory remains, may be
carried out even after the lapse of many weeks or even months.
Inhibitions of movement, anaesthesia, positive and negative
hallucinations, and delusions may also be made to persist for brief
periods after the termination of hypnosis; and organic effects, such as
the action of the bowels, the oncoming of sleep and the cessation of
pain, may be determined by post-hypnotic suggestion. In short, it may be
said that in a good subject all the kinds of suggestion which will take
effect during hypnosis will also be effective if given as post-hypnotic
suggestions.

_Theory of the Hypnotic State._--Very many so called theories of
hypnosis have been propounded, but few of them demand serious
consideration. One author ascribes all the symptoms to cerebral anaemia,
another to cerebral congestion, a third to temporary suppression of the
functions of the cerebrum, a fourth to abnormal cerebral excitability, a
fifth to the independent functioning of one hemisphere. Another seeks to
explain all the facts by saying that in hypnosis our normal
consciousness disappears and is replaced by a dream-consciousness; and
yet another by the assumption that every human organism comprises two
mental selves or personalities, a normal one and one which only comes
into activity during sleep and hypnosis. Most of these "theories" would,
even if true, carry us but a little way towards a complete understanding
of the facts. There is, however, one theory or principle of explanation
which is now gradually taking shape under the hands of a number of the
more penetrating workers in this field, and which does seem to render
intelligible many of the principle facts. This is the theory of _mental
dissociation_.

It is clear that a theory of hypnosis must attempt to give some account
of the peculiar condition of the brain which is undoubtedly present as
an essential feature of the state. It is therefore not enough to say
with Bernheim that hypnosis is a state of abnormally increased
suggestibility produced by suggestion; nor is it enough, though it is
partially true, to say that it is a state of mono-ideism or one of
abnormally great concentration of attention. Any theory must be stated
in terms of physiological psychology, it must take account of both the
psychical and the nervous peculiarities of the hypnotic state; it must
exhibit the physiological condition as in some degree similar to that
obtaining in normal sleep; but principally it must account for that
abnormally great receptivity for ideas, and that abnormally intense and
effective operation of ideas so received, which constitute abnormally
great suggestibility.

The theory of mental dissociation may be stated in purely mental terms,
or primarily in terms of nervous structure and function, and the latter
mode of statement is probably the more profitable at the present time.
The increased effectiveness of ideas might be due to one of two
conditions: (1) it might be that certain tracts of the brain or the
whole brain were in a condition of abnormally great excitability; or (2)
an idea might operate more effectively in the mind and on the body, not
because it, or the underlying brain-process was more intense than
normally, but because it worked out its effects free from the
interference of contrary or irrelevant ideas that might weaken its
force. It is along this second line that the theory of mental
dissociation attempts to explain the increased suggestibility of
hypnosis. To understand the theory we must bear in mind the nature of
mental process in general and of its nervous concomitants. Mental
process consists in the interplay, not merely of ideas, but rather of
complex dispositions which are the more or less enduring conditions of
the rise of ideas to consciousness. Each such disposition seems capable
of remaining inactive or quiescent for long periods, and of being
excited in various degrees, either by impressions made upon the
sense-organs or by the spread of excitement from other dispositions.
When its excitement rises above a certain pitch of intensity, the
corresponding idea rises to the focus of consciousness. These
dispositions are essential factors of all mental process, the essential
conditions of all mental retention. They may be called simply mental
dispositions, their nature being left undefined; but for our present
purpose it is advantageous to regard them as neural dispositions,
complex functional groups of nervous elements or neurones. The neurones
of each such group must be conceived as being so intimately connected
with one another that the excitement of any part of the group at once
spreads through the whole group or disposition, so that it always
functions as a unit. The whole cerebrum must be conceived as consisting
of a great number of such dispositions, inextricably interwoven, but
interconnected in orderly fashion with very various degrees of intimacy;
groups of dispositions are very intimately connected to form neural
systems, so that the excitement of any one member of such a system tends
to spread in succession to all the other members. On the other hand, it
is a peculiarity of the reciprocal relations of all such dispositions
and systems that the excitement of any one to such a degree that the
corresponding idea rises to consciousness prevents or inhibits the
excitement of others, i.e. all of them are in relations of reciprocal
inhibition with one another (see MUSCLE AND NERVE). The excitement of
dispositions associated together to form a system tends towards some end
which, either immediately or remotely, is an action, a bodily movement,
in many cases a movement of the organs of speech only. Now we know from
many exact experiments that the neural dispositions act and react upon
one another to some extent, even when they are excited only in so feeble
a degree that the corresponding ideas do not rise to consciousness. In
the normal state of the brain, then, when any idea is present to
consciousness, the corresponding neural disposition is in a state of
dominant excitement, but the intensity of that excitement is moderated,
depressed or partially inhibited by the sub-excitement of many rival or
competing dispositions of other systems with which it is connected.
Suppose now that all the nervous connexions between the multitudinous
dispositions of the cerebrum are by some means rendered less effective,
that the association-paths are partially blocked or functionally
depressed; the result will be that, while the most intimate connexions,
those between dispositions of any one system remain functional or
permeable, the weaker less intimate connexions, those between
dispositions belonging to different systems will be practically
abolished for the time being; each system of dispositions will then
function more or less as an isolated system, and its activity will no
longer be subject to the depressing or inhibiting influence of other
systems; therefore each system, on being excited in any way, will tend
to its end with more than normal force, being freed from all
interferences; that is to say, each idea or system of ideas will tend to
work itself out and to realize itself in action immediately, without
suffering the opposition of antagonistic ideas which, in the normal
state of the brain, might altogether prevent its realization in action.

The theory of mental dissociation assumes that the abnormal state of the
brain that obtains during hypnosis is of this kind, a temporary
functional depression of all, or of many of the associations or nervous
links between the neural dispositions; that is, it regards hypnosis as a
state of _relative dissociation_. The lighter the stage of hypnosis the
slighter is the degree of dissociation, the deeper the stage the more
nearly complete is the dissociation.

It is not essential that the theory should explain in what change this
stage of dissociation consists, but a view compatible with all that we
know of the functions of the central nervous system may be suggested.
The connexions between neural dispositions involve synapses or
cell-junctions, and these seem to be the places of variable resistance
which demarcate the dispositions and systems; and there is good reason
to think that their resistances vary with the state of the neurones
which they connect, being lowered when these are excited and raised when
their excitement ebbs. Now, in the waking state, the varied stimuli,
which constantly rain upon all the sense-organs, maintain the whole
cerebrum in a state of sub-excitement, keep all the cerebral neurones
partially charged with free nervous energy. When the subject lies down
to sleep or submits himself to the hypnotizer he arrests as far as
possible the flow of his thoughts, and the sensory stimuli are
diminished in number and intensity. Under these conditions the general
cerebral activity tends to subside, the free energy with which the
cerebral neurones are charged ebbs away, and the synaptic resistances
rise proportionally; then the effect of sensory impressions tends to be
confined to the lower nervous level, and the brain tends to come to
rest. If this takes place the condition of normal sleep is realized. But
in inducing hypnosis the operator, by means of his words and
manipulations, keeps one system of ideas and the corresponding neural
system in activity, namely, the ideas connected with himself; thus he
keeps open one channel of entry to the brain and mind, and through this
one open channel he can introduce whatever ideas he pleases; and the
ideas so introduced then operate with abnormally great effect because
they work in a free field, unchecked by rival ideas and tendencies.

This theory of relative dissociation has two great merits: in the first
place it goes far towards enabling us to understand in some degree most
of the phenomena of hypnosis; secondly, we have good evidence that
dissociation really occurs in deep hypnosis and in some allied states.
Any one may readily work out for himself the application of the theory
to the explanation of the power of the operator's suggestions to control
movement, to induce anaesthesia, hallucinations and delusions, and to
exert on the organic processes an influence greater than can be exerted
by mental processes in the normal state of the brain. But the positive
evidence of the occurrence of dissociation is a matter of great
psychological interest and its nature must be briefly indicated. The
phenomena of automatic speech and writing afford the best evidence of
cerebral dissociation. Many persons can, while in an apparently normal
or but very slightly abnormal condition, produce automatic writing, i.e.
intelligibly written sentences, in some cases long connected passages,
of whose import they have no knowledge, their self-conscious
intelligence being continuously directed to some other task. The
carrying out of post-hypnotic suggestions affords in many cases similar
evidence. Thus a subject may be told that after waking he will perform
some action when a given signal, such as a cough, is repeated for the
fifth time. In the post-hypnotic state he remains unaware of his
instructions, is not conscious of noting the signals, and yet carries
out the suggestion at the fifth signal, thereby proving that the signals
have been in some sense noted and counted. Many interesting varieties of
this experiment have been made, some of much greater complexity; but all
agreeing in indicating that the suggested action is prepared for and
determined by cerebral processes that do not affect the consciousness of
the subject, but seem to occur as a system of processes detached from
the main stream of cerebral activity; that is to say, they imply the
operation of relatively dissociated neural systems.

Many authorities go further than this; they argue that, since actions of
the kind described are determined by processes which involve operations,
such as counting, that we are accustomed to regard as distinctly mental
in character and that normally involve conscious activity, we must
believe that in these cases also consciousness or psychical activity is
involved, but that it remains as a separate system or stream of
consciousness concurrent with the normal or personal consciousness.

In recent years the study of various abnormal mental states, especially
the investigations by French physicians of severe forms of hysteria,
have brought to light many facts which seem to justify this assumption
of a secondary stream of consciousness, a co- or sub-consciousness
coexistent with the personal consciousness; although, from the nature of
the case, an absolute proof of such co-consciousness can hardly be
obtained. The co-consciousness seems to vary in degree of complexity and
coherence from a mere succession of fragmentary sensations to an
organized stream of mental activity, which may rival in all respects the
primary consciousness; and in cases of the latter type it is usual to
speak of the presence of a secondary personality. The co-consciousness
seems in the simpler cases, e.g. in cases of hysterical or hypnotic
anaesthesia, to consist of elements split off from the normal primary
consciousness, which remains correspondingly poorer; and the assumption
is usually made that such a stream of co-consciousness is the psychical
correlate of groups and systems of neurones dissociated from the main
mass of cerebral neurones. If, in spite of serious objections, we
entertain this conception, we find that it helps us to give some account
of various hypnotic phenomena that otherwise remain quite inexplicable;
some such conception seems to be required more particularly by the facts
of negative hallucination and the execution of post-hypnotic suggestions
involving such operations as counting and exact discrimination without
primary consciousness.

_Supernormal Hypnotic Phenomena._--The facts hitherto considered,
strange and perplexing as many of them are, do not seem to demand for
their explanation any principles of action fundamentally different from
those operative in the normal human mind. But much of the interest that
has centred in hypnotism in recent years has been due to the fact that
some of its manifestations seem to go beyond all such principles of
explanation, and to suggest the reality of modes of influence and action
that science has not hitherto recognized. Of these by far the best
attested are the post-hypnotic unconscious reckoning of time and
telepathy or "thought-transference" (for the latter see TELEPATHY). The
post-hypnotic reckoning and noting of the lapse of time seems in some
instances to have been carried out, in the absence of all extraneous
aids and with complete unconsciousness on the part of the normal
personality, with such extreme precision that the achievement cannot be
accounted for by any intensification of any faculty that we at present
recognize or understand. Thus, Dr Milne Bramwell has reported the case
of a patient who, when commanded in hypnosis to perform some simple
action after the lapse of many thousands of minutes, would carry out the
suggestion punctually to the minute, without any means of knowing the
exact time of day at which the suggestion was given or the time of day
at the moment its performance fell due; more recently a similar case,
even more striking in some respects, has been carefully observed and
described by Dr T. W. Mitchell. Other reported phenomena, such as
telaesthesia or clairvoyance, and telekinesia, are hardly sufficiently
well attested to demand serious consideration in this place.

_Medical Applications of Hypnotism._--The study and practice of
hypnotism is not yet, and probably never will be, regarded as a normal
part of the work of the general practitioner. Its successful application
demands so much time, tact, and special experience, that it will
probably remain, as it is now, and as it is perhaps desirable that it
should remain, a specialized branch of medical practice. In England it
is only in recent years that it has been possible for a medical man to
apply it in his practice without incurring professional odium and some
risk of loss of reputation. That, in certain classes of cases, it may
effect a cure or bring relief when all other modes of treatment are of
no avail is now rapidly becoming recognized; but it is less generally
recognized that it may be used with great advantage as a supplement to
other modes of treatment in relieving symptoms that are accentuated by
nervous irritability or mental disturbance. A third wide field of
usefulness lies before it in the cure of undesirable habits of many
kinds. Under the first heading may be put insomnia, neuralgia,
neurasthenia, hysteria in almost all its many forms; under the second,
inflammations such as that of chronic rheumatism, contractures and
paralyses resulting from gross lesion of the brain, epilepsy, dyspepsia,
menstrual irregularities, sea-sickness; under the third, inebriety, the
morphia and other drug habits, nail-biting, _enuresis nocturna_,
masturbation, constipation, facial and other twitchings. In pronounced
mental diseases hypnotism seems to be almost useless; for in general
terms it may be said that it can be applied most effectively where the
brain, the instrument through which it works, is sound and vigorous. The
widespread prejudice against the use of hypnotism is no doubt largely
due to the marvellous and (to most minds) mysterious character of the
effects producible by its means; and this prejudice may be expected to
diminish as our insight into the mode of its operation deepens. The more
purely bodily results achieved by hypnotic suggestion become in some
degree intelligible if we regard it as a powerful means of diverting
nervous energy from one channel or organ to others, so as to give
physiological rest to an overworked organ or tissue, or so as to lead to
the atrophy of one nervous habit and the replacement of it by a more
desirable habit. And in the cure of those disorders which involve a
large mental element the essential part played by it is to drive out
some habitually recurrent idea and to replace it by some idea,
expectation or conviction of healthy tendency.

It seems clear that the various systems of "mind-curing" in the hands of
persons lacking all medical training, which are now so frequently the
cause of distressing and needless disasters, owe their rapid spread to
the fact that the medical profession has hitherto neglected to attach
sufficient importance to the mental factor in the causation and cure of
disease; and it seems clear, too, that a more general and more
intelligent appreciation of the possibilities of hypnotic treatment
would constitute the best means at the disposal of the profession for
combating this growing evil.

_The Dangers of Hypnotism._--Much has been written on this head of late
years, and some of the enthusiastic advocates of hypnotic treatment have
done harm to their cause by ignoring or denying in a too thoroughgoing
manner the possibility of undesirable results of the spread of the
knowledge and practice of hypnotism. Like all powerful agencies,
chloroform or morphia, dynamite or strong electric currents, hypnotic
suggestion can only be safely used by those who have special knowledge
and experience, and, like them, it is liable to abuse. There is little
doubt that, if a subject is repeatedly hypnotized and made to entertain
all kinds of absurd delusions and to carry out very frequently
post-hypnotic suggestions, he may be liable to some ill-defined harm;
also, that an unprincipled hypnotizer might secure an undue influence
over a naturally weak subject.

But there is no ground for the belief that hypnotic treatment, applied
with good intentions and reasonable care and judgment, does or can
produce deleterious effects, such as weakening of the will or liability
to fall spontaneously into hypnosis. All physicians of large experience
in hypnotic practice are in agreement in respect to this point. But some
difference of opinion exists as to the possibility of deliberately
inducing a subject to commit improper or criminal actions during
hypnosis or by post-hypnotic suggestion. There is, however, no doubt
that subjects retain even in deep hypnosis a very considerable power of
resistance to any suggestion that is repugnant to their moral nature;
and it has been shown that, on some cases in which a subject in hypnosis
is made to perform some ostensibly criminal action, such as firing an
unloaded pistol at a bystander or putting poison into a cup for him to
drink, he is aware, however obscurely, of the unreal nature of the
situation. Nevertheless it must be admitted that a person lacking in
moral sentiments might be induced to commit actions from which in the
normal state he would abstain, if only from fear of punishment; and it
is probable that a skilful and evil-intentioned operator could in some
cases so deceive a well-disposed subject as to lead him into
wrong-doing. The proper precaution against such dangers is legislative
regulation of the practice of hypnotism such as is already enforced in
some countries.

  BIBLIOGRAPHY.--The literature of hypnotism has increased in volume at
  a rapid rate during recent years. Of recent writings the following may
  be mentioned as among the most important:--_Treatment by Hypnotism and
  Suggestion_ by C. Lloyd Tuckey, M.D. (5th ed., London, 1907);
  _Hypnotism, its History, Practice and Theory_, by J. Milne Bramwell,
  M.B. (2nd ed., London, 1906); _Hypnotism_, by Albert Moll (5th ed.,
  London, 1901). All these three books give good general accounts of
  hypnotism, the first being the most strictly medical, the last the
  most general in its treatment. See also _Hypnotism: or Suggestion in
  Psycho-Therapy_, by August Forel (translated from the 5th German ed.
  by G. H. W. Armit, London, 1906); a number of papers by Ed. Gurney,
  and by Ed. Gurney and F. W. H. Myers in _Proc. of the Soc. for
  Psychical Research_, especially "The Stages of Hypnotism," in vol.
  ii.; also some more recent papers in the same journal by other hands;
  chapter on Hypnotism in _Human Personality and its Survival of bodily
  Death_, by F. W. H. Myers (London, 1903); _The Psychology of
  Suggestion_, by Boris Sidis, Ph.D. (New York, 1898); "Zur Psychologie
  der Suggestion," by Prof. Th. Lipp, and other papers in the
  _Zeitschrift für Hypnotismus_. Of special historical interest are the
  following:--_Étude sur le zoomagnétisme_, par A. A. Liébeault (Paris,
  1883); _Hypnotisme, suggestion, psycho-thérapie_, par Prof. Bernheim
  (Paris, 1891); _Braid on Hypnotism_ (a new issue of James Braid's
  _Neurypnology_), edited by A. E. Waite (London, 1899); _Traité du
  somnambulisme_, by A. Bertrand (Paris, 1826). A full bibliography is
  appended to Dr Milne Bramwell's _Hypnotism_.     (W. McD.)



HYPOCAUST (Gr. [Greek: hypokauston: hypo], beneath, and [Greek: kauein],
to burn), the term given to the chamber formed under the floors of the
Roman baths, through which the hot air from the furnace passed,
sometimes to a single flue, as in the case of the _tepidarium_, but in
the _calidarium_ and sweating-room to a series of flues placed side by
side forming the lining of the walls. The floor of the hot-air chamber
consisted of tiles, 2 ft. square, laid on a bed of concrete; on this a
series of dwarf piers 2 ft. high were built of 8-in. square tiles placed
about 16 in. apart, which carried the floor of the hall or room; this
floor was formed of a bed of concrete covered with layers of pounded
bricks and marble cement, on which the marble pavement in slabs or
tesserae was laid. In colder countries, as for instance in Germany and
England, the living rooms were all heated in a similar way, and round
Trèves (Trier) both systems have been found in two or three Roman
villas, with the one flue for the ordinary rooms and several wall flues
for the hot baths. In England these hypocausts are found in every Roman
settlement, and the chief interest in these is centred in the
magnificent mosaic pavements with which the principal rooms were laid.
Many of the pavements found in London and elsewhere have been preserved
in the British or the Guildhall museums; and in some of the provincial
towns, such as Leicester and Lincoln, they remain _in situ_ many feet
below the present level of the town.



HYPOCHONDRIASIS (synonyms--"the spleen," "the vapours"), a medical term
(from [Greek: to hypochondrion, ta hypochondria], the soft part of the
body immediately under the [Greek: chondros] or cartilage of the
breast-bone) given by the ancients, and indeed by physicians down to the
time of William Cullen, to diseases or derangements of one or more of
the abdominal viscera. Cullen (_Clinical Lectures,_ 1777) classified it
amongst nervous diseases, and Jean Pierre Falret (1794-1870) more fully
described it as a morbid condition of the nervous system characterized
by depression of feeling and false beliefs as to an impaired state of
the health. The subjects of hypochondriasis are for the most part
members of families in which hereditary predisposition to degradation of
the nervous system is strong, or those who have suffered from morbid
influences affecting this system during the earlier years of life. It
may be dependent on depressing disease affecting the general system, but
under such circumstances it is generally so complicated with the
symptoms of hysteria as to render differentiation difficult (see
HYSTERIA). Hypochondriasis is often handed down from one generation to
another in its individual form, but it is also not unfrequently to be
met with in an individual as the sole manifestation in him of a family
tendency to insanity. In its most common form it is manifested by simple
false belief as to the state of the health, the intellect being
otherwise unaffected. We may instance the "vapourish" woman or the
"splenetic" as terms society has applied to its milder manifestations.
Such persons are constantly asserting a weak state of health although no
palpable cause can be discovered. In its more definite phases pain or
uneasy sensations are referred by the patient to some particular region,
generally the abdomen, the heart or the head. That these are subjective
is apparent from the fact that the general health is good: all the
functions of the various systems are duly performed; the patient eats
and sleeps well; and, when any circumstance temporarily overrides the
false belief, he is happy and comfortable. No appeal to the reason is of
any avail, and the hypochondriac idea so dominates his existence as to
render him unable to perform the ordinary duties of life. In its most
aggravated form hypochondriasis amounts to actual insanity, delusions
arising as to the existence of living creatures in the intestines or
brain, or to the effect that the body is materially changed; e.g. into
glass, wood, &c. The symptoms of this condition may be remittent; they
may even disappear for years, and only return on the advent of some
exciting cause. Suicide is occasionally committed in order to escape
from the constant misery. Recovery can only be looked for by placing the
patient under such morally hygienic conditions as may help to turn his
mind to other matters. (See also NEUROPATHOLOGY.)



HYPOCRISY, pretence, or false assumption of a high character, especially
in regard to religious belief or practice. The Greek [Greek:
hypokrisis], from which the word is derived through the Old French,
meant primarily the acting of a part on the stage, from [Greek:
hypokrinesthai], to give an answer, to speak dialogue, play a part on
the stage, hence to practice dissimulation.



HYPOSTASIS, in theology, a term frequently occurring in the Trinitarian
controversies of the 4th and 5th centuries. According to Irenaeus (i. 5,
4) it was introduced into theology by Gnostic writers, and in earliest
ecclesiastical usage appears, as among the Stoics, to have been
synonymous with [Greek: ousia]. Thus Dionysius of Rome (cf. Routh, _Rel.
Sacr._ iii. 373) condemns the attempt to sever the Godhead into three
separate _hypostases_ and three deities, and the Nicene Creed in the
anathemas speaks of [Greek: ex heteras hypostaseôs ê ousias].
Alongside, however, of this persistent interchange there was a desire to
distinguish between the terms, and to confine [Greek: hypostasis] to the
Divine _persons_. This tendency arose in Alexandria, and its progress
may be seen in comparing the early and later writings of Athanasius.
That writer, in view of the Arian trouble, felt that it was better to
speak of [Greek: ousia] as "the common undifferentiated substance of
Deity," and [Greek: hypostasis] as "Deity existing in a personal mode,
the substance of Deity with certain special properties" ([Greek: ousia
meta tinôn idiômatôn]). At the council of Alexandria in 362 the phrase
[Greek: treis hypostaseis] was permitted, and the work of this council
was supplemented by Basil, Gregory of Nazianzus and Gregory of Nyssa in
the formula [Greek: mia ousia, treis hypostaseis] or [Greek: mia ousia
en trisin hypostasesin].

  The results arrived at by these Cappadocian fathers were stated in a
  later age by John of Damascus (_De orth. fid._ iii. 6), quoted in R.
  L. Ottley, _The Doctrine of the Incarnation_, ii. 257.



HYPOSTYLE, in architecture, the term applied to a hall, the flat ceiling
of which is supported by columns, as in the Hall of Columns at Karnak.
In this case the columns flanking the central avenue are of greater
height than those of the side aisles, and this admits of openings in the
wall above the smaller columns, through which light is admitted over the
aisle roof, through clerestory windows.



HYPOSULPHITE OF SODA, the name originally given to the substance known
in chemistry as sodium thiosulphate, Na2S2O3; the earlier name is still
commonly used, especially by photographers, who employ this chemical as
a fixer. In systematic chemistry, sodium hyposulphite is a salt of
hyposulphurous acid, to which Schutzenberger gave the formula H2SO2, but
which Bernthsen showed to be H2S2O4. (See SULPHUR.)



HYPOTHEC (Lat. _hypotheca_, Gr. [Greek: hypothêkê]), in Roman law, the
most advanced form of the contract of pledge. A specific thing may be
given absolutely to a creditor on the understanding that it is to be
given back when the creditor's debt is paid; or the property in the
thing may be assigned to the creditor while the debtor is allowed to
remain in possession, the creditor as owner being able to take
possession if his debt is not discharged. Here we have the kind of
security known as pledge and mortgage respectively. In the _hypotheca_,
the property does not pass to the creditor, nor does he get possession,
but he acquires a preferential right to have his debt paid out of the
hypothecated property; that is, he can sell it and pay himself out of
the proceeds, or in default of a purchaser he can become the owner
himself. The name and the principle have passed into the law of
Scotland, which distinguishes between conventional hypothecs, as
_bottomry_ and _respondentia_, and tacit hypothecs established by law.
Of the latter the most important is the landlord's hypothec for rent
(corresponding to distress in the law of England), which extends over
the produce of the land and the cattle and sheep fed on it, and over
stock and horses used in husbandry. The law of agricultural hypothec
long caused much discontent in Scotland; its operation was restricted by
the Hypothec Amendment (Scotland) Act 1867, and finally by the Hypothec
Abolition (Scotland) Act 1880 it was enacted that the "landlord's right
of hypothec for the rent of land, including the rent of any buildings
thereon, exceeding two acres in extent, let for agriculture or pasture,
shall cease and determine." By the same act and by the Agricultural
Holdings (Scotland) Act 1883 other rights and remedies for rent, where
the right of hypothec had ceased, were given to the landlord.



HYPOTHESIS (from Gr. [Greek: hypotithenai], to put under; cf. Lat.
_suppositio_, from _sub-ponere_), in ordinary language, an explanation,
supposition or assumption, which is put forward in the absence of
ascertained facts or causes. Both in ordinary life and in the
acquisition of scientific knowledge hypothesis is all-important. A
detective's work consists largely in forming and testing hypothesis. If
an astronomer is confronted by some phenomenon which has no obvious
explanation he may postulate some set of conditions which from his
general knowledge of the subject would or might give rise to the
phenomenon in question; he then tests his hypothesis until he discovers
whether it does or does not conflict with the facts. An example of this
process is that of the discovery of the planet Neptune: certain
perturbations of the orbit of Uranus had been observed, and it was seen
that these could be explained on the hypothesis of the existence of a
then unknown planet, and this hypothesis was verified by actual
observation. The progress of inductive knowledge is by the formation of
successive hypotheses, and it frequently happens that the demolition of
one or even many hypotheses is the direct road to a new and accurate
hypothesis, i.e. to fresh knowledge. A hypothesis may, therefore, turn
out to be entirely wrong, yet it may be of the greatest practical use.

The recognition of the importance of hypotheses has led to various
attempts at drawing up exact rules for their formation, but logicians
are generally agreed that only very elementary principles can be laid
down. Thus a hypothesis must contain nothing which is at variance with
known facts or principles: it should not postulate conditions which
cannot be verified empirically. J. S. Mill (_Logic_ III. xiv. 4) laid
down the principle that a hypothesis is not "genuinely scientific" if it
is "destined always to remain a hypothesis": it must "be of such a
nature as to be either proved or disproved by comparison with observed
facts": in the same spirit Bacon said that in searching for causes in
nature "Deum semper excipimus." Mill's principle, though sound in the
abstract, has, except in a few cases, little practical value in
determining the admissibility of hypotheses, and in practice any rule
which tends to discourage hypothesis is in general undesirable. The most
satisfactory check on hypothesis is expert knowledge in the particular
field of research by which rigorous tests may be applied. This test is
roughly of two kinds, first by the ultimate principles or
presuppositions on which a particular branch of knowledge rests, and
second by the comparison of correlative facts. Useful light is shed on
this distinction by Lotze, who contrasts (_Logic_, § 273) _postulates_
("absolutely necessary assumptions without which the content of the
observation with which we are dealing would contradict the laws of our
thought") with _hypotheses_, which he defines as conjectures, which seek
"to fill up the postulate thus abstractly stated by specifying the
concrete causes, forces or processes, out of which the given phenomenon
really arose in this particular case, while in other cases maybe the
same postulate is to be satisfied by utterly different though equivalent
combinations of forces or active elements." Thus a hypothesis may be
ruled out by principles or postulates without any reference to the
concrete facts which belong to that division of the subject to explain
which the hypothesis is formulated. A true hypothesis, therefore, seeks
not merely to connect or colligate two separate facts, but to do this in
the light of and subject to certain fundamental principles. Various
attempts have been made to classify hypotheses and to distinguish
"hypothesis" from a "theory" or a mere "conjecture": none of these have
any great practical importance, the differences being only in degree,
not in kind.

The adjective "hypothetical" is used, in the same sense, both loosely in
contradistinction to "real" or "actual," and technically in the phrases
"hypothetical judgment" and "hypothetical syllogism." (See LOGIC and
SYLLOGISM.)

  See Naville, _La Logique de l'hypothèse_ (1880), and textbooks of
  logic, e.g. those of Jevons, Bosanquet, Joseph; Liebmann, _Der Klimax
  d. Theorien_.



HYPOTRACHELIUM (Gr. [Greek: hypotrachêlion], the lower part of the neck,
[Greek: trachêlos]), in classical architecture, the space between the
annulet of the echinus and the upper bed of the shafts, including,
according to C. R. Cockerell, the three grooves or sinkings found in
some of the older examples, as in the temple of Neptune at Paestum and
the temple of Aphaea at Aegina; there being only one groove in the
Parthenon, the Theseum and later examples. In the temple of Ceres and
the so-called Basilica at Paestum the hypotrachelium consists of a
concave sinking carved with vertical lines suggestive of leaves, the
tops of which project forward. A similar decoration is found in the
capital of the columns flanking the tomb of Agamemnon at Mycenae, but
here the hypotrachelium projects forward with a cavetto moulding, and is
carved with triple leaves like the buds of a rose. In the Roman Doric
Order the term was sometimes applied to that which is generally known as
the "necking," the space between the fillet and the annulet.



HYPSOMETER (Gr. [Greek: hypsos], height, [Greek: metron], a measure), an
instrument for measuring heights which employs the principles that the
boiling-point of a liquid is lowered by diminishing the pressure, and
that the barometric pressure varies with the height of the point of
observation. The instrument consists of a cylindrical vessel in which
the liquid, usually water, is boiled, surmounted by a jacketed column,
in the outer partitions of which the vapour circulates, while in the
central one a thermometer is placed. To deduce the height of the station
from the observed boiling-point, it is necessary to know the relation
existing between the boiling-point and pressure, and also between the
pressure and height of the atmosphere.



HYRACOIDEA, a suborder of ungulate mammals represented at the present
day only by the Syrian hyrax (_Procavia syriaca_), the "coney" of the
Bible, and its numerous African relatives, all of which may be included
in the single genus _Procavia_ (or _Hyrax_), and consequently in the
family _Procaviidae_. These creatures have no proper English name, and
are generally known as hyraxes, from the scientific term (_Hyrax_) by
which they were for many years designated--a term which has
unfortunately had to give place to the earlier _Procavia_. In size these
animals may be compared roughly to rabbits and hares; and they have
rodent-like habits, hunching up their backs after the fashion of some
foreign members of the hare-family, more especially the Liu-Kiu rabbit.
In the matter of nomenclature these animals have been singularly
unfortunate. In the title "hyrax" they have, for instance, usurped the
Greek name for the shrew-mouse; while in the Bible they have been given
the old English name for the rabbit. Perhaps rock-rabbit would be the
best name. At the Cape they are known to the Dutch as dass (badger),
which has been anglicized into "dassie."

[Illustration: FIG. 1.--The Cape Hyrax (_Procavia capensis_).]

  As regards the recent forms, the dentition in the fully adult animal
  consists only of incisors and cheek-teeth, the formula being _i._ ½,
  _c._ 0/0, _p._ 4/4 _m._ 3/3. There is, however, a minute upper canine
  developed at first, which is early shed; and in extinct forms this
  tooth was functional and molar-like. The upper incisors have
  persistent pulps, and are curved longitudinally, forming a semicircle
  as in rodents; they are, however, not flattened from before backwards
  as in that order, but prismatic, with an antero-external, an
  antero-internal and a posterior surface, the first two only being
  covered with enamel; their tips are consequently not chisel-shaped,
  but sharp-pointed. They are preceded by functional, rooted milk-teeth.
  The lower incisors have long tapering roots, but not of persistent
  growth; and are straight, directed somewhat forwards, with awl-shaped,
  tri-lobed crowns. Behind the incisors is a considerable gap, followed
  by the cheek-teeth, which are all contiguous, and formed almost
  exactly on the pattern of some of the perissodactyle ungulates. The
  milk-dentition includes three pairs of incisors and one of canines in
  each jaw. The hyoid arch is unlike that of any known mammal. The
  dorsal and lumbar vertebrae are very numerous, 28 to 30, of which 21
  or 22 bear ribs. The tail is extremely short. There are no clavicles.
  In the fore foot, the three middle toes are subequally developed, the
  fifth is present, but smaller, and the first is rudimentary, although,
  in one species at least, all its normal bones are present. The
  terminal phalanges of the four outer digits are small, somewhat
  conical and flattened in form. The carpus has a distinct os centrale.
  There is a slight ridge on the femur in the place of a third
  trochanter. The fibula is complete, thickest at its upper end, where
  it generally unites with the tibia. The articulation between the tibia
  and astragalus is more complex than in other mammals, the end of the
  malleolus entering into it. The hind-foot is very like that of a
  rhinoceros, having three well-developed toes. There is no trace of a
  first toe, and the fifth meta-tarsal is represented by a small nodule.
  The terminal phalange of the inner (or second) digit is deeply cleft,
  and has a peculiar long curved claw, the others having short broad
  nails. The stomach is formed upon much the same principle as that of
  the horse or rhinoceros, but is more elongated transversely and
  divided by a constriction into two cavities--a large left _cul de
  sac_, lined by a very dense white epithelium, and a right pyloric
  cavity, with a thick, soft, vascular lining. The intestinal canal is
  long, and has, in addition to the ordinary short, but capacious and
  sacculated caecum at the commencement of the colon, lower down, a pair
  of large, conical, pointed caeca. The liver is much subdivided, and
  there is no gall-bladder. The brain resembles that of typical
  ungulates far more than that of rodents. The testes are permanently
  abdominal. The ureters open into the fundus of the bladder as in some
  Rodents. The female has six teats, of which four are inguinal and two
  axillary, and the placenta is zonary and deciduous. There is a gland
  on the back.

  [Illustration: FIG. 2.--Skull and Dentition of Tree-Hyrax (_Procavia
  dorsalis_).]

  The more typical members of the genus are terrestrial in their habits,
  and their cheek-teeth have nearly the same pattern as in rhinoceroses;
  while the interval between the upper incisors is less than the width
  of the teeth; and the lower incisors are only slightly notched at the
  cutting edge. Vertebrae: C. 7, D. 22, L. 8, S. 6, C. 6. Of this form
  the earliest known species, _P. capensis_, is the type; but there are
  many other species, as _P. syriaca_, and _P. brucei_ from Syria and
  eastern Africa. They inhabit mountainous and rocky regions, and live
  on the ground. In a second section the molar teeth have the same
  pattern as in _Palaeotherium_ (except that the third lower molar has
  but two lobes); the interval between the upper incisors exceeds the
  width of the teeth; and the lower incisors have distinctly tri-lobed
  crowns. Vertebrae: C. 7, D. 21, L. 7, S. 5, C. 10. The members of this
  section frequent the trunks and large branches of trees, sleeping in
  holes. There are several species from Western and South Africa, as _P.
  arboreus_ and _P. dorsalis_. The members of both groups appear to have
  a power like that possessed by geckos of clinging to vertical surfaces
  of rocks and trees by the soles of their feet.

  _Extinct Hyracoids._--For many years extinct representatives of the
  Hyracoidea were unknown, partly owing to the fact that certain fossils
  were not recognized as really belonging to that group. The longest
  known of these was originally named _Leptodon graecus_, but, on
  account of the preoccupation of the generic title, the designation has
  been changed to _Pliohyrax graecus_. This animal, whose remains occur
  in the Lower Pliocene of both Attica and Samos, was about the size of
  a donkey, and possessed three pairs of upper incisor teeth, of which
  the innermost were large and trihedral, recalling those of the
  existing genus. On the other hand, the two outer pairs of incisors
  were in contact with one another and with the canines, so as to form
  on each side a series continuous with the cheek-teeth.

  The next representatives of the group occur in the Upper Eocene beds
  of the Fayum district of Egypt, where the genera _Saghatherium_ and
  _Megalohyrax_ occur. These are regarded as representing a distinct
  family, the _Saghatheriidae_, characterized by the possession of the
  full series of twenty-two teeth in the upper jaw, among which the
  first pair of incisors was modified to form trihedral rootless tusks,
  while the two remaining pairs were separated from one another and from
  the teeth in front by gaps. The canine was like a premolar, and in
  contact with the first tooth of that series; and the cheek-teeth were
  short-crowned, with the premolar simpler than the molars, and a third
  lobe to the last lower tooth of the latter series. The members of
  this genus were small or medium-sized ungulates with single-rooted
  incisors. On the other hand, the representatives of the contemporary
  genus _Megalohyrax_ were approximately as large as _Pliohyrax_, and in
  some instances had double roots to the second and third incisors.

  It is now possible to define the suborder Hyracoidea as including
  ungulates with a centrale in the carpus, plantigrade feet, in which
  the first and fifth toes are reduced in greater or less degree, and
  clavicles and a foramen in the lower end of the humerus are absent.
  The femur has a small third trochanter, the radius and ulna and tibia
  and fibula are respectively separate, at least in the young, and the
  fibula articulates with the astragalus. The earlier forms had the full
  series of 44 teeth, with the premolars simpler than the molars; but in
  the later types the canines and some of the incisors disappear, and at
  least the hinder premolars become molar-like. In all cases the first
  upper incisors are large and rootless.

  That the group originated in Africa there can be no reasonable doubt;
  and it is remarkable that so early as the Upper Eocene the types in
  existence differed comparatively little in structure from the modern
  forms. In fact the hyraxes were then almost as distinct from other
  mammals as they are at the present day.

  See also C. W. Andrews, _Descriptive Catalogue of the Tertiary
  Vertebrata of the Fayum_, British Museum (1906).     (R. L.*)



HYRCANIA. (1) An ancient district of Asia, south of the Caspian Sea, and
bounded on the E. by the river Oxus, called _Virkana_, or "Wolf's Land,"
in Old Persian. It was a wide and indefinite tract. Its chief city is
called Tape by Strabo, Zadracarta by Arrian (probably the modern
Astarabad). The latter is evidently the same as Carta, mentioned by
Strabo as an important city. Little is known of the history of the
country. Xenophon says it was subdued by the Assyrians; Curtius that
6000 Hyrcanians were in the army of Darius III. (2) Two towns named
Hyrcania are mentioned, one in Hyrcania, the other in Lydia. The latter
is said to have derived its name from a colony of Hyrcanians,
transported thither by the Persians.



HYRCANUS ([Greek: Hykanos]), a Greek surname, of unknown origin, borne
by several Jews of the Maccabaean period.

JOHN HYRCANUS I., high priest of the Jews from 135 to 105 B.C., was the
youngest son of Simon Maccabaeus. In 137 B.C. he, along with his brother
Judas, commanded the force which repelled the invasion of Judaea led by
Cendebeus, the general of Antiochus VII. _Sidetes_. On the assassination
of his father and two elder brothers by Ptolemy, governor of Jericho,
his brother-in-law, in February 135, he succeeded to the high priesthood
and the supreme authority in Judaea. While still engaged in the struggle
with Ptolemy, he was attacked by Antiochus with a large army (134), and
compelled to shut himself up in Jerusalem; after a severe siege peace
was at last secured only on condition of a Jewish disarmament, and the
payment of an indemnity and an annual tribute, for which hostages were
taken. In 129 he accompanied Antiochus as a vassal prince on his
ill-fated Parthian expedition; returning, however, to Judaea before
winter, he escaped the final disaster. By the judicious mission of an
embassy to Rome he now obtained confirmation of the alliance which his
father had previously made with the growing western power; at the same
time he availed himself of the weakened state of the Syrian monarchy
under Demetrius II. to overrun Samaria, and also to invade Idumaea,
which he completely subdued, compelling its inhabitants to receive
circumcision and accept the Jewish faith. After a long period of rest he
directed his arms against the town of Samaria, which, in spite of the
intervention of Antiochus, his sons Antigonus and Aristobulus ultimately
took, and by his orders razed to the ground (c. 100 B.C.). He died in
105, and was succeeded by Aristobulus, the eldest of his five sons. The
external policy of Hyrcanus was marked by considerable energy and tact,
and, aided as it was by favouring circumstances, was so successful as to
leave the Jewish nation in a position of independence and of influence
such as it had not known since the days of Solomon. During its later
years his reign was much disturbed, however, by the contentions for
ascendancy which arose between the Pharisees and Sadducees, the two
rival sects or parties which then for the first time (under those names
at least) came into prominence. Josephus has related the curious
circumstances under which he ultimately transferred his personal support
from the former to the latter.

JOHN HYRCANUS II., high priest from 78 to 40 B.C., was the eldest son of
Alexander Jannaeus by his wife Alexandra, and was thus a grandson of the
preceding. When his father died in 78, he was by his mother forthwith
appointed high priest, and on her death in 69 he claimed the succession
to the supreme civil authority also; but, after a brief and troubled
reign of three months, he was compelled to abdicate both kingly and
priestly dignities in favour of his more energetic and ambitious younger
brother Aristobulus II. In 63 it suited the policy of Pompey that he
should be restored to the high priesthood, with some semblance of
supreme command, but of much of this semblance even he was soon again
deprived by the arrangement of the pro-consul Gabinius, according to
which Palestine was in 57 B.C. divided into five separate circles
([Greek: synodoi, synedria]). For services rendered to Caesar after the
battle of Pharsalia, he was again rewarded with the sovereignty ([Greek:
prostasia tou ethnous], Jos. _Ant._ xx. 10) in 47 B.C., Antipater of
Idumaea, however, being at the same time made procurator of Judaea. In
41 B.C. he was practically superseded by Antony's appointment of Herod
and Phasael to be tetrarchs of Judaea; and in the following year he was
taken prisoner by the Parthians, deprived of his ears that he might be
permanently disqualified for priestly office, and carried to Babylon. He
was permitted in 33 B.C. to return to Jerusalem, where on a charge of
treasonable correspondence with Malchus, king of Arabia, he was put to
death in 30 B.C.

  See Josephus (_Ant._ xiii. 8-10; xiv. 5-13; _Bell. Jud._ i. 2; i.
  8-13). Also MACCABEES, _History_.     (J. H. A. H.)



HYSSOP (_Hyssopus officinalis_), a garden herb belonging to the natural
order _Labiatae_, formerly cultivated for use in domestic medicine. It
is a small perennial plant about 2 ft. high, with slender, quadrangular,
woody stems; narrowly elliptical, pointed, entire, dotted leaves, about
1 in. long and 1/3 in. wide, growing in pairs on the stem; and long
terminal, erect, half-whorled, leafy spikes of small violet-blue
flowers, which are in blossom from June to September. Varieties of the
plant occur in gardens with red and white flowers, also one having
variegated leaves. The leaves have a warm, aromatic, bitter taste, and
are believed to owe their properties to a volatile oil which is present
in the proportion of ¼ to ½%. Hyssop is a native of the south of Europe,
its range extending eastward to central Asia. A strong tea made of the
leaves, and sweetened with honey, was formerly used in pulmonary and
catarrhal affections, and externally as an application to bruises and
indolent swellings.

The hedge hyssop (_Gratiola officinalis_) belongs to the natural order
_Scrophulariaceae_, and is a native of marshy lands in the south of
Europe, whence it was introduced into Britain more than 300 years ago.
Like _Hyssopus officinalis_, it has smooth opposite entire leaves, but
the stems are cylindrical, the leaves twice the size, and the flowers
solitary in the axils of the leaves and having a yellowish-red veined
tube and bluish-white limb, while the capsules are oval and many-seeded.
The herb has a bitter, nauseous taste, but is almost odourless. In small
quantities it acts as a purgative, diuretic and emetic when taken
internally. It was formerly official in the Edinburgh Pharmacopoeia,
being esteemed as a remedy for dropsy. It is said to have formed the
basis of a celebrated nostrum for gout, called _Eau médicinale_, and in
former times was called _Gratia Dei_. When growing in abundance, as it
does in some damp pastures in Switzerland, it becomes dangerous to
cattle. G. _peruviana_ is known to possess similar properties.

  The hyssop (_'ezob_) of Scripture (Ex. xii. 22; Lev. xiv. 4, 6; Numb.
  xix. 6, 18; 1 Kings v. 13 (iv. 33); Ps. li. 9 (7); John xix. 29), a
  wall-growing plant adapted for sprinkling purposes, has long been the
  subject of learned disputation, the only point on which all have
  agreed being that it is not to be identified with the _Hyssopus
  officinalis_, which is not a native of Palestine. No fewer than
  eighteen plants have been supposed by various authors to answer the
  conditions, and Celsius has devoted more than forty pages to the
  discussion of their several claims. By Tristram (_Oxford Bible for
  Teachers_, 1880) and others the caper plant (_Capparis spinosa_) is
  supposed to be meant; but, apart from other difficulties, this
  identification is open to the objection that the caper seems to be, at
  least in one passage (Eccl. xii. 5), otherwise designated
  (_'abiy-yônah_). Thenius (on 1 Kings v. 13) suggests _Orthotrichum
  saxatile_. The most probable opinion would seem to be that found in
  Maimonides and many later writers, according to which the Hebrew
  _'ezob_ is to be identified with the Arabic _sa'atar_, now understood
  to be _Satureja Thymus_, a plant of very frequent occurrence in Syria
  and Palestine, with which _Thymus Serpyllum_, or wild thyme, and
  _Satureja Thymbra_ are closely allied. Its smell, taste and medicinal
  properties are similar to those of _H. officinalis_. In Morocco the
  _sa'atar_ of the Arabs is _Origanum compactum_; and it appears
  probable that several plants of the genera _Thymus_, _Origanum_ and
  others nearly allied in form and habit, and found in similar
  localities, were used under the name of hyssop.



HYSTASPES (the Greek form of the Persian _Vishtaspa_). (1) A
semi-legendary king (_kava_), praised by Zoroaster as his protector and
a true believer, son of Aurvataspa (Lohrasp). The later tradition and
the Shahname of Firdousi makes him (in the modern form Kai Gushtasp)
king of Iran. As Zoroaster probably preached his religion in eastern
Iran, Vishtaspa must have been a dynast in Bactria or Sogdiana. The
Zoroastrian religion was already dominant in Media in the time of the
Assyrian king Sargon (c. 715 B.C.), and had been propagated here
probably in much earlier times (cf. PERSIA); the time of Zoroaster and
Vishtaspa may therefore be put at c. 1000 B.C. (2) A Persian, father of
Darius I., under whose reign he was governor of Parthia, as Darius
himself mentions in the Behistun inscription (2. 65). By Ammianus
Marcellinus, xxiii. 6. 32, and by many modern authors he has been
identified with the protector of Zoroaster, which is equally impossible
for chronological and historical reasons, and from the evidence of the
development of Zoroastrianism itself (see PERSIA: _Ancient History_).
     (Ed. M.)



HYSTERESIS (Gr. [Greek: hysterêsis], from [Greek: hysterein], to lag
behind), a term added to the vocabulary of physical science by J. A.
Ewing, who defines it as follows: When there are two qualities M and N
such that cyclic variations of N cause cyclic variations of M, then if
the changes of M lag behind those of N, we may say that there is
hysteresis in the relation of M to N (_Phil. Trans._, 1885, 176, p.
524). The phenomenon is best known in connexion with magnetism. If an
iron bar is subjected to a magnetic force which is first gradually
increased to a maximum and then gradually diminished, the resulting
magnetization of the bar for any given value of the magnetic force will
be greater when the force is decreasing than when it is increasing; the
iron always tends to retain the magnetic condition which it has
previously acquired, and changes of its magnetization consequently lag
behind changes of the magnetic force. Thus there is hysteresis in the
relation of magnetization to magnetic force. In consequence of
hysteresis the process of magnetizing a piece of iron to a certain
intensity and then restoring it to its original condition, or of
effecting a double reversal of its magnetization, involves the
expenditure of energy, which is dissipated as heat in the iron.
Electrical generators and transformers often contain pieces of iron the
magnetization of which is reversed many times in a second, and in order
to economize power and to avoid undue heating it is essential that
hysteresis should in such cases be as small as possible. Iron and mild
steels showing remarkably little hysteresis are now specially
manufactured for use in the construction of electrical machinery. (See
MAGNETISM.)



HYSTERIA, a term applied to an affection which may manifest itself by a
variety of symptoms, and which depends upon a disordered condition of
the highest nervous centres. It is characterized by psychical
peculiarities, while in addition there is often derangement of the
functions subserved by the lower cerebral and spinal centres.
Histological examination of the nervous system has failed to disclose
associated structural alterations.

By the ancients and by modern physicians down to the time of Sydenham
the symptoms of hysteria were supposed to be directly due to
disturbances of the uterus (Gr. [Greek: hystera], whence the name). This
view is now universally recognized to be erroneous. The term
"functional" is often used by English neurologists as synonymous with
hysterical, a nomenclature which is tentatively advantageous since it is
at least non-committal. P. J. Möbius has defined hysteria as "a state in
which ideas control the body and produce morbid changes in its
functions." P. Janet, who has done much to popularize the psychical
origin of the affection, holds that there is "a limitation of the field
of consciousness" comparable to the contraction of the visual fields met
with in the disease. The hysterical subject, according to this view, is
incapable of taking into the field of consciousness all the impressions
of which the normal individual is conscious. Strong momentary
impressions are no longer controlled so efficiently because of the
defective simultaneous impressions of previous memories. Hence the
readiness with which the impulse of the moment is obeyed, the loss of
emotional control and the increased susceptibility to external
suggestion, which are so characteristic. A secondary subconscious mental
state is engendered by the relegation of less prominent impressions to a
lower sphere. The dual personality which is typically exemplified in
somnambulism and in the hypnotic state is thus induced. The explanation
of hysterical symptoms which are independent of the will, and of the
existence of which the individual may be unaware, is to be found in a
relative preponderance of this secondary subconscious state as compared
with the primary conscious personality. An elaboration of this theory
affords an explanation of hysterical symptoms dependent upon a "fixed
idea." The following definition of hysteria has recently been advanced
by J. F. F. Babinski: "Hysteria is a psychical condition manifesting
itself principally by signs that may be termed primary, and in an
accessory sense others that we may call secondary. The characteristic of
the primary signs is that they may be exactly reproduced in certain
subjects by suggestion and dispelled by persuasion. The characteristic
of the secondary signs is that they are closely related to the primary
phenomena."

The causes of hysteria may be divided into (a) the predisposing, such as
hereditary predisposition to nervous disease, sex, age and national
idiosyncrasy; and (b) the immediate, such as mental and physical
exhaustion, fright and other emotional influences, pregnancy, the
puerperal condition, diseases of the uterus and its appendages, and the
depressing influence of injury or general disease. Perhaps, taken over
all, hereditary predisposition to nerve-instability may be asserted as
the most prolific cause. There is frequently direct inheritance, and
cases of epilepsy and insanity or other form of nervous disease are
rarely wanting when the family history is carefully enquired into. As
regards age, the condition is apt to appear at the evolution periods of
life--puberty, pregnancy and the climacteric--without any further
assignable cause except that first spoken of. It is rare in young
children, but very frequent in girls between the ages of fifteen and
twenty-five, while it sometimes manifests itself in women at the
menopause. It is much more common in the female than in the male--in the
proportion of 20 to 1. Certain races are more liable to the disease than
others; thus the Latin races are much more prone to hysteria than are
those who come of a Teutonic stock, and in more aggravated and complex
forms. In England it has been asserted that an undue proportion of cases
occur among Jews. Occupation, or be it rather said want of occupation,
is a prolific cause. This is noticeable more especially in the higher
classes of society.

An hysterical attack may occur as an immediate sequel to an epileptic
fit. If the patient suffers only from _petit mal_ (see EPILEPSY),
unaccompanied by true epileptic fits, the significance of the hysterical
seizure, which is really a post-epileptic phenomenon, may remain
unrecognized.

It is convenient to group the very varied symptoms of hysteria into
paroxysmal and chronic. The popular term "hysterics" is applied to an
explosion of emotionalism, generally the result of mental excitement, on
which convulsive fits may supervene. The characters of these vary, and
may closely resemble epilepsy. The hysterical fit is generally preceded
by an aura or warning. This sometimes takes the form of a sensation as
of a lump in the throat (_globus hystericus_). The patient may fall, but
very rarely is injured in so doing. The eyes are often tightly closed,
the body and limbs become rigid, and the back may become so arched that
the patient rests on her heels and head (_opisthotonos_). This stage is
usually followed by violent struggling movements. There is no loss of
consciousness. The attack may last for half-an-hour or even longer.
Hysterical fits in their fully-developed form are rarely seen in
England, though common in France. In the chronic condition we find an
extraordinary complexity of symptoms, both physical and mental. The
physical symptoms are extremely diverse. There may be a paralysis of one
or more limbs associated with rigidity, which may persist for weeks,
months or years. In some cases, the patient is unable to walk; in others
there are peculiarities of the gait quite unlike anything met with in
organic disease. Perversions of sensation are usually present; a common
instance is the sensation of a nail being driven through the vertex of
the head (_clavus hystericus_). The region of the spine is a very
frequent seat of hysterical pain. Loss of sensation (_anaesthesia_), of
which the patient may be unaware, is of common occurrence. Very often
this sensory loss is limited exactly to one-half of the body, including
the leg, arm and face on that side (_hemianaesthesia_). Sensation to
touch, pain, heat and cold, and electrical stimuli may have completely
disappeared in the anaesthetic region. In other cases, the anaesthesia
is relative or it may be partial, certain forms of sensation remaining
intact. Anaesthesia is almost always accompanied by an inability to
recognize the exact position of the affected limb when the eyes are
closed. When hemianaesthesia is present, sight, hearing, taste and smell
are usually impaired on that side of the body. Often there is loss of
voice (hysterical aphonia). It is to such cases of hysterical paralysis
and sensory disturbance that the wonderful cures effected by quacks and
charlatans may be referred. The mental symptoms have not the same
tendency to pass away suddenly. They may be spoken of as
inter-paroxysmal and paroxysmal. The chief characteristics of the former
are extreme emotionalism combined with obstructiveness, a desire to be
an object of interest and a constant craving for sympathy which is often
procured at an immense sacrifice of personal comfort. Obstructiveness is
the invariable symptom. Hysteria may pass into absolute insanity.

The treatment of hysteria demands great tact and firmness on the part of
the physician. The affection is a definite entity and has to be clearly
distinguished from malingering, with which it is so often erroneously
regarded as synonymous. Drugs are of little value. The moral treatment
is all-important. In severe cases, removal from home surroundings and
isolation, either in a hospital ward or nursing home, are essential, in
order that full benefit may be derived from psychotherapeutic measures.

  BIBLIOGRAPHY.--Charcot, _Leçons sur les maladies du système nerveuse_
  (1877); S. Weir Mitchell, _Lectures on Diseases of the Nervous System
  especially in Women_ (1885); Buzzard, _Simulation of Hysteria by
  Organic Nervous Disease_ (1891); Pitres, _Leçons cliniques sur
  l'hystérie et l'hypnotisme_ (1891); Richer, _Études cliniques sur la
  grande hystérie_ (1891); Gilles de la Tourette, _Traité clinique et
  thérapeutique de l'hystérie_ (1891); Bastian, _Hysterical or
  Functional Paralysis_ (1893); Ormerod, Art. "Hysteria," in Clifford
  Allbutt's _System of Medicine_ (1899); Camus and Pagnez, _Isolement et
  Psychotherapie_ (1904).     (J. B. T.; E. Bra.)



HYSTERON-PROTERON (Gr. [Greek: hysteron], latter, and [Greek: proteron],
former), a figure of speech, in which the order of words or phrases is
inverted, and that which should logically or naturally come last is put
first, to secure emphasis for the principal idea; the classical example
is Virgil's "_moriamur et in media arma ruamus,_" "let us die and charge
into the thick of the fight" (Aen. ii. 358). The term is also applied to
any inversion in order of events, arguments, &c.



HYTHE, a market town and watering-place, one of the Cinque Ports, and a
municipal and parliamentary borough of Kent, England, 67 m. S.E. by E.
of London on a branch of the South Eastern & Chatham railway. Pop.
(1901) 5557. It is beautifully situated at the foot of a steep hill near
the eastern extremity of Romney Marsh, about half a mile from the sea,
and consists principally of one long street running parallel with the
shore, with which it is connected by a straight avenue of wych elms. On
account of its fine situation and picturesque and interesting
neighbourhood, it is a favourite watering-place. A sea-wall and parade
extend eastward to Sandgate, a distance of 3 m. There is communication
with Sandgate by means of a tramway along the front. On the slope of the
hill above the town stands the fine church of St Leonard, partly Late
Norman, with a very beautiful Early English chancel. The tower was
rebuilt about 1750. In a vault under the chancel there is a collection
of human skulls and bones supposed to be the remains of men killed in a
battle near Hythe in 456. Lionel Lukin (1742-1834), inventor of the
life-boat, is buried in the churchyard. Hythe possesses a guildhall
founded in 1794 and two hospitals, that of St Bartholomew founded by
Haimo, bishop of Rochester, in 1336, and that of St John (rebuilt in
1802), of still greater antiquity but unknown date, founded originally
for the reception of lepers. A government school of musketry, in which
instructors for the army are trained, was established in 1854, and has
been extended since, and the Shorncliffe military camp is within 2½ m.
of the town.

Lympne, which is now 3 m. inland, is thought to have been the original
harbour which gave Hythe a place among the Cinque Ports. The course of
the ancient estuary may be distinctly traced from here along the road to
Hythe, the sea-sand lying on the surface and colouring the soil. Here
are remains of a Roman fortress, and excavations have brought to light
many remains of the Roman _Portus Lemanis_. Large portions of the
fortress walls are standing. At the south-west corner is one of the
circular towers which occurred along the line of wall. The site is now
occupied by the fine old castellated mansion of Studfall castle,
formerly a residence of the archdeacons of Canterbury. The name denotes
a fallen place, and is not infrequently thus applied to ancient remains.
The church at Lympne is Early English, with a Norman tower built by
Archbishop Lanfranc, and Roman material may be traced in the walls. A
short distance east is Shipway or Shepway Cross, where some of the great
assemblies relating to the Cinque Ports were held. A mile north from
Hythe is Saltwood Castle, of very ancient origin, but rebuilt in the
time of Richard II. The castle was granted to the see of Canterbury in
1026, but escheated to the crown in the time of Henry II., when the
murder of Thomas à Beckett is said to have been concerted here, and
having been restored to the archbishops by King John remained a
residence of theirs until the time of Henry VIII. It was restored as a
residence in 1882. About 2 m. N.W. of Saltwood are remains of the
fortified 14th-century manor-house of Westenhanger. It is quadrangular
and surrounded by a moat, and of the nine towers (alternately square and
round) by which the walls were defended, three remain.

The parliamentary borough of Hythe, which includes Folkestone, Sandgate
and a number of neighbouring villages, returns one member. The town is
governed by a mayor, 4 aldermen and 12 councillors. Area 2617 acres.

Hythe (Heda, Heya, Hethe, Hithe, _i.e._ landing-place) was known as a
port in Saxon times, and was granted by Halfden, a Saxon thegn, to
Christ Church, Canterbury. In the Domesday Survey the borough is entered
among the archbishop's lands as appurtenant to his manor of Saltwood,
and the bailiff of the town was appointed by the archbishop. Hythe was
evidently a Cinque Port before the Conquest, as King John in 1205
confirmed the liberties, viz. freedom from toll, the right to be
impleaded only at the Shepway court, &c., which the townsmen had under
Edward the Confessor. The liberties of the Cinque Ports were confirmed
in Magna Carta and later by Edward I. in a general charter, which was
confirmed, often with additions, by subsequent kings down to James II.
John's charter to Hythe was confirmed by Henry IV., Henry V. and Henry
VI. These charters were granted to the Cinque Ports in return for the
fifty-seven ships which they supplied for the royal service, of which
five were contributed by Hythe. The ports were first represented in the
parliament of 1365, to which they each sent four members.

Hythe was governed by twelve jurats until 1574, when it was incorporated
by Elizabeth under the title of the mayor, jurats and commonalty of
Hythe; a fair for the sale of fish, &c., was also granted, to be held on
the feast of St Peter and St Paul. As the sea gradually retreated from
Hythe and the harbour became choked up with sand, the town suffered the
fate of other places near it, and lost its old importance.



I   the ninth letter of the English and Latin alphabet, the tenth in the
Greek and Phoenician, because in these the symbol Teth (the Greek
[theta]) preceded it. Teth was not included in the Latin alphabet
because that language had no sound corresponding to the Greek [theta],
but the symbol was metamorphosed and utilized as the numeral C = 100,
which took this form through the influence of the initial letter of the
Latin _centum_. The name of I in the Phoenician alphabet was _Yod_.
Though in form it seems the simplest of letters it was originally much
more complex. In Phoenician it takes the form [symbol], which is found
also in the earliest Syriac and Palestinian inscriptions with little
modification. Ultimately in Hebrew it became reduced to a very small
symbol, whence comes its use as a term of contempt for things of no
importance as in "not one _jot_ or tittle" (Matthew v. 18). The name
passed from Phoenician to Greek, and thence to the Latin of the vulgate
as _iota_, and from the Latin the English word is derived. Amongst the
Greeks of Asia it appears only as the simple upright I, but in some of
the oldest alphabets elsewhere, as Crete, Thera, Attica, Achaia and its
colonies in lower Italy, it takes the form [symbol] or S, while at
Corinth and Corcyra it appears first in a form closely resembling the
later Greek _sigma_ [Sigma]. It had originally no cross-stroke at top
and bottom. I being not _i_ but _z_. The Phoenician alphabet having no
vowel symbols, the value of _yod_ was that of the English _y_. In Greek,
where the consonant sound had disappeared or been converted into _h_, I
is regularly used as a vowel. Occasionally, as in Pamphylian, it is used
dialectically as a glide between _i_ and another vowel, as in the proper
name [Greek: Damatriius]. In Latin I was used alike for both vowel and
consonant, as in _iugum_ (yoke). The sound represented by it was
approximately that still assigned to _i_ on the continent. Neither Greek
nor Latin made any distinction in writing between short and long _i_,
though in the Latin of the Empire the long sound was occasionally
represented by a longer form of the symbol I. The dot over the _i_
begins in the 5th or 6th century A.D. In pronunciation the English short
_i_ is a more open sound than that of most languages, and does not
correspond to the Greek and Latin sound. Nor are the English short and
long _i_ of the same quality. The short _i_ in Sweet's terminology is a
high-front-wide vowel, the long _i_, in English often spelt _ee_ in
words like _seed_, is diphthonged, beginning like the short vowel but
becoming higher as it proceeds. The Latin short _i_, however, in final
syllables was open and ultimately became _e_, e.g. in the neuter of
_i_-stems as _utile_ from _utili-s_. Medially both the short and the
long sounds are very common in syllables which were originally
unaccented, because in such positions many other sounds passed into _i_:
_officio_ but _facio_, _redimo_ but _emo_, _quidlibet_ but _lubet_
(_libet_ is later); _collido_ but _laedo_, _fido_ from an older _feido_,
_istis_ (dative plural) from an earlier _istois_.     (P. Gi.)



IAMBIC, the term employed in prosody to denote a succession of verses,
each consisting of a foot or metre called an iambus ([Greek: iambos]),
formed of two syllables, of which the first is short and the second long
(u --). After the dactylic hexameter, the iambic trimeter was the most
popular metre of ancient Greece. Archilochus is said to have been the
inventor of this iambic verse, the [Greek: trimetros] consisting of
three iambic fed. In the Greek tragedians an iambic line is formed of
six feet arranged in obedience to the following scheme:--

  u   --  | u   --  | u   --  | u   --  | u   --  | u   --  |
  u  u  u | u  u  u | u  u  u | u  u  u | u  u  u |         |
  --  --  |         |  --  -- |         | --  --  |         |
  -- u  u |         | -- u  u |         |         |         |
  u  u -- |         |         |         |         |         |

Much of the beauty of the verse depends on the caesura, which is usually
In the middle of the third foot, and far less frequently in the middle
of the fourth. The English language runs more naturally in the iambic
metre than in any other. The normal blank verse in English is founded
upon an iambic basis, and Milton's line--

  And swims | or sinks | or wades | or creeps | or flies | --

exhibits it in its primitive form. The ordinary alexandrine of French
literature is a hexapod iambic, but in all questions of quantity in
modern prosody great care has to be exercised to recollect that all
ascriptions of classic names to modern forms of rhymed or blank verse
are merely approximate. The octosyllabic, or four-foot iambic metre, has
found great favour in English verse founded on old romances.
Decasyllabic iambic lines rhyming together form an "heroic" metre.



IAMBLICHUS (d. c. A.D. 330), the chief representative of Syrian
Neoplatonism, is only imperfectly known to us in the events of his life
and the details of his creed. We learn, however, from Suidas, and from
his biographer Eunapius, that he was born at Chalcis in Coele-Syria, the
scion of a rich and illustrious family, that he studied under Anatolius
and afterwards under Porphyry, the pupil of Plotinus, that he himself
gathered together a large number of disciples of different nations with
whom he lived on terms of genial friendship, that he wrote "various
philosophical books," and that he died during the reign of
Constantine,--according to Fabricius, before A.D. 333. His residence
(probably) at his native town of Chalcis was varied by a yearly visit
with his pupils to the baths of Gadara. Of the books referred to by
Suidas only a fraction has been preserved. His commentaries on Plato and
Aristotle, and works on the Chaldaean theology and on the soul, are
lost. For our knowledge of his system we are indebted partly to the
fragments of these writings preserved by Stobaeus and others, and to the
notices of his successors, especially Proclus, partly to his five extant
books, the sections of a great work on the Pythagorean philosophy.
Besides these, Proclus (412-485) seems to have ascribed to him[1] the
authorship of the celebrated book _On the Egyptian Mysteries_
(so-called), and although its differences in style and in some points of
doctrine from the writings just mentioned make it improbable that the
work was by Iamblichus himself, it certainly emanated from his school,
and in its systematic attempt to give a speculative justification of the
polytheistic cultus of the day, marks the turning-point in the history
of thought at which Iamblichus stood.

As a speculative theory Neoplatonism (q.v.) had received its highest
development from Plotinus. The modifications introduced by Iamblichus
were the elaboration in greater detail of its formal divisions, the more
systematic application of the Pythagorean number-symbolism, and chiefly,
under the influence of Oriental systems, the thorough-going mythic
interpretation of what the previous philosophy had still regarded as
notional. It is on the last account, probably, that Iamblichus was
looked upon with such extravagant veneration. As a philosopher he had
learning indeed, but little originality. His aim was to give a
philosophical rendering of the popular religion. By his contemporaries
he was accredited with miraculous powers (which he, however,
disclaimed), and by his followers in the decline of Greek philosophy,
and his admirers on its revival in the 15th and 16th centuries, his name
was scarcely mentioned without the epithet "divine" or "most divine,"
while, not content with the more modest eulogy of Eunapius that he was
inferior to Porphyry only in style, the emperor Julian regarded him as
not even second to Plato, and said that he would give all the gold of
Lydia for one epistle of Iamblichus.

Theoretically, the philosophy of Plotinus was an attempt to harmonize
the principles of the various Greek schools. At the head of his system
he placed the transcendent incommunicable one ([Greek: hen amethekton]),
whose first-begotten is intellect ([Greek: nous]), from which proceeds
soul ([Greek: psychê]), which in turn gives birth to [Greek: physis],
the realm of nature. Immediately after the absolute one, Iamblichus
introduced a second superexistent unity to stand between it and the many
as the producer of intellect, and made the three succeeding moments of
the development (intellect, soul and nature) undergo various
modifications. He speaks of them as intellectual ([Greek: theoi
noeroi]), supramundane ([Greek: hyperkosmioi]), and mundane gods
([Greek: egkosmioi]). The first of these--which Plotinus represented
under the three stages of (objective) being ([Greek: on]), (subjective)
life ([Greek: zôê]), and (realized) intellect ([Greek: nous])--is
distinguished by him into spheres of intelligible gods ([Greek: theoi
noêtoi]) and of intellectual gods ([Greek: theoi noeroi]), each
subdivided into triads, the latter sphere being the place of ideas, the
former of the archetypes of these ideas. Between these two worlds, at
once separating and uniting them, some scholars think there was inserted
by Iamblichus, as afterwards by Proclus, a third sphere partaking of the
nature of both ([Greek: theoi noêtoi kai noeroi]). But this supposition
depends on a merely conjectural emendation of the text. We read,
however, that "in the intellectual hebdomad he assigned the third rank
among the fathers to the Demiurge." The Demiurge, Zeus, or
world-creating potency, is thus identified with the perfected [Greek:
nous], the intellectual triad being increased to a hebdomad, probably
(as Zeller supposes) through the subdivision of its first two members.
As in Plotinus [Greek: nous] produced nature by mediation of [Greek:
psychê], so here the intelligible gods are followed by a triad of
psychic gods. The first of these is incommunicable and supramundane,
while the other two seem to be mundane though rational. In the third
class, or mundane gods ([Greek: theoi egkosmioi]), there is a still
greater wealth of divinities, of various local position, function, and
rank. We read of gods, angels, demons and heroes, of twelve heavenly
gods whose number is increased to thirty-six or three hundred and sixty,
and of seventy-two other gods proceeding from them, of twenty-one chiefs
([Greek: hegemones]) and forty-two nature-gods ([Greek: theoi
genesiourgoi]), besides guardian divinities, of particular individuals
and nations. The world is thus peopled by a crowd of superhuman beings
influencing natural events, possessing and communicating knowledge of
the future, and not inaccessible to prayers and offerings.

The whole of this complex theory is ruled by a mathematical formulism of
triad, hebdomad, &c., while the first principle is identified with the
monad, [Greek: nous] with the dyad, and [Greek: psychê] with the triad,
symbolic meanings being also assigned to the other numbers. "The
theorems of mathematics," he says, "apply absolutely to all things,"
from things divine to original matter ([Greek: hylê]). But though he
thus subjects all things to number, he holds elsewhere that numbers are
independent existences, and occupy a middle place between the limited
and unlimited.

Another difficulty of the system is the account given of nature. It is
said to be "bound by the indissoluble chains of necessity which men call
fate," as distinguished from divine things which are not subject to
fate. Yet, being itself the result of higher powers becoming corporeal,
a continual stream of elevating influence flows from them to it,
interfering with its necessary laws and turning to good ends the
imperfect and evil. Of evil no satisfactory account is given; it is said
to have been generated accidentally.

In his doctrine of man Iamblichus retains for the soul the middle place
between intellect and nature which it occupies in the universal order.
He rejects the passionless and purely intellectual character ascribed to
the human soul by Plotinus, distinguishing it sharply both from those
above and those below it. He maintains that it moves between the higher
and lower spheres, that it descends by a necessary law (not solely for
trial or punishment) into the body, and, passing perhaps from one human
body to another, returns again to the supersensible. This return is
effected by the virtuous activities which the soul performs through its
own power of free will, and by the assistance of the gods. These virtues
were classified by Porphyry as political, purifying ([Greek:
kathartikai]), theoretical, and paradigmatic; and to these Iamblichus
adds a fifth class of priestly virtues ([Greek: hieratikai aretai]), in
which the divinest part of the soul raises itself above intellect to
absolute being.

Iamblichus does not seem ever to have attained to that ecstatic
communion with and absorption in deity which was the aim of earlier
Neoplatonism, and which Plotinus enjoyed four times in his life,
Porphyry once. Indeed his tendency was not so much to raise man to God
as to bring the gods down to men--a tendency shown still more plainly in
the "Answer of Abamon the master to Porphyry's letter to Anebo and
solutions of the doubts therein expressed," afterwards entitled the
_Liber de mysteriis_, and ascribed to Iamblichus.

In answer to questions raised and doubts expressed by Porphyry, the
writer of this treatise appeals to the innate idea all men have of the
gods as testifying to the existence of divinities countless in number
and various in rank (to the correct arrangement of which he, like
Iamblichus, attaches the greatest importance). He holds with the latter
that above all principles of being and intelligence stands the absolute
one, from whom the first god and king spontaneously proceeds; while
after these follow the ethereal, empyrean, and heavenly gods, and the
various orders of archangels, angels, demons, and heroes distinguished
in nature, power, and activity, and in greater profusion than even the
imagination of Iamblichus had conceived. He says that all the gods are
good (though he in another place admits the existence of evil demons who
must be propitiated), and traces the source of evil to matter; rebuts
the objection that their answering prayer implies passivity on the part
of gods or demons; defends divination, soothsaying, and theurgic
practices as manifestations of the divine activity; describes the
appearances of the different sorts of divinities; discusses the various
kinds of sacrifice, which he says must be suitable to the different
natures of the gods, material and immaterial, and to the double
condition of the sacrificer as bound to the body or free from it
(differing thus in his psychology from Iamblichus); and, in conclusion,
states that the only way to happiness is through knowledge of and union
with the gods, and that theurgic practices alone prepare the mind for
this union--again going beyond his master, who held assiduous
contemplation of divine things to be sufficient. It is the passionless
nature of the soul which permits it to be thus united to divine
beings,--knowledge of this mystic union and of the worship associated
with it having been derived from the Egyptian priests, who learnt it
from Hermes.

On one point only does the author of the _De mysteriis_ seem not to go
so far as Iamblichus in thus making philosophy subservient to
priestcraft. He condemns as folly and impiety the worship of images of
the gods, though his master held that these _simulacra_ were filled with
divine power, whether made by the hand of man or (as he believed) fallen
from heaven. But images could easily be dispensed with from the point of
view of the writer, who not only held that all things were full of gods
([Greek: panta plêrê theôn], as Thales said), but thought that each man
had a special divinity of his own--an [Greek: idios daimôn]--as his
guard and companion.

  The following are the extant works of Iamblichus: (1) _On the
  Pythagorean_ (_Life_ [Greek: Peri tou Pythagorikou biou]), ed. T.
  Kiessling (1815), A. Nauck (St Petersburg, 1884); for a discussion of
  the authorities used see E. Rohde in _Rheinisches Museum_, xxvi.,
  xxvii. (1871, 1872); Eng. trans. by Thomas Taylor (1818), (2) The
  _Exhortation to Philosophy_ ([Greek: Logos protreptikos eis
  philosophian]), ed. T. Kiessling (1813); H. Piselli (1888). (3) The
  treatise _On the General Science of Mathematics_ ([Greek: Peri tês
  koinês mathêmatkês epistêmês]), ed. J. G. Friis (Copenhagen, 1790), N.
  Festa (Leipzig, 1891). (4) The book _On the Arithmetic of Nicomachus_
  ([Greek: Peri tês Nikomachou arithmêtikês eisagôgês]), along with
  fragments on fate ([Greek: Peri heimarmenês]) and prayer ([Greek: Peri
  euchês]), ed. S. Tennulius (1688), the _Arithmetic_ by H. Pistelli
  (1894). (5) The _Theological Principles of Arithmetic_ ([Greek:
  Theologoumena tês arithmêtikês])--the seventh book of the series--by
  F. Ast (Leipzig, 1817). Two lost books, treating of the physical and
  ethical signification of numbers, stood fifth and sixth, while books
  on music, geometry and astronomy followed. The emperor Julian had a
  great admiration for Iamblichus, whom he considered "intellectually
  not inferior to Plato"; but the _Letters to Iamblicus the Philosopher_
  which bear his name are now generally considered spurious.

  The so-called _Liber de mysteriis_ was first edited, with Latin
  translation and notes, by T. Gale (Oxford, 1678), and more recently by
  C. Parthey (Berlin, 1857); Eng. trans. by Thomas Taylor (1821).

  There is a monograph on Iamblichus by G. E. Hebenstreit (_De
  Iamblichi, philosophi Syri, doctrina_, Leipzig, 1764), and one of the
  _De myst._ by Harless (_Das Buch v. d. ägypt. Myst._, Munich, 1858).
  The best accounts of Iamblichus are those of Zeller, _Phil. d.
  Griechen_, iii. 2, pp. 613 sq., 2nd ed.; E. Vacherot, _Hist. de
  l'école d'Alexandrie_ (1846), ii. 57 sq.; J. Simon, _Hist. de l'école
  d'Alexandrie_ (1845); A. E. Chaignet, _Histoire de la psychologie des
  Grecs_ (Paris, 1893) v. 67-108; T. Whittaker, _The Neo-Platonists_
  (Cambridge, 1901).     (W. R. So.)


FOOTNOTE:

  [1] Besides the anonymous testimony prefixed to an ancient MS. of
    Proclus, _De Myst._ viii. 3 seems to be quoted by the latter as
    Iamblichus's. Cf. Meiners. "Judicium de libro qui de Myst. Aeg.
    inscribitur," in _Comment. Soc. Reg. Sci. Gott._, vol. iv., 1781, p.
    77.



IAMBLICHUS, of Syria, the earliest of the Greek romance writers,
flourished in the 2nd century A.D. He was the author of [Greek:
Babylôniaka], the loves of Rhodanes and Sinonis, of which an epitome is
preserved in Photius (cod. 94). Garmus, a legendary king of Babylon,
forces Sinonis to marry him and throws Rhodanes into prison. The lovers
manage to escape, and after many singular adventures, in which magic
plays a considerable part, Garmus is overthrown by Rhodanes, who becomes
king of Babylon. According to Suidas, Iamblichus was a freedman, and a
scholiast's note on Photius further informs us that he was a native
Syrian (not descended from Greek settlers); that he borrowed the
material for his romance from a love story told him by his Babylonian
tutor, and that he subsequently applied himself with great success to
the study of Greek. A MS. of the original in the library of the Escorial
is said to have been destroyed by fire in 1670. Only a few fragments
have been preserved, in addition to Photius's epitome.

  See _Scriptores erotici_, ed. A. Hirschig (1856) and R. Hercher
  (1858); A. Mai, _Scriptorum veterum nova collectio_, ii.; E. Rohde,
  _Der griechische Roman_ (1900).



IANNINA (i.e. "the city of St John"; Gr. _Ioannina_; Turk _Yaniá_; also
written Janina, Jannina, and, according to its Albanian pronunciation,
Yanina), the capital of the vilayet of Iannina, Albania, European
Turkey. Pop. (1905) about 22,000. The largest ethnical groups in the
population are the Albanian and Greek; the purest form of colloquial
Greek is spoken here among the wealthy and highly educated merchant
families. The position of Iannina is strikingly picturesque. At the foot
of the grey limestone mass of Mount Mitzekeli (1500 ft.), which forms
part of the fine range of hills running north from the Gulf of Arta,
there lies a valley (the _Hellopia_ of antiquity) partly occupied by a
lake; and the city is built on the slopes of a slight eminence,
stretching down to the western shore. It has greatly declined from the
state of barbaric prosperity which it enjoyed from 1788 to 1822, when it
was the seat of Ali Pasha (q.v.), and was estimated to have from 30,000
to 50,000 inhabitants. The fortress--Demir Kule or Iron Castle, which,
like the principal seraglio, was built on a promontory jutting into the
lake--is now in ruins. But the city is the seat of a Greek archbishop,
and still possesses many mosques and churches, besides synagogues, a
Greek college (gymnasium), a library and a hospital. Sayades (opposite
Corfu) and Arta are the places through which it receives its imports.
The rich gold and silver embroidery for which the city has long been
famous is still one of the notable articles in its bazaar; but the
commercial importance of Iannina has notably declined since the cession
of Arta and Thessaly to Greece in 1881. Iannina had previously been one
of the chief centres of the Thessalian grain trade; it now exports
little except cheese, hides, bitumen and sheepskins to the annual value
of about £120,000; the imports, which supply only the local demand for
provisions, textile goods, hardware, &c., are worth about double that
sum.

The lake of Iannina (perhaps to be identified with the Pambotus or
Pambotis of antiquity) is 6 m. long, and has an area of 24 sq.m., with
an extreme depth of less than 35 ft. In time of flood it is united with
the smaller lake of Labchistas to the north. There are no affluents of
any considerable size, and the only outlets are underground passages or
_katavothra_ extending for many miles through the calcareous rocks.

The theory supported by W. M. Leake (_Northern Greece_, London, 1835)
that the citadel of Iannina is to be identified with Dodona, is now
generally abandoned in favour of the claims of a more southern site. As
Anna Comnena, in describing the capture of the town ([Greek: ta
Ioannina]) by Bohemond in 1082, speaks of the walls as being
dilapidated, it may be supposed that the place existed before the 11th
century. It is mentioned from time to time in the Byzantine annals, and
on the establishment of the lordship of Epirus by Michael Angelus
Comnenus Ducas, it became his capital. In the middle ages it was
successively attacked by Serbs, Macedonians and Albanians; but it was in
possession of the successors of Michael when the forces of the Sultan
Murad appeared before it in 1430 (cf. Hahn, _Alban. Studien_, Jena
[1854], pp. 319-322). Since 1431 it has continued under Turkish rule.

  Descriptions of Iannina will be found in Holland's _Travels_ (1815);
  Hughes, _Travels in Greece_, &c. (1830); H. F. Tozer, _Researches in
  the Highlands of Turkey_ (London, 1869). See also ALBANIA and the
  authorities there cited.



IAPETUS, in Greek mythology, son of Uranus and Gaea, one of the Titans,
father of Atlas, Prometheus, Epimetheus and Menoetius, the
personifications of certain human qualities (Hesiod, _Theog._ 507). As a
punishment for having revolted against Zeus, he was imprisoned in
Tartarus (Homer, _Iliad_, viii. 479) or underneath the island of Inarime
off the coast of Campania (Silius Italicus xii. 148). Hyginus makes him
the son of Tartarus and Gaea, and one of the giants. Iapetus was
considered the original ancestor of the human race, as the father of
Prometheus and grandfather of Deucalion. The name is probably identical
with Japhet (Japheth), and the son of Noah in the Greek legend of the
flood becomes the ancestor of (Noah) Deucalion. Iapetus as the
representative of an obsolete order of things is described as warring
against the new order under Zeus, and is naturally relegated to
Tartarus.

  See F. G. Welcker, _Griechische Götterlehre_, i. (1857); C. H.
  Völcker, _Die Mythologie des Iapetischen Geschlechtes_ (1824); M.
  Mayer, _Giganten und Titanen_ (1887).



IAPYDES, or IAPODES, one of the three chief peoples of Roman Illyria.
They occupied the interior of the country on the north between the Arsia
(Arsa) and Tedanius (perhaps the Zermanja), which separated them from
the Liburnians. Their territory formed part of the modern Croatia. They
are described by Strabo as a mixed race of Celts and Illyrians, who used
Celtic weapons, tattooed themselves, and lived chiefly on spelt and
millet. They were a warlike race, addicted to plundering expeditions. In
129 B.C. C. Sempronius Tuditanus celebrated a triumph over them, and in
34 B.C. they were finally crushed by Augustus. They appear to have had a
_foedus_ with Rome, but subsequently rebelled.

  See Strabo iv. 207, vii. 313-315; Dio Cassius xlix. 35; Appian,
  _Illyrica_, 10, 14, 16; Livy, _Epit._ lix. 131; Tibullus iv. 1. 108;
  Cicero, _Pro Balbo_, 14.



IATROCHEMISTRY (coined from Gr. [Greek: iatros], a physician, and
"chemistry"), a stage in the history of chemistry, during which the
object of this science was held to be "not to make gold but to prepare
medicines." This doctrine dominated chemical thought during the 16th
century, its foremost supporters being Paracelsus, van Helmont and de la
Boë Sylvius. But it gave way to the new definition formulated by Boyle,
viz. that the proper domain of chemistry was "to determine the
composition of substances." (See CHEMISTRY: I. _History_; MEDICINE.)



IAZYGES, a tribe of Sarmatians first heard of on the Maeotis, where they
were among the allies of Mithradates the Great. Moving westward across
Scythia, and hence called Metanastae, they were on the lower Danube by
the time of Ovid, and about A.D. 50 occupied the plains east of the
Theiss. Here, under the general name of Sarmatae, they were a perpetual
trouble to the Roman province of Dacia. They were divided into freemen
and serfs (_Sarmatae Limigantes_), the latter of whom had a different
manner of life and were probably an older settled population enslaved by
nomad masters. They rose against them in A.D. 334, but were repressed by
foreign aid. Nothing is heard of Iazyges or Sarmatae after the Hunnish
invasions. Graves at Keszthely and elsewhere in the Theiss valley, shown
by their contents to belong to nomads of the first centuries A.D., are
referred to the Iazyges.     (E. H. M.)



IBADAN, a town of British West Africa, in Yorubaland, Southern Nigeria,
123 m. by rail N.E. of Lagos, and about 50 m. N.E. of Abeokuta. Pop.
1910 estimated at 150,000. The town occupies the slope of a hill, and
stretches into the valley through which the river Ona flows. It is
enclosed by mud walls, which have a circuit of 18 m., and is encompassed
by cultivated land 5 or 6 m. in breadth. The native houses are all low,
thatched structures, enclosing a square court, and the only break in the
mud wall is the door. There are numerous mosques, _orishas_
(idol-houses) and open spaces shaded with trees. There are a few
buildings in the European style. Most of the inhabitants are engaged in
agriculture; but a great variety of handicrafts is also carried on.
Ibadan is the capital of one of the Yoruba states and enjoys a large
measure of autonomy. Nominally the state is subject to the _alafin_
(ruler) of Oyo; but it is virtually independent. The administration is
in the hands of two chiefs, a civil and a military, the _bale_ and the
_balogun_; these together form the highest court of appeal. There is
also an _iyaloda_ or mother of the town, to whom are submitted all the
disputes of the women. Ibadan long had a feud with Abeokuta, but on the
establishment of the British protectorate the intertribal wars were
stopped. In 1862 the people of Ibadan destroyed Ijaya, a neighbouring
town of 60,000 inhabitants. A British resident and a detachment of Hausa
troops are stationed at Ibadan.

  See also YORUBAS, ABEOKUTA and LAGOS.



IBAGUÉ, or SAN BONIFACIO DE IBAGUÉ, a city of Colombia, and capital of
the department of Tolima, about 60 m. W. of Bogotá and 18 m. N.W. of the
Nevado de Tolima. Pop. (1900, estimate) 13,000. Ibagué is built on a
beautiful plain between the Chipalo and Combeima, small affluents of the
Cuello, a western tributary of the Magdalena. Its elevation, 4300 ft.
above the sea, gives it a mild, subtropical climate. The plain and the
neighbouring valleys produce cacao, tobacco, rice and sugar-cane. There
are two thermal springs in the vicinity, and undeveloped mines of
sulphur and silver. The city has an endowed college. It is an important
commercial centre, being on the road which crosses the Quindio pass, or
_paramo_, into the Cauca valley. Ibagué was founded in 1550 and was the
capital of the republic for a short time in 1854.



IBARRA, a city of Ecuador and capital of the province of Imbabura, about
50 m. N.N.E. of Quito, on a small fertile plain at the northern foot of
Imbabura volcano, 7300 ft. above sea-level. Pop. (1900, estimate) 5000.
It stands on the left bank of the Tahuando, a small stream whose waters
flow north and west to the Pacific through the Mira, and is separated
from the higher plateau of Quito by an elevated transverse ridge of
which the Imbabura and Mojanda volcanoes form a part. The surrounding
country is mountainous, the valleys being very fertile. Ibarra itself
has a mild, humid climate, and is set in the midst of orchards and
gardens. It is the see of a bishop and has a large number of churches
and convents, and many substantial residences. Ibarra has manufactures
of cotton and woollen fabrics, hats, sandals (_alpargates_), sacks and
rope from _cabulla_ fibre, laces, sugar and various kinds of distilled
spirits and cordials made from the sugar-cane grown in the vicinity.
Mules are bred for the Colombian markets of Pasto and Popayan. Ibarra
was founded in 1597 by Alvaro de Ibarra, the president of Quito. It has
suffered from the eruptions of Imbabura, and more severely from
earthquakes, that of 1859 causing great damage to its public buildings,
and the greater one of the 16th of August 1868 almost completely
destroyed the town and killed a large number of its inhabitants. The
village of Carranqui, 1¼ m. from Ibarra, is the birthplace of Atahualpa,
the Inca sovereign executed by Pizarro, and close by is the small lake
called Yaguarcocha where the army of Huaynacapac, the father of
Atahualpa, inflicted a bloody defeat on the Carranquis. Another
aboriginal battle-field is that of Hatuntaqui, near Ibarra, where
Huaynacapac won a decisive victory and added the greater part of Ecuador
to his realm. The whole region is full of _tolas_, or Indian burial
mounds.



IBERIANS (Iberi, [Greek: Ibêres]), an ancient people inhabiting parts of
the Spanish peninsula. Their ethnic affinities are not known, and our
knowledge of their history is comparatively slight. It is almost
impossible to make any statement in regard to them which will meet with
general agreement. At the same time, the general lines of Iberian
controversy are clear enough The principal sources of information about
the Iberians are (1) historical, (2) numismatic, (3) linguistic, (4)
anthropological.

1. _Historical._--The name seems to have been applied by the earlier
Greek navigators to the peoples who inhabited the eastern coast of
Spain; probably it originally meant those who dwelt by the river Iberus
(mod. _Ebro_). It is possible (Boudard, _Études sur l'alphabet ibérien_
(Paris, 1852) that the river-name itself represents the Basque phrase
_ibay-erri_ "the country of the river." On the other hand, even in older
Greek usage (as in Thuc. vi. 1) the term Iberia is said to have embraced
the country as far east as the Rhone (see Herodorus of Heraclea, _Fragm.
Hist. Gr._ ii. 34), and by the time of Strabo it was the common Greek
name for the Spanish peninsula. Iberians thus meant sometimes the
population of the peninsula in general and sometimes, it would appear,
the peoples of some definite race ([Greek: genos]) which formed one
element in that population. Of the tribal distribution of this race, of
its linguistic, social and political characteristics, and of the history
of its relation to the other peoples of Spain, we have only the most
general, fragmentary and contradictory accounts. On the whole, the
historical evidence indicates that in Spain, when it first became known
to the Greeks and Romans there existed many separate and variously
civilized tribes connected by at least apparent identity of race, and by
similarity (but not identity) of language, and sufficiently
distinguished by their general characteristics from Phoenicians, Romans
and Celts. The statement of Diodorus Siculus that the mingling of these
Iberians with the immigrant Celts gave rise to the Celtiberians is in
itself probable. Varro and Dionysius Afer proposed to identify the
Iberians of Spain with the Iberians of the Caucasus, the one regarding
the eastern, and other the western, settlements as the earlier.

2. _Numismatic._--Knowledge of ancient Iberian language and history is
mainly derived from a variety of coins, found widely distributed in the
peninsula,[1] and also in the neighbourhood of Narbonne. They are
inscribed in an alphabet which has many points of similarity with the
western Greek alphabets, and some with the Punic alphabet; but which
seems to retain a few characters from an older script akin to those of
Minoan Crete and Roman Libya.[2] The same Iberian alphabet is found also
rarely in inscriptions. The coinage began before the Roman conquest was
completed; the monetary system resembles that of the Roman republic,
with values analogous to _denarii_ and _quinarii_. The coin inscriptions
usually give only the name of the town, e.g. PLPLIS (Bilbilis), KLAQRIQS
(Calagurris), SEQBRICS (Segobriga), TMANIAV (Dumania). The types show
late Greek and perhaps also late Punic influence, but approximate later
to Roman models. The commonest reverse type, a charging horseman,
reappears on the Roman coins of Bilbilis, Osca, Segobriga and other
places. Another common type is one man leading two horses or brandishing
a sword or a bow. The obverse has usually a male head, sometimes
inscribed with what appears to be a native name.

3. _Linguistic._--The survival of the non-Aryan language among the
Basques around the west Pyrenees has suggested the attempt to interpret
by its means a large class of similar-sounding place-names of ancient
Spain, some of which are authenticated by their occurrence on the
inscribed coins, and to link it with other traces of non-Aryan speech
round the shores of the Western Mediterranean and on the Atlantic
seaboard of Europe. This phase of Iberian theory opens with K. W.
Humboldt (_Prüfung der Untersuchungen über die Urbewohner Hispaniens
vermittelst der waskischen Sprache_, Berlin, 1821), who contended that
there existed once a single great Iberian people, speaking a distinct
language of their own; that an essentially "Iberian" population was to
be found in Sicily, Sardinia and Corsica, in southern France, and even
in the British Isles; and that the Basques of the present day were
remnants of this race, which had elsewhere been expelled or absorbed.
This last was the central and the seminal idea of the work, and it has
been the point round which the battle of scholarship has mainly raged.
The principal evidence which Humboldt adduced in its support was the
possibility of explaining a vast number of the ancient topographical
names of Spain, and of other asserted Iberian districts, by the forms
and significations of Basque. In reply, Graslin (_De l'Ibérie_, Paris,
1839), maintained that the name Iberia was nothing but a Greek misnomer
of Spain, and that there was no proof that the Basque people had ever
occupied a wider area than at present; and Bladé (_Origine des Basques_,
Paris, 1869) took the same line of argument, holding that Iberia is a
purely geographical term, that there was no proper Iberian race, that
the Basques were always shut in by alien races, that their affinity is
still to seek, and that the whole Basque-Iberian theory is a figment.
His main contention has met with some acceptance,[3] but the great
current of ethnographical speculation still flows in the direction
indicated by Humboldt.

4. _Anthropological._--Humboldt's "Iberian theory" depended partly on
linguistic comparisons, but partly on his observation of widespread
similarity of physical type among the population of south-western
Europe. Since his time the anthropological researches of Broca, Thurnam
and Davis, Huxley, Busk, Beddoe, Virchow, Tubino and others have proved
the existence in Europe, from Neolithic times, of a race, small of
stature, with long or oval skulls, and accustomed to bury their dead in
tombs. Their remains have been found in Belgium and France, in Britain,
Germany and Denmark, as well as in Spain; and they bear a close
resemblance to a type which is common among the Basques as well as all
over the Iberian peninsula. This Neolithic race has consequently been
nicknamed "Iberians," and it is now common to speak of the "Iberian"
ancestry of the people of Britain, recognizing the racial
characteristics of "Iberians" in the "small swarthy Welshman," the
"small dark Highlander," and the "Black Celts to the west of the
Shannon," as well as in the typical inhabitants of Aquitania and
Brittany.[4] Later investigators went further. M. d'Arbois de
Jubainville, for example (_Les Premiers habitants de l'Europe_, Paris,
1877), maintained that besides possessing Spain, Gaul, Italy and the
British Isles, "Iberian" peoples penetrated into the Balkan peninsula,
and occupied a part of northern Africa, Corsica and Sardinia; and it is
now generally accepted that a race with fairly uniform characteristics
was at one time in possession of the south of France (or at least of
Aquitania), the whole of Spain from the Pyrenees to the straits, the
Canary Islands (the Guanches) a part of northern Africa and Corsica.
Whether this type is more conveniently designated by the word _Iberian_,
or by some other name ("Eur-african," "Mediterranean," &c.) is a matter
of comparative indifference, provided that there is no misunderstanding
as to the steps by which the term _Iberian_ attained its meaning in
modern anthropology.

  AUTHORITIES.--K. W. von Humboldt, "Über die cantabrische oder
  baskische Sprache" in Adelung, _Mithridates_ iv. (1817), and _Prüfung
  d. Untersuchungen ü. die Urbewohner Hispaniens vermittelst der
  waskischen Sprache_ (Berlin, 1821); L. F. Graslin, _De l'Ibérie_
  (Paris, 1838); T. B. G. M. Bory de St Vincent, _Essai géologique sur
  le genre humain_ (1838); G. Lagneau, "Sur l'ethnologie des peuples
  ibériens," in _Bull. soc. anthrop._ (1867), pp. 146-161; J. F. Bladé,
  _Études sur l'origine des Basques_ (Paris, 1869), _Défense des
  études_, &c. (Paris, 1870); Phillips, _Die Einwanderung der Iberer in
  die pyren. Halbinsel_ (Vienna, 1870), _Über das iberische Alphabet_
  (Vienna, 1870); W. Boyd Dawkins, "The Northern Range of the Basques,"
  in _Fortnightly Rev._ N.S. xvi. 323-337 (1874); W. T. van Eys, "La
  Langue ibérienne et la langue basque," in _Revue de linguistique_, pp.
  3-15 (1874); W. Webster, "The Basque and the Kelt," in _Journ.
  Anthrop. Inst._ v. 5-29 (1875); F. M. Tubino, _Los Aborigines ibericos
  o los Berberos en la peninsula_ (Madrid, 1876); A. Luchaire, _Les
  Origines linguistiques de l'Aquitaine_ (Paris, 1877); W. Boyd Dawkins,
  _Early Man in Britain_ (London, 1880); A. Castaing, "Les Origines des
  Aquitains," _Mém. Soc. Eth._ N.S. 1, pp. 183-328 (1884); G. C. C.
  Gerland, "Die Basken und die Iberer" in Gröber, _Grundriss d. roman.
  Philologie_, 1, pp. 313-334 (1888); M. H. d'Arbois de Jubainville,
  _Les Premiers habitants de l'Europe_ (1889-1894); J. F. Bladé, _Les
  Vascons avant leur établissement en Novempopulanie_, Agen. (1891); W.
  Webster, "The Celt-iberians," _Academy_ xl. 268-269 (and consequent
  correspondence) (1891); J. Rhys, "The Inscriptions and Language of the
  Northern Picts," _Proc. Soc. Ant. Scot._ xxvi. 263-351 (1892); F.
  Fita, "El Vascuence en las inscripciones ógmicas," _Bol. Real. Acad.
  Hist. Madrid_ (June 1893), xxii. 579-587; G. v. d. Gabelentz,
  "Baskisch u. Berberisch," _Sitz. k. preuss. Akad. Wiss._ 593-613
  (Berlin, 1893), _Die Verwandtschaft der Baskischen mit der
  Berber-Sprache Nordafrikas nachgewiesen_ (Braunschweig, 1894); M. H.
  d'Arbois de Jubainville, "Les Celtes en Espagne," _Rev. celtique_,
  xiv. 357-395 (1894); G. Buschan, "Über die iberische Rasse,"
  _Ausland_, lxvi. 342-344 (1894); F. Olóriz y Aguilera, _Distribucion
  geografica del indice cefalico en España_ (Madrid, 1894), "La Talla
  humana en España" in _Discursos R. Acad. Medicina_ xxxvi. 389 (Madrid,
  1896); R. Collignon, "La Race basque," _L'Anthropologie_, v. 276-287
  (1894); T. de Aranzadi, "Le Peuple basque, résumé" _Bull. soc.
  d'anth._ 510-520 (1894), "Consideraciones acerca de la raza basca"
  _Euskel-Erria_ xxxv. 33, 65, 97, 129 (1896); H. Schuchhardt,
  _Baskische Studien_, i. "Über die Entstehung der Bezugsformen des
  baskischen Zeitworts"; _Denkschriften der K. Akad. der Wiss._,
  Phil.-Hist., Classe, Bd. 42, Abh. 3. (Wien, 1893); Ph. Salmon, _Rev.
  mens. Éc. d'anthr._ v. 155-181, 214-220 (1895); R. Collignon, "Anthr.
  du S.-O. de la France," _Mém. Soc. Anthr._ § 3. 1. 4. p. 1-129 (1895),
  _Ann. de géogr._ v. 156-166 (1896), and with J. Deniker, "Les Maures
  de Sénégal," _L'Anthr._ vii. 57-69 (1897); G. Hervé, _Rev. mens. Éc.
  d'anthr._ vi. 97-109 (1896); G. Sergi, _Africa: Anthropologia della
  stirpe Camitica_ (Turin, 1897), _Arii ed Italici_ (1898); L. de Hoyos
  Sainz, "L'Anthropologie et la préhistorique en Espagne et en Portugal
  en 1897," _L'Anthropologie_, ix. 37-51 (1898); J. Deniker (see
  Collignon) "Les Races de l'Europe," _L'Anthropologie_, ix. 113-133
  (1898); M. Gèze, "De quelques rapports entre les langues berbère et
  basque," _Mém. soc. arch. du Midi de la France_, xiii. See also the
  works quoted in the footnotes; and the bibliography under BASQUES.
       (J. L. M.)


FOOTNOTES:

  [1] For the prehistoric civilization of the peninsula as a whole see
    SPAIN.

  [2] P. A. Boudard's _Études sur l'alphabet ibérien_ (Paris, 1852).
    and _Numismatique ibérienne_ (Béziers, 1859); Aloiss Heiss, _Notes
    sur les monnaies celtibériennes_ (Paris, 1865), and _Description
    générale des monnaies antiques de l'Espagne_ (Paris, 1870); Phillips,
    _Über das iberische Alphabet_ (Vienna, 1870), _Die Einwanderung der
    Iberer in die pyren. Halbinsel_ (Vienna, 1870); W. M. Flinders
    Petrie, _Journ. Anthr. Inst._ xxix. (1899) 204, and above all E.
    Hübner, _Monumenta linguae Ibericae_.

  [3] W. van Eys, for example, "La Langue ibérienne et la langue
    basque," in _Revue de linguistique_, goes against Humboldt; but
    Prince Napoleon and to a considerable extent A. Luchaire maintain the
    justice of his method and the value of many of his results. See
    Luchaire, _Les Origines linguistiques de l'Aquitaine_ (Paris, 1877).

  [4] Compare the interesting résumé of the whole question in Boyd
    Dawkins's _Early Man in Britain_ (London, 1880).



IBEX, one of the names of the Alpine wild goat, otherwise known as the
steinbok and bouquetin, and scientifically as _Capra ibex_. Formerly the
ibex was common on the mountain-ranges of Germany, Switzerland and
Tirol, but is now confined to the Alps which separate Valais from
Piedmont, and to the lofty peaks of Savoy, where its existence is mainly
due to game-laws. The ibex is a handsome animal, measuring about 4½ ft.
in length and standing about 40 in. at the shoulder. The skin is covered
in summer with a short fur of an ashy-grey colour, and in winter with
much longer yellowish-brown hair concealing a dense fur beneath. The
horns of the male rise from the crest of the skull, and after bending
gradually backwards terminate in smooth tips; the front surface of the
remainder carrying bold transverse ridges or knots. About 1 yd. is the
maximum recorded length of ibex-horns. The fact that the fore-legs are
somewhat shorter than those behind enables the ibex to ascend mountain
slopes with more facility than it can descend, while its hoofs are as
hard as steel, rough underneath and when walking over a flat surface
capable of being spread out. These, together with its powerful sinews,
enable it to take prodigious leaps, to balance itself on the smallest
foothold and to scale almost perpendicular rocks. Ibex live habitually
at a greater height than chamois or any other Alpine mammals, their
vertical limit being the line of perpetual snow. There they rest in
sunny nooks during the day, descending at night to the highest woods to
graze. Ibex are gregarious, feeding in herds of ten to fifteen
individuals; but the old males generally live apart from, and usually at
greater elevations than, the females and young. They utter a sharp
whistling sound not unlike that of the chamois, but when greatly
irritated or frightened make a peculiar snorting noise. The period of
gestation in the female is ninety days, after which she
produces--usually at the end of June--a single young one which is able
at once to follow its mother. Kids when caught young and fed on goat's
milk can be readily tamed; and in the 16th century young tamed ibex were
frequently driven to the mountains along with the goats, in whose
company they would afterwards return. Even wild ibex have been known to
stray among the herds of goats, although they shun the society of
chamois. Its flesh is said to resemble mutton, but has a flavour of
game.

[Illustration: The Ibex (_Capra ibex_).]

By naturalists the name "ibex" has been extended to embrace all the
kindred species of wild goats, while by sportsmen it is used in a still
more elastic sense, to include not only the true wild goat (known in
India as the Sind ibex) but even the short-horned _Hemitragus hylocrius_
of the Nilgiris. Dealing only with species zoologically known as ibex,
the one nearest akin to the European kind is the Asiatic or Siberian
ibex (_Capra sibirica_), which, with several local phases, extends from
the northern side of Kashmir over an enormous area in Central Asia.
These ibex, especially the race from the Thian Shan, are incomparably
finer than the European species, their bold knotted horns sometimes
attaining a length of close on 60 in. The Arabian, or Nubian, ibex (_C.
nubiana_) is characterized by the more slender type of horn, in which
the front edge is much narrower; while the Simien ibex (_C. vali_) of
Central Abyssinia is a very large and dark-coloured animal, with the
horns black instead of brownish, and bearing only slightly marked front
ridges. The Caucasian ibex (_C. caucasica_), or tur, is a wholly
fox-coloured animal, in which the horns are still flatter in front, and
thus depart yet further from the ibex type. In the Spanish ibex (_C.
pyrenaica_) the horns are flattened, with ill-defined knobs, and a
spiral twist. (See GOAT.)     (W. H. F.; R. L.*)



IBIS, one of the sacred birds of the ancient Egyptians. James Bruce
identified this bird with the _Abu-Hannes_ or "Father John" of the
Abyssinians, and in 1790 it received from Latham (_Index
ornithologicus_, p. 706) the name of _Tantalus aethiopicus_. This
determination was placed beyond question by Cuvier (_Ann. du Muséum_,
iv. 116-135) and Savigny (_Hist. nat. et mythol. de l'ibis_) in 1805.
They, however, removed it from the Linnaean genus _Tantalus_ and,
Lacépède having some years before founded a genus _Ibis_, it was
transferred thither, and is now generally known as _I. aethiopica_,
though some speak of it as _I. religiosa_. No attempt can here be made
to treat the ibis from a mythological or antiquarian point of view.
Savigny's memoir contains a great deal of matter on the subject.
Wilkinson (_Ancient Egyptians_, ser. 2, vol. ii. pp. 217-224) added some
of the results of later research, and Renouf in his _Hibbert Lectures_
explains the origin of the myth.

The ibis is chiefly an inhabitant of the Nile basin from Dongola
southward, as well as of Kordofan and Sennar; whence about midsummer it
moves northwards to Egypt.[1] In Lower Egypt it bears the name of
_Abu-mengel_, or "father of the sickle," from the form of its bill, but
it does not stay long in that country, disappearing when the Nile has
subsided. Hence most travellers have failed to meet with it there[2]
(since their acquaintance with the birds of Egypt is limited to those
which frequent the country in winter), and writers have denied generally
to this species a place in its modern fauna (cf. Shelley, _Birds of
Egypt_, p. 261). However, in 1864, von Heuglin (_Journ. für
Ornithologie_, 1865, p. 100) saw a young bird which had been shot in the
Delta, and E. C. Taylor (_Ibis_, 1878, p. 372) saw an adult which had
been killed near Lake Menzal in 1877. The story told to Herodotus of its
destroying snakes is, according to Savigny, devoid of truth, but Cuvier
states that he discovered partly digested remains of a snake in the
stomach of a mummied ibis.

The ibis is somewhat larger than a curlew, _Numenius arquata_, which
bird it resembles, with a much stouter bill and stouter legs. The head
and greater part of the neck are bare and black. The plumage is white,
except the primaries, which are black, and a black plume, formed by the
secondaries, tertials and lower scapulars, and richly glossed with
bronze, blue and green, which curves gracefully over the hind-quarters.
The bill and feet are also black. The young lack the ornamental plume,
and in them the head and neck are clothed with short black feathers,
while the bill is yellow. The nest is placed in bushes or high trees,
the bird generally building in companies, and in the middle of August
von Heuglin (_Orn. Nord-Ost-Afrikas_, p. 1138) found that it had from
two to four young or much incubated eggs.[3] These are of a dingy white,
splashed, spotted and speckled with reddish-brown.

Congeneric with the typical ibis are two or three other species, the _I.
melanocephala_ of India, the _I. molucca_ or _I. strictipennis_, of
Australia, and the _I. bernieri_ of Madagascar, all of which closely
resemble _I. aethiopica_; while many other forms not very far removed
from it, though placed by authors in distinct genera,[4] are known.
Among these are several beautiful species such as the Japanese
_Geronticus nippon_, the _Lophotibis cristata_ of Madagascar, and the
scarlet ibis,[5] _Eudocimus ruber_, of America. The glossy ibis,
_Plegadis falcinellus_, found throughout the West Indies, Central and
the south-eastern part of North America, as well as in many parts of
Europe (whence it not unfrequently strays to the British Islands),
Africa, Asia and Australia. This bird, believed to be the second kind of
ibis spoken of by Herodotus, is rather smaller than the sacred ibis, and
mostly of a dark chestnut colour with brilliant green and purple
reflections on the upper parts, exhibiting, however, when young none of
the rufous hue. This species lays eggs of a deep sea-green colour,
having wholly the character of heron's eggs, and it often breeds in
company with herons, while the eggs of all other ibises whose eggs are
known resemble those of the sacred ibis. Though ibises resemble the
curlews externally, there is no affinity between them. The _Ibididae_
are more nearly related to the storks, _Ciconiidae_, and still more to
the spoonbills, _Plataleidae_, with which latter many systematists
consider them to form one group, the _Hemiglottides_ of Nitzsch.
Together these groups form the sub-order _Ciconiae_ of the order
_Ciconiiformes_. The true ibises are also to be clearly separated from
the wood-ibises, _Tantalidae_, of which there are four or five species,
by several not unimportant structural characters. Fossil remains of a
true ibis, _I. pagana_, have been found in considerable numbers in the
middle Tertiary beds of France.[6]     (A. N.)


FOOTNOTES:

  [1] It has been said to occur occasionally in Europe (Greece and
    southern Russia).

  [2] E. C. Taylor remarked (_Ibis_, 1859, p. 51), that the buff-backed
    heron, _Ardea bubulcus_, was made by the tourists' dragomans to do
    duty for the "sacred ibis," and this seems to be no novel practice,
    since by it, or something like it, Hasselqvist was misled, and
    through him Linnaeus.

  [3] The ibis has more than once nested in the gardens of the
    Zoological Society in London, and even reared its young there.

  [4] For some account of these may be consulted Dr Reichenow's paper
    in _Journ. für Ornithologie_ (1877), pp. 143-156; Elliot's in _Proc.
    Zool. Society_ (1877), pp. 477-510; and that of Oustalet in _Nouv.
    Arch. du Muséum_, ser. 2, vols. i. pp. 167-184.

  [5] It is a popular error--especially among painters--that this bird
    was the sacred ibis of the Egyptians.

  [6] The name "_Ibis_" was selected as the title of an ornithological
    magazine, frequently referred to in this and other articles, which
    made its first appearance in 1859.



IBLIS, or EBLIS, in Moslem mythology the counterpart of the Christian
and Jewish devil. He figures oftener in the Koran under the name
Shaitan, Iblis being mentioned 11 times, whereas Shaitan appears in 87
passages. He is chief of the spirits of evil, and his personality is
adapted to that of his Jewish prototype. Iblis rebelled against Allah
and was expelled from Paradise. The Koranic legend is that his fall was
a punishment for his refusal to worship Adam. Condemned to death he was
afterwards respited till the judgment day (Koran vii. 13).

  See Gustav Weil, _The Bible, the Koran and the Talmud_ (London, 1846).



IBN 'ABD RABBIHI [Abu 'Umar Ahmad ibn Mahommed ibn 'Abd Rabbihi]
(860-940), Arabian poet, was born in Cordova and descended from a freed
slave of Hisham, the second Spanish Omayyad caliph. He enjoyed a great
reputation for learning and eloquence. No diwan of his is extant, but
many selections from his poems are given in the _Yatimat ud-Dahr_, i.
412-436 (Damascus, 1887). More widely known than his poetry is his great
anthology, the _'Iqd ul-Farid_ ("The Precious Necklace"), a work divided
into twenty-five sections, the thirteenth being named the middle jewel
of the necklace, the chapters on either side of this being named after
other jewels. It is an _adab_ book (see ARABIA: _Literature_, section
"Belles Lettres") resembling Ibn Qutaiba's _'Uyun ul-Akhbar_, from which
it borrows largely. It has been printed, several times in Cairo (1876,
1886, &c.).     (G. W. T.)



IBN 'ARABI [Muhyiuddin Abu 'Abdallah ibn ul-'Arabi] (1165-1240), Moslem
theologian and mystic, was born in Murcia and educated in Seville. When
thirty-eight he travelled in Egypt, Arabia, Bagdad, Mosul and Asia
Minor, after which he lived in Damascus for the rest of his life. In law
he was a Zahirite, in theology a mystic of the extreme order, though
professing orthodox Ash'arite theology and combating in many points the
Indo-Persian mysticism (pantheism). He claims to have had conversations
with all the prophets past and future, and reports conversations with
God himself. Of his numerous works about 150 still exist. The most
extensive is the twelve-volume _Futuhat ul-Makkiyat_ ("Meccan
Revelations"), a general encyclopaedia of Sufic beliefs and doctrines.
Numerous extracts from this work are contained in Sha'rani's (d. 1565)
manual of Sufic dogma (_Yawaqit_) published several times in Cairo. A
short account of these works is given in A. von Kremer's _Geschichte der
herrschenden Ideen des Islams_, pp. 102-109 (Leipzig, 1868). Another
characteristic and more accessible work of Ibn 'Arabi is the _Fusus
ul-Hikam_, on the nature and importance of the twenty-seven chief
prophets, written in 1230 (ed. Bulaq, 1837) and with the _Commentary_
(Cairo, 1891) of Qashani (d. 1350); cf. analysis by M. Schreiner in
_Journal of German Oriental Society_, lii. 516-525.

  Of some 289 works said to have been written by Ibn 'Arabi 150 are
  mentioned in C. Brockelmann's _Gesch. der arabischen Litteratur_, vol.
  i. (Weimar, 1898), pp. 441-448. See also R. A. Nicholson, _A Literary
  History of the Arabs_, pp. 399-404 (London, 1907).     (G. W. T.)



IBN ATHIR, the family name of three brothers, all famous in Arabian
literature, born at Jazirat ibn 'Umar in Kurdistan. The eldest brother,
known as MAJD UD-DIN (1149-1210), was long in the service of the amir of
Mosul, and was an earnest student of tradition and language. His
dictionary of traditions (_Kitab un-Nihaya_) was published at Cairo
(1893), and his dictionary of family names (_Kitab ul-Murassa'_) has
been edited by Seybold (Weimar, 1896). The youngest brother, known as
DIYA UD-DIN (1163-1239), served Saladin from 1191 on, then his son,
al-Malik ul-Afdal, and was afterwards in Egypt, Samosata, Aleppo, Mosul
and Bagdad. He was one of the most famous aesthetic and stylistic
critics in Arabian literature. His _Kitab ul-Mathal_, published in Bulaq
in 1865 (cf. _Journal of the German Oriental Society_, xxxv. 148, and
Goldziher's _Abhandlungen_, i. 161 sqq.), contains some very
independent criticism of ancient and modern Arabic verse. Some of his
letters have been published by D. S. Margoliouth "On the Royal
Correspondence of Diya ed-Din el-Jazari" in the _Actes du dixième
congrès international des orientalistes_, sect. 3, pp. 7-21.

The brother best known by the simple name of Ibn Athir was ABU-L-HASAN
'IZZUDDIN MAHOMMED IBN UL-ATHIR (1160-1234), who devoted himself to the
study of history and tradition. At the age of twenty-one he settled with
his father in Mosul and continued his studies there. In the service of
the amir for many years, he visited Bagdad and Jerusalem and later
Aleppo and Damascus. He died in Mosul. His great history, the _Kamil_,
extends to the year 1231; it has been edited by C. J. Tornberg, _Ibn
al-Athiri Chronicon quod perfectissimum inscribitur_ (14 vols., Leiden,
1851-1876), and has been published in 12 vols. in Cairo (1873 and 1886).
The first part of this work up to A.H. 310 (A.D. 923) is an abbreviation
of the work of Tabari (q.v.) with additions. Ibn Athir also wrote a
history of the Atabegs of Mosul, published in the _Recueil des
historiens des croisades_ (vol. ii., Paris); a work (_Usd ul-Ghaba_),
giving an account of 7500 companions of Mahomet (5 vols., Cairo, 1863),
and a compendium (the _Lubab_) of Sam'ani's _Kitab ul-Ansab_ (cf. F.
Wüstenfeld's _Specimen el-Lobabi_, Göttingen, 1835).     (G. W. T.)



IBN BATUTA, i.e. ABU ABDULLAH MAHOMMED, surnamed IBN BATUTA (1304-1378),
the greatest of Moslem travellers, was born at Tangier in 1304. He
entered on his travels at twenty-one (1325) and closed them in 1355. He
began by traversing the coast of the Mediterranean from Tangier to
Alexandria, finding time to marry two wives on the road. After some stay
at Cairo, then probably the greatest city in the world (excluding
China), and an unsuccessful attempt to reach Mecca from Aidhab on the
west coast of the Red Sea, he visited Palestine, Aleppo and Damascus. He
then made the pilgrimage to Mecca and Medina, and visited the shrine of
Ali at Mashhad-Ali, travelling thence to Basra, and across the mountains
of Khuzistan to Isfahan, thence to Shiraz and back to Kufa and Bagdad.
After an excursion to Mosul and Diarbekr, he made the _haj_ a second
time, staying at Mecca three years. He next sailed down the Red Sea to
Aden (then a place of great trade), the singular position of which he
describes, noticing its dependence for water-supply upon the great
cisterns restored in modern times. He continued his voyage down the
African coast, visiting, among other places, Mombasa and Quiloa (Kilwa).
Returning north he passed by the chief cities of Oman to New Ormuz
(Hurmuz), which had about 15 years before, c. 1315, been transferred to
its famous island-site from the mainland (Old Ormuz). After visiting
other parts of the gulf he crossed the breadth of Arabia to Mecca,
making the _haj_ for the third time. Crossing the Red Sea, he made a
journey of great hardship to Syene, and thence along the Nile to Cairo.
After this, travelling through Syria, he made a circuit among the petty
Turkish states into which Asia Minor was divided after the fall of the
kingdom of Rum (Iconium). He now crossed the Black Sea to Kaffa, then
mainly occupied by the Genoese, and apparently the first Christian city
he had seen, for he was much perturbed by the bell-ringing. He next
travelled into Kipchak (the Mongol khanate of Russia), and joined the
camp of the reigning khan Mahommed Uzbeg, from whom the great and
heterogeneous _Uzbeg_ race is perhaps named. Among other places in this
empire he travelled to Bolghar (54° 54´ N.) in order to witness the
shortness of the summer night, and desired to continue his travels north
into the "Land of Darkness" (in the extreme north of Russia), of which
wonderful things were told, but was obliged to forego this. Returning to
the khan's camp he joined the cortège of one of the Khatuns, who was a
Greek princess by birth (probably illegitimate) and in her train
travelled to Constantinople, where he had an interview with the emperor
Andronikos III. the Younger (1328-1341). He tells how, as he passed the
city gates, he heard the guards muttering _Sarakinu_. Returning to the
court of Uzbeg, at Sarai on the Volga, he crossed the steppes to
Khwarizm and Bokhara; thence through Khorasan and Kabul, and over the
Hindu Kush (to which he gives that name, its first occurrence). He
reached the Indus, on his own statement, in September, 1333. This
closes the first part of his narrative.

From Sind, which he traversed to the sea and back again, he proceeded to
Multan, and eventually, on the invitation of Mahommed Tughlak, the
reigning sovereign, to Delhi. Mahommed was a singular character, full of
pretence at least to many accomplishments and virtues, the founder of
public charities, and a profuse patron of scholars, but a parricide, a
fratricide, and as madly capricious, bloodthirsty and unjust as
Caligula. "No day did his palace gate fail to witness the elevation of
some abject to affluence and the torture and murder of some living
soul." He appointed the traveller to be kazi of Delhi, with a present of
12,000 silver dinars (rupees), and an annual salary of the same amount,
besides an assignment of village lands. In the sultan's service Ibn
Batuta remained eight years; but his good fortune stimulated his natural
extravagance, and his debts soon amounted to four or five times his
salary. At last he fell into disfavour and retired from court, only to
be summoned again on a congenial duty. The emperor of China, last of the
Mongol dynasty, had sent a mission to Delhi, and the Moor was to
accompany the return embassy (1342). The party travelled through central
India to Cambay and thence sailed to Calicut, classed by the traveller
with the neighbouring Kaulam (Quilon), Alexandria, Sudak in the Crimea,
and Zayton (Amoy harbour) in China, as one of the greatest trading
havens in the world--an interesting enumeration from one who had seen
them all. The mission party was to embark in Chinese junks (the word
used) and smaller vessels, but that carrying the other envoys and the
presents, which started before Ibn Batuta was ready, was wrecked
totally; the vessel that he had engaged went off with his property, and
he was left on the beach of Calicut. Not daring to return to Delhi, he
remained about Honore and other cities of the western coast, taking part
in various adventures, among others the capture of Sindabur (Goa), and
visiting the Maldive Islands, where he became kazi, and married four
wives, and of which he has left the best medieval account, hardly
surpassed by any modern. In August 1344 he left the Maldives for Ceylon;
here he made the pilgrimage to the "Footmark of our Father Adam." Thence
he betook himself to Maabar (the Coromandel coast), where he joined a
Mussulman adventurer, residing at Madura, who had made himself master of
much of that region. After once more visiting Malabar, Canara and the
Maldives, he departed for Bengal, a voyage of forty-three days, landing
at Sadkawan (Chittagong). In Bengal he visited the famous Moslem saint
Shaykh Jalaluddin, whose shrine (_Shah Jalal_ at Silhet) is still
maintained. Returning to the delta, he took ship at Sunarganw (near
Dacca) on a junk bound for Java (i.e. _Java Minor_ of Marco Polo, or
Sumatra). Touching the coast of Arakan or Burma, he reached Sumatra in
forty days, and was provided with a junk for China by Malik al Dhahir, a
zealous disciple of Islam, which had recently spread among the states on
the northern coast of that island. Calling (apparently) at Cambodia on
his way, Ibn Batuta reached China at Zayton (Amoy harbour), famous from
Marco Polo; he also visited Sin Kalan or Canton, and professes to have
been in Khansa (_Kinsay_ of Marco Polo, i.e. Hangchau), and Khanbalik
(_Cambaluc_ or Peking). The truth of his visit to these two cities, and
especially to the last, has been questioned. The traveller's history,
not least in China, singularly illustrates the free masonry of Islam,
and its power of carrying a Moslem doctor over the known world of Asia
and Africa. On his way home he saw the great bird _Rukh_ (evidently,
from his description, an island lifted by refraction); revisited
Sumatra, Malabar, Oman, Persia, Bagdad, and crossed the great desert to
Palmyra and Damascus, where he got his first news of home, and heard of
his father's death fifteen years before. Diverging to Hamath and Aleppo,
on his return to Damascus, he found the Black Death raging, so that two
thousand four hundred died in one day. Revisiting Jerusalem and Cairo he
made the _haj_ a fourth time, and finally reappeared at Fez (visiting
Sardinia _en route_) on the 8th of November 1349, after twenty-four
years' absence. Morocco, he felt, was, after all, the best of countries.
"The _dirhems_ of the West are but little; but then you get more for
them." After going home to Tangier, Ibn Batuta crossed into Spain and
made the round of Andalusia, including Gibraltar, which had just then
stood a siege from the "Roman tyrant Adfunus" (Alphonso XI. of Castile,
1312-1350). In 1352 the restless man started for Central Africa, passing
by the oases of the Sahara (where the houses were built of rock-salt, as
Herodotus tells, and roofed with camel skins) to Timbuktu and Gogo on
the Niger, a river which he calls the Nile, believing it to flow down
into Egypt, an opinion maintained by some up to the date of Lander's
discovery. Being then recalled by his own king, he returned to Fez
(early in 1354) via Takadda, Haggar and Tuat. Thus ended his
twenty-eight years' wanderings which in their main lines alone exceeded
75,000 m. By royal order he dictated his narrative to Mahommed Ibn
Juzai, who concludes the work, 13th of December 1355 (A.D.) with the
declaration: "This Shaykh is the traveller of our age; and he who should
call him the traveller of the whole body of Islam would not exceed the
truth." Ibn Batuta died in 1378, aged seventy-three.

  Ibn Batuta's travels have only been known in Europe during the 19th
  century; at first merely by Arabic abridgments in the Gotha and
  Cambridge libraries. Notices or extracts had been published by Seetzen
  (c. 1808), Kosegarten (1818), Apetz (1819), and Burckhardt (1819),
  when in 1829 Dr S. Lee published for the Oriental Translation Fund a
  version from the abridged MSS. at Cambridge, which attracted much
  interest. The French capture of Constantina afforded MSS. of the
  complete work, one of them the autograph of Ibn Juzai. And from these,
  after versions of fragments by various French scholars, was derived at
  last (1858-1859) the standard edition and translation of the whole by
  M. Défrémery and Dr Sanguinetti, in 4 vols. See also Sir Henry Yule,
  Cathay, ii. 397-526; C. Raymond Beazley, _Dawn of Modern Geography_,
  iii. 535-538. Though there are some singular chronological
  difficulties in the narrative, and a good many cursory inaccuracies
  and exaggerations, there is no part of it except, perhaps, certain
  portions of the journeys in north China, which is open to doubt. The
  accounts of the Maldive Islands, and of the Negro countries on the
  Niger, are replete with interesting and accurate particulars. The
  former agrees surprisingly with that given by the only other foreign
  resident we know of, Pyrard de la Val, two hundred and fifty years
  later. Ibn Batuta's statements and anecdotes regarding the showy
  virtues and solid vices of Sultan Muhammad Tughlak are in entire
  agreement with Indian historians, and add many fresh details.
       (H. Y.; C. R. B.)



IBN DURAID [Abu Bakr Mahommed ibn ul-Hasan ibn Duraid ul-Azdi]
(837-934), Arabian poet and philologist, was born at Basra of south
Arabian stock. At his native place he was trained under various
teachers, but fled in 871 to Oman at the time Basra was attacked by the
negroes, known as the Zanj, under Muhallabi. After living twelve years
in Oman he went to Persia, and, under the protection of the governor,
'Abdallah ibn Mahommed ibn Mikal, and his son, Isma'il, wrote his chief
works. In 920 he went to Bagdad, where he received a pension from the
caliph Moqtadir.

  The _Maqsura_, a poem in praise of Ibn Mikal and his son, has been
  edited by A. Haitsma (1773) E. Scheidius (1786) and N. Boyesen (1828).
  Various commentaries on the poem exist in MS. (cf. C. Brockelmann,
  _Gesch. der ar. Lit._, i. 211 ff., Weimar, 1898), The _Jamhara
  fi-l-Lugha_ is a large dictionary written in Persian but not printed.
  Another work is the _Kitab ul-Ishtiqaq_ ("Book of Etymology"), edited
  by F. Wüstenfeld (Göttingen, 1854); it was written in opposition to
  the anti-Arabian party to show the etymological connexion of the
  Arabian tribal names.     (G. W. T.)



IBN FARADI [Abu-l-Walid 'Abdallah ibn ul-Faradi] (962-1012), Arabian
historian, was born at Cordova and studied law and tradition. In 992 he
made the pilgrimage and proceeded to Egypt and Kairawan, studying in
these places. After his return in 1009 he became cadi in Valencia, and
was killed at Cordova when the Berbers took the city.

  His chief work is the _History of the Learned Men of Andalusia_,
  edited by F. Codera (Madrid, 1891-1892). He wrote also a history of
  the poets of Andalusia.     (G. W. T.)



IBN FARID [Abu-l-Qasim 'Umar ibn ul-Farid] (1181-1235), Arabian poet,
was born in Cairo, lived for some time in Mecca and died in Cairo. His
poetry is entirely Sufic, and he was esteemed the greatest mystic poet
of the Arabs. Some of his poems are said to have been written in
ecstasies. His diwan has been published with commentary at Beirut, 1887,
&c.; with the commentaries of Burini (d. 1615) and 'Abdul-Ghani (d.
1730) at Marseilles, 1853, and at Cairo; and with the commentary of
Rushayyid Ghalib (19th century) at Cairo, 1893. One of the separate
poems was edited by J. von Hammer Purgstall as _Das arabische hohe Lied
der Liebe_ (Vienna, 1854).

  See R. A. Nicholson, _A Literary History of the Arabs_ (London, 1907),
  pp. 394-398.     (G. W. T.)



IBN GABIROL [SOLOMON BEN JUDAH], Jewish poet and philosopher, was born
at Malaga, probably about 1021. The early part of his troublous life was
spent at Saragossa, but few personal details of it are recorded. His
parents died while he was a child and he was under the protection first
of a certain Jekuthiel, who died in 1039, and afterwards of Samuel
ha-Nagid, the well-known patron of learning. His passionate disposition,
however, embittered no doubt by his misfortunes, involved him in
frequent difficulties and led to his quarrelling with Samuel. It is
generally agreed that he died young, although the date is uncertain. Al
Harizi[1] says at the age of twenty-nine, and Moses b. Ezra[2] about
thirty, but Abraham Zaccuto[3] states that he died (at Valencia) in
1070. M. Steinschneider[4] accepts the date 1058.

His literary activity began early. He is said to have composed poems at
the age of sixteen, and elegies by him are extant on Hai Gaon (died in
1038) and Jekuthiel (died in 1039), each of which was written probably
soon after the death of the person commemorated. About the same time he
also wrote his _'Anaq_, a poem on grammar, of which only 97 lines out of
400 are preserved. Moses ben Ezra says of him that he imitated Moslem
models, and was the first to open to Jewish poets the door of
versification,[5] meaning that he first popularized the use of Arabic
metres in Hebrew. It is as a poet that he has been known to the Jews to
the present day, and admired for the youthful freshness and beauty of
his work, in which he may be compared to the romantic school in France
and England in the early 19th century. Besides his lyrical and satirical
poems, he contributed many of the finest compositions to the liturgy
(some of them with the acrostic "Shelomoh ha-qato"), which are widely
different from the artificial manner of the earlier payyetanim. The best
known of his longer liturgical compositions are the philosophical
_Kether Malkuth_ (for the Day of Atonement) and the _Azharoth_, on the
613 precepts (for _Shebhu'oth_). Owing to his pure biblical style he had
an abiding influence on subsequent liturgical writers.

Outside the Jewish community he was known as the philosopher Avicebron
(Avencebrol, Avicebrol, &c.) The credit of identifying this name as a
medieval corruption of Ibn Gabirol is due to S. Munk, who showed that
selections made by Shem Tobh Palqera (or Falqera) from the Meqor Hayyim
(the Hebrew translation of an Arabic original) by Ibn Gabirol,
corresponded to the Latin _Fons Vitae_ of Avicebron. The Latin version,
made by Johannes Hispalensis and Gundisalvi about one hundred years
after the author's death, had at once become known among the Schoolmen
of the 12th century and exerted a powerful influence upon them, although
so little was known of the author that it was doubted whether he was a
Christian or a Moslem. The teaching of the _Fons Vitae_ was entirely new
to the country of its origin, and being drawn largely from Neoplatonic
sources could not be expected to find favour with Jewish thinkers. Its
distinctive doctrines are: (1) that all created beings, spiritual or
corporeal, are composed of matter and form, the various species of
matter being but varieties of the universal matter, and similarly all
forms being contained in one universal form; (2) that between the primal
One and the intellect (the [Greek: nous] of Plotinus) there is
interposed the divine Will, which is itself divine and above the
distinction of form and matter, but is the cause of their union in the
being next to itself, the intellect, in which Avicebron holds that the
distinction does exist. The doctrine that there is a material, as well
as a formal, element in all created beings was explicitly adopted from
Avicebron by Duns Scotus (as against the view of Albertus Magnus and
Thomas Aquinas), and perhaps his exaltation of the will above the
intellect is due to the same influence. Avicebron develops his
philosophical system throughout quite independently of his religious
views--a practice wholly foreign to Jewish teachers, and one which could
not be acceptable to them. Indeed, this charge is expressly brought
against him by Abraham ben David of Toledo (died in 1180). It is
doubtless this non-religious attitude which accounts for the small
attention paid to the _Fons Vitae_ by the Jews, as compared with the
wide influence of the philosophy of Maimonides.

The other important work of Ibn Gabirol is _Islah al-akhlaq_ (the
improvement of character), a popular work in Arabic, translated into
Hebrew (_Tiqqun middoth ha-nephesh_) by Judah ibn Tibbon. It is widely
different in treatment from the _Fons_, being intended as a practical
not a speculative work.

The collection of moral maxims, compiled in Arabic but best known (in
the Hebrew translation of Judah ibn Tibbon) as _Mibhar ha-peninim_, is
generally ascribed to Ibn Gabirol, though on less certain grounds.

  BIBLIOGRAPHY.--Texts of the liturgical poems are to be found in the
  prayer-books: others in Dukes and Edelmann, _Treasures of Oxford_
  (Oxford, 1850); Dukes, _Shire Shelomoh_ (Hanover, 1858); S. Sachs,
  _Shir ha-shirim asher li-Shelomoh_ (Paris, 1868, incomplete); Brody,
  _Die weltlichen Gedichte des ... Gabirol_ (Berlin, 1897, &c.).

  "Avencebrolis Fons Vitae" (Latin text) in Clemens Bäumker's _Beiträge
  zur Gesch. d. Philosophie_, Bd. i. Hefte 2-4 (Münster, 1892); _The
  Improvement of the Moral Qualities_ [Arabic and English] ed. by S. S.
  Wise (New York, 1901); _A Choice of Pearls_ [Hebrew and English] ed.
  by Ascher (London, 1859).

  On the philosophy in general: S. Munk, _Mélanges_ (quoted above);
  Guttmann, _Die Philosophie des Sal.-ibn Gabirol_ (Göttingen, 1889); D.
  Kaufmann, _Studien über Sal.-ibn Gabirol_ (Budapest, 1899); S.
  Horovitz, "Die Psychologie Ibn Gabirols," in the _Jahresbericht des
  jüd. theol. Seminars Fränckel'scher Stiftung_ (Breslau, 1900);
  Wittmann, "Zur Stellung Avencebrols ..." (in Bäumker's _Beiträge_, Bd.
  v. Heft 1, Münster, 1905).     (A. Cy.)


FOOTNOTES:

  [1] _Jud. Har. Macamæ_, ed. Lagarde (Göttingen, 1883), p. 89, l. 61.

  [2] See the passage quoted by Munk, _Mélanges de philosophie arabe et
    juive_ (Paris, 1859), pp. 264 and 517.

  [3] _Liber Juchassin_, ed. Filipowski (London, 1857), p. 217.

  [4] _Hebr. Übersetzungen_ (Berlin, 1893), § 219, note 70; cf.
    Kaufmann, _Studien über Sal.-ibn Gabirol_ (Budapest, 1899), p. 79,
    note 2.

  [5] See Munk, _op. cit._ pp. 515-516, transl. on pp. 263-264. Metre
    had been already used by Dunash.



IBN HAUKAL, strictly IBN HAUQAL, a 10th century Arabian geographer.
Nothing is known of his life. His work on geography, written in 977, is
only a revision and extension of the _Masalik ul-Mamalik_ of
al-Istakhri, who wrote in 951. This itself was a revised edition of the
_Kitab ul-Ashkal_ or _Suwar ul-Aqalim_ of Abu Zaid ul-Balkhi, who wrote
about 921. Ibn Haukal's work was published by M. J. de Goeje (Leiden,
1873). An anonymous epitome of the book was written in 1233.

  See M. J. de Goeje, "Die Istahri-Balhi Frage," in the _Zeitschrift der
  deutschen Morgenländischen Gesellschaft_, xxv. 42 sqq.



IBN HAZM [Abu Mahommed 'Ali ibn Ahmad ibn Hazm] (994-1064), Moslem
theologian, was born in a suburb of Cordova. He studied history, law and
theology, and became a vizier as his father had been before him, but was
deposed for heresy, and spent the rest of his life quietly in the
country. In legal matters he belonged first to the Shafi'ite school, but
came to adopt the views of the Zahirites, who admitted only the external
sense of the Koran and tradition, disallowing the use of analogy
(_Qiyas_) and _Taqlid_ (appeal to the authority of an imam), and
objecting altogether to the use of individual opinion (_Ra'y_). Every
sentence of the Koran was to be interpreted in a general and universal
sense; the special application to the circumstances of the time it was
written was denied. Every word of the Koran was to be taken in a literal
sense, but that sense was to be learned from other uses in the Koran
itself, not from the meaning in other literature of the time. The
special feature of Ibn Hazm's teaching was that he extended the
application of these principles from the study of law to that of
dogmatic theology. He thus found himself in opposition at one time to
the Mo'tazilites, at another to the Ash'arites. He did not, however,
succeed in forming a school. His chief work is the _Kitab ul-Milal
wan-Nihal_, or "Book of Sects" (published in Cairo, 1899).

  For his teaching cf. I. Goldziher, _Die Zahiriten_, pp. 116-172
  (Leipzig, (1884), and M. Schreiner in the _Journal of the German
  Oriental Society_, lii. 464-486. For a list of his other works see C.
  Brockelmann's _Geschichte der arabischen Literatur_, vol. i. (Weimar,
  1898), p. 400.     (G. W. T.)



IBN HISHAM [Abu Mahommed 'Abdulmalik ibn Hisham ibn Ayyub ul-Himyari]
(d. 834), Arabian biographer, studied in Kufa but lived afterwards in
Fostat (old Cairo), where he gained a name as a grammarian and student
of language and history. His chief work is his edition of Ibn Ishaq's
(q.v.) _Life of the Apostle of God_, which has been edited by F.
Wüstenfeld (Göttingen, 1858-1860). An abridged German translation has
been made by G. Weil (Stuttgart, 1864; cf. P. Brönnle, _Die
Commentatoren des Ibn Ishaq und ihre Scholien_, Halle, 1895). Ibn Hisham
is said to have written a work explaining the difficult words which
occur in poems on the life of the Apostle, and another on the
genealogies of the Himyarites and their princes.     (G. W. T.)



IBN ISHAQ [Mahommed ibn Ishaq Abu 'Abdallah] (d. 768), Arabic historian,
lived in Medina, where he interested himself to such an extent in the
details of the Prophet's life that he was attacked by those to whom his
work seemed to have a rationalistic tendency. He consequently left
Medina in 733, and went to Alexandria, then to Kufa and Hira, and
finally to Bagdad, where the caliph Mansur provided him with the means
of writing his great work. This was the _Life of the Apostle of God_,
which is now lost and is known to us only in the recension of Ibn Hisham
(q.v.). The work has been attacked by Arabian writers (as in the
_Fihrist_) as untrustworthy, and it seems clear that he introduced
forged verses (cf. _Journal of the German Oriental Society_, xiv. 288
sqq.). It remains, however, one of the most important works of the age.
     (G. W. T.)



IBN JUBAIR [Abu-l Husain Mahommed ibn Ahmad ibn Jubair] (1145-1217),
Arabian geographer, was born in Valencia. At Granada he studied the
Koran, tradition, law and literature, and later became secretary to the
Mohad governor of that city. During this time he composed many poems. In
1183 he left the court and travelled to Alexandria, Jerusalem, Medina,
Mecca, Damascus, Mosul and Bagdad, returning in 1185 by way of Sicily.

  The _Travels of Ibn Jubair_ were edited by W. Wright (Leiden, 1852);
  and a new edition of this text, revised by M. J. de Goeje, was
  published by the Gibb Trustees (London, 1907). The part relating to
  Sicily was published, with French translation and notes, by M. Amari
  in the _Journal asiatique_ (1845-1846) and a French translation alone
  of the same part by G. Crolla in _Museon_, vi. 123-132.     (G. W. T.)



IBN KHALDUN [Abu Zaid ibn Mahommed ibn Mahommed ibn Khaldun]
(1332-1406), Arabic historian, was born at Tunis. He studied the various
branches of Arabic learning with great success. In 1352 he obtained
employment under the Marinid sultan Abu Inan (Faris I.) at Fez. In the
beginning of 1356, his integrity having been suspected, he was thrown
into prison until the death of Abu Inan in 1358, when the vizier
al-Hasan ibn Omar set him at liberty and reinstated him in his rank and
offices. He here continued to render great service to Abu Salem (Ibrahim
III.), Abu Inan's successor, but, having offended the prime minister, he
obtained permission to emigrate to Spain, where, at Granada, he was
received with great cordiality by Ibn al Ahmar, who had been greatly
indebted to his good offices when an exile at the court of Abu Salem.
The favours he received from the sovereign excited the jealousy of the
vizier, and he was driven back to Africa (1364), where he was received
with great cordiality by the sultan of Bougie, Abu Abdallah, who had
been formerly his companion in prison. On the fall of Abu Abdallah Ibn
Khaldun raised a large force amongst the desert Arabs, and entered the
service of the sultan of Tlemçen. A few years later he was taken
prisoner by Abdalaziz ('Abd ul 'Aziz), who had defeated the sultan of
Tlemçen and seized the throne. He then entered a monastic establishment,
and occupied himself with scholastic duties, until in 1370 he was sent
for to Tlemçen by the new sultan. After the death of 'Abd ul 'Aziz he
resided at Fez, enjoying the patronage and confidence of the regent.
After some further vicissitudes in 1378 he entered the service of the
sultan of his native town of Tunis, where he devoted himself almost
exclusively to his studies and wrote his history of the Berbers. Having
received permission to make the pilgrimage to Mecca, he reached Cairo,
where he was presented to the sultan, al-Malik udh-Dhahir Barkuk, who
insisted on his remaining there, and in the year 1384 made him grand
cadi of the Malikite rite for Cairo. This office he filled with great
prudence and probity, removing many abuses in the administration of
justice in Egypt. At this time the ship in which his wife and family,
with all his property, were coming to join him, was wrecked, and every
one on board lost. He endeavoured to find consolation in the completion
of his history of the Arabs of Spain. At the same time he was removed
from his office of cadi, which gave him more leisure for his work. Three
years later he made the pilgrimage to Mecca, and on his return lived in
retirement in the Fayum until 1399, when he was again called upon to
resume his functions as cadi. He was removed and reinstated in the
office no fewer than five times.

In 1400 he was sent to Damascus, in connexion with the expedition
intended to oppose Timur or Tamerlane. When Timur had become master of
the situation, Ibn Khaldun let himself down from the walls of the city
by a rope, and presented himself before the conqueror, who permitted him
to return to Egypt. Ibn Khaldun died on the 16th of March 1406, at the
age of sixty-four.

  The great work by which he is known is a "Universal History," but it
  deals more particularly with the history of the Arabs of Spain and
  Africa. Its Arabic title is _Kitab ul'Ibar, wa diwan el Mubtada wa'l
  Khabar, fi ayyam ul 'Arab wa'l'Ajam wa'l Berber_; that is, "The Book
  of Examples and the Collection of Origins and Information respecting
  the History of the Arabs, Foreigners and Berbers." It consists of
  three books, an introduction and an autobiography. Book i. treats of
  the influence of civilization upon man; book ii. of the history of the
  Arabs and other peoples from the remotest antiquity until the author's
  own times; book iii. of the history of the Berber tribes and of the
  kingdoms founded by that race in North Africa. The introduction is an
  elaborate treatise on the science of history and the development of
  society, and the autobiography contains the history, not only of the
  author himself, but of his family and of the dynasties which ruled in
  Fez, Tunis and Tlemçen during his lifetime. An edition of the Arabic
  text has been printed at Bulaq, (7 vols., 1867) and a part of the work
  has been translated by the late Baron McG. de Slane under the title of
  _Histoire des Berbères_ (Algiers, 1852-1856); it contains an admirable
  account of the author and analysis of his work. Vol. i., the
  _Muqaddama_ (preface), was published by M. Quatremère (3 vols., Paris,
  1858), often republished in the East, and a French translation was
  made by McG. de Slane (3 vols., Paris, 1862-1868). The parts of the
  history referring to the expeditions of the Franks into Moslem lands
  were edited by C. J. Tornberg (Upsala, 1840), and the parts treating
  of the Banu-l Ahmar kings of Granada were translated into French by M.
  Gaudefroy-Demombynes in the _Journal asiatique_, ser. 9, vol. xiii.
  The _Autobiography_ of Ibn Khaldun was translated into French by de
  Slane in the _Journal asiatique_, ser. 4, vol. iii. For an English
  appreciation of the philosophical spirit of Ibn Khaldun see R. Flint's
  _History of the Philosophy of History_ (Edinburgh, 1893), pp. 157-170.
       (E. H. P.; G. W. T.)



IBN KHALLIKAN [Abu-l 'Abbas Ahmad ibn Khallikan] (1211-1282), Arabian
biographer, was born at Arbela, the son of a professor reputed to be
ascended from the Barmecides of the court of Harun al-Rashid. When
eighteen he went to Aleppo, where he studied for six years, then to
Damascus, and in 1238 to Alexandria and Cairo. In 1252 he married and
became chief cadi of Syria in Damascus in 1261. Having held this office
for ten years, he was professor in Cairo until 1278, when he again took
office in Damascus for three years. In 1281 he accepted a professorship
in the same city, but died in the following year.

  His great work is the _Kitab Wafayat ul-A'yan_, "The Obituaries of
  Eminent Men." It contains in alphabetical order the lives of the most
  celebrated persons of Moslem history and literature, except those of
  Mahomet, the four caliphs and the companions of Mahomet and their
  followers (the _Tabiun_). The work is anecdotal and contains many
  brief extracts from the poetry of the writers. It was published by F.
  Wüstenfeld (Göttingen, 1835-1843), in part by McG. de Slane (Paris,
  1838-1842), and also in Cairo (1859 and 1882). An English translation
  by McG. de Slane was published for the Oriental Translation Fund in 4
  vols. (London, 1842-1871). Thirteen extra biographies from a
  manuscript in Amsterdam were published by Pijnappel (Amsterdam, 1845).
  A Persian translation exists in manuscript, and various extracts from
  the work are known. Several supplements to the book have been written,
  the best known being that of Mahommed ibn Shakir (d. 1362), published
  at Cairo 1882. A collection of poems by Ibn Khallikan is also extant.
       (G. W. T.)



IBN QUTAIBA, or KOTAIBA [Abu Mahommed ibn Muslim ibn Qutaiba] (828-889),
Arabian writer, was born at Bagdad or Kufa, and was of Iranian descent,
his father belonging to Merv. Having studied tradition and philology he
became cadi in Dinawar and afterwards teacher in Bagdad, where he died.
He was the first representative of the eclectic school of Bagdad
philologists that succeeded the schools of Kufa and Basra (see ARABIA:
_Literature_, section "Grammar"). Although engaged also in theological
polemic (cf. I. Goldziher, _Muhammedanische Studien_, ii. 136, Halle,
1890), his chief works were directed to the training of the ideal
secretary. Of these five may be said to form a series. The _Adab
ul-Katib_ ("Training of the Secretary") contains instruction in writing
and is a compendium of Arabic style. It has been edited by Max Grünert
(Leiden, 1900). The _Kitab ush-Sharab_ is still in manuscript. The
_Kitab ul-Ma'arif_ has been edited by F. Wüstenfeld as the _Handbuch der
Geschichte_[1] (Göttingen, 1850); the _Kitab ush-Shi'r wash-Shu'arai_
("Book of Poetry and Poets") edited by M. J. de Goeje (Leiden, 1904).[2]
The fifth and most important is the _'Uyun ul-Akhbar_, which deals in
ten books with lordship, war, nobility, character, science and
eloquence, asceticism, friendship, requests, foods and women, with many
illustrations from history, poetry and proverb (ed. C. Brockelmann,
Leiden, 1900 sqq.).

  For other works (which were much quoted by later Arabian writers) see
  C. Brockelmann, _Gesch. der arabischen Literatur_, vol. i. (Weimar,
  1898), pp. 120-122.     (G. W. T.)


FOOTNOTES:

  [1] Summary in E. G. Browne, _A Literary History of Persia_ (London,
    1902), pp. 387 f.

  [2] The preface was translated into German by Theodor Nöldeke in his
    _Beiträge_ (Hanover, 1864), pp. 1-51.



IBN SA'D [Abu 'Abdallah Mahommed ibn Sa'd ibn Mani' uz-Zuhri, often
called Katib ul-Waqidi ("secretary of Waqidi") of Basra] (d. 845),
Arabian biographer, received his training in tradition from Waqidi and
other celebrated teachers. He lived for the most part in Bagdad, and had
the reputation of being both trustworthy and accurate in his writings,
which, in consequence, were much used by later writers. His work, the
_Kitab ul-Tabaqat ul-Kabir_ (15 vols.) contains the lives of Mahomet,
his Companions and Helpers (including those who fought at Badr as a
special class) and of the following generation (the Followers) who
received their traditions from the personal friends of the Prophet.

  This work has been edited under the superintendence of E. Sachau
  (Leiden, 1904 sqq.); cf. O. Loth, _Das Classenbuch des Ibn Sa'd_
  (Leipzig, 1869).     (G. W. T.)



IBN TIBBON, a family of Jewish translators, who flourished in Provence
in the 12th and 13th centuries. They all made original contributions to
philosophical and scientific literature, but their permanent fame is
based on their translations. Between them they rendered into Hebrew all
the chief Jewish writings of the middle ages. These Hebrew translations
were, in their turn, rendered into Latin (by Buxtorf and others) and in
this form the works of Jewish authors found their way into the learned
circles of Europe. The chief members of the Ibn Tibbon family were (1)
JUDAH BEN SAUL (1120-1190), who was born in Spain but settled in Lunel.
He translated the works of Bahya, Halevi, Saadiah and the grammatical
treatises of Janah. (2) His son, SAMUEL (1150-1230), translated the
_Guide of the Perplexed_ by Maimonides. He justly termed his father "the
father of the Translators," but Samuel's own method surpassed his
father's in lucidity and fidelity to the original. (3) Son of Samuel,
MOSES (died 1283). He translated into Hebrew a large number of Arabic
books (including the Arabic form of Euclid). The Ibn Tibbon family thus
rendered conspicuous services to European culture, and did much to
further among Jews who did not understand Arabic the study of science
and philosophy.     (I. A.)



IBN TUFAIL, or TOFAIL [Abu Bakr Mahommed ibn 'Abd-ul-Malik ibn Tufail
ul-Qaisi] (d. 1185), Moslem philosopher, was born at Guadix near
Granada. There he received a good training in philosophy and medicine,
and is said to have been a pupil of Avempace (q.v.). He became secretary
to the governor of Granada, and later physician and vizier to the Mohad
caliph, Abu Ya'qub Yusuf. He died at Morocco.

  His chief work is a philosophical romance, in which he describes the
  awakening and growth of intellect in a child removed from the
  influences of ordinary life. Its Arabic title is _Risalat Hayy ibn
  Yaqzan_; it was edited by E. Pococke as _Philosophus autodidactus_
  (Oxford, 1671; 2nd ed., 1700), and with a French translation by L.
  Gauthier (Algiers, 1900). An English translation by S. Ockley was
  published in 1708 and has been reprinted since. A Spanish translation
  by F. Pons Boigues was published at Saragossa (1900). Another work of
  Ibn Tufail, the _Kitab Asrar ul-Hikma ul-mashraqiyya_ ("Secrets of
  Eastern Science"), was published at Bulaq (1882); cf. S. Munk,
  _Mélanges_ (1859), pp. 410 sqq., and T. J. de Boer, _Geschichte der
  Philosophie im Islam_ (Stuttgart, 1901), pp. 160 sqq. (also an English
  translation).     (G. W. T.)



IBN USAIBI'A [Muwaffaquddin Abu-l-'Abbas Ahmad ibn ul-Qasim ibn Abi
Usaibi'a] (1203-1270), Arabian physician, was born at Damascus, the son
of an oculist, and studied medicine at Damascus and Cairo. In 1236 he
was appointed by Saladin physician to a new hospital in Cairo, but
surrendered the appointment the following year to take up a post given
him by the amir of Damascus in Salkhad near that city. There he lived
and died. He wrote '_Uyun ul-Anba'fi Tabaqat ul-Atibba_' or "Lives of
the Physicians," which in its first edition (1245-1246) was dedicated to
the vizier of Damascus. This he enlarged, though it is uncertain whether
the new edition was made public in the lifetime of the author.

  Edition by A. Müller (Königsberg, 1884).     (G. W. T.)



IBO, a district of British West Africa, on the lower Niger immediately
above the delta, and mainly on the eastern bank of the river. The chief
town, frequently called by the same name (more correctly Abo or Áboh),
lies on a creek which falls into the main stream about 150 m. from its
mouth and contains from 6000 to 8000 inhabitants. The Ibo are a strong
well-built Negro race. Their women are distinguished by their
embonpoint. The language of the Ibo is one of the most widely spoken on
the lower Niger. The Rev. J. F. Schön began its reduction in 1841, and
in 1861 he published a grammar (_Oku Ibo Grammatical Elements_, London,
Church Miss. Soc.). (See NIGERIA.)



IBRAHIM AL-MAUSILI (742-804), Arabian singer, was born of Persian
parents settled in Kufa. In his early years his parents died and he was
trained by an uncle. Singing, not study, attracted him, and at the age
of twenty-three he fled to Mosul, where he joined a band of wild youths.
After a year he went to Rai (Rei, Rhagae), where he met an ambassador of
the caliph Mansur, who enabled him to come to Basra and take singing
lessons. His fame as a singer spread, and the caliph Mahdi brought him
to the court. There he remained a favourite under Hadi, while Harun
al-Rashid kept him always with him until his death, when he ordered his
son (Ma'mun) to say the prayer over his corpse. Ibrahim, as might be
expected, was no strict Moslem. Two or three times he was knouted and
imprisoned for excess in wine-drinking, but was always taken into favour
again. His powers of song were far beyond anything else known at the
time. Two of his pupils, his son Ishaq and Muhariq, attained celebrity
after him.

  See the Preface to W. Ahlwardt's _Abu Nowas_ (Greifswald, 1861), pp.
  13-18, and the many stories of his life in the _Kitab ul-Aghani_, v.
  2-49.     (G. W. T.)



IBRAHIM PASHA (1789-1848), Egyptian general, is sometimes spoken of as
the adopted son of Mehemet Ali, pasha of Egypt. He is also and more
commonly called his son. He was born in his father's native town, Kavala
in Thrace. During his father's struggle to establish himself in Egypt,
Ibrahim, then sixteen years of age, was sent as a hostage to the Ottoman
capitan pasha (admiral), but when Mehemet Ali was recognized as pasha,
and had defeated the English expedition under General A. M. Fraser, he
was allowed to return to Egypt. When Mehemet Ali went to Arabia to
prosecute the war against the Wahhabis in 1813, Ibrahim was left in
command in Upper Egypt. He continued the war with the broken power of
the Mamelukes, whom he suppressed. In 1816 he succeeded his brother
Tusun in command of the Egyptian forces in Arabia. Mehemet Ali had
already begun to introduce European discipline into his army, and
Ibrahim had probably received some training, but his first campaign was
conducted more in the old Asiatic style than his later operations. The
campaign lasted two years, and terminated in the destruction of the
Wahhabis as a political power. Ibrahim landed at Yembo, the port of
Medina, on the 30th of September 1816. The holy cities had been
recovered from the Wahhabis, and Ibrahim's task was to follow them into
the desert of Nejd and destroy their fortresses. Such training as the
Egyptian troops had received, and their artillery, gave them a marked
superiority in the open field. But the difficulty of crossing the desert
to the Wahhabi stronghold of Deraiya, some 400 m. east of Medina, and
the courage of their opponents, made the conquest a very arduous one.
Ibrahim displayed great energy and tenacity, sharing all the hardships
of his army, and never allowing himself to be discouraged by failure. By
the end of September 1818 he had forced the Wahhabi leader to surrender,
and had taken Deraiya, which he ruined. On the 11th of December 1819 he
made a triumphal entry into Cairo. After his return he gave effective
support to the Frenchman, Colonel Sève (Suleiman Pasha), who was
employed to drill the army on the European model. Ibrahim set an example
by submitting to be drilled as a recruit. When in 1824 Mehemet Ali was
appointed governor of the Morea by the sultan, who desired his help
against the insurgent Greeks, he sent Ibrahim with a squadron and an
army of 17,000 men. The expedition sailed on the 10th of July 1824, but
was for some months unable to do more than come and go between Rhodes
and Crete. The fear of the Greek fire ships stopped his way to the
Morea. When the Greek sailors mutinied from want of pay, he was able to
land at Modon on the 26th of February 1825. He remained in the Morea
till the capitulation of the 1st of October 1828 was forced on him by
the intervention of the Western powers. Ibrahim's operations in the
Morea were energetic and ferocious. He easily defeated the Greeks in the
open field, and though the siege of Missolonghi proved costly to his own
troops and to the Turks who operated with him, he brought it to a
successful termination on the 24th of April 1826. The Greek guerrilla
bands harassed his army, and in revenge he desolated the country and
sent thousands of the inhabitants into slavery in Egypt. These measures
of repression aroused great indignation in Europe, and led first to the
intervention of the English, French and Russian squadrons (see NAVARINO,
BATTLE OF), and then to the landing of a French expeditionary force. By
the terms of the capitulation of the 1st of October 1828, Ibrahim
evacuated the country. It is fairly certain that the Turkish government,
jealous of his power, had laid a plot to prevent him and his troops from
returning to Egypt. English officers who saw him at Navarino describe
him as short, grossly fat and deeply marked with smallpox. His obesity
did not cause any abatement of activity when next he took the field. In
1831, his father's quarrel with the Porte having become flagrant,
Ibrahim was sent to conquer Syria. He carried out his task with truly
remarkable energy. He took Acre after a severe siege on the 27th of May
1832, occupied Damascus, defeated a Turkish army at Homs on the 8th of
July, defeated another Turkish army at Beilan on the 29th of July,
invaded Asia Minor, and finally routed the grand vizier at Konia on the
21st of December. The convention of Kutaiah on the 6th of May left Syria
for a time in the hands of Mehemet Ali. Ibrahim was undoubtedly helped
by Colonel Sève and the European officers in his army, but his
intelligent docility to their advice, as well as his personal hardihood
and energy, compare most favourably with the sloth, ignorance and
arrogant conceit of the Turkish generals opposed to him. He is entitled
to full credit for the diplomatic judgment and tact he showed in
securing the support of the inhabitants, whom he protected and whose
rivalries he utilized. After the campaign of 1832 and 1833 Ibrahim
remained as governor in Syria. He might perhaps have administered
successfully, but the exactions he was compelled to enforce by his
father soon ruined the popularity of his government and provoked
revolts. In 1838 the Porte felt strong enough to renew the struggle, and
war broke out once more. Ibrahim won his last victory for his father at
Nezib on the 24th of June 1839. But Great Britain and Austria intervened
to preserve the integrity of Turkey. Their squadrons cut his
communications by sea with Egypt, a general revolt isolated him in
Syria, and he was finally compelled to evacuate the country in February
1841. Ibrahim spent the rest of his life in peace, but his health was
ruined. In 1846 he paid a visit to western Europe, where he was received
with some respect and a great deal of curiosity. When his father became
imbecile in 1848 he held the regency till his own death on the 10th of
November 1848.

  See Edouard Gouin, _L'Égypte au XIX^e siècle_ (Paris, 1847); Aimé
  Vingtrinier, _Soliman-Pasha_ (_Colonel Sève_) (Paris, 1886). A great
  deal of unpublished material of the highest interest with regard to
  Ibrahim's personality and his system in Syria is preserved in the
  British Foreign Office archives; for references to these see
  _Cambridge Mod. Hist._ x. 852, bibliography to chap. xvii.



IBSEN, HENRIK (1828-1906), Norwegian dramatic and lyric poet, eldest son
of Knud Henriksen Ibsen, a merchant, and of his wife Marichen Cornelia
Altenburg, was born at Skien on the 20th of March 1828. For five
generations the family had consisted on the father's side of a blending
of the Danish, German and Scottish races, with no intermixture of pure
Norwegian. In 1836 Knud Ibsen became insolvent, and the family withdrew,
in great poverty, to a cottage in the outskirts of the town. After brief
schooling at Skien, Ibsen was, towards the close of 1843, apprenticed to
an apothecary in Grimstad; here he remained through seven dreary years
of drudgery, which set their mark upon his spirit. In 1847, in his
nineteenth year, he began to write poetry. He made a gloomy and almost
sinister impression upon persons who met him at this time, and one of
his associates of those days has recorded that Ibsen "walked about
Grimstad like a mystery sealed with seven seals." He had continued, by
assiduous reading, his self-education, and in 1850 he contrived to come
up as a student to Christiania. In the same year he published his first
work, the blank-verse tragedy of _Catilina_, under the pseudonym
Brynjolf Bjarme. A second drama, _The Viking's Barrow_, was acted (but
not printed) a few months later; Ibsen was at this time entirely under
the influence of the Danish poet Oehlenschläger. During the next year or
two he made a very precarious livelihood in Christiania as a journalist,
but in November 1851 he had the good fortune to be appointed
"stage-poet" at the little theatre of Bergen, with a small but regular
salary. He was practically manager at this house, and he also received a
travelling stipend. In 1852, therefore, he went for five months to study
the stage, to Copenhagen and to Dresden. Among many dramatic experiments
which Ibsen made in Bergen, the most considerable and most satisfactory
is the saga-drama of _Mistress Inger at Östraat_, which was produced in
1855; and printed at Christiania in 1857; here are already perceptible
some qualities of his mature character. Much less significant, although
at the time more successful, is _The Feast at Solhaug_, a tragedy
produced in Bergen in 1856; here for a moment Ibsen abandoned his own
nascent manner for an imitation of the popular romantic dramatist of
Denmark, Henrik Hertz. It is noticeable that Ibsen, by far the most
original of modern writers for the stage, was remarkably slow in
discovering the true bent of his genius. His next dramatic work was the
romantic tragedy of _Olaf Liljekrans_, performed in 1857, but unprinted
until 1898. This was the last play Ibsen wrote in Bergen. In the summer
of the former year his five years' appointment came to an end, and he
returned to Christiania. Almost immediately he began the composition of
a work which showed an extraordinary advance on all that he had written
before, the beautiful saga-drama of _The Warriors in Helgeland_, in
which he threw off completely the influence of the Danish romantic
tragedians, and took his material directly from the ancient Icelandic
sources. This play marks an epoch in the development of Norwegian
literature. It was received by the managers, both in Christiania and
Copenhagen, with contemptuous disapproval, and in the autumn of 1857
Ibsen could not contrive to produce it even at the new theatre of which
he was now the manager. _The Warriors_ was printed at Christiania in
1858, but was not acted anywhere until 1861. During these years Ibsen
suffered many reverses and humiliations, but he persisted in his own
line in art. Some of his finest short poems, among others the admirable
seafaring romance, _Terje Vigen_, belong to the year 1860. The
annoyances which Ibsen suffered, and the retrograde and ignorant
conditions which he felt around him in Norway, developed the ironic
qualities in his genius, and he became an acid satirist. The brilliant
rhymed drama, _Love's Comedy_, a masterpiece of lyric wit and incisive
vivacity, was published in 1862. This was a protest against the
conventionality which deadens the beauty of all the formal relations
between men and women, and against the pettiness, the publicity, and the
prosiness of betrothed and married life among the middle classes in
Norway; it showed how society murders the poetry of love. For some time
past Ibsen had been meditating another saga-drama in prose, and in 1864
this appeared, _Kongsemnerne_ (The Pretenders). These works, however,
now so universally admired, contained an element of strangeness which
was not welcome when they were new. Ibsen's position in Christiania grew
more and more disagreeable, and he had positive misfortunes which added
to his embarrassment. In 1862 his theatre became bankrupt, and he was
glad to accept the poorly-paid post of "aesthetic adviser" at the other
house. An attempt to obtain a poet's pension (_digtergage_) was
unsuccessful; the Storthing, which had just voted one to Björnson,
refused to do the same for Ibsen. His cup was full of disillusion and
bitterness, and in April 1864 he started, by Berlin and Trieste,
ultimately to settle in Rome. His anger and scorn gave point to the
satirical arrows which he shot back to his thankless fatherland from
Italy in the splendid poem of _Brand_, published in Copenhagen in 1866,
a fierce attack on the Laodicean state of religious and moral sentiment
in the Norway of that day; the central figure, the stern priest Brand,
who attempts to live like Christ and is snubbed and hounded away by his
latitudinarian companions, is one of the finest conceptions of a modern
poet. Ibsen had scarcely closed _Brand_ before he started a third
lyrico-dramatic satire. _Peer Gynt_ (1867), which remains, in a
technical sense, the most highly finished of all his metrical works. In
_Brand_ the hero had denounced certain weaknesses which Ibsen saw in the
Norwegian character, but these and other faults are personified in the
hero of _Peer Gynt_; or rather, in this figure the poet pictured, in a
type, the Norwegian nation in all the egotism, vacillation, and
lukewarmness which he believed to be characteristic of it. Ibsen,
however, acted better than he preached, and he soon forgot his
abstraction in the portrait of Peer Gynt as a human individual. In this
magnificent work modern Norwegian literature first rises to a level with
the finest European poetry of the century. In 1869 Ibsen wrote the
earliest of his prose dramas, the political comedy, _The Young Men's
League_, in which for the first time he exercised his extraordinary gift
for perfectly natural and yet pregnant dialogue. Ibsen was in Egypt, in
October 1869, when his comedy was put on the stage in Christiania, amid
violent expressions of hostility; on hearing the news, he wrote his
brilliant little poem of defiance, called _At Port Saïd_. By this time,
however, he had become a successful author; _Brand_ sold largely, and
has continued to be the most popular of Ibsen's writings. In 1866,
moreover, the Storthing had been persuaded to vote him a "poet's
pension," and there was now an end of Ibsen's long struggle with
poverty. In 1868 he left Rome, and settled in Dresden until 1874, when
he returned to Norway. But after a short visit he went back to Germany,
and lived first at Dresden, afterwards at Munich, and did not finally
settle in Christiania until 1891. His shorter lyrical poems were
collected in 1871, and in that year his name and certain of his writings
were for the first time mentioned to the English public. At this time he
was revising his old works, which were out of print, and which he would
not resign again to the reading world until he had subjected them to
what in some instances (for example, _Mistress Inger at Östraat_)
amounted to practical recomposition. In 1873 he published a double
drama, each part of which was of unusual bulk, the whole forming the
tragedy of _Emperor and Galilean_; this, Ibsen's latest historical play,
has for subject the unsuccessful struggle of Julian the Apostate to hold
the world against the rising tide of Christianity. The work is of an
experimental kind, and takes its place between the early poetry and the
later prose of the author. Compared with the series of plays which Ibsen
had already inaugurated with _The Young Men's League_, _Emperor and
Galilean_ preserves a colour of idealism and even of mysticism which was
for many years to be absent from Ibsen's writings, but to reappear in
his old age with _The Master-builder_. There is some foundation for the
charge that Ibsen has made his romantic Greek emperor needlessly
squalid, and that he has robbed him, at last, too roughly of all that
made him a sympathetic exponent of Hellenism. Ibsen was now greatly
occupied by the political spectacle of Germany at war first in Denmark,
then in France, and he believed that all things were conspiring to start
a new epoch of individualism. He was therefore deeply disgusted by the
Paris commune, and disappointed by the conservative reaction which
succeeded it. This disillusion in political matters had a very direct
influence upon Ibsen's literary work. It persuaded him that nothing
could be expected in the way of reform from democracies, from large
blind masses of men moved capriciously in any direction, but that the
sole hope for the future must lie in the study of personality, in the
development of individual character. He set himself to diagnose the
conditions of society, which he had convinced himself lay sick unto
death. Hitherto Ibsen had usually employed rhymed verse for his dramatic
compositions, or, in the case of his saga-plays, a studied and
artificial prose. Now, in spite of the surprising achievements of his
poetry, he determined to abandon versification, and to write only in the
language of everyday conversation. In the first drama of this his new
period, _The Pillars of Society_ (1877), he dealt with the problem of
hypocrisy in a small commercial centre of industry, and he drew in the
Bernick family a marvellous picture of social egotism in a prosperous
seaport town. There was a certain similarity between this piece and _A
Doll's House_ (1879), although the latter was much the more successful
in awakening curiosity. Indeed, no production of Ibsen's has been so
widely discussed as this, which is nevertheless not the most coherently
conceived of his plays. Here also, social hypocrisy, was the object of
the playwright's satire, but this time mainly in relation to marriage.
In _A Doll's House_ Ibsen first developed his views with regard to the
individualism of woman. In his previous writings he had depicted woman
as a devoted and willing sacrifice to man; here he begins to explain
that she has no less a duty to herself, and must keep alive her own
conception of honour and of responsibility. The conclusion of _A Doll's
House_ was violently and continuously discussed through the length and
breadth of Europe, and to the situation of Nora Helmer is probably due
more than to anything else the long tradition that Ibsen is "immoral."
He braved convention still more audaciously in _Ghosts_ (1881), perhaps
the most powerful of the series of plays in which Ibsen diagnoses the
diseases of modern society. It was received in Norway with a tumult of
ill-will, and the author was attacked no less venomously than he had
been twenty years before. Ibsen was astonished and indignant at the
reception given to _Ghosts_, and at the insolent indifferentism of the
majority to all ideas of social reform. He wrote, more as a pamphlet
than as a play, what is yet one of the most effective of his comedies,
_An Enemy of the People_ (1882). Dr Stockmann, the hero of that piece,
discovers that the drainage system of the bathing-station on which the
little town depends is faulty, and the water impure and dangerous. He
supposes that the corporation will be grateful to have these
deficiencies pointed out; on the contrary, they hound him out of their
midst as an "enemy of the people." In this play occurs Ibsen's famous
and typical saying, "a minority may be right--a majority is always
wrong." This polemical comedy seemed at first to be somewhat weakened by
the personal indignation which runs through it, but it has held the
stage. Ibsen's next drama, _The Wild Duck_ (1884), was written in
singular contrast with the zest and fire which had inspired _An Enemy of
the People_. Here he is squalid and pessimistic to a degree elsewhere
unparalleled in his writings; it is not quite certain that he is not
here guilty of a touch of parody of himself. The main figure of the play
is an unhealthy, unlucky enthusiast, who goes about making hopeless
mischief by exposing weak places in the sordid subterfuges of others.
This drama contains a figure, Hjálmar Ekdal, who claims the bad
pre-eminence of being the meanest scoundrel in all drama. _The Wild
Duck_ is the darkest, the least relieved, of Ibsen's studies of social
life, and his object in composing it is not obvious. With _Rosmersholm_
(1886) he rose to the height of his genius again; this is a mournful,
but neither a pessimistic nor a cynical play. The fates which hang round
the contrasted lives of Rosmer and Rebecca, the weak-willed scrupulous
man and the strong-willed unshrinking woman, the old culture and the
new, the sickly conscience and the robust one, create a splendid
dramatic antithesis. Ibsen then began to compose a series of dramas, of
a more and more symbolical and poetic character; the earliest of these
was the mystical _The Lady from the Sea_ (1888). At Christmas 1890 he
brought out _Hedda Gabler_; two years later _The Master-builder_
(_Bygmester Solnaes_), in which many critics see the highest attainment
of his genius; at the close of 1894 _Little Eyolf_; in 1896 _John
Gabriel Borkman_; and in 1900 _When We Dead Awaken_. On the occasion of
his seventieth birthday (1898) Ibsen was the recipient of the highest
honours from his own country and of congratulations and gifts from all
parts of the world. A colossal bronze statue of him was erected outside
the new National Theatre, Christiania, in September 1899. In 1901 his
health began to decline, and he was ordered by the physician to abandon
every species of mental effort. The evil advanced, and he became
unconscious of the passage of events. After lingering in this sad
condition he died, without suffering, on the 23rd of May 1906, and was
accorded a public funeral, with the highest national honours.

No recent writer belonging to the smaller countries of Europe has had so
widely spread a fame as that of Ibsen, and although the value of his
dramatic work is still contested, it has received the compliment of
vivacious discussion in every part of the world. There would, perhaps,
have been less violence in this discussion if it had been perceived that
the author does not pose as a moral teacher, but as an imaginative
investigator. He often and with much heat insisted that he was not
called upon as a poet to suggest a remedy for the diseases of society,
but to diagnose them. In this he was diametrically opposed to Tolstoi,
who admitted that he wrote his books for the healing of the nations. If
the subjects which Ibsen treats, or some of them, are open to
controversy, we are at least on firm ground in doing homage to the
splendour of his art as a playwright. He reintroduced into modern
dramatic literature something of the velocity and inevitability of Greek
tragic intrigue. It is very rarely that any technical fault can be found
with the architecture of his plots, and his dialogue is the most
lifelike that the modern stage has seen. His long apprenticeship to the
theatre was of immense service to him in this respect. In every country,
though least perhaps in England, the influence of Ibsen has been marked
in the theatrical productions of the younger school. Even in England, on
the rare occasions when his dramas are acted, they awaken great interest
among intelligent playgoers.

  The editions of Ibsen's works are numerous, but the final text is
  included in the _Samlede Vaerker_, with a bibliography by J. B.
  Halvorsen, published in Copenhagen, in 10 vols. (1898-1902). They have
  been translated into the principal European languages, and into
  Japanese. The study of Ibsen in English was begun by Mr Gosse in 1872,
  and continued by Mr William Archer, whose version of Ibsen's prose
  dramas appeared in 5 vols. (1890, 1891; new and revised edition,
  1906). Other translators have been Mr C. Herford, Mr R. A.
  Streatfield, Miss Frances Lord and Mr Adie. His _Correspondence_ was
  edited, in 2 vols., under the supervision of his son, Sigurd Ibsen, in
  1904 (Eng. trans., 1905). Critical studies on the writings and
  position of Ibsen are innumerable, and only those which were
  influential in guiding opinion, during the early part of his career,
  in the various countries, can be mentioned here: Georg Brandes
  _Ästhetiske Studier_ (Copenhagen, 1868); Les Quesnel, _Poésie
  scandinave_ (Paris 1874); Valfrid Valsenius, _Henrik Ibsen_
  (Helsingfors, 1879); Edmund Gosse, _Studies in Northern Literature_
  (London, 1879); L. Passarge, _Henrik Ibsen_ (Leipzig, 1883); G.
  Brandes, _Björnson och Ibsen_ (Stockholm, 1882); Henrik Jaeger,
  _Henrik Ibsen 1828-1888_ (Copenhagen, 1888; Eng. trans., 1890); T.
  Terwey, _Henrik Ibsen_ (Amsterdam, 1882); G. Bernard Shaw, _The
  Quintessence of Ibsen_ (London, 1892). In France Count Moritz Prozor
  carried on an ardent propaganda in favour of Ibsen from 1885, and
  Jules Lemaître's articles in his _Les Contemporains_ and _Impressions
  de théâtre_ did much to encourage discussion. W. Archer forwarded the
  cause in England from 1878 onwards. In Germany Ibsen began to be known
  in 1866, when John Grieg, P. F. Siebold and Adolf Strodtmann
  successively drew attention to his early dramas; but his real
  popularity among the Germans dates from 1880.     (E. G.)



IBYCUS, of Rhegium in Italy, Greek lyric poet, contemporary of Anacreon,
flourished in the 6th century B.C. Notwithstanding his good position at
home, he lived a wandering life, and spent a considerable time at the
court of Polycrates, tyrant of Samos. The story of his death is thus
related: While in the neighbourhood of Corinth, the poet was mortally
wounded by robbers. As he lay dying he saw a flock of cranes flying
overhead, and called upon them to avenge his death. The murderers betook
themselves to Corinth, and soon after, while sitting in the theatre, saw
the cranes hovering above. One of them, either in alarm or jest,
ejaculated, "Behold the avengers of Ibycus," and thus gave the clue to
the detection of the crime (Plutarch, _De Garrulitate_, xiv.). The
phrase, "the cranes of Ibycus," passed into a proverb among the Greeks
for the discovery of crime through divine intervention. According to
Suidas, Ibycus wrote seven books of lyrics, to some extent mythical and
heroic, but mainly erotic (Cicero, _Tusc. Disp._ iv. 33), celebrating
the charms of beautiful youths and girls. F. G. Welcker suggests that
they were sung by choruses of boys at the "beauty competitions" held at
Lesbos. Although the metre and dialect are Dorian, the poems breathe the
spirit of Aeolian melic poetry.

  The best editions of the fragments are by F. W. Schneidewin (1833) and
  Bergk, _Poëtae lyrici Graeci_.



ICA (YCA, or ECCA), a city of southern Peru and the capital of a
department of the same name, 170 m. S.S.E. of Lima, and 46 m. by rail
S.E. of Pisco; its port on the Pacific coast. Pop. (1906, official
estimate) 6000. It lies in a valley of the foothills of the Cordillera
Occidental, which is watered by the Rio de Ica, is made highly fertile
by irrigation, and is filled with vineyards and cotton fields; between
this valley and the coast is a desert. The original town was founded in
1563, 4 m. E. of its present site, but it was destroyed by the
earthquake of 1571, and again by that of 1664, after which the present
town was laid out near the ruins. In 1882 a Chilean marauding expedition
inflicted great damage to private property in the town and vicinity.
These repeated disasters give the place a partially ruined appearance,
but it has considerable commercial and industrial prosperity. It has a
large cotton factory and there are some smaller industries. Wine-making
is one of the principal industries of the valley, and much brandy,
called _pisco_, is exported from Pisco. A new industry is that of drying
the fruits for which this region is celebrated. Ica is the seat of a
national college.

The department of ICA lies between the Western Cordillera and the
Pacific coast, and extends from the department of Lima S.E. to that of
Arequipa. Pop. (1906, official estimate) 68,220; area 8721 sq. m. Ica is
in the rainless region of Peru, and the greater part of its surface is
barren. It is crossed by the rivers Pisco, Ica and Grande, whose
tributaries drain the western slope of the Cordillera, and whose valleys
are fertile and highly cultivated. The valley of the Nasca, a tributary
of the Grande, is celebrated for an extensive irrigating system
constructed by the natives before the discovery of America. The
principal products of the department are cotton, grapes, wine, spirits,
sugar and fruit. These are two good ports on the northern coast, Tambo
de Mora and Pisco, the latter being connected with the capital by a
railway across the desert, 46 m. long.



ICE (a word common to Teutonic languages; cf. Ger. _Eis_), the solid
crystalline form which water assumes when exposed to a sufficiently low
temperature. It is a colourless crystalline substance, assuming forms
belonging to the hexagonal system, and distinguished by a well-marked
habit of twinning, which occasions the beautiful "ice flowers" displayed
by hoar-frost. It is frequently precipitated as hoar-frost, snow or
hail; and in the glaciers and snows of lofty mountain systems or of
regions of high latitude it exists on a gigantic scale, being
especially characteristic of the seas and lands around the poles. In
various regions, especially in France and Italy, great quantities of ice
form in caves, which, in virtue of their depth below the earth's
surface, their height above the sea-level, or their exposure to suitable
winds, or to two or more of these conditions in combination, are
unaffected by ordinary climatic changes, so that the mean annual
temperature is sufficiently low to ensure the permanency of the ice. The
temperature at which water freezes, and also at which ice melts, is so
readily determined that it is employed as one of the standard
temperatures in the graduation of ordinary thermometer scales, this
temperature being the zero of the Centigrade and Réaumur scales, and 32°
of the Fahrenheit (see THERMOMETRY). In the act of freezing, water,
though its temperature remains unchanged, undergoes a remarkable
expansion so that ice at 0° C. is less dense than water--a fact
demonstrated by its power of floating. The sub-aqueous retention of
"ground-ice" or "anchor-ice," which forms in certain circumstances at
the bottom of streams or pools in which there are many eddies, is due to
the cohesion between it and the stones or rocks which compose the bed of
the streams or pools. As water expands on freezing, so conversely ice
contracts on melting; and the ice-cold water thus formed continues to
contract when heated until it has reached its point of maximum density,
the temperature at which this occurs being about 39° Fahr, or 4° C.
Above this point water continuously expands, and at no temperature is it
less dense than ice as is shown by the following table:--

  Density of ice at      0°C. =  .9175
     "       water at    0°C. =  .99988
     "          "        4°C. = 1.00000
     "          "       10°C. =  .99976
     "          "      100°C. =  .95866

Under the influence of heat, ice itself behaves as most solids do,
contracting when cooled, expanding when heated. According to Plücker,
the coefficient of cubical dilatation at moderately low temperatures is
0.0001585. From a series of elaborate experiments, Person deduced 0.505
as the specific heat of ice, or about half that of water.

Though no rise of temperature accompanies the melting of ice, there is
yet a definite quantity of heat absorbed, namely, about 80 calories per
gram; this is called the latent heat of fusion of water (see FUSION).
The same amount of heat is evolved when water becomes ice. That ice can
be melted by increase of pressure was first pointed out by James Thomson
in 1849. He showed that, since water expands on freezing, the laws of
thermodynamics require that its freezing-point must be lowered by
increase of pressure; and he calculated that for every additional
atmosphere of pressure the freezing-point of water was lowered by
0.0075°. This result was verified by his brother, Sir William Thomson
(Lord Kelvin), in 1850. The Thomsons and H. L. F. Helmholtz successfully
applied this behaviour of ice under pressure to the explanation of many
properties of the substance. When two blocks of ice at 0° C. are pressed
together or even simply laid in contact, they gradually unite along
their touching surfaces till they form one block. This "regelation" is
due to the increased pressure at the various points of contact causing
the ice there to melt and cool. The water so formed tends to escape,
thus relieving the pressure for an instant, refreezing and returning to
the original temperature. This succession of melting and freezing, with
their accompanying thermal effects, goes on until the two blocks are
cemented into one.

Ice forms over fresh water if the temperature of the air has been for a
sufficient time at or below the freezing-point; but not until the whole
mass of water has been cooled down to its point of maximum density, so
that the subsequent cooling of the surface can give rise to no
convection currents, is freezing possible. Sea-water, in the most
favourable circumstances, does not freeze till its temperature is
reduced to about -2° C.; and the ice, when formed, is found to have
rejected four-fifths of the salt which was originally present. In the
upper provinces of India water is made to freeze during cold clear
nights by leaving it overnight in porous vessels, or in bottles which
are enwrapped in moistened cloth. The water then freezes in virtue of
the cold produced by its own evaporation or by the drying of the
moistened wrapper. In Bengal the natives resort to a still more
elaborate forcing of the conditions. Pits are dug about 2 ft. deep and
filled three-quarters full with dry straw, on which are set flat porous
pans containing the water to be frozen. Exposed overnight to a cool dry
gentle wind from the north-west, the water evaporates at the expense of
its own heat, and the consequent cooling takes place with sufficient
rapidity to overbalance the slow influx of heat from above through the
cooled dense air or from below through the badly conducting straw.

  See WATER, and for the manufacture of ice see REFRIGERATING.



ICEBERG (from ice and _Berg_, Ger. for hill, mountain), a floating mass
of ice broken from the end of a glacier or from an ice-sheet. The word
is sometimes, but rarely, applied to the arch of an Arctic glacier
viewed from the sea. It is more commonly used to describe huge floating
masses of ice that drift from polar regions into navigable waters. They
are occasionally encountered far beyond the polar regions, rising into
beautiful forms with breakers roaring into their caves and streams of
water pouring from their pinnacles in the warmer air. When, however,
they rest in comparatively warm water, melting takes place most rapidly
at the base and they frequently overturn. Only one-ninth of the mass of
ice is seen above water. When a glacier descends to the sea, as in
Alaska, and "advances into water, the depth of which approaches its
thickness, the ends are broken off and the detached masses float away as
icebergs. Many of the bergs are overturned, or at least tilted, as they
set sail. If this does not happen at once it is likely to occur later as
the result of the wave-cutting and melting which disturb their
equilibrium" (T. C. Chamberlin and R. D. Salisbury, _Geology: Processes
and their Results_, 1905). These bergs carry a load of débris from the
glacier and gradually strew their load upon the sea floor. They do not
travel far before losing all stony and earthy débris, but glacial
material found in dredgings shows that icebergs occasionally carry their
load far from land. The structure of the iceberg varies with its origin
and is always that of the glacier or ice-sheet from which it was broken.
The breaking off of the ice-sheet from a Greenland glacier is called
locally the "calving" of the glacier. The constantly renewed material
from which the icebergs are formed is brought down by the motion of the
glacier. The ice-sheet cracks at the end, and masses break off, owing to
the upward pressure of the water upon the lighter ice which is pushed
into it. This is accomplished with considerable violence. The
disintegration of an Arctic ice-sheet is a simpler matter, as the ice is
already floating.



ICELAND (Dan. _Island_), an island in the North Atlantic Ocean,
belonging to Denmark. Its extreme northerly point is touched by the
Arctic Circle; it lies between 13° 22´ and 24° 35´ W., and between 63°
12´ and 66° 33´ N., and has an area of 40,437 sq. m. Its length is 298
m. and its breadth 194 m., the shape being a rough oval, broken at the
north-west, where a peninsula, diversified by a great number of fjords,
projects from the main portion of the island. The total length of the
coast-line is about 3730 m., of which approximately one-third belongs to
the north-western peninsula. Iceland is a plateau or tableland, built up
of volcanic rocks of older and younger formation, and pierced on all
sides by fjords and valleys. Compared with the tableland, the lowlands
have a relatively small area, namely, one-fourteenth of