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Title: Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 2 - "Ehud" to "Electroscope"
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 9, Slice 2 - "Ehud" to "Electroscope"" ***

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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) dP stands for the partial-derivative symbol, or curled 'd'.

(6) [oo] stands for the infinity symbol, and [int] for the integral
      symbol.

(7) The following typographical errors have been corrected:

    ARTICLE EKATERINOSLAV: "Nearly 40,000 persons find occupation in
      factories, the most important being iron-works and agricultural
      machinery works, though there are also tobacco ... " 'important'
      amended from 'imporant'.

    ARTICLE ELASTICITY: "The limits of perfect elasticity as regards
      change of shape, on the other hand, are very low, if they exist at
      all, for glasses and other hard, brittle solids; but a class of
      metals including copper, brass, steel, and platinum are very
      perfectly elastic as regards distortion, provided that the
      distortion is not too great." Missing 'and' after 'steel'.

    ARTICLE ELASTICITY: "The parts of the radii vectors within the
     sphere ..." 'vectors' amended from 'vectores'.

    ARTICLE ELBE: "Its total length is 725 m., of which 190 are in
      Bohemia, 77 in the kingdom of Saxony, and 350 in Prussia, the
      remaining 108 being in Hamburg and other states of Germany." 'Its'
      amended from 'it'.

    ARTICLE ELBE: "Finally, in 1870, 1,000,000 thalers were paid to
      Mecklenburg and 85,000 thalers to Anhalt, which thereupon abandoned
      all claims to levy tolls upon the Elbe shipping, and thus
      navigation on the river became at last entirely free. 'Anhalt'
      amended from 'Anhal'.

    ARTICLE ELBE: "... after driving back at Lobositz the Austrian
      forces which were hastening to their assistance; but only nine
      months later he lost his reputation for "invincibility" by his
      crushing defeat at Kolin ..." 'assistance' amended from
      'asistance'.

    ARTICLE ELECTRICITY: "De la Rive reviews the subject in his large
      Treatise on Electricity and Magnetism, vol. ii. ch. iii. The writer
      made a contribution to the discussion in 1874 ..." 'Magnetism'
      amended from 'Magnestism'.

    ARTICLE ELECTRICITY SUPPLY: "... or by means of overhead wires
      within restricted areas, but the limitations proved uneconomical
      and the installations were for the most part merged into larger
      undertakings sanctioned by parliamentary powers." 'limitations'
      amended from 'limitatons'.

    ARTICLE ELECTROKINETICS: "A vector can most conveniently be
      represented by a symbol such as a + ib, where a stands for any
      length of a units measured horizontally and b for a length b units
      measured vertically, and the symbol i is a sign of perpendicularity
      ..." 'symbol' amended from 'smybol'.

    ARTICLE ELECTROSCOPE: "The collapse of the gold-leaf is observed
      through an aperture in the case by a microscope, and the time taken
      by the gold-leaf to fall over a certain distance is proportional to
      the ionizing current, that is, to the intensity of the
      radioactivity of the substance. 'microscope' amended from
      'miscroscope'.



          ENCYCLOPAEDIA BRITANNICA

  A DICTIONARY OF ARTS, SCIENCES, LITERATURE
           AND GENERAL INFORMATION

              ELEVENTH EDITION


            VOLUME IX, SLICE II

           Ehud to Electroscope



ARTICLES IN THIS SLICE:


  EHUD                                ELBERFELD
  EIBENSTOCK                          ELBEUF
  EICHBERG, JULIUS                    ELBING
  EICHENDORFF, JOSEPH, FREIHERR VON   ELBOW
  EICHHORN, JOHANN GOTTFRIED          ELBURZ
  EICHHORN, KARL FRIEDRICH            ELCHE
  EICHSTÄTT                           ELCHINGEN
  EICHWALD, KARL EDUARD VON           ELDAD BEN MA[H.]LI
  EIDER (river of Prussia)            ELDER (ruler or officer)
  EIDER (duck)                        ELDER (shrubs and trees)
  EIFEL                               ELDON, JOHN SCOTT
  EIFFEL TOWER                        EL DORADO
  EILDON HILLS                        ELDUAYEN, JOSÉ DE
  EILENBURG                           ELEANOR OF AQUITAINE
  EINBECK                             ELEATIC SCHOOL
  EINDHOVEN                           ELECAMPANE
  EINHARD                             ELECTION (politics)
  EINHORN, DAVID                      ELECTION (English law choice)
  EINSIEDELN                          ELECTORAL COMMISSION
  EISENACH                            ELECTORS
  EISENBERG                           ELECTRA
  EISENERZ                            ELECTRICAL MACHINE
  EISLEBEN                            ELECTRIC EEL
  EISTEDDFOD                          ELECTRICITY
  EJECTMENT                           ELECTRICITY SUPPLY
  EKATERINBURG                        ELECTRIC WAVES
  EKATERINODAR                        ELECTROCHEMISTRY
  EKATERINOSLAV (Russian government)  ELECTROCUTION
  EKATERINOSLAV (Russian town)        ELECTROKINETICS
  EKHOF, KONRAD                       ELECTROLIER
  EKRON                               ELECTROLYSIS
  ELABUGA                             ELECTROMAGNETISM
  ELAM                                ELECTROMETALLURGY
  ELAND                               ELECTROMETER
  ELASTICITY                          ELECTRON
  ELATERITE                           ELECTROPHORUS
  ELATERIUM                           ELECTROPLATING
  ELBA                                ELECTROSCOPE
  ELBE



EHUD, in the Bible, a "judge" who delivered Israel from the Moabites
(Judg. iii. 12-30). He was sent from Ephraim to bear tribute to Eglon
king of Moab, who had crossed over the Jordan and seized the district
around Jericho. Being, like the Benjamites, left-handed (cf. xx. 16), he
was able to conceal a dagger and strike down the king before his
intentions were suspected. He locked Eglon in his chamber and escaped.
The men from Mt Ephraim collected under his leadership and by seizing
the fords of the Jordan were able to cut off the Moabites. He is called
the son of Gera a Benjamite, but since both Ehud and Gera are tribal
names (2 Sam. xvi. 5, 1 Chron. viii. 3, 5 sq.) it has been thought that
this notice is not genuine. The tribe of Benjamin rarely appears in the
old history of the Hebrews before the time of Saul. See further
BENJAMIN; JUDGES.



EIBENSTOCK, a town of Germany, in the kingdom of Saxony, near the Mulde,
on the borders of Bohemia, 17 m. by rail S.S.E. of Zwickau. Pop. (1905)
7460. It is a principal seat of the tambour embroidery which was
introduced in 1775 by Clara Angermann. It possesses chemical and tobacco
manufactories, and tin and iron works. It has also a large cattle
market. Eibenstock, together with Schwarzenberg, was acquired by
purchase in 1533 by Saxony and was granted municipal rights in the
following year.



EICHBERG, JULIUS (1824-1893), German musical composer, was born at
Düsseldorf on the 13th of June 1824. When he was nineteen he entered the
Brussels Conservatoire, where he took first prizes for violin-playing
and composition. For eleven years he occupied the post of professor in
the Conservatoire of Geneva. In 1857 he went to the United States,
staying two years in New York and then proceeding to Boston, where he
became director of the orchestra at the Boston Museum. In 1867 he
founded the Boston Conservatory of Music. Eichberg published several
educational works on music; and his four operettas, _The Doctor of
Alcantara_, _The Rose of Tyrol_, _The Two Cadis_ and _A Night in Rome_,
were highly popular. He died in Boston on the 18th of January 1893.



EICHENDORFF, JOSEPH, FREIHERR VON (1788-1857), German poet and
romance-writer, was born at Lubowitz, near Ratibor, in Silesia, on the
10th of March 1788. He studied law at Halle and Heidelberg from 1805 to
1808. After a visit to Paris he went to Vienna, where he resided until
1813, when he joined the Prussian army as a volunteer in the famous
Lützow corps. When peace was concluded in 1815, he left the army, and in
the following year he was appointed to a judicial office at Breslau. He
subsequently held similar offices at Danzig, Königsberg and Berlin.
Retiring from public service in 1844, he lived successively in Danzig,
Vienna, Dresden and Berlin. He died at Neisse on the 26th of November
1857. Eichendorff was one of the most distinguished of the later members
of the German romantic school. His genius was essentially lyrical. Thus
he is most successful in his shorter romances and dramas, where
constructive power is least called for. His first work, written in 1811,
was a romance, _Ahnung und Gegenwart_ (1815). This was followed at short
intervals by several others, among which the foremost place is by
general consent assigned to _Aus dem Leben eines Taugenichts_ (1826),
which has often been reprinted. Of his dramas may be mentioned _Ezzelin
von Romano_ (1828); and _Der letzte Held von Marienburg_ (1830), both
tragedies; and a comedy, _Die Freier_ (1833). He also translated several
of Calderon's religious dramas (_Geistliche Schauspiele_, 1846). It is,
however, through his lyrics (_Gedichte_, first collected 1837) that
Eichendorff is best known; he is the greatest lyric poet of the romantic
movement. No one has given more beautiful expression than he to the
poetry of a wandering life; often, again, his lyrics are exquisite word
pictures interpreting the mystic meaning of the moods of nature, as in
_Nachts_, or the old-time mystery which yet haunts the twilight forests
and feudal castles of Germany, as in the dramatic lyric _Waldesgespräch_
or _Auf einer Burg_. Their language is simple and musical, which makes
them very suitable for singing, and they have been often set, notably by
Schubert and Schumann.

In the later years of his life Eichendorff published several works on
subjects in literary history and criticism such as _Über die ethische
und religiöse Bedeutung der neuen romantischen Poesie in Deutschland_
(1847), _Der deutsche Roman des 18. Jahrhunderts in seinem Verhältniss
zum Christenthum_ (1851), and _Geschichte der poetischen Litteratur
Deutschlands_ (1856), but the value of these works is impaired by the
author's reactionary standpoint. An edition of his collected works in
six volumes, appeared at Leipzig in 1870.

  Eichendorff's _Sämtliche Werke_ appeared in 6 vols., 1864 (reprinted
  1869-1870); his _Sämtliche poetische Werke_ in 4 vols. (1883). The
  latest edition is that edited by R. von Gottschall in 4 vols. (1901).
  A good selection edited by M. Kaoch will be found in vol. 145 of
  Kürschner's _Deutsche Nationalliteratur_ (1893). Eichendorff's
  critical writings were collected in 1866 under the title _Vermischte
  Schriften_ (5 vols.). Cp. H. von Eichendorff's biographical
  introduction to the _Sämtliche Werke_; also H. Keiter, _Joseph von
  Eichendorff_ (Cologne, 1887); H.A. Krüger, _Der junge Eichendorff_
  (Oppeln, 1898).



EICHHORN, JOHANN GOTTFRIED (1752-1827), German theologian, was born at
Dörrenzimmern, in the principality of Hohenlohe-Oehringen, on the 16th
of October 1752. He was educated at the state school in Weikersheim,
where his father was superintendent, at the gymnasium at Heilbronn and
at the university of Göttingen (1770-1774), studying under J.D.
Michaelis. In 1774 he received the rectorship of the gymnasium at
Ohrdruf, in the duchy of Gotha, and in the following year was made
professor of Oriental languages at Jena. On the death of Michaelis in
1788 he was elected professor _ordinarius_ at Göttingen, where he
lectured not only on Oriental languages and on the exegesis of the Old
and New Testaments, but also on political history. His health was
shattered in 1825, but he continued his lectures until attacked by fever
on the 14th of June 1827. He died on the 27th of that month. Eichhorn
has been called "the founder of modern Old Testament criticism." He
first properly recognized its scope and problems, and began many of its
most important discussions. "My greatest trouble," he says in the
preface to the second edition of his _Einleitung_, "I had to bestow on a
hitherto unworked field--on the investigation of the inner nature of the
Old Testament with the help of the Higher Criticism (not a new name to
any humanist)." His investigations led him to the conclusion that "most
of the writings of the Hebrews have passed through several hands." He
took for granted that all the so-called supernatural facts relating to
the Old and New Testaments were explicable on natural principles. He
sought to judge them from the standpoint of the ancient world, and to
account for them by the superstitious beliefs which were then generally
in vogue. He did not perceive in the biblical books any religious ideas
of much importance for modern times; they interested him merely
historically and for the light they cast upon antiquity. He regarded
many books of the Old Testament as spurious, questioned the genuineness
of _2 Peter_ and _Jude_, denied the Pauline authorship of _Timothy_ and
_Titus_, and suggested that the canonical gospels were based upon
various translations and editions of a primary Aramaic gospel. He did
not appreciate as sufficiently as David Strauss and the Tübingen critics
the difficulties which a natural theory has to surmount, nor did he
support his conclusions by such elaborate discussions as they deemed
necessary.

  His principal works were--_Geschichte des Ostindischen Handels vor
  Mohammed_ (Gotha, 1775); _Allgemeine Bibliothek der biblischen
  Literatur_ (10 vols., Leipzig, 1787-1801); _Einleitung in das Alte
  Testament_ (3 vols., Leipzig, 1780-1783); _Einleitung in das Neue
  Testament_ (1804-1812); _Einleitung in die apokryphischen Bücher des
  Alten Testaments_ (Gött., 1795); _Commentarius in apocalypsin Joannis_
  (2 vols., Gött., 1791); _Die Hebr. Propheten_ (3 vols., Gött.,
  1816-1819); _Allgemeine Geschichte der Cultur und Literatur des neuern
  Europa_ (2 vols., Gött., 1796-1799); _Literärgeschichte_ (1st vol.,
  Gött., 1799, 2nd ed. 1813, 2nd vol. 1814); _Geschichte der Literatur
  von ihrem Anfange bis auf die neuesten Zeiten_ (5 vols., Gött.,
  1805-1812); _Übersicht der Französischen Revolution_ (2 vols., Gött.,
  1797); _Weltgeschichte_ (3rd ed., 5 vols., Gött., 1819-1820);
  _Geschichte der drei letzten Jahrhunderte_ (3rd ed., 6 vols., Hanover,
  1817-1818); _Urgeschichte des erlauchten Hauses der Welfen_ (Hanover,
  1817).

  See R.W. Mackay, _The Tübingen School and its Antecedents_ (1863), pp.
  103 ff.; Otto Pfleiderer, _Development of Theology_ (1890), p. 209;
  T.K. Cheyne, _Founders of Old Testament Criticism_ (1893), pp. 13 ff.



EICHHORN, KARL FRIEDRICH (1781-1854), German jurist, son of the
preceding, was born at Jena on the 20th of November 1781. He entered the
university of Göttingen in 1797. In 1805 he obtained the professorship
of law at Frankfort-on-Oder, holding it till 1811, when he accepted the
same chair at Berlin. On the call to arms in 1813 he became a captain of
horse, and received at the end of the war the decoration of the Iron
Cross. In 1817 he was offered the chair of law at Göttingen, and,
preferring it to the Berlin professorship, taught there with great
success till ill-health compelled him to resign in 1828. His successor
in the Berlin chair having died in 1832, he again entered on its duties,
but resigned two years afterwards. In 1832 he also received an
appointment in the ministry of foreign affairs, which, with his labours
on many state committees and his legal researches and writings, occupied
him till his death at Cologne on the 4th of July 1854. Eichhorn is
regarded as one of the principal authorities on German constitutional
law. His chief work is _Deutsche Staats- und Rechtsgeschichte_
(Göttingen, 1808-1823, 5th ed. 1843-1844). In company with Savigny and
J.F.L. Göschen he founded the _Zeitschrift für geschichtliche
Rechtswissenschaft_. He was the author besides of _Einleitung in das
deutsche Privatrecht mit Einschluss des Lehnrechts_ (Gött., 1823) and
the _Grundsätze des Kirchenrechts der Katholischen und der Evangelischen
Religionspartei in Deutschland_, 2 Bde. (ib., 1831-1833).

  See Schulte, _Karl Friedrich Eichhorn, sein Leben und Wirken_ (1884).



EICHSTÄTT, a town and episcopal see of Germany, in the kingdom of
Bavaria, in the deep and romantic valley of the Altmühl, 35 m. S. of
Nuremberg, on the railway to Ingolstadt and Munich. Pop. (1905) 7701.
The town, with its numerous spires and remains of medieval
fortifications, is very picturesque. It has an Evangelical and seven
Roman Catholic churches, among the latter the cathedral of St Wilibald
(first bishop of Eichstätt),--with the tomb of the saint and numerous
pictures and relics,--the church of St Walpurgis, sister of Wilibald,
whose remains rest in the choir, and the Capuchin church, a copy of the
Holy Sepulchre. Of its secular buildings the most noticeable are the
town hall and the Leuchtenberg palace, once the residence of the prince
bishops and later of the dukes of Leuchtenberg (now occupied by the
court of justice of the district), with beautiful grounds. The
Wilibaldsburg, built on a neighbouring hill in the 14th century by
Bishop Bertold of Hohenzollern, was long the residence of the prince
bishops of Eichstätt, and now contains an historical museum. There are
an episcopal lyceum, a clerical seminary, a classical and a modern
school, and numerous religious houses. The industries of the town
include bootmaking, brewing and the production of lithographic stones.

Eichstätt (Lat. _Aureatum_ or _Rubilocus_) was originally a Roman
station which, after the foundation of the bishopric by Boniface in 745,
developed into a considerable town, which was surrounded with walls in
908. The bishops of Eichstätt were princes of the Empire, subject to the
spiritual jurisdiction of the archbishops of Mainz, and ruled over
considerable territories in the Circle of Franconia. In 1802 the see was
secularized and incorporated in Bavaria. In 1817 it was given, with the
duchy of Leuchtenberg, as a mediatized domain under the Bavarian crown,
by the king of Bavaria to his son-in-law Eugène de Beauharnais,
ex-viceroy of Italy, henceforth styled duke of Leuchtenberg. In 1855 it
reverted to the Bavarian crown.



EICHWALD, KARL EDUARD VON (1795-1876), Russian geologist and physician,
was born at Mitau in Courland on the 4th of July 1795. He became doctor
of medicine and professor of zoology in Kazañ in 1823; four years later
professor of zoology and comparative anatomy at Vilna; in 1838 professor
of zoology, mineralogy and medicine at St Petersburg; and finally
professor of palaeontology in the institute of mines in that city. He
travelled much in the Russian empire, and was a keen observer of its
natural history and geology. He died at St Petersburg on the 10th of
November 1876. His published works include _Reise auf dem Caspischen
Meere und in den Caucasus_, 2 vols. (Stuttgart and Tübingen, 1834-1838);
_Die Urwelt Russlands_ (St Petersburg, 1840-1845); _Lethaea Rossica, ou
paléontologie de la Russie_, 3 vols. (Stuttgart, 1852-1868), with
Atlases.



EIDER, a river of Prussia, in the province of Schleswig-Holstein. It
rises to the south of Kiel, in Lake Redder, flows first north, then west
(with wide-sweeping curves), and after a course of 117 m. enters the
North Sea at Tönning. It is navigable up to Rendsburg, and is embanked
through the marshes across which it runs in its lower course. Since the
reign of Charlemagne, the Eider (originally _Ägyr Dör_--Neptune's gate)
was known as _Romani terminus imperii_ and was recognized as the
boundary of the Empire in 1027 by the emperor Conrad II., the founder of
the Salian dynasty. In the controversy arising out of the
Schleswig-Holstein Question, which culminated in the war of Austria and
Prussia against Denmark in 1864, the Eider gave its name to the "Eider
Danes," the _intransigeant_ Danish party which maintained that Schleswig
(Sonderjylland, South Jutland) was by nature and historical tradition an
integral part of Denmark. The Eider Canal (_Eider-Kanal_), which was
constructed between 1777 and 1784, leaves the Eider at the point where
the river turns to the west and enters the Bay of Kiel at Holtenau. It
was hampered by six sluices, but was used annually by some 4000 vessels,
and until its conversion in 1887-1895 into the Kaiser Wilhelm Canal
afforded the only direct connexion between the North Sea and the Baltic.



EIDER (Icelandic, _Ædur_), a large marine duck, the _Somateria
mollissima_ of ornithologists, famous for its down, which, from its
extreme lightness and elasticity, is in great request for filling
bed-coverlets. This bird generally frequents low rocky islets near the
coast, and in Iceland and Norway has long been afforded every
encouragement and protection, a fine being inflicted for killing it
during the breeding-season, or even for firing a gun near its haunts,
while artificial nesting-places are in many localities contrived for its
further accommodation. From the care thus taken of it in those countries
it has become exceedingly tame at its chief resorts, which are strictly
regarded as property, and the taking of eggs or down from them, except
by authorized persons, is severely punished by law. In appearance the
eider is somewhat clumsy, though it flies fast and dives admirably. The
female is of a dark reddish-brown colour barred with brownish-black. The
adult male in spring is conspicuous by his pied plumage of velvet-black
beneath, and white above: a patch of shining sea-green on his head is
only seen on close inspection. This plumage he is considered not to
acquire until his third year, being when young almost exactly like the
female, and it is certain that the birds which have not attained their
full dress remain in flocks by themselves without going to the
breeding-stations. The nest is generally in some convenient corner among
large stones, hollowed in the soil, and furnished with a few bits of dry
grass, seaweed or heather. By the time that the full number of eggs
(which rarely if ever exceeds five) is laid the down is added. Generally
the eggs and down are taken at intervals of a few days by the owners of
the "eider-fold," and the birds are thus kept depositing both during the
whole season; but some experience is needed to ensure the greatest
profit from each commodity. Every duck is ultimately allowed to hatch an
egg or two to keep up the stock, and the down of the last nest is
gathered after the birds have left the spot. The story of the drake's
furnishing down, after the duck's supply is exhausted is a fiction. He
never goes near the nest. The eggs have a strong flavour, but are much
relished by both Icelanders and Norwegians. In the Old World the eider
breeds in suitable localities from Spitsbergen to the Farne Islands off
the coast of Northumberland--where it is known as St Cuthbert's duck.
Its food consists of marine animals (molluscs and crustaceans), and
hence the young are not easily reared in captivity. The eider of the New
World differs somewhat, and has been described as a distinct species
(_S. dresseri_). Though much diminished in numbers by persecution, it is
still abundant on the coast of Newfoundland and thence northward. In
Greenland also eiders are very plentiful, and it is supposed that
three-fourths of the supply of down sent to Copenhagen comes from that
country. The limits of the eider's northern range are not known, but the
Arctic expedition of 1875 did not meet with it after leaving the Danish
settlements, and its place was taken by an allied species, the king-duck
(_S. spectabilis_), a very beautiful bird which sometimes appears on the
British coast. The female greatly resembles that of the eider, but the
male has a black chevron on his chin and a bright orange prominence on
his forehead, which last seems to have given the species its English
name. On the west coast of North America the eider is represented by a
species (_S. v-nigrum_) with a like chevron, but otherwise resembling
the Atlantic bird. In the same waters two other fine species are also
found (_S. fischeri_ and _S. stelleri_), one of which (the latter) also
inhabits the Arctic coast of Russia and East Finmark and has twice
reached England. The Labrador duck (_S. labradoria_), now extinct, also
belongs to this group.     (A. N.)



EIFEL, a district of Germany, in the Prussian Rhine Province, between
the Rhine, the Moselle and the frontier of the grand duchy of Luxemburg.
It is a hilly region, most elevated in the eastern part (Hohe Eifel),
where there are several points from 2000 up to 2410 ft. above sea-level.
In the west is the Schneifels or Schnee-Eifel; and the southern part,
where the most picturesque scenery and chief geological interest is
found, is called the Vorder Eifel.

The Eifel is an ancient massif of folded Devonian rocks upon the margins
of which, near Hillesheim and towards Bitburg and Trier, rest
unconformably the nearly undisturbed sandstones, marls and limestones of
the Trias. On the southern border, at Wittlich, the terrestrial deposits
of the Permian Rothliegende are also met with. The slates and sandstones
of the Lower Devonian form by far the greater part of the region; but
folded amongst these, in a series of troughs running from south-west to
north-east lie the fossiliferous limestones of the Middle Devonian, and
occasionally, as for example near Büdesheim, a few small patches of the
Upper Devonian. Upon the ancient floor of folded Devonian strata stand
numerous small volcanic cones, many of which, though long extinct, are
still very perfect in form. The precise age of the eruptions is
uncertain. The only sign of any remaining volcanic activity is the
emission in many places of carbon dioxide and of heated waters. There is
no historic or legendary record of any eruption, but nevertheless the
eruptions must have continued to a very recent geological period. The
lavas of Papenkaule are clearly posterior to the excavation of the
valley of the Kyll, and an outflow of basalt has forced the Uess to seek
a new course. The volcanic rocks occur both as tuffs and as lava-flows.
They are chiefly leucite and nepheline rocks, such as leucitite,
leucitophyre and nephelinite, but basalt and trachyte also occur. The
leucite lavas of Niedermendig contain haüyne in abundance. The most
extensive and continuous area of volcanic rocks is that surrounding the
Laacher See and extending eastwards to Neuwied and Coblenz and even
beyond the Rhine.

The numerous so-called crater-lakes or _maare_ of the Eifel present
several features of interest. They do not, as a rule, lie in true
craters at the summit of volcanic cones, but rather in hollows which
have been formed by explosions. The most remarkable group is that of
Daun, where the three depressions of Gemünd, Weinfeld and Schalkenmehren
have been hollowed out in the Lower Devonian strata. The first of these
shows no sign of either lavas or scoriae, but volcanic rocks occur on
the margins of the other two. The two largest lakes in the Eifel region,
however, are the Laacher See in the hills west of Andernach on the
Rhine, and the Pulvermaar S.E. of the Daun group, with its shores of
peculiar volcanic sand, which also appears in its waters as a black
powder (_pulver_).



EIFFEL TOWER. Erected for the exposition of 1889, the Eiffel Tower, in
the Champ de Mars, Paris, is by far the highest artificial structure in
the world, and its height of 300 metres (984 ft.) surpasses that of the
obelisk at Washington by 429 ft., and that of St Paul's cathedral by 580
ft. Its framework is composed essentially of four uprights, which rise
from the corners of a square measuring 100 metres on the side; thus the
area it covers at its base is nearly 2½ acres. These uprights are
supported on huge piers of masonry and concrete, the foundations for
which were carried down, by the aid of iron caissons and compressed air,
to a depth of about 15 metres on the side next the Seine, and about 9
metres on the other side. At first they curve upwards at an angle of
54°; then they gradually become straighter, until they unite in a single
shaft rather more than half-way up. The first platform, at a height of
57 metres, has an area of 5860 sq. yds., and is reached either by
staircases or lifts. The next, accessible by lifts only, is 115 metres
up, and has an area of 32 sq. yds; while the third, at 276, supports a
pavilion capable of holding 800 persons. Nearly 25 metres higher up
still is the lantern, with a gallery 5 metres in diameter. The work of
building this structure, which is mainly composed of iron lattice-work,
was begun on the 28th of January 1887, and the full height was reached
on the 13th of March 1889. Besides being one of the sights of Paris, to
which visitors resort in order to enjoy the extensive view that can be
had from its higher galleries on a clear day, the tower is used to some
extent for scientific and semi-scientific purposes; thus meteorological
observations are carried on. The engineer under whose direction the
tower was constructed was Alexandre Gustave Eiffel (born at Dijon on the
15th of December 1832), who had already had a wide experience in the
construction of large metal bridges, and who designed the huge sluices
for the Panama Canal, when it was under the French company.



EILDON HILLS, a group of three conical hills, of volcanic origin, in
Roxburghshire, Scotland, 1 m. S. by E. of Melrose, about equidistant
from Melrose and St Boswells stations on the North British railway. They
were once known as Eldune--the _Eldunum_ of Simeon of Durham (fl.
1130)--probably derived from the Gaelic _aill_, "rock," and _dun_,
"hill"; but the name is also said to be a corruption of the Cymric
_moeldun_, "bald hill." The northern peak is 1327 ft. high, the central
1385 ft. and the southern 1216 ft. Whether or not the Roman station of
_Trimontium_ was situated here is matter of controversy. According to
General William Roy (1726-1790) Trimontium--so called, according to this
theory, from the triple Eildon heights--was Old Melrose; other
authorities incline to place the station on the northern shore of the
Solway Firth. The Eildons have been the subject of much legendary lore.
Michael Scot (1175-1234), acting as a confederate of the Evil One (so
the fable runs) cleft Eildon Hill, then a single cone, into the three
existing peaks. Another legend states that Arthur and his knights sleep
in a vault beneath the Eildons. A third legend centres in Thomas of
Erceldoune. The Eildon Tree Stone, a large moss-covered boulder, lying
on the high road as it bends towards the west within 2 m. of Melrose,
marks the spot where the Fairy Queen led him into her realms in the
heart of the hills. Other places associated with this legend may still
be identified. Huntly Banks, where "true Thomas" lay and watched the
queen's approach, is half a mile west of the Eildon Tree Stone, and on
the west side of the hills is Bogle Burn, a streamlet that feeds the
Tweed and probably derives its name from his ghostly visitor. Here, too,
is Rhymer's glen, although the name was invented by Sir Walter Scott,
who added the dell to his Abbotsford estate. Bowden, to the south of the
hills, was the birthplace of the poets Thomas Aird (1802-1876) and James
Thomson, and its parish church contains the burial-place of the dukes of
Roxburghe. Eildon Hall is a seat of the duke of Buccleuch.



EILENBURG, a town of Germany, in the Prussian province of Saxony, on an
island formed by the Mulde, 31 m. E. from Halle, at the junction of the
railways Halle-Cottbus and Leipzig-Eilenburg. Pop. (1905) 15,145. There
are three churches, two Evangelical and one Roman Catholic. The
industries of the town include the manufacture of chemicals, cloth,
quilting, calico, cigars and agricultural implements, bleaching, dyeing,
basket-making, carriage-building and trade in cattle. In the
neighbourhood is the iron foundry of Erwinhof. Opposite the town, on the
steep left bank of the Mulde, is the castle from which it derives its
name, the original seat of the noble family of Eulenburg. This castle
(Ilburg) is mentioned in records of the reigns of Henry the Fowler as an
important outpost against the Sorbs and Wends. The town itself,
originally called Mildenau, is of great antiquity. It is first mentioned
as a town in 981, when it belonged to the house of Wettin and was the
chief town of the East Mark. In 1386 it was incorporated in the
margraviate of Meissen. In 1815 it passed to Prussia.

  See Gundermann, _Chronik der Stadt Eilenburg_ (Eilenburg, 1879).



EINBECK, or EIMBECK, a town of Germany, in the Prussian province of
Hanover, on the Ilm, 50 m. by rail S. of Hanover. Pop. (1905) 8709. It
is an old-fashioned town with many quaint wooden houses, notable among
them the "Northeimhaus," a beautiful specimen of medieval architecture.
There are several churches, among them the Alexanderkirche, containing
the tombs of the princes of Grubenhagen, and a synagogue. The schools
include a _Realgymnasium_ (i.e. predominantly for "modern" subjects),
technical schools for the advanced study of machine-making, for weaving
and for the textile industries, a preparatory training-college and a
police school. The industries include brewing, weaving and the
manufacture of cloth, carpets, tobacco, sugar, leather-grease, toys and
roofing-felt.

Einbeck grew up originally round the monastery of St Alexander (founded
1080), famous for its relic of the True Blood. It is first recorded as a
town in 1274, and in the 14th century was the seat of the princes of
Grubenhagen, a branch of the ducal house of Brunswick. The town
subsequently joined the Hanseatic League. In the 15th century it became
famous for its beer ("Eimbecker," whence the familiar "Bock"). In 1540
the Reformation was introduced by Duke Philip of
Brunswick-Saltzderhelden (d. 1551), with the death of whose son Philip
II. (1596) the Grubenhagen line became extinct. In 1626, during the
Thirty Years' War, Einbeck was taken by Pappenheim and in October 1641
by Piccolomini. In 1643 it was evacuated by the Imperialists. In 1761
its walls were razed by the French.

  See H.L. Harland, _Gesch. der Stadt Einbeck_, 2 Bde. (Einbeck,
  1854-1859; abridgment, ib. 1881).



EINDHOVEN, a town in the province of North Brabant, Holland, and a
railway junction 8 m. by rail W. by S. of Helmond. Pop. (1900) 4730.
Like Tilburg and Helmond it has developed in modern times into a
flourishing industrial centre, having linen, woollen, cotton, tobacco
and cigar, matches, &c., factories and several breweries.



EINHARD (c. 770-840), the friend and biographer of Charlemagne; he is
also called Einhartus, Ainhardus or Heinhardus, in some of the early
manuscripts. About the 10th century the name was altered into Agenardus,
and then to Eginhardus, or Eginhartus, but, although these variations
were largely used in the English and French languages, the form
Einhardus, or Einhartus, is unquestionably the right one.

According to the statement of Walafrid Strabo, Einhard was born in the
district which is watered by the river Main, and his birth has been
fixed at about 770. His parents were of noble birth, and were probably
named Einhart and Engilfrit; and their son was educated in the monastery
of Fulda, where he was certainly residing in 788 and in 791. Owing to
his intelligence and ability he was transferred, not later than 796,
from Fulda to the palace of Charlemagne by abbot Baugulf; and he soon
became very intimate with the king and his family, and undertook various
important duties, one writer calling him _domesticus palatii regalis_.
He was a member of the group of scholars who gathered around Charlemagne
and was entrusted with the charge of the public buildings, receiving,
according to a fashion then prevalent, the scriptural name of Bezaleel
(Exodus xxxi. 2 and xxxv. 30-35) owing to his artistic skill. It has
been supposed that he was responsible for the erection of the basilica
at Aix-la-Chapelle, where he resided with the emperor, and the other
buildings mentioned in chapter xvii. of his _Vita Karoli Magni_, but
there is no express statement to this effect. In 806 Charlemagne sent
him to Rome to obtain the signature of Pope Leo III. to a will which he
had made concerning the division of his empire; and it was possibly
owing to Einhard's influence that in 813, after the death of his two
elder sons, the emperor made his remaining son, Louis, a partner with
himself in the imperial dignity. When Louis became sole emperor in 814
he retained his father's minister in his former position; then in 817
made him tutor to his son, Lothair, afterwards the emperor Lothair I.;
and showed him many other marks of favour. Einhard married Emma, or
Imma, a sister of Bernharius, bishop of Worms, and a tradition of the
12th century represented this lady as a daughter of Charlemagne, and
invented a romantic story with regard to the courtship which deserves to
be noticed as it frequently appears in literature. Einhard is said to
have visited the emperor's daughter regularly and secretly, and on one
occasion a fall of snow made it impossible for him to walk away without
leaving footprints, which would lead to his detection. This risk,
however, was obviated by the foresight of Emma, who carried her lover
across the courtyard of the palace; a scene which was witnessed by
Charlemagne, who next morning narrated the occurrence to his
counsellors, and asked for their advice. Very severe punishments were
suggested for the clandestine lover, but the emperor rewarded the
devotion of the pair by consenting to their marriage. This story is, of
course, improbable, and is further discredited by the fact that Einhard
does not mention Emma among the number of Charlemagne's children.
Moreover, a similar story has been told of a daughter of the emperor
Henry III. It is uncertain whether Einhard had any children. He
addressed a letter to a person named Vussin, whom he calls _fili_ and
_mi nate_, but, as Vussin is not mentioned in documents in which his
interests as Einhard's son would have been concerned, it is possible
that he was only a young man in whom he took a special interest. In
January 815 the emperor Louis I. bestowed on Einhard and his wife the
domains of Michelstadt and Mulinheim in the Odenwald, and in the charter
conveying these lands he is called simply Einhardus, but, in a document
dated the 2nd of June of the same year, he is referred to as abbot.
After this time he is mentioned as head of several monasteries: St
Peter, Mount Blandin and St Bavon at Ghent, St Servais at Maastricht, St
Cloud near Paris, and Fontenelle near Rouen, and he also had charge of
the church of St John the Baptist at Pavia.

During the quarrels which took place between Louis I. and his sons, in
consequence of the emperor's second marriage, Einhard's efforts were
directed to making peace, but after a time he grew tired of the troubles
and intrigues of court life. In 818 he had given his estate at
Michelstadt to the abbey of Lorsch, but he retained Mulinheim, where
about 827 he founded an abbey and erected a church, to which he
transported some relics of St Peter and St Marcellinus, which he had
procured from Rome. To Mulinheim, which was afterwards called
Seligenstadt, he finally retired in 830. His wife, who had been his
constant helper, and whom he had not put away on becoming an abbot, died
in 836, and after receiving a visit from the emperor, Einhard died on
the 14th of March 840. He was buried at Seligenstadt, and his epitaph
was written by Hrabanus Maurus. Einhard was a man of very short
stature, a feature on which Alcuin wrote an epigram. Consequently he was
called _Nardulus_, a diminutive form of Einhardus, and his great
industry and activity caused him to be likened to an ant. He was also a
man of learning and culture. Reaping the benefits of the revival of
learning brought about by Charlemagne, he was on intimate terms with
Alcuin, was well versed in Latin literature, and knew some Greek. His
most famous work is his _Vita Karoli Magni_, to which a prologue was
added by Walafrid Strabo. Written in imitation of the _De vitis
Caesarum_ of Suetonius, this is the best contemporary account of the
life of Charlemagne, and could only have been written by one who was
very intimate with the emperor and his court. It is, moreover, a work of
some artistic merit, although not free from inaccuracies. It was written
before 821, and having been very popular during the middle ages, was
first printed at Cologne in 1521. G.H. Pertz collated more than sixty
manuscripts for his edition of 1829, and others have since come to
light. Other works by Einhard are: _Epistolae_, which are of
considerable importance for the history of the times; _Historia
translationis beatorum Christi martyrum Marcellini et Petri_, which
gives a curious account of how the bones of these martyrs were stolen
and conveyed to Seligenstadt, and what miracles they wrought; and _De
adoranda cruce_, a treatise which has only recently come to light, and
which has been published by E. Dümmler in the _Neues Archiv der
Gesellschaft für ältere deutsche Geschichtskunde_, Band xi. (Hanover,
1886). It has been asserted that Einhard was the author of some of the
Frankish annals, and especially of part of the annals of Lorsch
(_Annales Laurissenses majores_), and part of the annals of Fulda
(_Annales Fuldenses_). Much discussion has taken place on this question,
and several of the most eminent of German historians, Ranke among them,
have taken part therein, but no certain decision has been reached.

  The literature on Einhard is very extensive, as nearly all those who
  deal with Charlemagne, early German and early French literature, treat
  of him. Editions of his works are by A. Teulet, _Einhardi omnia quae
  extant opera_ (Paris, 1840-1843), with a French translation; P. Jaffé,
  in the _Bibliotheca rerum Germanicarum_, Band iv. (Berlin, 1867); G.H.
  Pertz in the _Monumenta Germaniae historica_, Bände i. and ii.
  (Hanover, 1826-1829), and J.P. Migne in the _Patrologia Latina_, tomes
  97 and 104 (Paris, 1866). The _Vita Karoli Magni_, edited by G.H.
  Pertz and G. Waitz, has been published separately (Hanover, 1880).
  Among the various translations of the _Vita_ may be mentioned an
  English one by W. Glaister (London, 1877) and a German one by O. Abel
  (Leipzig, 1893). For a complete bibliography of Einhard, see A.
  Potthast, _Bibliotheca historica_, pp. 394-397 (Berlin, 1896), and W.
  Wattenbach, _Deutschlands Geschichtsquellen_, Band i. (Berlin, 1904).
       (A. W. H.*)



EINHORN, DAVID (1809-1879), leader of the Jewish reform movement in the
United States of America, was born in Bavaria. He was a supporter of the
principles of Abraham Geiger (q.v.), and while still in Germany
advocated the introduction of prayers in the vernacular, the exclusion
of nationalistic hopes from the synagogue service, and other ritual
modifications. In 1855 he migrated to America, where he became the
acknowledged leader of reform, and laid the foundation of the régime
under which the mass of American Jews (excepting the newly arrived
Russians) now worship. In 1858 he published his revised prayer book,
which has formed the model for all subsequent revisions. In 1861 he
strongly supported the anti-slavery party, and was forced to leave
Baltimore where he then ministered. He continued his work first in
Philadelphia and later in New York.     (I. A.)



EINSIEDELN, the most populous town in the Swiss canton of Schwyz. It is
built on the right bank of the Alpbach (an affluent of the Sihl), at a
height of 2908 ft. above the sea-level on a rather bare moorland, and by
rail is 25 m. S.E. of Zürich, or by a round-about railway route about 38
m. north of Schwyz, with which it communicates directly over the Hacken
Pass (4649 ft.) or the Holzegg Pass (4616 ft.). In 1900 the population
was 8496, all (save 75) Romanists and all (save 111) German-speaking.
The town is entirely dependent on the great Benedictine abbey that rises
slightly above it to the east. Close to its present site Meinrad, a
hermit, was murdered in 861 by two robbers, whose crime was made known
by Meinrad's two pet ravens. Early in the 10th century Benno, a hermit,
rebuilt the holy man's cell, but the abbey proper was not founded till
about 934, the church having been consecrated (it is said by Christ
Himself) in 948. In 1274 the dignity of a prince of the Holy Roman
Empire was confirmed by the emperor to the reigning abbot. Originally
under the protection of the counts of Rapperswil (to which town on the
lake of Zürich the old pilgrims' way still leads over the Etzel Pass,
3146 ft., with its chapel and inn), this position passed by marriage
with their heiress in 1295 to the Laufenburg or cadet line of the
Habsburgs, but from 1386 was permanently occupied by Schwyz. A black
wooden image of the Virgin and the fame of St Meinrad caused the throngs
of pilgrims to resort to Einsiedeln in the middle ages, and even now it
is much frequented, particularly about the 14th of September. The
existing buildings date from the 18th century only, while the treasury
and the library still contain many precious objects, despite the sack by
the French in 1798. There are now about 100 fully professed monks, who
direct several educational institutions. The Black Virgin has a special
chapel in the stately church. Zwingli was the parish priest of
Einsiedeln 1516-1518 (before he became a Protestant), while near the
town Paracelsus (1493-1541), the celebrated philosopher, was born.

  See Father O. Ringholz, _Geschichte d. fürstl. Benediktinerstiftes
  Einsiedeln_, vol. i. (to 1526), (Einsiedeln, 1904).     (W. A. B. C.)



EISENACH, a town of Germany, second capital of the grand-duchy of
Saxe-Weimar-Eisenach, lies at the north-west foot of the Thuringian
forest, at the confluence of the Nesse and Hörsel, 32 m. by rail W. from
Erfurt. Pop. (1905) 35,123. The town mainly consists of a long street,
running from east to west. Off this are the market square, containing
the grand-ducal palace, built in 1742, where the duchess Hélène of
Orleans long resided, the town-hall, and the late Gothic St
Georgenkirche; and the square on which stands the Nikolaikirche, a fine
Romanesque building, built about 1150 and restored in 1887. Noteworthy
are also the Klemda, a small castle dating from 1260; the Lutherhaus, in
which the reformer stayed with the Cotta family in 1498; the house in
which Sebastian Bach was born, and that (now a museum) in which Fritz
Reuter lived (1863-1874). There are monuments to the two former in the
town, while the resting-place of the latter in the cemetery is marked by
a less pretentious memorial. Eisenach has a school of forestry, a school
of design, a classical school (_Gymnasium_) and modern school
(_Realgymnasium_), a deaf and dumb school, a teachers' seminary, a
theatre and a Wagner museum. The most important industries of the town
are worsted-spinning, carriage and wagon building, and the making of
colours and pottery. Among others are the manufacture of cigars, cement
pipes, iron-ware and machines, alabaster ware, shoes, leather, &c.,
cabinet-making, brewing, granite quarrying and working, tile-making, and
saw- and corn-milling.

The natural beauty of its surroundings and the extensive forests of the
district have of late years attracted many summer residents.
Magnificently situated on a precipitous hill, 600 ft. above the town to
the south, is the historic Wartburg (q.v.), the ancient castle of the
landgraves of Thuringia, famous as the scene of the contest of
Minnesingers immortalized in Wagner's Tannhäuser, and as the place where
Luther, on his return from the diet of Worms in 1521, was kept in hiding
and made his translation of the Bible. On a high rock adjacent to the
Wartburg are the ruins of the castle of Mädelstein.

Eisenach (_Isenacum_) was founded in 1070 by Louis II. the Springer,
landgrave of Thuringia, and its history during the middle ages was
closely bound up with that of the Wartburg, the seat of the landgraves.
The Klemda, mentioned above, was built by Sophia (d. 1284), daughter of
the landgrave Louis IV., and wife of Duke Henry II. of Brabant, to
defend the town against Henry III., margrave of Meissen, during the
succession contest that followed the extinction of the male line of the
Thuringian landgraves in 1247. The principality of Eisenach fell to the
Saxon house of Wettin in 1440, and in the partition of 1485 formed part
of the territories given to the Ernestine line. It was a separate Saxon
duchy from 1596 to 1638, from 1640 to 1644, and again from 1662 to
1741, when it finally fell to Saxe-Weimar. The town of Eisenach, by
reason of its associations, has been a favourite centre for the
religious propaganda of Evangelical Germany, and since 1852 it has been
the scene of the annual conference of the German Evangelical Church,
known as the Eisenach conference.

  See Trinius, _Eisenach und Umgebung_ (Minden, 1900); and H.A. Daniel,
  _Deutschland_ (Leipzig, 1895), and further references in U. Chevalier,
  "Répertoire des sources," &c., _Topo-bibliogr._ (Montbéliard,
  1894-1899), s.v.



EISENBERG (_Isenberg_), a town of Germany, in the duchy of
Saxe-Altenburg, on a plateau between the rivers Saale and Elster, 20 m.
S.W. from Zeitz, and connected with the railway Leipzig-Gera by a branch
to Crossen. Pop. (1905) 8824. It possesses an old castle, several
churches and monuments to Duke Christian of Saxe-Eisenberg (d. 1707),
Bismarck, and the philosopher Karl Christian Friedrich Krause (q.v.).
Its principal industries are weaving, and the manufacture of machines,
ovens, furniture, pianos, porcelain and sausages.

  See Back, _Chronik der Sladt und des Amtes Eisenberg_ (Eisenb., 1843).



EISENERZ ("Iron ore"), a market-place and old mining town in Styria,
Austria, 68 m. N.W. of Graz by rail. Pop. (1900) 6494. It is situated in
a deep valley, dominated on the east by the Pfaffenstein (6140 ft.), on
the west by the Kaiserschild (6830 ft.), and on the south by the Erzberg
(5030 ft.). It has an interesting example of a medieval fortified
church, a Gothic edifice founded by Rudolph of Habsburg in the 13th
century and rebuilt in the 16th. The Erzberg or Ore Mountain furnishes
such rich ore that it is quarried in the open air like stone, in the
summer months. There is documentary evidence of the mines having been
worked as far back as the 12th century. They afford employment to two or
three thousand hands in summer and about half as many in winter, and
yield some 800,000 tons of iron per annum. Eisenerz is connected with
the mines by the Erzberg railway, a bold piece of engineering work, 14
m. long, constructed on the Abt's rack-and-pinion system. It passes
through some beautiful scenery, and descends to Vordernberg (pop. 3111),
an important centre of the iron trade situated on the south side of the
Erzberg. Eisenerz possesses, in addition, twenty-five furnaces, which
produce iron, and particularly steel, of exceptional excellence. A few
miles to the N.W. of Eisenerz lies the castle of Leopoldstein, and near
it the beautiful Leopoldsteiner Lake. This lake, with its dark-green
water, situated at an altitude of 2028 ft., and surrounded on all sides
by high peaks, is not big, but is very deep, having a depth of 520 ft.



EISLEBEN (Lat. _Islebia_), a town of Germany, in the Prussian province
of Saxony, 24 m. W. by N. from Halle, on the railway to Nordhausen and
Cassel. Pop. (1905) 23,898. It is divided into an old and a new town
(Altstadt and Neustadt). Among its principal buildings are the church of
St Andrew (Andreaskirche), which contains numerous monuments of the
counts of Mansfeld; the church of St Peter and St Paul
(Peter-Paulkirche), containing the font in which Luther was baptized;
the royal gymnasium (classical school), founded by Luther shortly before
his death in 1546; and the hospital. Eisleben is celebrated as the place
where Luther was born and died. The house in which he was born was
burned in 1689, but was rebuilt in 1693 as a free school for orphans.
This school fell into decay under the régime of the kingdom of
Westphalia, but was restored in 1817 by King Frederick William III. of
Prussia, who, in 1819, transferred it to a new building behind the old
house. The house in which Luther died was restored towards the end of
the 19th century, and his death chamber is still preserved. A bronze
statue of Luther by Rudolf Siemering (1835-1905) was unveiled in 1883.
Eisleben has long been the centre of an important mining district
(Luther was a miner's son), the principal products being silver and
copper. It possesses smelting works and a school of mining.

The earliest record of Eisleben is dated 974. In 1045, at which time it
belonged to the counts of Mansfeld, it received the right to hold
markets, coin money, and levy tolls. From 1531 to 1710 it was the seat
of the cadet line of the counts of Mansfeld-Eisleben. After the
extinction of the main line of the counts of Mansfeld, Eisleben fell to
Saxony, and, in the partition of Saxony by the congress of Vienna in
1815, was assigned to Prussia.

  See G. Grössler, _Urkundliche Gesch. Eislebens bis zum Ende des 12.
  Jahrhunderts_ (Halle, 1875); _Chronicon Islebiense; Eisleben
  Stadtchronik aus den Jahren_ 1520-1738, edited from the original, with
  notes by Grössler and Sommer (Eisleben, 1882).



EISTEDDFOD (plural Eisteddfodau), the national bardic congress of Wales,
the objects of which are to encourage bardism and music and the general
literature of the Welsh, to maintain the Welsh language and customs of
the country, and to foster and cultivate a patriotic spirit amongst the
people. This institution, so peculiar to Wales, is of very ancient
origin.[1] The term _Eisteddfod_, however, which means "a session" or
"sitting," was probably not applied to bardic congresses before the 12th
century.

The Eisteddfod in its present character appears to have originated in
the time of Owain ap Maxen Wledig, who at the close of the 4th century
was elected to the chief sovereignty of the Britons on the departure of
the Romans. It was at this time, or soon afterwards, that the laws and
usages of the Gorsedd were codified and remodelled, and its motto of "Y
gwir yn erbyn y byd" (The truth against the world) given to it. "Chairs"
(with which the Eisteddfod as a national institution is now inseparably
connected) were also established, or rather perhaps resuscitated, about
the same time. The chair was a kind of convention where disciples were
trained, and bardic matters discussed preparatory to the great Gorsedd,
each chair having a distinctive motto. There are now existing four
chairs in Wales,--namely, the "royal" chair of Powys, whose motto is "A
laddo a leddir" (He that slayeth shall be slain); that of Gwent and
Glamorgan, whose motto is "Duw a phob daioni" (God and all goodness);
that of Dyfed, whose motto is "Calon wrth galon" (Heart with heart); and
that of Gwynedd, or North Wales, whose motto is "Iesu," or "O Iesu! na'd
gamwaith" (Jesus, or Oh Jesus! suffer not iniquity).

The first Eisteddfod of which any account seems to have descended to us
was one held on the banks of the Conway in the 6th century, under the
auspices of Maelgwn Gwynedd, prince of North Wales. Maelgwn on this
occasion, in order to prove the superiority of vocal song over
instrumental music, is recorded to have offered a reward to such bards
and minstrels as should swim over the Conway. There were several
competitors, but on their arrival on the opposite shore the harpers
found themselves unable to play owing to the injury their harps had
sustained from the water, while the bards were in as good tune as ever.
King Cadwaladr also presided at an Eisteddfod about the middle of the
7th century.

Griffith ap Cynan, prince of North Wales, who had been born in Ireland,
brought with him from that country many Irish musicians, who greatly
improved the music of Wales. During his long reign of 56 years he
offered great encouragement to bards, harpers and minstrels, and framed
a code of laws for their better regulation. He held an Eisteddfod about
the beginning of the 12th century at Caerwys in Flintshire, "to which
there repaired all the musicians of Wales, and some also from England
and Scotland." For many years afterwards the Eisteddfod appears to have
been held triennially, and to have enforced the rigid observance of the
enactments of Griffith ap Cynan. The places at which it was generally
held were Aberffraw, formerly the royal seat of the princes of North
Wales; Dynevor, the royal castle of the princes of South Wales; and
Mathrafal, the royal palace of the princes of Powys: and in later times
Caerwys in Flintshire received that honourable distinction, it having
been the princely residence of Llewelyn the Last. Some of these
Eisteddfodau were conducted in a style of great magnificence, under the
patronage of the native princes. At Christmas 1107 Cadwgan, the son of
Bleddyn ap Cynfyn, prince of Powys, held an Eisteddfod in Cardigan
Castle, to which he invited the bards, harpers and minstrels, "the best
to be found in all Wales"; and "he gave them chairs and subjects of
emulation according to the custom of the feasts of King Arthur." In 1176
Rhys ab Gruffydd, prince of South Wales, held an Eisteddfod in the same
castle on a scale of still greater magnificence, it having been
proclaimed, we are told, a year before it took place, "over Wales,
England, Scotland, Ireland and many other countries."

On the annexation of Wales to England, Edward I. deemed it politic to
sanction the bardic Eisteddfod by his famous statute of Rhuddlan. In the
reign of Edward III. Ifor Hael, a South Wales chieftain, held one at his
mansion. Another was held in 1451, with the permission of the king, by
Griffith ab Nicholas at Carmarthen, in princely style, where Dafydd ab
Edmund, an eminent poet, signalized himself by his wonderful powers of
versification in the Welsh metres, and whence "he carried home on his
shoulders the silver chair" which he had fairly won. Several
Eisteddfodau, were held, one at least by royal mandate, in the reign of
Henry VII. In 1523 one was held at Caerwys before the chamberlain of
North Wales and others, by virtue of a commission issued by Henry VIII.
In the course of time, through relaxation of bardic discipline, the
profession was assumed by unqualified persons, to the great detriment of
the regular bards. Accordingly in 1567 Queen Elizabeth issued a
commission for holding an Eisteddfod at Caerwys in the following year,
which was duly held, when degrees were conferred on 55 candidates,
including 20 harpers. From the terms of the royal proclamation we find
that it was then customary to bestow "a silver harp" on the chief of the
faculty of musicians, as it had been usual to reward the chief bard with
"a silver chair." This was the last Eisteddfod appointed by royal
commission, but several others of some importance were held during the
16th and 17th centuries, under the patronage of the earl of Pembroke,
Sir Richard Neville, and other influential persons. Amongst these the
last of any particular note was one held in Bewper Castle, Glamorgan, by
Sir Richard Basset in 1681.

During the succeeding 130 years Welsh nationality was at its lowest ebb,
and no general Eisteddfod on a large scale appears to have been held
until 1819, though several small ones were held under the auspices of
the Gwyneddigion Society, established in 1771,--the most important being
those at Corwen (1789), St Asaph (1790) and Caerwys (1798).

At the close of the Napoleonic wars, however, there was a general
revival of Welsh nationality, and numerous Welsh literary societies were
established throughout Wales, and in the principal English towns. A
large Eisteddfod was held under distinguished patronage at Carmarthen in
1819, and from that time to the present they have been held (together
with numerous local Eisteddfodau), almost without intermission,
annually. The Eisteddfod at Llangollen in 1858 is memorable for its
archaic character, and the attempts then made to revive the ancient
ceremonies, and restore the ancient vestments of druids, bards and
ovates.

To constitute a provincial Eisteddfod it is necessary that it should be
proclaimed by a graduated bard of a Gorsedd a year and a day before it
takes place. A local one may be held without such a proclamation. A
provincial Eisteddfod generally lasts three, sometimes four days. A
president and a conductor are appointed for each day. The proceedings
commence with a Gorsedd meeting, opened with sound of trumpet and other
ceremonies, at which candidates come forward and receive bardic degrees
after satisfying the presiding bard as to their fitness. At the
subsequent meetings the president gives a brief address; the bards
follow with poetical addresses; adjudications are made, and prizes and
medals with suitable devices are given to the successful competitors for
poetical, musical and prose compositions, for the best choral and solo
singing, and singing with the harp or "Pennillion singing"[2] as it is
called, for the best playing on the harp or stringed or wind
instruments, as well as occasionally for the best specimens of
handicraft and art. In the evening of each day a concert is given,
generally attended by very large numbers. The great day of the
Eisteddfod is the "chair" day--usually the third or last day--the grand
event of the Eisteddfod being the adjudication on the chair subject, and
the chairing and investiture of the fortunate winner. This is the
highest object of a Welsh bard's ambition. The ceremony is an imposing
one, and is performed with sound of trumpet. (See also the articles
BARD, CELT: _Celtic Literature_, and WALES.)     (R. W.*)


FOOTNOTE:

  [1] According to the Welsh Triads and other historical records, the
    _Gorsedd_ or assembly (an essential part of the modern Eisteddfod,
    from which indeed the latter sprung) is as old at least as the time
    of Prydain the son of Ædd the Great, who lived many centuries before
    the Christian era. Upon the destruction of the political ascendancy
    of the Druids, the Gorsedd lost its political importance, though it
    seems to have long afterwards retained its institutional character as
    the medium for preserving the laws, doctrines and traditions of
    bardism.

  [2] According to Jones's _Bardic Remains_, "To sing 'Pennillion' with
    a Welsh harp is not so easily accomplished as may be imagined. The
    singer is obliged to follow the harper, who may change the tune, or
    perform variations _ad libitum_, whilst the vocalist must keep time,
    and end precisely with the strain. The singer does not commence with
    the harper, but takes the strain up at the second, third or fourth
    bar, as best suits the 'pennill' he intends to sing.... Those are
    considered the best singers who can adapt stanzas of various metres
    to one melody, and who are acquainted with the twenty-four measures
    according to the bardic laws and rules of composition."



EJECTMENT (Lat. e, out, and _jacere_, to throw), in English law, an
action for the recovery of the possession of land, together with damages
for the wrongful withholding thereof. In the old classifications of
actions, as real or personal, this was known as a mixed action, because
its object was twofold, viz. to recover both the realty and personal
damages. It should be noted that the term "ejectment" applies in law to
distinct classes of proceedings--ejectments as between rival claimants
to land, and ejectments as between those who hold, or have held, the
relation of landlord and tenant. Under the Rules of the Supreme Court,
actions in England for the recovery of land are commenced and proceed in
the same manner as ordinary actions. But the historical interest
attaching to the action of ejectment is so great as to render some
account of it necessary.

The form of the action as it prevailed in the English courts down to the
Common Law Procedure Act 1852 was a series of fictions, among the most
remarkable to be found in the entire body of English law. A, the person
claiming title to land, delivered to B, the person in possession, a
declaration in ejectment in which C and D, fictitious persons, were
plaintiff and defendant. C stated that A had devised the land to him for
a term of years, and that he had been ousted by D. A notice signed by D
informed B of the proceedings, and advised him to apply to be made
defendant in D's place, as he, D, having no title, did not intend to
defend the suit. If B did not so apply, judgment was given against D,
and possession of the lands was given to A. But if B did apply, the
Court allowed him to defend the action only on condition that he
admitted the three fictitious averments--the lease, the entry and the
ouster--which, together with title, were the four things necessary to
maintain an action of ejectment. This having been arranged the action
proceeded, B being made defendant instead of D. The names used for the
fictitious parties were John Doe, plaintiff, and Richard Roe, defendant,
who was called "the casual ejector." The explanation of these mysterious
fictions is this. The writ _de ejectione firmae_ was invented about the
beginning of the reign of Edward III. as a remedy to a lessee for years
who had been ousted of his term. It was a writ of trespass, and carried
damages, but in the time of Henry VII., if not before that date, the
courts of common law added thereto a species of remedy neither warranted
by the original writ nor demanded by the declaration, viz. a judgment to
recover so much of the term as was still to run, and a writ of
possession thereupon. The next step was to extend the remedy--limited
originally to leaseholds--to cases of disputed title to freeholds. This
was done indirectly by the claimant entering on the land and there
making a lease for a term of years to another person; for it was only a
term that could be recovered by the action, and to create a term
required actual possession in the granter. The lessee remained on the
land, and the next person who entered even by chance was accounted an
ejector of the lessee, who then served upon him a writ of trespass and
ejectment. The case then went to trial as on a common action of
trespass; and the claimant's title, being the real foundation of the
lessee's right, was thus indirectly determined. These proceedings might
take place without the knowledge of the person really in possession; and
to prevent the abuse of the action a rule was laid down that the
plaintiff in ejectment must give notice to the party in possession, who
might then come in and defend the action. When the action came into
general use as a mode of trying the title to freeholds, the actual
entry, lease and ouster which were necessary to found the action were
attended with much inconvenience, and accordingly Lord Chief Justice
Rolle during the Protectorate (c. 1657) substituted for them the
fictitious averments already described. The action of ejectment is now
only a curiosity of legal history. Its fictitious suitors were swept
away by the Common Law Procedure Act of 1852. A form of writ was
prescribed, in which the person in possession of the disputed premises
by name and all persons entitled to defend the possession were informed
that the plaintiff claimed to be entitled to possession, and required to
appear in court to defend the possession of the property or such part of
it as they should think fit. In the form of the writ and in some other
respects ejectment still differed from other actions. But, as already
mentioned, it has now been assimilated (under the name of action for the
recovery of lands) to ordinary actions by the Rules of the Supreme
Court. It is commenced by writ of summons, and--subject to the rules as
to summary judgments (_v. inf._)--proceeds along the usual course of
pleadings and trial to judgment; but is subject to one special rule,
viz: that except by leave of the Court or a judge the only claims which
may be joined with one for recovery of land are claims in respect of
arrears of rent or double value for holding over, or mesne profits (i.e.
the value of the land during the period of illegal possession), or
damages for breach of a contract under which the premises are held or
for any wrong or injury to the premises claimed (R.S.C., O. xviii. r.
2). These claims were formerly recoverable by an independent action.

With regard to actions for the recovery of land--apart from the
relationship of landlord and tenant--the only point that need be noted
is the presumption of law in favour of the actual possessor of the land
in dispute. Where the action is brought by a landlord against his
tenant, there is of course no presumption against the landlord's title
arising from the tenant's possession. By the Common Law Procedure Act
1852 (ss. 210-212) special provision was made for the prompt recovery of
demised premises where half a year's rent was in arrear and the landlord
was entitled to re-enter for non-payment. These provisions are still in
force, but advantage is now more generally taken of the summary judgment
procedure introduced by the Rules of the Supreme Court (Order 3, r. 6.).
This procedure may be adopted when (a) the tenant's term has expired,
(b) or has been duly determined by notice to quit, or (c) has become
liable to forfeiture for non-payment of rent, and applies not only to
the tenant but to persons claiming under him. The writ is specially
endorsed with the plaintiff's claim to recover the land with or without
rent or mesne profits, and summary judgment obtained if no substantial
defence is disclosed. Where an action to recover land is brought against
the tenant by a person claiming adversely to the landlord, the tenant is
bound, under penalty of forfeiting the value of three years' improved or
rack rent of the premises, to give notice to the landlord in order that
he may appear and defend his title. Actions for the recovery of land,
other than land belonging to spiritual corporations and to the crown,
are barred in 12 years (Real Property Limitation Acts 1833 (s. 29) and
1874 (s. 1). A landlord can recover possession in the county court (i.)
by an action for the recovery of possession, where neither the value of
the premises nor the rent exceeds £100 a year, and the tenant is holding
over (County Courts Acts of 1888, s. 138, and 1903, s. 3); (ii.) by "an
action of ejectment," where (a) the value or rent of the premises does
not exceed £100, (b) half a year's rent is in arrear, and (c) no
sufficient distress (see RENT) is to be found on the premises (Act of
1888, s. 139; Act of 1903, s. 3; County Court Rules 1903, Ord. v. rule
3). Where a tenant at a rent not exceeding £20 a year of premises at
will, or for a term not exceeding 7 years, refuses nor neglects, on the
determination or expiration of his interest, to deliver up possession,
such possession may be recovered by proceedings before justices under
the Small Tenements Recovery Act 1838, an enactment which has been
extended to the recovery of allotments. Under the Distress for Rent Act
1737, and the Deserted Tenements Act 1817, a landlord can have himself
put by the order of two justices into premises deserted by the tenant
where half a year's rent is owing and no sufficient distress can be
found.

In _Ireland_, the practice with regard to the recovery of land is
regulated by the Rules of the Supreme Court 1891, made under the
Judicature (Ireland) Act 1877; and resembles that of England. Possession
may be recovered summarily by a special indorsement of the writ, as in
England; and there are analogous provisions with regard to the recovery
of small tenements (see Land Act, 1860 ss. 84 and 89). The law with
regard to the ejectment or eviction of tenants is consolidated by the
Land Act 1860. (See ss. 52-66, 68-71, and further under LANDLORD AND
TENANT.)

In _Scotland_, the recovery of land is effected by an action of
"removing" or summary ejection. In the case of a tenant "warning" is
necessary unless he is bound by his lease to remove without warning. In
the case of possessors without title, or a title merely precarious, no
warning is needed. A summary process of removing from small holdings is
provided for by Sheriff Courts (Scotland) Acts of 1838 and 1851.

In the United States, the old English action of ejectment was adopted to
a very limited extent, and where it was so adopted has often been
superseded, as in Connecticut, by a single action for all cases of
ouster, disseisin or ejectment. In this action, known as an action of
disseisin or ejectment, both possession of the land and damages may be
recovered. In some of the states a tenant against whom an action of
ejectment is brought by a stranger is bound under a penalty, as in
England, to give notice of the claim to the landlord in order that he
may appear and defend his title.

In _French law_ the landlord's claim for rent is fairly secured by the
hypothec, and by summary powers which exist for the seizure of the
effects of defaulting tenants. Eviction or annulment of a lease can only
be obtained through the judicial tribunals. The Civil Code deals with
the position of a tenant in case of the sale of the property leased. If
the lease is by authentic act (_acte authentique_) or has an ascertained
date, the purchaser cannot evict the tenant unless a right to do so was
reserved on the lease (art. 1743), and then only on payment of an
indemnity (arts. 1744-1747). If the lease is not by authentic act, or
has not an ascertained date, the purchaser is not liable for indemnity
(art. 1750). The tenant of rural lands is bound to give the landlord
notice of acts of usurpation (art. 1768). There are analogous provisions
in the Civil Codes of Belgium (arts. 1743 et seq.), Holland (arts. 1613,
1614), Portugal (art. 1572); and see the German Civil Code (arts. 535 et
seq.). In many of the colonies there are statutory provisions for the
recovery of land or premises on the lines of English law (cf. Ontario,
Rev. Stats. 1897, c. 170. ss. 19 et seq.; Manitoba, Rev. Stats. 1902, c.
1903). In others (e.g. New Zealand, Act. No. 55 of 1893, ss. 175-187;
British Columbia, Revised Statutes, 1897, c. 182: Cyprus, Ord. 15 of
1895) there has been legislation similar to the Small Tenements Recovery
Act 1838.

  AUTHORITIES.--_English Law_: Cole on _Ejectment_; Digby, _History of
  Real Property_ (3rd ed., London, 1884); Pollock and Maitland, _History
  of English Law_ (Cambridge, 1895); Foa, _Landlord and Tenant_ (4th
  ed., London, 1907); Fawcett, _Landlord and Tenant_ (London, 1905).
  _Irish Law_: Nolan and Kane's _Statutes relating to the Law of
  Landlord and Tenant_ (5th ed., Dublin, 1898); Wylie's _Judicature
  Acts_ (Dublin, 1900). _Scots Law_: Hunter on _Landlord and Tenant_
  (4th ed., Edin., 1878); Erskine's _Principles_ (20th ed., Edin.,
  1903). _American Law: Two Centuries' Growth of American Law_ (New York
  and London, 1901); Bouvier's _Law Dictionary_ (Boston and London,
  1897); Stimson, _American Statute Law_ (Boston, 1886).     (A. W. R.)



EKATERINBURG, a town of Russia, in the government of Perm, 311 m. by
rail S.E. of the town of Perm, on the Iset river, near the E. foot of
the Ural Mountains, in 56° 49' N. and 60° 35' E., at an altitude of 870
ft. above sea-level. It is the most important town of the Urals. Pop.
(1860) 19,830; (1897) 55,488. The streets are broad and regular, and
several of the houses of palatial proportions. In 1834 Ekaterinburg was
made the see of a suffragan bishop of the Orthodox Greek Church. There
are two cathedrals--St Catherine's, founded in 1758, and that of the
Epiphany, in 1774--and a museum of natural history, opened in 1853.
Ekaterinburg is the seat of the central mining administration of the
Ural region, and has a chemical laboratory for the assay of gold, a
mining school, the Ural Society of Naturalists, and a magnetic and
meteorological observatory. Besides the government mint for copper
coinage, which dates from 1735, the government engineering works, and
the imperial factory for the cutting and polishing of malachite, jasper,
marble, porphyry and other ornamental stones, the industrial
establishments comprise candle, paper, soap and machinery works, flour
and woollen mills, and tanneries. There is a lively trade in cattle,
cereals, iron, woollen and silk goods, and colonial products; and two
important fairs are held annually. Nearly forty gold and platinum mines,
over thirty iron-works, and numerous other factories are scattered over
the district, while wheels, travelling boxes, hardware, boots and so
forth are extensively made in the villages. Ekaterinburg took its origin
from the mining establishments founded by Peter the Great in 1721, and
received its name in honour of his wife, Catherine I. Its development
was greatly promoted in 1763 by the diversion of the Siberian highway
from Verkhoturye to this place.



EKATERINODAR, a town of South Russia, chief town of the province of
Kubañ, on the right bank of the river Kubañ, 85 m. E.N.E. of
Novo-rossiysk on the railway to Rostov-on-Don, and in 45° 3' N. and 38°
50' E. It is badly built, on a swampy site exposed to the inundations of
the river; and its houses, with few exceptions, are slight structures of
wood and plaster. Founded by Catherine II. in 1794 on the site of an old
town called Tmutarakan, as a small fort and Cossack settlement, its
population grew from 9620 in 1860 to 65,697 in 1897. It has various
technical schools, an experimental fruit-farm, a military hospital, and
a natural history museum. A considerable trade is carried on, especially
in cereals.



EKATERINOSLAV, a government of south Russia, having the governments of
Poltava and Kharkov on the N., the territory of the Don Cossacks on the
E., the Sea of Azov and Taurida on the S., and Kherson on the W. Area,
24,478 sq. m. Its surface is undulating steppe, sloping gently south and
north, with a few hills reaching 1200 ft. in the N.E., where a slight
swelling (the Don Hills) compels the Don to make a great curve
eastwards. Another chain of hills, to which the eastward bend of the
Dnieper is due, rises in the west. These hills have a crystalline core
(granites, syenites and diorites), while the surface strata belong to
the Carboniferous, Permian, Cretaceous and Tertiary formations. The
government is rich in minerals, especially in coal--the mines lie in the
middle of the Donets coalfield--iron ores, fireclay and rock-salt, and
every year the mining output increases in quantity, especially of coal
and iron. Granite, limestone, grindstone, slate, with graphite,
manganese and mercury are found. The government is drained by the
Dnieper, the Don and their tributaries (e.g. the Donets and Volchya) and
by several affluents (e.g. the Kalmius) of the Sea of Azov. The soil is
the fertile black earth, but the crops occasionally suffer from drought,
the average annual rainfall being only 15 in. Forests are scarce. Pop.
(1860) 1,138,750; (1897) 2,118,946, chiefly Little Russians, with Great
Russians, Greeks (48,740), Germans (80,979), Rumanians and a few
gypsies. Jews constitute 4.7% of the population. The estimated
population in 1906 was 2,708,700.

Wheat and other cereals are extensively grown; other noteworthy crops
are potatoes, tobacco and grapes. Nearly 40,000 persons find occupation
in factories, the most important being iron-works and agricultural
machinery works, though there are also tobacco, glass, soap and candle
factories, potteries, tanneries and breweries. In the districts of
Mariupol the making of agricultural implements and machinery is carried
on extensively as a domestic industry in the villages. Bees are kept in
very considerable numbers. Fishing employs many persons in the Don and
the Dnieper. Cereals are exported in large quantities via the Dnieper,
the Sevastopol railway, and the port of Mariupol. The chief towns of the
eight districts, with their populations in 1897, are Ekaterinoslav
(135,552 inhabitants in 1900), Alexandrovsk (28,434), Bakhmut (30,585),
Mariupol (31,772), Novomoskovsk (12,862), Pavlograd (17,188),
Slavyanoserbsk (3120), and Verkhne-dnyeprovsk (11,607).



EKATERINOSLAV, a town of Russia, capital of the government of the same
name, on the right bank of the Dnieper above the rapids, 673 m. by rail
S.S.W. of Moscow, in 48° 21' N. and 35° 4' E., at an altitude of 210 ft.
Pop. (1861) 18,881, without suburbs; (1900) 135,552. If the suburb of
Novyikoindak be included, the town extends for upwards of 4 m. along the
river. The oldest part lies very low and is much exposed to floods.
Contiguous to the towns on the N.W. is the royal village of Novyimaidani
or the New Factories. The bishop's palace, mining academy,
archaeological museum and library are the principal public buildings.
The house now occupied by the Nobles Club was formerly inhabited by the
author and statesman Potemkin. Ekaterinoslav is a rapidly growing city,
with a number of technical schools, and is an important depot for timber
floated down the Dnieper, and also for cereals. Its iron-works,
flour-mills and agricultural machinery works give occupation to over
5000 persons. In fact since 1895 the city has become the centre of
numerous Franco-Belgian industrial undertakings. In addition to the
branches just mentioned, there are tobacco factories and breweries.
Considerable trade is carried on in cattle, cereals, horses and wool,
there being three annual fairs. On the site of the city there formerly
stood the Polish castle of Koindak, built in 1635, and destroyed by the
Cossacks. The existing city was founded by Potemkin in 1786, and in the
following year Catherine II. laid the foundation-stone of the cathedral,
though it was not actually built until 1830-1835. On the south side of
it is a bronze statue of the empress, put up in 1846. Paul I. changed
the name of the city to Novo-rossiysk, but the original name was
restored in 1802.



EKHOF, KONRAD (1720-1778), German actor, was born in Hamburg on the 12th
of August 1720. In 1739 he became a member of Johann Friedrich
Schönemann's (1704-1782) company in Lüneburg, and made his first
appearance there on the 15th of January 1740 as Xiphares in Racine's
_Mithridate_. From 1751 the Schönemann company performed mainly in
Hamburg and at Schwerin, where Duke Christian Louis II. of
Mecklenburg-Schwerin made them comedians to the court. During this
period Ekhof founded a theatrical academy, which, though short-lived,
was of great importance in helping to raise the standard of German
acting and the status of German actors. In 1757 Ekhof left Schönemann to
join Franz Schuch's company at Danzig; but he soon returned to Hamburg,
where, in conjunction with two other actors, he succeeded Schönemann in
the direction of the company. He resigned this position, however, in
favour of H.G. Koch, with whom he acted until 1764, when he joined K.E.
Ackermann's company. In 1767 was founded the National Theatre at
Hamburg, made famous by Lessing's _Hamburgische Dramaturgie_, and Ekhof
was the leading member of the company. After the failure of the
enterprise Ekhof was for a time in Weimar, and ultimately became
co-director of the new court theatre at Gotha. This, the first
permanently established theatre in Germany, was opened on the 2nd of
October 1775. Ekhof's reputation was now at its height; Goethe called
him the only German tragic actor; and in 1777 he acted with Goethe and
Duke Charles Augustus at a private performance at Weimar, dining
afterwards with the poet at the ducal table. He died on the 16th of June
1778. His versatility may be judged from the fact that in the comedies
of Goldoni and Molière he was no less successful than in the tragedies
of Lessing and Shakespeare. He was regarded by his contemporaries as an
unsurpassed exponent of naturalness on the stage; and in this respect he
has been not unfairly compared with Garrick. His fame, however, was
rapidly eclipsed by that of Friedrich U.L. Schröder. His literary
efforts were chiefly confined to translations from French authors.

  See H. Uhde, biography of Ekhof in vol. iv. of _Der neue Plutarch_
  (1876), and J. Rüschner, _K. Ekhofs Leben und Wirken_ (1872). Also H.
  Devrient, _J.F. Schönemann und seine Schauspielergesellschaft_ (1895).



EKRON (better, as in the Septuagint and Josephus, ACCARON, [Greek:
Akkarôn]), a royal city of the Philistines commonly identified with the
modern Syrian village of `Akir, 5 m. from Ramleh, on the southern slope
of a low ridge separating the plain of Philistia from Sharon. It lay
inland and off the main line of traffic. Though included by the
Israelites within the limits of the tribe of Judah, and mentioned in
Judges xix. as one of the cities of Dan, it was in Philistine possession
in the days of Samuel, and apparently maintained its independence.
According to the narrative of the Hebrew text, here differing from the
Greek text and Josephus (which read Askelon), it was the last town to
which the ark was transferred before its restoration to the Israelites.
Its maintenance of a sanctuary of Baal Zebub is mentioned in 2 Kings i.
From Assyrian inscriptions it has been gathered that Padi, king of
Ekron, was for a time the vassal of Hezekiah of Judah, but regained his
independence when the latter was hard pressed by Sennacherib. A notice
of its history in 147 B.C. is found in 1 Macc. x. 89; after the fall of
Jerusalem A.D. 70 it was settled by Jews. At the time of the crusades it
was still a large village. Recently a Jewish agricultural colony has
been settled there. The houses are built of mud, and in the absence of
visible remains of antiquity, the identification of the site is
questionable. The neighbourhood is fertile.     (R. A. S. M.)



ELABUGA, a town of Russia, in the government of Vyatka, on the Kama
river, 201 m. by steamboat down the Volga from Kazan and then up the
Kama. It has flour-mills, and carries on a brisk trade in exporting
corn. Pop. (1897) 9776.

The famous _Ananiynskiy Mogilnik_ (burial-place) is on the right bank of
the Kama, 3 m. above the town. It was discovered in 1858, was excavated
by Alabin, Lerch and Nevostruyev, and has since supplied extremely
valuable collections belonging to the Stone, Bronze and Iron Ages. It
consisted of a mound, about 500 ft. in circumference, adorned with
decorated stones (which have disappeared), and contained an inner wall,
65 ft. in circumference, made of uncemented stone flags. Nearly fifty
skeletons were discovered, mostly lying upon charred logs, surrounded
with cinerary urns filled with partially burned bones. A great variety
of bronze decorations and glazed clay pearls were strewn round the
skeletons. The knives, daggers and arrowpoints are of slate, bronze and
iron, the last two being very rough imitations of stone implements. One
of the flags bore the image of a man, without moustaches or beard,
dressed in a costume and helmet recalling those of the Circassians.



ELAM, the name given in the Bible to the province of Persia called
Susiana by the classical geographers, from Susa or Shushan its capital.
In one passage, however (Ezra iv. 9), it is confined to Elymais, the
north-western part of the province, and its inhabitants distinguished
from those of Shushan, which elsewhere (Dan. viii. 2) is placed in Elam.
Strabo (xv. 3. 12, &c.) makes Susiana a part of Persia proper, but a
comparison of his account with those of Ptolemy (vi. 3. 1, &c.) and
other writers would limit it to the mountainous district to the east of
Babylonia, lying between the Oroatis and the Tigris, and stretching from
India to the Persian Gulf. Along with this mountainous district went a
fertile low tract of country on the western side, which also included
the marshes at the mouths of the Euphrates and Tigris and the
north-eastern coast land of the Gulf. This low tract, though producing
large quantities of grain, was intensely hot in summer; the high
regions, however, were cool and well watered.

The whole country was occupied by a variety of tribes, speaking
agglutinative dialects for the most part, though the western districts
were occupied by Semites. Strabo (xi. 13. 3, 6), quoting from Nearchus,
seems to include the Susians under the Elymaeans, whom he associates
with the Uxii, and places on the frontiers of Persia and Susa; but
Pliny more correctly makes the Eulaeus the boundary between Susiana and
Elymais (_N.H._ vi. 29-31). The Uxii are described as a robber tribe in
the mountains adjacent to Media, and their name is apparently to be
identified with the title given to the whole of Susiana in the Persian
cuneiform inscriptions, _Uwaja_, i.e. "Aborigines." Uwaja is probably
the origin of the modern Khuzistan, though Mordtmann would derive the
latter from [Arab script] "a sugar-reed." Immediately bordering on the
Persians were the Amardians or Mardians, as well as the people of
Khapirti (Khatamti, according to Scheil), the name given to Susiana in
the Neo-Susian texts. Khapirti appears as Apir in the inscriptions of
Mal-Amir, which fix the locality of the district. Passing over the
Messabatae, who inhabited a valley which may perhaps be the modern
Mah-Sabadan, as well as the level district of Yamutbal or Yatbur which
separated Elam from Babylonia, and the smaller districts of Characene,
Cabandene, Corbiana and Gabiene mentioned by classical authors, we come
to the fourth principal tribe of Susiana, the Cissii (Aesch. _Pers._ 16;
Strabo xv. 3. 2) or Cossaei (Strabo xi. 5. 6, xvi. 11. 17; Arr. _Ind._
40; Polyb. v. 54, &c.), the Kassi of the cuneiform inscriptions. So
important were they, that the whole of Susiana was sometimes called
Cissia after them, as by Herodotus (iii. 91, v. 49, &c.). In fact
Susiana was only a late name for the country, dating from the time when
Susa had been made a capital of the Persian empire. In the Sumerian
texts of Babylonia it was called Numma, "the Highlands," of which Elamtu
or Elamu, "Elam," was the Semitic translation. Apart from Susa, the most
important part of the country was Anzan (Anshan, contracted Assan),
where the native population maintained itself unaffected by Semitic
intrusion. The exact position of Anzan is still disputed, but it
probably included originally the site of Susa and was distinguished from
it only when Susa became the seat of a Semitic government. In the
lexical tablets Anzan is given as the equivalent of Elamtu, and the
native kings entitle themselves kings of "Anzan and Susa," as well as
"princes of the Khapirti."

The principal mountains of Elam were on the north, called Charbanus and
Cambalidus by Pliny (vi. 27, 31), and belonging to the Parachoathras
chain. There were numerous rivers flowing into either the Tigris or the
Persian Gulf. The most important were the Ulai or Eulaeus (_Kuran_) with
its tributary the Pasitigris, the Choaspes (_Kerkhah_), the Coprates
(river of _Diz_ called Itite in the inscriptions), the Hedyphon or
Hedypnus (_Jerrahi_), and the Croatis (_Hindyan_), besides the
monumental Surappi and Ukni, perhaps to be identified with the Hedyphon
and Oroatis, which fell into the sea in the marshy region at the mouth
of the Tigris. Shushan or Susa, the capital now marked by the mounds of
_Shush_, stood near the junction of the Choaspes and Eulaeus (see SUSA);
and Badaca, Madaktu in the inscriptions, lay between the _Shapur_ and
the river of _Diz_. Among the other chief cities mentioned in the
inscriptions may be named Naditu, Khaltemas, Din-sar, Bubilu, Bit-imbi,
Khidalu and Nagitu on the sea-coast. Here, in fact, lay some of the
oldest and wealthiest towns, the sites of which have, however, been
removed inland by the silting up of the shore. J. de Morgan's
excavations at Susa have thrown a flood of light on the early history of
Elam and its relations to Babylon. The earliest settlement there goes
back to neolithic times, but it was already a fortified city when Elam
was conquered by Sargon of Akkad (3800 B.C.) and Susa became the seat of
a Babylonian viceroy. From this time onward for many centuries it
continued under Semitic suzerainty, its high-priests, also called "Chief
Envoys of Elam, Sippara and Susa," bearing sometimes Semitic, sometimes
native "Anzanite" names. One of the kings of the dynasty of Ur built at
Susa. Before the rise of the First Dynasty of Babylon, however, Elam had
recovered its independence, and in 2280 B.C. the Elamite king
Kutur-Nakhkhunte made a raid in Babylonia and carried away from Erech
the image of the goddess Nana. The monuments of many of his successors
have been discovered by de Morgan and their inscriptions deciphered by
v. Scheil. One of them was defeated by Ammi-zadoq of Babylonia (c. 2100
B.C.); another would have been the Chedor-laomer (Kutur-Lagamar) of
Genesis xiv. One of the greatest builders among them was Untas-GAL (the
pronunciation of the second element in the name is uncertain). About
1330 B.C. Khurba-tila was captured by Kuri-galzu III., the Kassite king
of Babylonia, but a later prince Kidin-Khutrutas avenged his defeat, and
Sutruk-Nakhkhunte (1220 B.C.) carried fire and sword through Babylonia,
slew its king Zamama-sum-iddin and carried away a stela of Naram-Sin and
the famous code of laws of Khammurabi from Sippara, as well as a stela
of Manistusu from Akkuttum or Akkad. He also conquered the land of
Asnunnak and carried off from Padan a stela belonging to a refugee from
Malatia. He was succeeded by his son who was followed on the throne by
his brother, one of the great builders of Elam. In 750 B.C. Umbadara was
king of Elam; Khumban-igas was his successor in 742 B.C. In 720 B.C. the
latter prince met the Assyrians under Sargon at Dur-ili in Yamutbal, and
though Sargon claims a victory the result was that Babylonia recovered
its independence under Merodach-baladan and the Assyrian forces were
driven north. From this time forward it was against Assyria instead of
Babylonia that Elam found itself compelled to exert its strength, and
Elamite policy was directed towards fomenting revolt in Babylonia and
assisting the Babylonians in their struggle with Assyria. In 716 B.C.
Khumban-igas died and was followed by his nephew, Sutruk-Nakhkhunte. He
failed to make head against the Assyrians; the frontier cities were
taken by Sargon and Merodach-baladan was left to his fate. A few years
later (704 B.C.) the combined forces of Elam and Babylonia were
overthrown at Kis, and in the following year the Kassites were reduced
to subjection. The Elamite king was dethroned and imprisoned in 700 B.C.
by his brother Khallusu, who six years later marched into Babylonia,
captured the son of Sennacherib, whom his father had placed there as
king, and raised a nominee of his own, Nergal-yusezib, to the throne.
Khallusu was murdered in 694 B.C., after seeing the maritime part of his
dominions invaded by the Assyrians. His successor Kudur-Nakhkhunte
invaded Babylonia; he was repulsed, however, by Sennacherib, 34 of his
cities were destroyed, and he himself fled from Madaktu to Khidalu. The
result was a revolt in which he was killed after a reign of ten months.
His brother Umman-menan at once collected allies and prepared for
resistance to the Assyrians. But the terrible defeat at Khalule broke
his power; he was attacked by paralysis shortly afterwards, and
Khumba-Khaldas II. followed him on the throne (689 B.C.). The new king
endeavoured to gain Assyrian favour by putting to death the son of
Merodach-baladan, but was himself murdered by his brothers Urtaki and
Teumman (681 B.C.), the first of whom seized the crown. On his death
Teumman succeeded and almost immediately provoked a quarrel with
Assur-bani-pal by demanding the surrender of his nephews who had taken
refuge at the Assyrian court. The Assyrians pursued the Elamite army to
Susa, where a battle was fought on the banks of the Eulaeus, in which
the Elamites were defeated, Teumman captured and slain, and Umman-igas,
the son of Urtaki, made king, his younger brother Tammaritu being given
the district of Khidalu. Umman-igas afterwards assisted in the revolt of
Babylonia under Samas-sum-yukin, but his nephew, a second Tammaritu,
raised a rebellion against him, defeated him in battle, cut off his head
and seized the crown. Tammaritu marched to Babylonia; while there, his
officer Inda-bigas made himself master of Susa and drove Tammaritu to
the coast whence he fled to Assur-bani-pal. Inda-bigas was himself
overthrown and slain by a new pretender, Khumba-Khaldas III., who was
opposed, however, by three other rivals, two of whom maintained
themselves in the mountains until the Assyrian conquest of the country,
when Tammaritu was first restored and then imprisoned, Elam being
utterly devastated. The return of Khumba-Khaldas led to a fresh Assyrian
invasion; the Elamite king fled from Madaktu to Dur-undasi; Susa and
other cities were taken, and the Elamite army almost exterminated on the
banks of the Itite. The whole country was reduced to a desert, Susa was
plundered and razed to the ground, the royal sepulchres were desecrated,
and the images of the gods and of 32 kings "in silver, gold, bronze and
alabaster," were carried away. All this must have happened about 640
B.C. After the fall of the Assyrian empire Elam was occupied by the
Persian Teispes, the forefather of Cyrus, who, accordingly, like his
immediate successors, is called in the inscriptions "king of Anzan."
Susa once more became a capital, and on the establishment of the Persian
empire remained one of the three seats of government, its language, the
Neo-Susian, ranking with the Persian of Persepolis and the Semitic of
Babylon as an official tongue. In the reign of Darius, however, the
Susianians attempted to revolt, first under Assina or Atrina, the son of
Umbadara, and later under Martiya, the son of Issainsakria, who called
himself Immanes; but they gradually became completely Aryanized, and
their agglutinative dialects were supplanted by the Aryan Persian from
the south-east.

Elam, "the land of the cedar-forest," with its enchanted trees, figured
largely in Babylonian mythology, and one of the adventures of the hero
Gilgamesh was the destruction of the tyrant Khumbaba who dwelt in the
midst of it. A list of the Elamite deities is given by Assur-bani-pal;
at the head of them was In-Susinak, "the lord of the Susians,"--a title
which went back to the age of Babylonian suzerainty,--whose image and
oracle were hidden from the eyes of the profane. Nakhkhunte, according
to Scheil, was the Sun-goddess, and Lagamar, whose name enters into that
of Chedor-laomer, was borrowed from Semitic Babylonia.

  See W.K. Loftus, _Chaldaea and Susiana_ (1857); A. Billerbeck, _Susa_
  (1893); J. de Morgan, _Mémoires de la Délégation en Perse_ (9 vols.,
  1899-1906).     (A. H. S.)



ELAND (= elk), the Dutch name for the largest of the South African
antelopes (_Taurotragus oryx_), a species near akin to the kudu, but
with horns present in both sexes, and their spiral much closer, being in
fact screw-like instead of corkscrew-like. There is also a large dewlap,
while old bulls have a thick forelock. In the typical southern form the
body-colour is wholly pale fawn, but north of the Orange river the body
is marked by narrow vertical white lines, this race being known as _T.
oryx livingstonei_. In Senegambia the genus is represented by _T.
derbianus_, a much larger animal, with a dark neck; while in the
Bahr-el-Ghazal district there is a gigantic local race of this species
(_T. derbianus giganteus_).     (R. L.*)



ELASTICITY. 1. Elasticity is the property of recovery of an original
size or shape. A body of which the size, or shape, or both size and
shape, have been altered by the application of forces may, and generally
does, tend to return to its previous size and shape when the forces
cease to act. Bodies which exhibit this tendency are said to be
_elastic_ (from Greek, [Greek: elaunein], to drive). All bodies are more
or less elastic as regards size; and all solid bodies are more or less
elastic as regards shape. For example: gas contained in a vessel, which
is closed by a piston, can be compressed by additional pressure applied
to the piston; but, when the additional pressure is removed, the gas
expands and drives the piston outwards. For a second example: a steel
bar hanging vertically, and loaded with one ton for each square inch of
its sectional area, will have its length increased by about seven
one-hundred-thousandths of itself, and its sectional area diminished by
about half as much; and it will spring back to its original length and
sectional area when the load is gradually removed. Such changes of size
and shape in bodies subjected to forces, and the recovery of the
original size and shape when the forces cease to act, become conspicuous
when the bodies have the forms of thin wires or planks; and these
properties of bodies in such forms are utilized in the construction of
spring balances, carriage springs, buffers and so on.

It is a familiar fact that the hair-spring of a watch can be coiled and
uncoiled millions of times a year for several years without losing its
elasticity; yet the same spring can have its shape permanently altered
by forces which are much greater than those to which it is subjected in
the motion of the watch. The incompleteness of the recovery from the
effects of great forces is as important a fact as the practical
completeness of the recovery from the effects of comparatively small
forces. The fact is referred to in the distinction between "perfect"
and "imperfect" elasticity; and the limitation which must be imposed
upon the forces in order that the elasticity may be perfect leads to the
investigation of "limits of elasticity" (see §§ 31, 32 below). Steel
pianoforte wire is perfectly elastic within rather wide limits, glass
within rather narrow limits; building stone, cement and cast iron appear
not to be perfectly elastic within any limits, however narrow. When the
limits of elasticity are not exceeded no injury is done to a material or
structure by the action of the forces. The strength or weakness of a
material, and the safety or insecurity of a structure, are thus closely
related to the elasticity of the material and to the change of size or
shape of the structure when subjected to forces. The "science of
elasticity" is occupied with the more abstract side of this relation,
viz. with the effects that are produced in a body of definite size,
shape and constitution by definite forces; the "science of the strength
of materials" is occupied with the more concrete side, viz. with the
application of the results obtained in the science of elasticity to
practical questions of strength and safety (see STRENGTH OF MATERIALS).

2. _Stress._--Every body that we know anything about is always under the
action of forces. Every body upon which we can experiment is subject to
the force of gravity, and must, for the purpose of experiment, be
supported by other forces. Such forces are usually applied by way of
pressure upon a portion of the surface of the body; and such pressure is
exerted by another body in contact with the first. The supported body
exerts an equal and opposite pressure upon the supporting body across
the portion of surface which is common to the two. The same thing is
true of two portions of the same body. If, for example, we consider the
two portions into which a body is divided by a (geometrical) horizontal
plane, we conclude that the lower portion supports the upper portion by
pressure across the plane, and the upper portion presses downwards upon
the lower portion with an equal pressure. The pressure is still exerted
when the plane is not horizontal, and its direction may be obliquely
inclined to, or tangential to, the plane. A more precise meaning is
given to "pressure" below. It is important to distinguish between the
two classes of forces: forces such as the force of gravity, which act
all through a body, and forces such as pressure applied over a surface.
The former are named "body forces" or "volume forces," and the latter
"surface tractions." The action between two portions of a body separated
by a geometrical surface is of the nature of surface traction. Body
forces are ultimately, when the volumes upon which they act are small
enough, proportional to the volumes; surface tractions, on the other
hand, are ultimately, when the surfaces across which they act are small
enough, proportional to these surfaces. Surface tractions are always
exerted by one body upon another, or by one part of a body upon another
part, across a surface of contact; and a surface traction is always to
be regarded as one aspect of a "stress," that is to say of a pair of
equal and opposite forces; for an equal traction is always exerted by
the second body, or part, upon the first across the surface.

3. The proper method of estimating and specifying stress is a matter of
importance, and its character is necessarily mathematical. The
magnitudes of the surface tractions which compose a stress are estimated
as so much force (in dynes or tons) per unit of area (per sq. cm. or per
sq. in.). The traction across an assigned plane at an assigned point is
measured by the mathematical limit of the fraction F/S, where F denotes
the numerical measure of the force exerted across a small portion of the
plane containing the point, and S denotes the numerical measure of the
area of this portion, and the limit is taken by diminishing S
indefinitely. The traction may act as "tension," as it does in the case
of a horizontal section of a bar supported at its upper end and hanging
vertically, or as "pressure," as it does in the case of a horizontal
section of a block resting on a horizontal plane, or again it may act
obliquely or even tangentially to the separating plane. Normal tractions
are reckoned as positive when they are tensions, negative when they are
pressures. Tangential tractions are often called "shears" (see § 7
below). Oblique tractions can always be resolved, by the vector law,
into normal and tangential tractions. In a fluid at rest the traction
across any plane at any point is normal to the plane, and acts as
pressure. For the complete specification of the "state of stress" at any
point of a body, we should require to know the normal and tangential
components of the traction across every plane drawn through the point.
Fortunately this requirement can be very much simplified (see §§ 6, 7
below).

  4. In general let [nu] denote the direction of the normal drawn in a
  specified sense to a plane drawn through a point O of a body; and let
  T{[nu]} denote the traction exerted across the plane, at the point O,
  by the portion of the body towards which [nu] is drawn upon the
  remaining portion. Then T{[nu]} is a vector quantity, which has a
  definite magnitude (estimated as above by the limit of a fraction of
  the form F/S) and a definite direction. It can be specified completely
  by its components X{[nu]}, Y{[nu]}, Z{[nu]}, referred to fixed
  rectangular axes of x, y, z. When the direction of [nu] is that of the
  axis of x, in the positive sense, the components are denoted by X_x,
  Y_x, Z_x; and a similar notation is used when the direction of [nu] is
  that of y or z, the suffix x being replaced by y or z.

5. Every body about which we know anything is always in a state of
stress, that is to say there are always internal forces acting between
the parts of the body, and these forces are exerted as surface tractions
across geometrical surfaces drawn in the body. The body, and each part
of the body, moves under the action of all the forces (body forces and
surface tractions) which are exerted upon it; or remains at rest if
these forces are in equilibrium. This result is expressed analytically
by means of certain equations--the "equations of motion" or "equations
of equilibrium" of the body.

  Let [rho] denote the density of the body at any point, X, Y, Z, the
  components parallel to the axes of x, y, z of the body forces,
  estimated as so much force per unit of mass; further let f_x, f_y, f_z
  denote the components, parallel to the same axes, of the acceleration
  of the particle which is momentarily at the point (x, y, z). The
  equations of motion express the result that the rates of change of the
  momentum, and of the moment of momentum, of any portion of the body
  are those due to the action of all the forces exerted upon the portion
  by other bodies, or by other portions of the same body. For the
  changes of momentum, we have three equations of the type
      _ _ _                 _ _            _ _ _
     / / /                 / /            / / /
     | | |[rho]Xdx dy dz + | |X_[nu] dS = | | |[rho]f_x dx dy dz,  (1)
    _/_/_/                _/_/           _/_/_/

  in which the volume integrations are taken through the volume of the
  portion of the body, the surface integration is taken over its
  surface, and the notation X_[nu] is that of § 4, the direction of [nu]
  being that of the normal to this surface drawn outwards. For the
  changes of moment of momentum, we have three equations of the type
      _ _ _                         _ _
     / / /                         / /
     | | |[rho](yZ - zY)dx dy dz + | |(yZ_[nu] - zY_[nu])dS =
    _/_/_/                        _/_/
         _ _ _
        / / /
        | | |[rho](yf_z - zf_y)dx dy dz. (2)
       _/_/_/

  The equations (1) and (2) are the equations of motion of any kind of
  body. The equations of equilibrium are obtained by replacing the
  right-hand members of these equations by zero.

  6. These equations can be used to obtain relations between the values
  of X_[nu], Y_[nu], ... for different directions [nu]. When the
  equations are applied to a very small volume, it appears that the
  terms expressed by surface integrals would, unless they tend to zero
  limits in a higher order than the areas of the surfaces, be very great
  compared with the terms expressed by volume integrals. We conclude
  that the surface tractions on the portion of the body which is bounded
  by any very small closed surface, are ultimately in equilibrium. When
  this result is interpreted for a small portion in the shape of a
  tetrahedron, having three of its faces at right angles to the
  co-ordinate axes, it leads to three equations of the type

    X_[nu] = X_x cos(x, [nu]) + X_y cos(y, [nu]) + X_z cos(z, [nu]), (1)

  where [nu] is the direction of the normal (drawn outwards) to the
  remaining face of the tetrahedron, and (x, [nu]) ... denote the angles
  which this normal makes with the axes. Hence X_[nu], ... for any
  direction [nu] are expressed in terms of X_x,.... When the above
  result is interpreted for a very small portion in the shape of a cube,
  having its edges parallel to the co-ordinate axes, it leads to the
  equations

    Y_z = Z_y,   Z_x = X_z,   X_y = Y_x.  (2)

  When we substitute in the general equations the particular results
  which are thus obtained, we find that the equations of motion take
  such forms as

             dPX_x   dPX_y   dPZ_x
    [rho]X + ----- + ----- + ----- = [rho] f_x,  (3)
              dPx     dPy     dPz

  and the equations of moments are satisfied identically. The equations
  of equilibrium are obtained by replacing the right-hand members by
  zero.

7. A state of stress in which the traction across any plane of a set of
parallel planes is normal to the plane, and that across any
perpendicular plane vanishes, is described as a state of "simple
tension" ("simple pressure" if the traction is negative). A state of
stress in which the traction across any plane is normal to the plane,
and the traction is the same for all planes passing through any point,
is described as a state of "uniform tension" ("uniform pressure" if the
traction is negative). Sometimes the phrases "isotropic tension" and
"hydrostatic pressure" are used instead of "uniform" tension or
pressure. The distinction between the two states, simple tension and
uniform tension, is illustrated in fig. 1.

[Illustration: FIG. 1.]

A state of stress in which there is purely tangential traction on a
plane, and no normal traction on any perpendicular plane, is described
as a state of "shearing stress." The result (2) of § 6 shows that
tangential tractions occur in pairs. If, at any point, there is
tangential traction, in any direction, on a plane parallel to this
direction, and if we draw through the point a plane at right angles to
the direction of this traction, and therefore containing the normal to
the first plane, then there is equal tangential traction on this second
plane in the direction of the normal to the first plane. The result is
illustrated in fig. 2, where a rectangular block is subjected on two
opposite faces to opposing tangential tractions, and is held in
equilibrium by equal tangential tractions applied to two other faces.

[Illustration: FIG. 2.]

Through any point there always pass three planes, at right angles to
each other, across which there is no tangential traction. These planes
are called the "principal planes of stress," and the (normal) tractions
across them the "principal stresses." Lines, usually curved, which have
at every point the direction of a principal stress at the point, are
called "lines of stress."

8. It appears that the stress at any point of a body is completely
specified by six quantities, which can be taken to be the X_x, Y_y, Z_z
and Y_z, Z_x, X_y of § 6. The first three are tensions (pressures if
they are negative) across three planes parallel to fixed rectangular
directions, and the remaining three are tangential tractions across the
same three planes. These six quantities are called the "components of
stress." It appears also that the components of stress are connected
with each other, and with the body forces and accelerations, by the
three partial differential equations of the type (3) of § 6. These
equations are available for the purpose of determining the state of
stress which exists in a body of definite form subjected to definite
forces, but they are not sufficient for the purpose (see § 38 below). In
order to effect the determination it is necessary to have information
concerning the constitution of the body, and to introduce subsidiary
relations founded upon this information.

9. The definite mathematical relations which have been found to connect
the components of stress with each other, and with other quantities,
result necessarily from the formation of a clear conception of the
nature of stress. They do not admit of experimental verification,
because the stress within a body does not admit of direct measurement.
Results which are deduced by the aid of these relations can be compared
with experimental results. If any discrepancy were observed it would not
be interpreted as requiring a modification of the concept of stress, but
as affecting some one or other of the subsidiary relations which must
be introduced for the purpose of obtaining the theoretical result.

10. _Strain._--For the specification of the changes of size and shape
which are produced in a body by any forces, we begin by defining the
"average extension" of any linear element or "filament" of the body. Let
l0 be the length of the filament before the forces are applied, l its
length when the body is subjected to the forces. The average extension
of the filament is measured by the fraction (l - l0)/l0. If this
fraction is negative there is "contraction." The "extension at a point"
of a body in any assigned direction is the mathematical limit of this
fraction when one end of the filament is at the point, the filament has
the assigned direction, and its length is diminished indefinitely. It is
clear that all the changes of size and shape of the body are known when
the extension at every point in every direction is known.

  The relations between the extensions in different directions around
  the same point are most simply expressed by introducing the extensions
  in the directions of the co-ordinate axes and the angles between
  filaments of the body which are initially parallel to these axes. Let
  e_(xx), e_(yy), e_(zz) denote the extensions parallel to the axes of
  x, y, z, and let e_(yz), e_(zx), e_(xy) denote the cosines of the
  angles between the pairs of filaments which are initially parallel to
  the axes of y and z, z and x, x and y. Also let e denote the extension
  in the direction of a line the direction cosines of which are l, m, n.
  Then, if the changes of size and shape are slight, we have the
  relation

    e = e_(xx)l² + e_(yy)m² + e_(zz)n² + e_(yz)mn + e_(zx)nl + e_(xy)lm.

The body which undergoes the change of size or shape is said to be
"strained," and the "strain" is determined when the quantities e_(xx),
e_(yy), e_(zz) and e_(yz), e_(zx), e_(xy) defined above are known at
every point of it. These quantities are called "components of strain."
The three of the type e_(xx) are extensions, and the three of the type
e_(yz) are called "shearing strains" (see § 12 below).

11. All the changes of relative position of particles of the body are
known when the strain is known, and conversely the strain can be
determined when the changes of relative position are given. These
changes can be expressed most simply by the introduction of a vector
quantity to represent the displacement of any particle.

  When the body is deformed by the action of any forces its particles
  pass from the positions which they occupied before the action of the
  forces into new positions. If x, y, z are the co-ordinates of the
  position of a particle in the first state, its co-ordinates in the
  second state may be denoted by x + u, y + v, z + w. The quantities, u,
  v, w are the "components of displacement." When these quantities are
  small, the strain is connected with them by the equations

    e_(xx) = dPu/dPx,  e_(yy) = dPv/dPy,  e_(zz) = dPw/dPz,        \
                                                                   |
             dPw   dPv            dPu   dPw            dPv   dPu    >(1)
    e_(yz) = --- + ---,  e_(zx) = --- + ---,  e_(xy) = --- + --- . |
             dPy   dPz            dPz   dPx            dPx   dPy   /

12. These equations enable us to determine more exactly the nature of
the "shearing strains" such as e_(xy). Let u, for example, be of the
form sy, where s is constant, and let v and w vanish. Then e_(xy) = s,
and the remaining components of strain vanish. The nature of the strain
(called "simple shear") is simply appreciated by imagining the body to
consist of a series of thin sheets, like the leaves of a book, which lie
one over another and are all parallel to a plane (that of x, z); and the
displacement is seen to consist in the shifting of each sheet relative
to the sheet below in a direction (that of x) which is the same for all
the sheets. The displacement of any sheet is proportional to its
distance y from a particular sheet, which remains undisplaced. The
shearing strain has the effect of distorting the shape of any portion of
the body without altering its volume. This is shown in fig. 3, where a
square ABCD is distorted by simple shear (each point moving parallel to
the line marked xx) into a rhombus A'B'C'D', as if by an extension of
the diagonal BD and a contraction of the diagonal AC, which extension
and contraction are adjusted so as to leave the area unaltered. In the
general case, where u is not of the form sy and v and w do not vanish,
the shearing strains such as e_(xy) result from the composition of pairs
of simple shears of the type which has just been explained.

  13. Besides enabling us to express the extension in any direction and
  the changes of relative direction of any filaments of the body, the
  components of strain also express the changes of size of volumes and
  areas. In particular, the "cubical dilatation," that is to say, the
  increase of volume per unit of volume, is expressed by the quantity

                                dPu   dPv   dPw
    e_(xx) + e_(yy) + e_(zz) or --- + --- + ---.
                                dPx   dPy   dPz

  When this quantity is negative there is "compression."

[Illustration: FIG. 3.]

14. It is important to distinguish between two types of strain: the
"rotational" type and the "irrotational" type. The distinction is
illustrated in fig. 3, where the figure A"B"C"D" is obtained from the
figure ABCD by contraction parallel to AC and extension parallel to BD,
and the figure A'B'C'D' can be obtained from ABCD by the same
contraction and extension followed by a rotation through the angle
A"OA'. In strains of the irrotational type there are at any point three
filaments at right angles to each other, which are such that the
particles which lie in them before strain continue to lie in them after
strain. A small spherical element of the body with its centre at the
point becomes a small ellipsoid with its axes in the directions of these
three filaments. In the case illustrated in the figure, the lines of the
filaments in question, when the figure ABCD is strained into the figure
A"B"C"D", are OA, OB and a line through O at right angles to their
plane. In strains of the rotational type, on the other hand, the single
existing set of three filaments (issuing from a point) which cut each
other at right angles both before and after strain do not retain their
directions after strain, though one of them may do so in certain cases.
In the figure, the lines of the filaments in question, when the figure
ABCD is strained into A'B'C'D', are OA, OB and a line at right angles to
their plane before strain, and after strain they are OA', OB', and the
same third line. A rotational strain can always be analysed into an
irrotational strain (or "pure" strain) followed by a rotation.

  Analytically, a strain is irrotational if the three quantities

    dPw   dPv    dPu   dPw    dPv   dPu
    --- - ---,   --- - ---,   --- - ---.
    dPy   dPz    dPz   dPx    dPx   dPy

  vanish, rotational if any one of them is different from zero. The
  halves of these three quantities are the components of a vector
  quantity called the "rotation."

  15. Whether the strain is rotational or not, there is always one set
  of three linear elements issuing from any point which cut each other
  at right angles both before and after strain. If these directions are
  chosen as axes of x, y, z, the shearing strains e_(yz), e_(zx), e_(xy)
  vanish at this point. These directions are called the "principal axes
  of strain," and the extensions in the directions of these axes the
  "principal extensions."

16. It is very important to observe that the relations between
components of strain and components of displacement imply relations
between the components of strain themselves. If by any process of
reasoning we arrive at the conclusion that the state of strain in a body
is such and such a state, we have a test of the possibility or
impossibility of our conclusion. The test is that, if the state of
strain is a possible one, then there must be a displacement which can
be associated with it in accordance with the equations (1) of § 11.

  We may eliminate u, v, w from these equations. When this is done we
  find that the quantities e_(xx), ... e_(yz) are connected by the two
  sets of equations

    dP²e_(yy)   dP²e_(zz)   dP²e_(yz)   \
    --------- + --------- = ---------   |
       dPz²       dPy²       dPydPz     |
                                        |
    dP²e_(zz)   dP²e_(xx)   dP²e_(zx)   |
    --------- + --------- = ---------    > (1)
       dPx²       dPz²       dPzdPx     |
                                        |
    dP²e_(xx)   dP²e_(yy)   dP²e_(xy)   |
    --------- + --------- = ---------   |
       dPy²       dPx²       dPxdPy     /

  and

      dP²e_(xx)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   \
    2 --------- = --- ( - -------- + -------- + -------- )  |
       dPydPz     dPx  \    dPx        dPy        dPz   /   |
                                                            |
      dP²e_(yy)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   |
    2 --------- = --- (   -------- - -------- + -------- )   > (2)
       dPzdPx     dPy  \    dPx        dPy        dPz   /   |
                                                            |
      dP²e_(zz)   dP   /  dPe_(yz)   dPe_(zx)   dPe_(xy)\   |
    2 --------- = --- (   -------- + -------- - -------- )  |
       dPxdPy     dPz  \    dPx        dPy        dPz   /   /

These equations are known as the _conditions of compatibility of
strain-components_. The components of strain which specify any possible
strain satisfy them. Quantities arrived at in any way, and intended to
be components of strain, if they fail to satisfy these equations, are
not the components of any possible strain; and the theory or speculation
by which they are reached must be modified or abandoned.

  When the components of strain have been found in accordance with these
  and other necessary equations, the displacement is to be found by
  solving the equations (1) of § 11, considered as differential
  equations to determine u, v, w. The most general possible solution
  will differ from any other solution by terms which contain arbitrary
  constants, and these terms represent a possible displacement. This
  "complementary displacement" involves no strain, and would be a
  possible displacement of an ideal perfectly rigid body.

17. The relations which connect the strains with each other and with the
displacement are geometrical relations resulting from the definitions of
the quantities and not requiring any experimental verification. They do
not admit of such verification, because the strain within a body cannot
be measured. The quantities (belonging to the same category) which can
be measured are displacements of points on the surface of a body. For
example, on the surface of a bar subjected to tension we may make two
fine transverse scratches, and measure the distance between them before
and after the bar is stretched. For such measurements very refined
instruments are required. Instruments for this purpose are called
barbarously "extensometers," and many different kinds have been devised.
From measurements of displacement by an extensometer we may deduce the
average extension of a filament of the bar terminated by the two
scratches. In general, when we attempt to measure a strain, we really
measure some displacements, and deduce the values, not of the strain at
a point, but of the average extensions of some particular linear
filaments of a body containing the point; and these filaments are, from
the nature of the case, nearly always superficial filaments.

18. In the case of transparent materials such as glass there is
available a method of studying experimentally the state of strain within
a body. This method is founded upon the result that a piece of glass
when strained becomes doubly refracting, with its optical principal axes
at any point in the directions of the principal axes of strain (§ 15) at
the point. When the piece has two parallel plane faces, and two of the
principal axes of strain at any point are parallel to these faces,
polarized light transmitted through the piece in a direction normal to
the faces can be used to determine the directions of the principal axes
of the strain at any point. If the directions of these axes are known
theoretically the comparison of the experimental and theoretical results
yields a test of the theory.

19. _Relations between Stresses and Strains._--The problem of the
extension of a bar subjected to tension is the one which has been most
studied experimentally, and as a result of this study it is found that
for most materials, including all metals except cast metals, the
measurable extension is proportional to the applied tension, provided
that this tension is not too great. In interpreting this result it is
assumed that the tension is uniform over the cross-section of the bar,
and that the extension of longitudinal filaments is uniform throughout
the bar; and then the result takes the form of a law of proportionality
connecting stress and strain: The tension is proportional to the
extension. Similar results are found for the same materials when other
methods of experimenting are adopted, for example, when a bar is
supported at the ends and bent by an attached load and the deflexion is
measured, or when a bar is twisted by an axial couple and the relative
angular displacement of two sections is measured. We have thus very
numerous experimental verifications of the famous law first enunciated
by Robert Hooke in 1678 in the words "_Ut Tensio sic vis_"; that is,
"the Power of any spring is in the same proportion as the Tension
(--stretching) thereof." The most general statement of Hooke's Law in
modern language would be:--_Each of the six components of stress at any
point of a body is a linear function of the six components of strain at
the point._ It is evident from what has been said above as to the nature
of the measurement of stresses and strains that this law in all its
generality does not admit of complete experimental verification, and
that the evidence for it consists largely in the agreement of the
results which are deduced from it in a theoretical fashion with the
results of experiments. Of such results one of a general character may
be noted here. If the law is assumed to be true, and the equations of
motion of the body (§ 5) are transformed by means of it into
differential equations for determining the components of displacement,
these differential equations admit of solutions which represent periodic
vibratory displacements (see § 85 below). The fact that solid bodies can
be thrown into states of isochronous vibration has been emphasized by
G.G. Stokes as a peremptory proof of the truth of Hooke's Law.

20. According to the statement of the generalized Hooke's Law the
stress-components vanish when the strain-components vanish. The
strain-components contemplated in experiments upon which the law is
founded are measured from a zero of reckoning which corresponds to the
state of the body subjected to experiment before the experiment is made,
and the stress-components referred to in the statement of the law are
those which are called into action by the forces applied to the body in
the course of the experiment. No account is taken of the stress which
must already exist in the body owing to the force of gravity and the
forces by which the body is supported. When it is desired to take
account of this stress it is usual to suppose that the strains which
would be produced in the body if it could be freed from the action of
gravity and from the pressures of supports are so small that the strains
produced by the forces which are applied in the course of the experiment
can be compounded with them by simple superposition. This supposition
comes to the same thing as measuring the strain in the body, not from
the state in which it was before the experiment, but from an ideal state
(the "unstressed" state) in which it would be entirely free from
internal stress, and allowing for the strain which would be produced by
gravity and the supporting forces if these forces were applied to the
body when free from stress. In most practical cases the initial strain
to be allowed for is unimportant (see §§ 91-93 below).

21. Hooke's law of proportionality of stress and strain leads to the
introduction of important physical constants: the _moduluses of
elasticity_ of a body. Let a bar of uniform section (of area [omega]) be
stretched with tension T, which is distributed uniformly over the
section, so that the stretching force is Tw[omega], and let the bar be
unsupported at the sides. The bar will undergo a longitudinal extension
of magnitude T/E, where E is a constant quantity depending upon the
material. This constant is called _Young's modulus_ after Thomas Young,
who introduced it into the science in 1807. The quantity E is of the
same nature as a traction, that is to say, it is measured as a force
estimated per unit of area. For steel it is about 2.04×10^12 dynes per
square centimetre, or about 13,000 tons per sq. in.

22. The longitudinal extension of the bar under tension is not the only
strain in the bar. It is accompanied by a lateral contraction by which
all the transverse filaments of the bar are shortened. The amount of
this contraction is [sigma]T/E, where [sigma] is a certain number called
_Poisson's ratio_, because its importance was at first noted by S.D.
Poisson in 1828. Poisson arrived at the existence of this contraction,
and the corresponding number [sigma], from theoretical considerations,
and his theory led him to assign to [sigma] the value ¼. Many
experiments have been made with the view of determining [sigma], with
the result that it has been found to be different for different
materials, although for very many it does not differ much from ¼. For
steel the best value (Amagat's) is 0.268. Poisson's theory admits of
being modified so as to agree with the results of experiment.

23. The behaviour of an elastic solid body, strained within the limits
of its elasticity, is entirely determined by the constants E and [sigma]
if the body is _isotropic_, that is to say, if it has the same quality
in all directions around any point. Nevertheless it is convenient to
introduce other constants which are related to the action of particular
sorts of forces. The most important of these are the "modulus of
compression" (or "bulk modulus") and the "rigidity" (or "modulus of
shear"). To define the _modulus of compression_, we suppose that a solid
body of any form is subjected to uniform hydrostatic pressure of amount
p. The state of stress within it will be one of uniform pressure, the
same at all points, and the same in all directions round any point.
There will be compression, the same at all points, and proportional to
the pressure; and the amount of the compression can be expressed as p/k.
The quantity k is the modulus of compression. In this case the linear
contraction in any direction is p/3k; but in general the linear
extension (or contraction) is not one-third of the cubical dilatation
(or compression).

24. To define the _rigidity_, we suppose that a solid body is subjected
to forces in such a way that there is shearing stress within it. For
example, a cubical block may be subjected to opposing tractions on
opposite faces acting in directions which are parallel to an edge of the
cube and to both the faces. Let S be the amount of the traction, and let
it be uniformly distributed over the faces. As we have seen (§ 7), equal
tractions must act upon two other faces in suitable directions in order
to maintain equilibrium (see fig. 2 of § 7). The two directions involved
may be chosen as axes of x, y as in that figure. Then the state of
stress will be one in which the stress-component denoted by X_y is equal
to S, and the remaining stress-components vanish; and the strain
produced in the body is shearing strain of the type denoted by e _(xy).
The amount of the shearing strain is S/µ, and the quantity µ is the
"rigidity."

25. The modulus of compression and the rigidity are quantities of the
same kind as Young's modulus. The modulus of compression of steel is
about 1.43 × 10^12 dynes per square centimetre, the rigidity is about
8.19 × 10^11 dynes per square centimetre. It must be understood that the
values for different specimens of nominally the same material may differ
considerably.

  The modulus of compression k and the rigidity µ of an isotropic
  material are connected with the Young's modulus E and Poisson's ratio
  [sigma] of the material by the equations

    k = E/3(1 - 2[sigma]),   µ = E/2(1 + [sigma]).

  26. Whatever the forces acting upon an isotropic solid body may be,
  provided that the body is strained within its limits of elasticity,
  the strain-components are expressed in terms of the stress-components
  by the equations

    e_(xx) = (X_x - [sigma]Y_y - [sigma]Z_z)/E,  e_(yz) = Y_z/µ, \
    e_(yy) = (Y_y - [sigma]Z_z - [sigma]X_x)/E,  e_(zx) = Z_x/µ,  > (1)
    e_(zz) = (Z_z - [sigma]X_x - [sigma]Y_y)/E,  e_(xy) = X_y/µ. /

  If we introduce a quantity [lambda], of the same nature as E or µ, by
  the equation

    [lambda] = E[sigma]/(1 + [sigma])(1 - 2[sigma]),  (2)

  we may express the stress-components in terms of the strain-components
  by the equations

    X_x = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2µe_(xx), Y_z = µe_(yz), \
    Y_y = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2µe_(yy), Z_x = µe_(zx),  > (3)
    Z_z = [lambda][e_(xx) + e_(yy) + e_(zz)] + 2µe_(zz), X_y = µe_(xy); /

  and then the behaviour of the body under the action of any forces
  depends upon the two constants [lambda] and µ. These two constants
  were introduced by G. Lamé in his treatise of 1852. The importance of
  the quantity µ had been previously emphasized by L.J. Vicat and G.G.
  Stokes.

  27. The potential energy per unit of volume (often called the
  "resilience") stored up in the body by the strain is equal to

    ½([lambda] + 2µ)(e_(xx) + e_(yy) + e_(zz))² + ½µ[e²_(yz) + e²_(zx) +
      e²_(xy) - 4e_(yy)e_(zz) - 4e_(zz)e_(xx) - 4e_(xx)e_(yy)],

  or the equivalent expression

    ½[(X²_x + Y²_y + Z²_z) - 2[sigma](Y_yZ_z + Z_zX_x + X_xY_y) +
      2(1 + [sigma])(Y²_z + Z²_x + X²_y)]/E.

  The former of these expressions is called the
  "strain-energy-function."

28. The Young's modulus E of a material is often determined
experimentally by the direct method of the extensometer (§ 17), but more
frequently it is determined indirectly by means of a result obtained in
the theory of the flexure of a bar (see §§ 47, 53 below). The rigidity µ
is usually determined indirectly by means of results obtained in the
theory of the torsion of a bar (see §§ 41, 42 below). The modulus of
compression k may be determined directly by means of the piezometer, as
was done by E.H. Amagat, or it may be determined indirectly by means of
a result obtained in the theory of a tube under pressure, as was done by
A. Mallock (see § 78 below). The value of Poisson's ratio [sigma] is
generally inferred from the relation connecting it with E and µ or with
E and k, but it may also be determined indirectly by means of a result
obtained in the theory of the flexure of a bar (§ 47 below), as was done
by M.A. Cornu and A. Mallock, or directly by a modification of the
extensometer method, as has been done recently by J. Morrow.

29. The _elasticity of a fluid_ is always expressed by means of a single
quantity of the same kind as the _modulus of compression_ of a solid
body. To any increment of pressure, which is not too great, there
corresponds a proportional cubical compression, and the amount of this
compression for an increment [delta]p of pressure can be expressed as
[delta]p/k. The quantity that is usually tabulated is the reciprocal of
k, and it is called the _coefficient of compressibility_. It is the
amount of compression per unit increase of pressure. As a physical
quantity it is of the same dimensions as the reciprocal of a pressure
(or of a force per unit of area). The pressures concerned are usually
measured in atmospheres (1 atmosphere = 1.014 × 10^6 dynes per sq. cm.).
For water the coefficient of compressibility, or the compression per
atmosphere, is about 4.5 × 10^-5. This gives for k the value 2.22 ×
10^10 dynes per sq. cm. The Young's modulus and the rigidity of a fluid
are always zero.

30. The relations between stress and strain in a material which is not
isotropic are much more complicated. In such a material the Young's
modulus depends upon the direction of the tension, and its variations
about a point are expressed by means of a surface of the fourth degree.
The Poisson's ratio depends upon the direction of the contracted lateral
filaments as well as upon that of the longitudinal extended ones. The
rigidity depends upon both the directions involved in the specification
of the shearing stress. In general there is no simple relation between
the Young's moduluses and Poisson's ratios and rigidities for assigned
directions and the modulus of compression. Many materials in common use,
all fibrous woods for example, are actually _aeolotropic_ (that is to
say, are not isotropic), but the materials which are aeolotropic in the
most regular fashion are natural crystals. The elastic behaviour of
crystals has been studied exhaustively by many physicists, and in
particular by W. Voigt. The strain-energy-function is a homogeneous
quadratic function of the six strain-components, and this function may
have as many as 21 independent coefficients, taking the place in the
general case of the 2 coefficients [lambda], µ which occur when the
material is isotropic--a result first obtained by George Green in 1837.
The best experimental determinations of the coefficients have been made
indirectly by Voigt by means of results obtained in the theories of the
torsion and flexure of aeolotropic bars.

31. _Limits of Elasticity._--A solid body which has been strained by
considerable forces does not in general recover its original size and
shape completely after the forces cease to act. The strain that is left
is called _set_. If set occurs the elasticity is said to be
"imperfect," and the greatest strain (or the greatest load) of any
specified type, for which no set occurs, defines the "limit of perfect
elasticity" corresponding to the specified type of strain, or of stress.
All fluids and many solid bodies, such as glasses and crystals, as well
as some metals (copper, lead, silver) appear to be perfectly elastic as
regards change of volume within wide limits; but malleable metals and
alloys can have their densities permanently increased by considerable
pressures. The limits of perfect elasticity as regards change of shape,
on the other hand, are very low, if they exist at all, for glasses and
other hard, brittle solids; but a class of metals including copper,
brass, steel, and platinum are very perfectly elastic as regards
distortion, provided that the distortion is not too great. The question
can be tested by observation of the torsional elasticity of thin fibres
or wires. The limits of perfect elasticity are somewhat ill-defined,
because an experiment cannot warrant us in asserting that there is no
set, but only that, if there is any set, it is too small to be observed.

32. A different meaning may be, and often is, attached to the phrase
"limits of elasticity" in consequence of the following experimental
result:--Let a bar be held stretched under a moderate tension, and let
the extension be measured; let the tension be slightly increased and the
extension again measured; let this process be continued, the tension
being increased by equal increments. It is found that when the tension
is not too great the extension increases by equal increments (as nearly
as experiment can decide), but that, as the tension increases, a stage
is reached in which the extension increases faster than it would do if
it continued to be proportional to the tension. The beginning of this
stage is tolerably well marked. Some time before this stage is reached
the limit of perfect elasticity is passed; that is to say, if the load
is removed it is found that there is some permanent set. The limiting
tension beyond which the above law of proportionality fails is often
called the "limit of _linear_ elasticity." It is higher than the limit
of perfect elasticity. For steel bars of various qualities J.
Bauschinger found for this limit values varying from 10 to 17 tons per
square inch. The result indicates that, when forces which produce any
kind of strain are applied to a solid body and are gradually increased,
the strain at any instant increases proportionally to the forces up to a
stage beyond that at which, if the forces were removed, the body would
completely recover its original size and shape, but that the increase of
strain ceases to be proportional to the increase of load when the load
surpasses a certain limit. There would thus be, for any type of strain,
a _limit of linear elasticity_, which exceeds the limit of perfect
elasticity.

33. A body which has been strained beyond the limit of linear elasticity
is often said to have suffered an "over-strain." When the load is
removed, the _set_ which can be observed is not entirely permanent; but
it gradually diminishes with lapse of time. This phenomenon is named
"elastic after-working." If, on the other hand, the load is maintained
constant, the strain is gradually increased. This effect indicates a
gradual flowing of solid bodies under great stress; and a similar effect
was observed in the experiments of H. Tresca on the punching and
crushing of metals. It appears that all solid bodies under sufficiently
great loads become "plastic," that is to say, they take a set which
gradually increases with the lapse of time. No plasticity is observed
when the limit of linear elasticity is not exceeded.

34. The values of the elastic limits are affected by overstrain. If the
load is maintained for some time, and then removed, the limit of linear
elasticity is found to be higher than before. If the load is not
maintained, but is removed and then reapplied, the limit is found to be
lower than before. During a period of rest a test piece recovers its
elasticity after overstrain.

35. The effects of repeated loading have been studied by A. Wöhler, J.
Bauschinger, O. Reynolds and others. It has been found that, after many
repetitions of rather rapidly alternating stress, pieces are fractured
by loads which they have many times withstood. It is not certain whether
the fracture is in every case caused by the gradual growth of minute
flaws from the beginning of the series of tests, or whether the elastic
quality of the material suffers deterioration apart from such flaws. It
appears, however, to be an ascertained result that, so long as the limit
of linear elasticity is not exceeded, repeated loads and rapidly
alternating loads do not produce failure of the material.

36. The question of the conditions of safety, or of the conditions in
which rupture is produced, is one upon which there has been much
speculation, but no completely satisfactory result has been obtained. It
has been variously held that rupture occurs when the numerically
greatest principal stress exceeds a certain limit, or when this stress
is tension and exceeds a certain limit, or when the greatest difference
of two principal stresses (called the "stress-difference") exceeds a
certain limit, or when the greatest extension or the greatest shearing
strain or the greatest strain of any type exceeds a certain limit. Some
of these hypotheses appear to have been disproved. It was held by G.F.
Fitzgerald (_Nature_, Nov. 5, 1896) that rupture is not produced by
pressure symmetrically applied all round a body, and this opinion has
been confirmed by the recent experiments of A. Föppl. This result
disposes of the greatest stress hypothesis and also of the greatest
strain hypothesis. The fact that short pillars can be crushed by
longitudinal pressure disposes of the greatest tension hypothesis, for
there is no tension in the pillar. The greatest extension hypothesis
failed to satisfy some tests imposed by H. Wehage, who experimented with
blocks of wrought iron subjected to equal pressures in two directions at
right angles to each other. The greatest stress-difference hypothesis
and the greatest shearing strain hypothesis would lead to practically
identical results, and these results have been held by J.J. Guest to
accord well with his experiments on metal tubes subjected to various
systems of combined stress; but these experiments and Guest's conclusion
have been criticized adversely by O. Mohr, and the question cannot be
regarded as settled. The fact seems to be that the conditions of rupture
depend largely upon the nature of the test (tensional, torsional,
flexural, or whatever it may be) that is applied to a specimen, and that
no general formula holds for all kinds of tests. The best modern
technical writings emphasize the importance of the limits of linear
elasticity and of tests of dynamical resistance (§ 87 below) as well as
of statical resistance.

37. The question of the conditions of rupture belongs rather to the
science of the strength of materials than to the science of elasticity
(§ 1); but it has been necessary to refer to it briefly here, because
there is no method except the methods of the theory of elasticity for
determining the state of stress or strain in a body subjected to forces.
Whatever view may ultimately be adopted as to the relation between the
conditions of safety of a structure and the state of stress or strain in
it, the calculation of this state by means of the theory or by
experimental means (as in § 18) cannot be dispensed with.

  38. _Methods of determining the Stress in a Body subjected to given
  Forces._--To determine the state of stress, or the state of strain, in
  an isotropic solid body strained within its limits of elasticity by
  given forces, we have to use (i.) the equations of equilibrium, (ii.)
  the conditions which hold at the bounding surface, (iii.) the
  relations between stress-components and strain-components, (iv.) the
  relations between strain-components and displacement. The equations of
  equilibrium are (with notation already used) three partial
  differential equations of the type

    dPX_x   dPX_y   dPZ_z
    ----- + ----- + ----- + [rho]X = 0.  (1)
     dPx     dPy     dPz

  The conditions which hold at the bounding surface are three equations
  of the type

    X_x cos(x, [nu]) + X_y cos(y, [nu]) + Z_x cos(z, [nu]) = X`_[nu], (2)

  where [nu] denotes the direction of the outward-drawn normal to the
  bounding surface, and X`_[nu] denotes the x-component of the applied
  surface traction. The relations between stress-components and
  strain-components are expressed by either of the sets of equations (1)
  or (3) of § 26. The relations between strain-components and
  displacement are the equations (1) of § 11, or the equivalent
  conditions of compatibility expressed in equations (1) and (2) of §
  16.

  39. We may proceed by either of two methods. In one method we
  eliminate the stress-components and the strain-components and retain
  only the components of displacement. This method leads (with notation
  already used) to three partial differential equations of the type

                   dP   /dPu   dPv   dPw\      /dP²u   dP²u   dP²u\
    ([lambda] + µ) --- ( --- + --- + --- ) + µ( ---- + ---- + ---- ) + [rho]X = 0, (3)
                   dPx  \dPx   dPy   dPz/      \dPx²   dPy²   dPz²/

  and three boundary conditions of the type
                                                  _
                          /dPu   dPv   dPw\      |               dPu
    [lambda] cos(x, [nu])( --- + --- + --- ) + µ | 2 cos(x, [nu])---
                          \dPx   dPy   dPz/      |_              dPx
                                                             _
                     /dPv   dPu\                 /dPu   dPw\  |
      + cos(y, [nu])( -- + --   ) + cos(z, [nu])( -- + --   ) | = X`_[nu], (4)
                     \dPx   dPy/                 \dPz   dPx/ _|

  In the alternative method we eliminate the strain-components and the
  displacements. This method leads to a system of partial differential
  equations to be satisfied by the stress-components. In this system
  there are three equations of the type

    dPX_x   dPX_y   dPX_z
    ----- + ----- + ----- + [rho]X = 0,  (1 _bis_)
     dPx     dPy     dPz

  three of the type

    dP²X_x   dP²X_x   dP²X_x        1      dP²
    ------ + ------ + ------ + ----------- --- (X_x + Y_y + Z_z) =
     dPx²     dPy²     dPz²    1 + [sigma] dPx²

          [sigma]       /dPX   dPY   dPZ\           dPX
      -  ---------[rho]( --- + --- + --- ) - 2[rho] ---,  (5)
         1-[sigma]      \dPx   dPy   dPz/           dPx

  and three of the type

    dP²Y_z   dP²Y_z   dP²Y_z        1       dP²
    ------ + ------ + ------ + ----------- ------ (X_x + Y_y + Z_z) =
     dPx²     dPy²     dPz²    1 + [sigma] dPydPz

              /dPZ   dPY\
      - [rho]( --- + --- ), (6)
              \dPy   dPz/

  the equations of the two latter types being necessitated by the
  conditions of compatibility of strain-components. The solutions of
  these equations have to be adjusted so that the boundary conditions of
  the type (2) may be satisfied.

  40. It is evident that whichever method is adopted the mathematical
  problem is in general very complicated. It is also evident that, if we
  attempt to proceed by help of some intuition as to the nature of the
  stress or strain, our intuition ought to satisfy the tests provided by
  the above systems of equations. Neglect of this precaution has led to
  many errors. Another source of frequent error lies in the neglect of
  the conditions in which the above systems of equations are correct.
  They are obtained by help of the supposition that the relative
  displacements of the parts of the strained body are small. The
  solutions of them must therefore satisfy the test of smallness of the
  relative displacements.

41. Torsion.--As a first example of the application of the theory we
take the problem of the torsion of prisms. This problem, considered
first by C.A. Coulomb in 1784, was finally solved by B. de Saint-Venant
in 1855. The problem is this:--A cylindrical or prismatic bar is held
twisted by terminal couples; it is required to determine the state of
stress and strain in the interior. When the bar is a circular cylinder
the problem is easy. Any section is displaced by rotation about the
central-line through a small angle, which is proportional to the
distance z of the section from a fixed plane at right angles to this
line. This plane is a terminal section if one of the two terminal
sections is not displaced. The angle through which the section z rotates
is [tau]z, where [tau] is a constant, called the amount of the twist;
and this constant [tau] is equal to G/µI, where G is the twisting
couple, and I is the moment of inertia of the cross-section about the
central-line. This result is often called "Coulomb's law." The stress
within the bar is shearing stress, consisting, as it must, of two sets
of equal tangential tractions on two sets of planes which are at right
angles to each other. These planes are the cross-sections and the axial
planes of the bar. The tangential traction at any point of the
cross-section is directed at right angles to the axial plane through the
point, and the tangential traction on the axial plane is directed
parallel to the length of the bar. The amount of either at a distance r
from the axis is µ[tau]r or Gr/I. The result that G = µ[tau]I can be
used to determine µ experimentally, for [tau] may be measured and G and
I are known.

42. When the cross-section of the bar is not circular it is clear that
this solution fails; for the existence of tangential traction, near the
prismatic bounding surface, on any plane which does not cut this surface
at right angles, implies the existence of traction applied to this
surface. We may attempt to modify the theory by retaining the
supposition that the stress consists of shearing stress, involving
tangential traction distributed in some way over the cross-sections.
Such traction is obviously a necessary constituent of any stress-system
which could be produced by terminal couples around the axis. We should
then know that there must be equal tangential traction directed along
the length of the bar, and exerted across some planes or other which are
parallel to this direction. We should also know that, at the bounding
surface, these planes must cut this surface at right angles. The
corresponding strain would be shearing strain which could involve (i.) a
sliding of elements of one cross-section relative to another, (ii.) a
relative sliding of elements of the above mentioned planes in the
direction of the length of the bar. We could conclude that there may be
a longitudinal displacement of the elements of the cross-sections. We
should then attempt to satisfy the conditions of the problem by
supposing that this is the character of the strain, and that the
corresponding displacement consists of (i.) a rotation of the
cross-sections in their planes such as we found in the case of the
circle, (ii.) a distortion of the cross-sections into curved surfaces by
a displacement (w) which is directed normally to their planes and varies
in some manner from point to point of these planes. We could show that
all the conditions of the problem are satisfied by this assumption,
provided that the longitudinal displacement (w), considered as a
function of the position of a point (x, y) in the cross-section,
satisfies the equation

  dP²w   dP²w
  ---- + ---- = 0,  (1)
  dPx²   dPy²

and the boundary condition

   / dPw         \                  / dPw         \
  (  --- - [tau]y ) cos(x, [nu]) + (  --- + [tau]x ) cos(y, [nu]) = 0, (2)
   \ dPx         /                  \ dPy         /

where [tau] denotes the amount of the twist, and [nu] the direction of
the normal to the boundary. The solution is known for a great many forms
of section. (In the particular case of a circular section w vanishes.)
The tangential traction at any point of the cross-section is directed
along the tangent to that curve of the family [psi] = const. which
passes through the point, [psi] being the function determined by the
equations

  dPw         /dP[psi]    \    dPw           /dP[psi]    \
  --- = [tau]( ------- + y ),  --- = - [tau]( ------- + x ).
  dPx         \  dPy      /    dPy           \  dPx      /

The amount of the twist [tau] produced by terminal couples of magnitude
G is G/C, where C is a constant, called the "torsional rigidity" of the
prism, and expressed by the formula
         _  _  _                         _
        /  /  |  /dP[psi]\²    /dP[psi]\² |
  C = µ |  |  | ( ------- ) + ( ------- ) | dxdy,
       _/ _/  |_ \  dPx  /     \  dPy  / _|

the integration being taken over the cross-section. When the coefficient
of µ in the expression for C is known for any section, µ can be
determined by experiment with a bar of that form of section.

43. The distortion of the cross-sections into curved surfaces is shown
graphically by drawing the contour lines (w = const.). In general the
section is divided into a number of compartments, and the portions that
lie within two adjacent compartments are respectively concave and
convex. This result is illustrated in the accompanying figures (fig. 4
for the ellipse, given by x²/b² + y²/c² = 1; fig. 5 for the equilateral
triangle, given by (x + (1/3)a) [x² - 3y² - (4/3)ax + (4/9)a²] = 0; fig.
6 for the square).

[Illustration: FIG. 4.]

44. The distribution of the shearing stress over the cross-section is
determined by the function [psi], already introduced. If we draw the
curves [psi] = const., corresponding to any form of section, for
equidifferent values of the constant, the tangential traction at any
point on the cross-section is directed along the tangent to that curve
of the family which passes through the point, and the magnitude of it is
inversely proportional to the distance between consecutive curves of the
family. Fig. 7 illustrates the result in the case of the _equilateral_
triangle. The boundary is, of course, one of the lines. The "lines of
shearing stress" which can thus be drawn are in every case identical
with the lines of flow of frictionless liquid filling a cylindrical
vessel of the same cross-section as the bar, when the liquid circulates
in the plane of the section with uniform spin. They are also the same as
the contour lines of a flexible and slightly extensible membrane, of
which the edge has the same form as the bounding curve of the
cross-section of the bar, when the membrane is fixed at the edge and
slightly deformed by uniform pressure.

[Illustration: FIG. 5.]

[Illustration: FIG. 6.]

[Illustration: FIG. 7.]

45. Saint-Venant's theory shows that the true torsional rigidity is in
general less than that which would be obtained by extending Coulomb's
law (G = µ[tau]I) to sections which are not circular. For an elliptic
cylinder of sectional area [omega] and moment of inertia I about its
central-line the torsional rigidity is µ[omega]^4/4[pi]²I, and this
formula is not far from being correct for a very large number of
sections. For a bar of square section of side a centimetres, the
torsional rigidity in C.G.S. units is (0.1406)µa^4 approximately, µ
being expressed in dynes per square centimetre. How great the defect of
the true value from that given by extending Coulomb's law may be in the
case of sections with projecting corners is shown by the diagrams (fig.
8 especially no. 4). In these diagrams the upper of the two numbers
under each figure indicates the fraction which the true torsional
rigidity corresponding to the section is of that value which would be
obtained by extending Coulomb's law; and the lower of the two numbers
indicates the ratio which the torsional rigidity for a bar of the
corresponding section bears to that of a bar of circular section of the
same material and of equal sectional area. These results have an
important practical application, inasmuch as they show that
strengthening ribs and projections, such as are introduced in
engineering to give stiffness to beams, have the reverse of a good
effect when torsional stiffness is an object, although they are of great
value in increasing the resistance to bending. The theory shows further
that the resistance to torsion is very seriously diminished when there
is in the surface any dent approaching to a re-entrant angle. At such a
place the shearing strain tends to become infinite, and some permanent
set is produced by torsion. In the case of a section of any form, the
strain and stress are greatest at points on the contour, and these
points are in many cases the points of the contour which are nearest to
the centroid of the section. The theory has also been applied to show
that a longitudinal flaw near the axis of a shaft transmitting a
torsional couple has little influence on the strength of the shaft, but
that in the neighbourhood of a similar flaw which is much nearer to the
surface than to the axis the shearing strain may be nearly doubled, and
thus the possibility of such flaws is a source of weakness against which
special provision ought to be made.

[Illustration: FIG. 8.--Diagrams showing Torsional Rigidities.

  (1) Rectilineal square. .84346. .88326.
  (2) Square with curved corners and hollow sides. .8186. .8666.
  (3) Square with acute angles and hollow sides. .7783. .8276.
  (4) Star with four rounded points, being a curve of the eighth degree.
        .5374. .6745.
  (5) Equilateral triangle. .60000. .72552.]

[Illustration: FIG. 9.]

46. _Bending of Beams._--As a second example of the application of the
general theory we take the problem of the flexure of a beam. In this
case also we begin by forming a simple intuition as to the nature of the
strain and the stress. On the side of the beam towards the centre of
curvature the longitudinal filaments must be contracted, and on the
other side they must be extended. If we assume that the cross-sections
remain plane, and that the central-line is unaltered in length, we see
(at once from fig. 9) that the extensions (or contractions) are given by
the formula y/R, where y denotes the distance of a longitudinal filament
from the plane drawn through the unstrained central-line at right-angles
to the plane of bending, and R is the radius of curvature of the curve
into which this line is bent (shown by the dotted line in the figure).
Corresponding to this strain there must be traction acting across the
cross-sections. If we assume that there is no other stress, then the
magnitude of the traction in question is Ey/R, where E is Young's
modulus, and it is tension on the side where the filaments are extended
and pressure on the side where they are contracted. If the plane of
bending contains a set of principal axes of the cross-sections at their
centroids, these tractions for the whole cross-section are equivalent to
a couple of moment EI/R, where I now denotes the moment of inertia of
the cross-section about an axis through its centroid at right angles to
the plane of bending, and the plane of the couple is the plane of
bending. Thus a beam of any form of section can be held bent in a
"principal plane" by terminal couples of moment M, that is to say by a
"bending moment" M; the central-line will take a curvature M/EI, so that
it becomes an arc of a circle of radius EI/M; and the stress at any
point will be tension of amount My/I, where y denotes distance (reckoned
positive towards the side remote from the centre of curvature) from that
plane which initially contains the central-line and is at right angles
to the plane of the couple. This plane is called the "neutral plane."
The restriction that the beam is bent in a principal plane means that
the plane of bending contains one set of principal axes of the
cross-sections at their centroids; in the case of a beam of rectangular
section the plane would bisect two opposite edges at right angles. In
order that the theory may hold good the radius of curvature must be very
large.

47. In this problem of the bending of a beam by terminal couples the
stress is tension, determined as above, and the corresponding strain
consists therefore of longitudinal extension of amount My/EI or y/R
(contraction if y is negative), accompanied by lateral contraction of
amount [sigma]My/EI or [sigma]y/R (extension if y is negative), [sigma]
being Poisson's ratio for the material. Our intuition of the nature of
the strain was imperfect, inasmuch as it took no account of these
lateral strains. The necessity for introducing them was pointed out by
Saint-Venant. The effect of them is a change of shape of the
cross-sections in their own planes. This is shown in an exaggerated way
in fig. 10, where the rectangle ABCD represents the cross-section of the
unstrained beam, or a rectangular portion of this cross-section, and the
curvilinear figure A'B'C'D' represents in an exaggerated fashion the
cross-section (or the corresponding portion of the cross-section) of the
same beam, when bent so that the centre of curvature of the central-line
(which is at right angles to the plane of the figure) is on the line EF
produced beyond F. The lines A'B' and C'D' are approximately circles of
radii R/[sigma], when the central-line is a circle of radius R, and
their centres are on the line FE produced beyond E. Thus the neutral
plane, and each of the faces that is parallel to it, becomes strained
into an _anticlastic surface_, whose principal curvatures are in the
ratio [sigma] : 1. The general appearance of the bent beam is shown in
an exaggerated fashion in fig. 11, where the traces of the surface into
which the neutral plane is bent are dotted. The result that the ratio of
the principal curvatures of the anticlastic surfaces, into which the top
and bottom planes of the beam (of rectangular section) are bent, is
Poisson's ratio [sigma], has been used for the experimental
determination of [sigma]. The result that the radius of curvature of the
bent central-line is EI/M is used in the experimental determination of
E. The quantity EI is often called the "flexural rigidity" of the beam.
There are two principal flexural rigidities corresponding to bending in
the two principal planes (cf. § 62 below).

[Illustration: FIG. 10.]

[Illustration: FIG. 11.]

[Illustration: FIG. 12.]

48. That this theory requires modification, when the load does not
consist simply of terminal couples, can be seen most easily by
considering the problem of a beam loaded at one end with a weight W, and
supported in a horizontal position at its other end. The forces that are
exerted at any section p, to balance the weight W, must reduce
statically to a vertical force W and a couple, and these forces arise
from the action of the part Ap on the part Bp (see fig. 12), i.e. from
the stresses across the section at p. The couple is equal to the moment
of the applied load W about an axis drawn through the centroid of the
section p at right angles to the plane of bending. This moment is called
the "bending moment" at the section, it is the product of the load W and
the distance of the section from the loaded end, so that it varies
uniformly along the length of the beam. The stress that suffices in the
simpler problem gives rise to no vertical force, and it is clear that in
addition to longitudinal tensions and pressures there must be tangential
tractions on the cross-sections. The resultant of these tangential
tractions must be a force equal to W, and directed vertically; but the
direction of the traction at a point of the cross-section need not in
general be vertical. The existence of tangential traction on the
cross-sections implies the existence of equal tangential traction,
directed parallel to the central-line, on some planes or other which are
parallel to this line, the two sets of tractions forming a shearing
stress. We conclude that such shearing stress is a necessary constituent
of the stress-system in the beam bent by terminal transverse load. We
can develop a theory of this stress-system from the assumptions (i.)
that the tension at any point of the cross-section is related to the
bending moment at the section by the same law as in the case of uniform
bending by terminal couples; (ii.) that, in addition to this tension,
there is at any point shearing stress, involving tangential tractions
acting in appropriate directions upon the elements of the
cross-sections. When these assumptions are made it appears that there is
one and only one distribution of shearing stress by which the conditions
of the problem can be satisfied. The determination of the amount and
direction of this shearing stress, and of the corresponding strains and
displacements, was effected by Saint-Venant and R.F.A. Clebsch for a
number of forms of section by means of an analysis of the same kind as
that employed in the solution of the torsion problem.

[Illustration: Fig. 13.]

  49. Let l be the length of the beam, x the distance of the section p
  from the fixed end A, y the distance of any point below the horizontal
  plane through the centroid of the section at A, then the bending
  moment at p is W(l - x), and the longitudinal tension P or X_x at any
  point on the cross-section is - W(l - x)y/I, and this is related to
  the bending moment exactly as in the simpler problem.

  50. The expressions for the shearing stresses depend on the shape of
  the cross-section. Taking the beam to be of isotropic material and the
  cross-section to be an ellipse of semiaxes a and b (fig. 13), the a
  axis being vertical in the unstrained state, and drawing the axis z at
  right angles to the plane of flexure, we find that the vertical
  shearing stress U or X_y at any point (y, z) on any cross-section is

    2W[(a² - y²){2a²(1 + [sigma]) + b²} - z²a²(1 - 2[sigma])]
    ---------------------------------------------------------.
                 [pi]a³b(1 + [sigma])(3a² + b²)

  The resultant of these stresses is W, but the amount at the centroid,
  which is the maximum amount, exceeds the average amount, W/[pi]ab, in
  the ratio

    {4a²(1 + [sigma]) + 2b²}/(3a² + b²)(1 + [sigma]).

  If [sigma] = ¼, this ratio is 7/5 for a circle, nearly 4/3 for a flat
  elliptic bar with the longest diameter vertical, nearly 8/5 for a flat
  elliptic bar with the longest diameter horizontal.

  In the same problem the horizontal shearing stress T or Z_x at any
  point on any cross-section is of amount

      4Wyz{a²(1 + [sigma]) + b²[sigma]}
    - ---------------------------------.
       [pi]a³b(1 + [sigma])(3a² + b²)

  The resultant of these stresses vanishes; but, taking as before
  [sigma] = ¼, and putting for the three cases above a = b, a = 10b, b =
  10a, we find that the ratio of the maximum of this stress to the
  average vertical shearing stress has the values 3/5, nearly 1/15, and
  nearly 4. Thus the stress T is of considerable importance when the
  beam is a plank.

  As another example we may consider a circular tube of external radius
  r0 and internal radius r1. Writing P, U, T for X_x, X_y, Z_x, we find

                  4W
    P = - -----------------(l - x)y,
          [pi](r0^4 - r1^4)
                                         _
                      W                 |                /
    U = ------------------------------- |(3 + 2[sigma]) (r0² + r1² - y²
        2(1 + [sigma])[pi](r0^4 - r1^4) |_               \
                                                 _
           r0²r1²            \                    |
       - ---------- (y² - z²) ) - (1 - 2[sigma])z²|
         (y² + z²)²          /                   _|

                      W
  T = - ------------------------------
        (1 + [sigma])[pi](r0^4 - r1^4)
     _                                         _
    |                                 r0²r1²    |
    | 1 + 2[sigma] + (3 + 2[sigma]) ----------  | yz;
    |_                              (y² + z²)² _|

  and for a tube of radius r and small thickness t the value of P and
  the maximum values of U and T reduce approximately to

    P = - W(l - x)y/[pi]r³t

    U_max. = W/[pi]rt,  T_max. = W/2[pi]rt.

  The greatest value of U is in this case approximately twice its
  average value, but it is possible that these results for the bending
  of very thin tubes may be seriously at fault if the tube is not
  plugged, and if the load is not applied in the manner contemplated in
  the theory (cf. § 55). In such cases the extensions and contractions
  of the longitudinal filaments may be practically confined to a small
  part of the material near the ends of the tube, while the rest of the
  tube is deformed without stretching.

51. The tangential tractions U, T on the cross-sections are necessarily
accompanied by tangential tractions on the longitudinal sections, and on
each such section the tangential traction is parallel to the central
line; on a vertical section z = const. its amount at any point is T, and
on a horizontal section y = const. its amount at any point is U.

The internal stress at any point is completely determined by the
components P, U, T, but these are not principal stresses (§ 7). Clebsch
has given an elegant geometrical construction for determining the
principal stresses at any point when the values of P, U, T are known.

[Illustration: FIG. 14.]

  From the point O (fig. 14) draw lines OP, OU, OT, to represent the
  stresses P, U, T at O, on the cross-section through O, in magnitude,
  direction and sense, and compound U and T into a resultant represented
  by OE; the plane EOP is a principal plane of stress at O, and the
  principal stress at right angles to this plane vanishes. Take M the
  middle point of OP, and with centre M and radius ME describe a circle
  cutting the line OP in A and B; then OA and OB represent the
  magnitudes of the two remaining principal stresses. On AB describe a
  rectangle ABDC so that DC passes through E; then OC is the direction
  of the principal stress represented in magnitude by OA, and OD is the
  direction of the principal stress represented in magnitude by OB.

[Illustration: FIG. 15.]

52. As regards the strain in the beam, the longitudinal and lateral
extensions and contractions depend on the bending moment in the same way
as in the simpler problem; but, the bending moment being variable, the
anticlastic curvature produced is also variable. In addition to these
extensions and contractions there are shearing strains corresponding to
the shearing stresses T, U. The shearing strain corresponding to T
consists of a relative sliding parallel to the central-line of different
longitudinal linear elements combined with a relative sliding in a
transverse horizontal direction of elements of different cross-sections;
the latter of these is concerned in the production of those
displacements by which the variable anticlastic curvature is brought
about; to see the effect of the former we may most suitably consider,
for the case of an elliptic cross-section, the distortion of the shape
of a rectangular portion of a plane of the material which in the natural
state was horizontal; all the boundaries of such a portion become
parabolas of small curvature, which is variable along the length of the
beam, and the particular effect under consideration is the change of the
transverse horizontal linear elements from straight lines such as HK to
parabolas such as H'K' (fig. 15); the lines HL and KM are parallel to
the central-line, and the figure is drawn for a plane above the neutral
plane. When the cross-section is not an ellipse the character of the
strain is the same, but the curves are only approximately parabolic.

The shearing strain corresponding to U is a distortion which has the
effect that the straight vertical filaments become curved lines which
cut the longitudinal filaments obliquely, and thus the cross-sections do
not remain plane, but become curved surfaces, and the tangent plane to
any one of these surfaces at the centroid cuts the central line
obliquely (fig. 16). The angle between these tangent planes and the
central-line is the same at all points of the line; and, if it is
denoted by ½[pi] + s0, the value of s0 is expressible as

  shearing stress at centroid
  ---------------------------,
    rigidity of material

and it thus depends on the shape of the cross-section; for the elliptic
section of § 50 its value is

    4W    2a²(1 + [sigma]) + b²
  ------- ---------------------;
  E[pi]ab       3a² + b²

for a circle (with [sigma] = ¼) this becomes 7W/2E[pi]a². The vertical
filament through the centroid of any cross-section becomes a cubical
parabola, as shown in fig. 16, and the contour lines of the curved
surface into which any cross-section is distorted are shown in fig. 17
for a circular section.

[Illustration: FIG. 16.]

53. The deflection of the beam is determined from the equation

  curvature of central line = bending moment ÷ flexural rigidity,

and the special conditions at the supported end; there is no alteration
of this statement on account of the shears. As regards the special
condition at an end which is _encastrée_, or built in, Saint-Venant
proposed to assume that the central tangent plane of the cross-section
at the end is vertical; with this assumption the tangent to the central
line at the end is inclined downwards and makes an angle s0 with the
horizontal (see fig. 18); it is, however, improbable that this condition
is exactly realized in practice. In the application of the theory to the
experimental determination of Young's modulus, the small angle which the
central-line at the support makes with the horizontal is an unknown
quantity, to be eliminated by observation of the deflection at two or
more points.

54. We may suppose the displacement in a bent beam to be produced by the
following operations: (1) the central-line is deflected into its curved
form, (2) the cross-sections are rotated about axes through their
centroids at right angles to the plane of flexure so as to make angles
equal to ½[pi] + s0 with the central-line, (3) each cross-section is
distorted in its own plane in such a way that the appropriate variable
anticlastic curvature is produced, (4) the cross-sections are further
distorted into curved surfaces. The contour lines of fig. 17 show the
disturbance from the central tangent plane, not from the original
vertical plane.

[Illustration: FIG. 17.]

55. _Practical Application of Saint-Venant's Theory._--The theory above
described is exact provided the forces applied to the loaded end, which
have W for resultant, are distributed over the terminal section in a
particular way, not likely to be realized in practice; and the
application to practical problems depends on a principle due to
Saint-Venant, to the effect that, except for comparatively small
portions of the beam near to the loaded and fixed ends, the resultant
only is effective, and its mode of distribution does not seriously
affect the internal strain and stress. In fact, the actual stress is
that due to forces with the required resultant distributed in the manner
contemplated in the theory, superposed upon that due to a certain
distribution of forces on each terminal section which, if applied to a
rigid body, would keep it in equilibrium; according to Saint-Venant's
principle, the stresses and strains due to such distributions of force
are unimportant except near the ends. For this principle to be exactly
applicable it is necessary that the length of the beam should be very
great compared with any linear dimension of its cross-section; for the
practical application it is sufficient that the length should be about
ten times the greatest diameter.

56. In recent years the problem of the bending of a beam by loads
distributed along its length has been much advanced. It is now
practically solved for the case of a load distributed uniformly, or
according to any rational algebraic law, and it is also solved for the
case where the thickness is small compared with the length and depth, as
in a plate girder, and the load is distributed in any way. These
solutions are rather complicated and difficult to interpret. The case
which has been worked out most fully is that of a transverse load
distributed uniformly along the length of the beam. In this case two
noteworthy results have been obtained. The first of these is that the
central-line in general suffers extension. This result had been found
experimentally many years before. In the case of the plate girder loaded
uniformly along the top, this extension is just half as great as the
extension of the central-line of the same girder when free at the ends,
supported along the base, and carrying the same load along the top. The
second noteworthy result is that the curvature of the strained
central-line is not proportional to the bending moment. Over and above
the curvature which would be found from the ordinary relation--

  curvature of central-line = bending moment ÷ flexural rigidity,

there is an additional curvature which is the same at all the
cross-sections. In ordinary cases, provided the length is large compared
with any linear dimension of the cross-section, this additional
curvature is small compared with that calculated from the ordinary
formula, but it may become important in cases like that of suspension
bridges, where a load carried along the middle of the roadway is
supported by tensions in rods attached at the sides.

[Illustration: FIG. 18.]

57. When the ordinary relation between the curvature and the bending
moment is applied to the calculation of the deflection of _continuous
beams_ it must not be forgotten that a correction of the kind just
mentioned may possibly be requisite. In the usual method of treating the
problem such corrections are not considered, and the ordinary relation
is made the basis of the theory. In order to apply this relation to the
calculation of the deflection, it is necessary to know the bending
moment at every point; and, since the pressures of the supports are not
among the data of the problem, we require a method of determining the
bending moments at the supports either by calculation or in some other
way. The calculation of the bending moment can be replaced by a method
of graphical construction, due to Mohr, and depending on the two
following theorems:--

(i.) The curve of the central-line of each span of a beam, when the
bending moment M is given,[1] is identical with the catenary or
funicular curve passing through the ends of the span under a
(fictitious) load per unit length of the span equal to M/EI, the
horizontal tension in the funicular being unity.

(ii.) The directions of the tangents to this funicular curve at the ends
of the span are the same for all statically equivalent systems of
(fictitious) load.

When M is known, the magnitude of the resultant shearing stress at any
section is dM/dx, where x is measured along the beam.

[Illustration: FIG. 19.]

[Illustration: FIG. 20.]

  58. Let l be the length of a span of a loaded beam (fig. 19), M1 and
  M2 the bending moments at the ends, M the bending moment at a section
  distant x from the end (M1), M' the bending moment at the same section
  when the same span with the same load is simply supported; then M is
  given by the formula

                l - x      x
    M = M' + M1 ----- + M2 --,
                  l        l

  and thus a fictitious load statically equivalent to M/EI can be easily
  found when M' has been found. If we draw a curve (fig. 20) to pass
  through the ends of the span, so that its ordinate represents the
  value of M'/EI, the corresponding fictitious loads are statically
  equivalent to a single load, of amount represented by the area of the
  curve, placed at the point of the span vertically above the centre of
  gravity of this area. If PN is the ordinate of this curve, and if at
  the ends of the span we erect ordinates in the proper sense to
  represent M1/EI and M2/EI, the bending moment at any point is
  represented by the length PQ.[2] For a uniformly distributed load the
  curve of M' is a parabola M' = ½wx(l - x), where w is the load per
  unit of length; and the statically equivalent fictitious load is
  (1/12)wl³/EI placed at the middle point G of the span; also the loads
  statically equivalent to the fictitious loads M1(l - x)/lEI and
  M2x/lEI are ½M1l/EI and ½M2l/EI placed at the points g, g' of
  trisection of the span. The funicular polygon for the fictitious loads
  can thus be drawn, and the direction of the central-line at the
  supports is determined when the bending moments at the supports are
  known.

  [Illustration: FIG. 21.]

  59. When there is more than one span the funiculars in question may be
  drawn for each of the spans, and, if the bending moments at the ends
  of the extreme spans are known, the intermediate ones can be
  determined. This determination depends on two considerations: (1) the
  fictitious loads corresponding to the bending moment at any support
  are proportional to the lengths of the spans which abut on that
  support; (2) the sides of two funiculars that end at any support
  coincide in direction. Fig. 21 illustrates the method for the case of
  a uniform beam on three supports A, B, C, the ends A and C being
  freely supported. There will be an unknown bending moment M0 at B, and
  the system[3] of fictitious loads is (1/12)wAB³/EI at G the middle
  point of AB, (1/12)wBC³/EI at G' the middle point of BC, -½M0AB/EI at
  g and -½M0BC/EI at g', where g and g' are the points of trisection
  nearer to B of the spans AB, BC. The centre of gravity of the two
  latter is a fixed point independent of M0, and the line VK of the
  figure is the vertical through this point. We draw AD and CE to
  represent the loads at G and G' in magnitude; then D and E are fixed
  points. We construct any triangle UVW whose sides UV, UW pass through
  D, B, and whose vertices lie on the verticals gU, VK, g'W; the point F
  where VW meets DB is a fixed point, and the lines EF, DK are the two
  sides (2, 4) of the required funiculars which do not pass through A, B
  or C. The remaining sides (1, 3, 5) can then be drawn, and the side 3
  necessarily passes through B; for the triangle UVW and the triangle
  whose sides are 2, 3, 4 are in perspective.

  [Illustration: FIG. 22.]

  The bending moment M0 is represented in the figure by the vertical
  line BH where H is on the continuation of the side 4, the scale being
  given by

    BH     ½M0BC
    -- = ---------- ;
    CE   (1/12)wBC³

  this appears from the diagrams of forces, fig. 22, in which the
  oblique lines are marked to correspond to the sides of the funiculars
  to which they are parallel.

  In the application of the method to more complicated cases there are
  two systems of fixed points corresponding to F, by means of which the
  sides of the funiculars are drawn.

60. _Finite Bending of Thin Rod._--The equation

  curvature = bending moment ÷ flexural rigidity

may also be applied to the problem of the flexure in a principal plane
of a very thin rod or wire, for which the curvature need not be small.
When the forces that produce the flexure are applied at the ends only,
the curve into which the central-line is bent is one of a definite
family of curves, to which the name _elastica_ has been given, and there
is a division of the family into two species according as the external
forces are applied directly to the ends or are applied to rigid arms
attached to the ends; the curves of the former species are characterized
by the presence of inflections at all the points at which they cut the
line of action of the applied forces.

[Illustration: FIG. 23.]

  We select this case for consideration. The problem of determining the
  form of the curve (cf. fig. 23) is mathematically identical with the
  problem of determining the motion of a simple circular pendulum
  oscillating through a finite angle, as is seen by comparing the
  differential equation of the curve

       d²[phi]
    EI ------- + W sin [phi] = 0
         ds²

  with the equation of motion of the pendulum

      d²[phi]
    l ------- + g sin [phi] = 0.
        dt²

  The length L of the curve between two inflections corresponds to the
  time of oscillation of the pendulum from rest to rest, and we thus
  have

    L [root](W/EI) = 2K,

  where K is the real quarter period of elliptic functions of modulus
  sin ½[alpha], and [alpha] is the angle at which the curve cuts the
  line of action of the applied forces. Unless the length of the rod
  exceeds [pi][root](EI/W) it will not bend under the force, but when
  the length is great enough there may be more than two points of
  inflection and more than one bay of the curve; for n bays (n + 1
  inflections) the length must exceed n[pi][root](EI/W). Some of the
  forms of the curve are shown in fig. 24.

  [Illustration: FIG. 24.]

  For the form d, in which two bays make a figure of eight, we have

    L[root](W/EI) = 4.6, [alpha] = 130°

  approximately. It is noteworthy that whenever the length and force
  admit of a sinuous form, such as [alpha] or b, with more than two
  inflections, there is also possible a crossed form, like e, with two
  inflections only; the latter form is stable and the former unstable.

61. The particular case of the above for which [alpha] is very small is
a curve of sines of small amplitude, and the result in this case has
been applied to the problem of the buckling of struts under thrust. When
the strut, of length L', is maintained upright at its lower end, and
loaded at its upper end, it is simply contracted, unless L'²W >
¼[pi]²EI, for the lower end corresponds to a point at which the tangent
is vertical on an elastica for which the line of inflections is also
vertical, and thus the length must be half of one bay (fig. 25, a). For
greater lengths or loads the strut tends to bend or buckle under the
load. For a very slight excess of L'²W above ¼[pi]²EI, the theory on
which the above discussion is founded, is not quite adequate, as it
assumes the central-line of the strut to be free from extension or
contraction, and it is probable that bending without extension does not
take place when the length or the force exceeds the critical value but
slightly. It should be noted also that the formula has no application to
short struts, as the theory from which it is derived is founded on the
assumption that the length is great compared with the diameter (cf. §
56).

[Illustration: Fig. 25.]

The condition of buckling, corresponding to the above, for a long strut,
of length L', when both ends are free to turn is L'²W > [pi]²EI; for the
central-line forms a complete bay (fig. 25, b); if both ends are
maintained in the same vertical line, the condition is L'²W > 4[pi]²EI,
the central-line forming a complete bay and two half bays (fig. 25, c).

[Illustration: Fig. 26.]

62. In our consideration of flexure it has so far been supposed that the
bending takes place in a principal plane. We may remove this restriction
by resolving the forces that tend to produce bending into systems of
forces acting in the two principal planes. To each plane there
corresponds a particular flexural rigidity, and the systems of forces in
the two planes give rise to independent systems of stress, strain and
displacement, which must be superposed in order to obtain the actual
state. Applying this process to the problem of §§ 48-54, and supposing
that one principal axis of a cross-section at its centroid makes an
angle [theta] with the vertical, then for any shape of section the
neutral surface or locus of unextended fibres cuts the section in a line
DD', which is conjugate to the vertical diameter CP with respect to any
ellipse of inertia of the section. The central-line is bent into a plane
curve which is not in a vertical plane, but is in a plane through the
line CY which is perpendicular to DD' (fig. 26).

63. _Bending and Twisting of Thin Rods._--When a very thin rod or wire
is bent and twisted by applied forces, the forces on any part of it
limited by a normal section are balanced by the tractions across the
section, and these tractions are statically equivalent to certain forces
and couples at the centroid of the section; we shall call them the
_stress-resultants_ and the _stress-couples_. The stress-couples consist
of two flexural couples in the two principal planes, and the torsional
couple about the tangent to the central-line. The torsional couple is
the product of the torsional rigidity and the twist produced; the
torsional rigidity is exactly the same as for a straight rod of the same
material and section twisted without bending, as in Saint-Venant's
torsion problem (§ 42). The twist [tau] is connected with the
deformation of the wire in this way: if we suppose a very small ring
which fits the cross-section of the wire to be provided with a pointer
in the direction of one principal axis of the section at its centroid,
and to move along the wire with velocity v, the pointer will rotate
about the central-line with angular velocity [tau]v. The amount of the
flexural couple for either principal plane at any section is the product
of the flexural rigidity for that plane, and the resolved part in that
plane of the curvature of the central line at the centroid of the
section; the resolved part of the curvature along the normal to any
plane is obtained by treating the curvature as a vector directed along
the normal to the osculating plane and projecting this vector. The
flexural couples reduce to a single couple in the osculating plane
proportional to the curvature when the two flexural rigidities are
equal, and in this case only.

The stress-resultants across any section are tangential forces in the
two principal planes, and a tension or thrust along the central-line;
when the stress-couples and the applied forces are known these
stress-resultants are determinate. The existence, in particular, of the
resultant tension or thrust parallel to the central-line does not imply
sensible extension or contraction of the central filament, and the
tension per unit area of the cross-section to which it would be
equivalent is small compared with the tensions and pressures in
longitudinal filaments not passing through the centroid of the section;
the moments of the latter tensions and pressures constitute the flexural
couples.

64. We consider, in particular, the case of a naturally straight spring
or rod of circular section, radius c, and of homogeneous isotropic
material. The torsional rigidity is ¼E[pi]c^4/(1 + [sigma]); and the
flexural rigidity, which is the same for all planes through the
central-line, is ¼E[pi]c^4; we shall denote these by C and A
respectively. The rod may be held bent by suitable forces into a curve
of double curvature with an amount of twist [tau], and then the
torsional couple is C[tau], and the flexural couple in the osculating
plane is A/[rho], where [rho] is the radius of circular curvature. Among
the curves in which the rod can be held by forces and couples applied at
its ends only, one is a circular helix; and then the applied forces and
couples are equivalent to a wrench about the axis of the helix.

  Let [alpha] be the angle and r the radius of the helix, so that [rho]
  is r sec²[alpha]; and let R and K be the force and couple of the
  wrench (fig. 27).

  Then the couple formed by R and an equal and opposite force at any
  section and the couple K are equivalent to the torsional and flexural
  couples at the section, and this gives the equations for R and K

          sin [alpha] cos³ [alpha]           cos [alpha]
    R = A ------------------------ - C[tau] ------------,
                    r²                            r

          cos³ [alpha]
    K = A ------------ + C[tau] sin [alpha].
               r

  The thrust across any section is R sin [alpha] parallel to the tangent
  to the helix, and the shearing stress-resultant is R cos [alpha] at
  right angles to the osculating plane.

  [Illustration: FIG. 27.]

  When the twist is such that, if the rod were simply unbent, it would
  also be untwisted, [tau] is (sin [alpha] cos [alpha])/r, and then,
  restoring the values of A and C, we have

         E[pi]c^4   [sigma]
    R =  -------- ----------- sin [alpha] cos² [alpha],
           4r²    1 + [sigma]

        E[pi]c^4  1 + [sigma] cos² [alpha]
    K = --------  ------------------------ cos [alpha].
            4r          1 + [sigma]

  65. The theory of spiral springs affords an application of these
  results. The stress-couples called into play when a naturally helical
  spring ([alpha], r) is held in the form of a helix ([alpha]', r'), are
  equal to the differences between those called into play when a
  straight rod of the same material and section is held in the first
  form, and those called into play when it is held in the second form.

  Thus the torsional couple is

       /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha] \
    C ( ------------------------- - ------------------------ ),
       \           r'                          r            /

  and the flexural couple is

       /cos² [alpha]'   cos² [alpha]\
    A ( ------------- - ------------ ).
       \     r'              r      /

  The wrench (R, K) along the axis by which the spring can be held in
  the form ([alpha]', r') is given by the equations

          sin [alpha]'  /cos² [alpha]'   cos² [alpha]\
    R = A ------------ ( ------------- - ------------ ) -
              r'        \       r'            r      /

         cos [alpha]'  /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha]\
      C ------------- ( ------------------------- - ----------------------- ),
              r'       \           r'                          r           /

                        /cos² [alpha]'   cos² [alpha]\
    K = A cos [alpha]' ( ------------- - ------------ ) +
                        \     r'               r     /

                      /sin [alpha]' cos [alpha]'   sin [alpha] cos [alpha]\
      C sin [alpha]' ( ------------------------- - ----------------------- ).
                      \           r'                           r          /

  When the spring is slightly extended by an axial force F, = -R, and
  there is no couple, so that K vanishes, and [alpha]', r' differ very
  little from [alpha], r, it follows from these equations that the axial
  elongation, [delta]x, is connected with the axial length x and the
  force F by the equation

        E[pi]c^4        sin [alpha]       [delta]x
    F = -------- ------------------------ --------,
          4r²    1 + [sigma] cos² [alpha]     x

  and that the loaded end is rotated about the axis of the helix through
  a small angle

    4[sigma]Fxr cos [alpha]
    -----------------------
           E[pi]c^4

  the sense of the rotation being such that the spring becomes more
  tightly coiled.

66. A horizontal pointer attached to a vertical spiral spring would be
made to rotate by loading the spring, and the angle through which it
turns might be used to measure the load, at any rate, when the load is
not too great; but a much more sensitive contrivance is the twisted
strip devised by W.E. Ayrton and J. Perry. A very thin, narrow
rectangular strip of metal is given a permanent twist about its
longitudinal middle line, and a pointer is attached to it at right
angles to this line. When the strip is subjected to longitudinal tension
the pointer rotates through a considerable angle. G.H. Bryan (_Phil.
Mag._, December 1890) has succeeded in constructing a theory of the
action of the strip, according to which it is regarded as a strip of
_plating_ in the form of a right helicoid, which, after extension of the
middle line, becomes a portion of a slightly different helicoid; on
account of the thinness of the strip, the change of curvature of the
surface is considerable, even when the extension is small, and the
pointer turns with the generators of the helicoid.

  If b stands for the breadth and t for the thickness of the strip, and
  [tau] for the permanent twist, the approximate formula for the angle
  [theta] through which the strip is untwisted on the application of a
  load W was found to be

                        Wb[tau](1 + [sigma])
    [theta] = ---------------------------------------.
                     /    (1 + [sigma])   b^4[tau]²\
              2Et^3 ( 1 + ------------- - --------- )
                     \        30              t²   /

  The quantity b[tau] which occurs in the formula is the total twist in
  a length of the strip equal to its breadth, and this will generally be
  very small; if it is small of the same order as t/b, or a higher
  order, the formula becomes ½Wb[tau](1+[sigma])/Et^3, with sufficient
  approximation, and this result appears to be in agreement with
  observations of the behaviour of such strips.

67. _Thin Plate under Pressure._--The theory of the deformation of
plates, whether plane or curved, is very intricate, partly because of
the complexity of the kinematical relations involved. We shall here
indicate the nature of the effects produced in a thin plane plate, of
isotropic material, which is slightly bent by pressure. This theory
should have an application to the stress produced in a ship's plates. In
the problem of the cylinder under internal pressure (§ 77 below) the
most important stress is the circumferential tension, counteracting the
tendency of the circular filaments to expand under the pressure; but in
the problem of a plane plate some of the filaments parallel to the plane
of the plate are extended and others are contracted, so that the
tensions and pressures along them give rise to resultant couples but not
always to resultant forces. Whatever forces are applied to bend the
plate, these couples are always expressible, at least approximately in
terms of the principal curvatures produced in the surface which, before
strain, was the middle plane of the plate. The simplest case is that of
a rectangular plate, bent by a distribution of couples applied to its
edges, so that the middle surface becomes a cylinder of large radius R;
the requisite couple per unit of length of the straight edges is of
amount C/R, where C is a certain constant; and the requisite couple per
unit of length of the circular edges is of amount C[sigma]/R, the latter
being required to resist the tendency to anticlastic curvature (cf. §
47). If normal sections of the plate are supposed drawn through the
generators and circular sections of the cylinder, the action of the
neighbouring portions on any portion so bounded involves flexural
couples of the above amounts. When the plate is bent in any manner, the
curvature produced at each section of the middle surface may be regarded
as arising from the superposition of two cylindrical curvatures; and the
flexural couples across normal sections through the lines of curvature,
estimated per unit of length of those lines, are C(1/R1 + [sigma]/R2)
and C(1/R2 + [sigma]/R1), where R1 and R2 are the principal radii of
curvature. The value of C for a plate of small thickness 2h is
(2/3)Eh^3/(1 - [sigma]²). Exactly as in the problem of the beam (§§ 48,
56), the action between neighbouring portions of the plate generally
involves shearing stresses across normal sections as well as flexural
couples; and the resultants of these stresses are determined by the
conditions that, with the flexural couples, they balance the forces
applied to bend the plate.

[Illustration: FIG. 28.]

  68. To express this theory analytically, let the middle plane of the
  plate in the unstrained position be taken as the plane of (x, y), and
  let normal sections at right angles to the axes of x and y be drawn
  through any point. After strain let w be the displacement of this
  point in the direction perpendicular to the plane, marked p in fig.
  28. If the axes of x and y were parallel to the lines of curvature at
  the point, the flexural couple acting across the section normal to x
  (or y) would have the axis of y (or x) for its axis; but when the
  lines of curvature are inclined to the axes of co-ordinates, the
  flexural couple across a section normal to either axis has a component
  about that axis as well as a component about the perpendicular axis.
  Consider an element ABCD of the section at right angles to the axis of
  x, contained between two lines near together and perpendicular to the
  middle plane. The action of the portion of the plate to the right upon
  the portion to the left, across the element, gives rise to a couple
  about the middle line (y) of amount, estimated per unit of length of
  that line, equal to

       /dP²w          dP²w\
    C ( ---- + [sigma]---- ), = G1,
       \dPx²          dPy²/

  say, and to a couple, similarly estimated, about the normal (x) of
  amount

                   dP²w
    -C(1-[sigma]) ------, = H,
                  dPxdPy

  say. The corresponding couples on an element of a section at right
  angles to the axis of y, estimated per unit of length of the axis of
  x, are of amounts

        /dP²w          dP²w\
     -C( ---- + [sigma]---- ), = G2
        \dPy²          dPx²/

  say, and -H. The resultant S1 of the shearing stresses on the element
  ABCD, estimated as before, is given by the equation

         dPG1   dPH
    S1 = ---- - ---
         dPx    dPy

  (cf. § 57), and the corresponding resultant S2 for an element
  perpendicular to the axis of y is given by the equation

          dPH   dPG2
    S2= - --- - ----.
          dPx   dPy

  If the plate is bent by a pressure p per unit of area, the equation of
  equilibrium is

    dPS1   dPS2
    ---- + ---- = p, or, in terms of w,
    dPx    dPy

    dP^4w   dP^4w     dP^4w     p
    ----- + ----- + 2-------- = --.
    dPx^4   dPy^4    dPx²dPy²   C

  This equation, together with the special conditions at the rim,
  suffices for the determination of w, and then all the quantities here
  introduced are determined. Further, the most important of the
  stress-components are those which act across elements of normal
  sections: the tension in direction x, at a distance z from the middle
  plane measured in the direction of p, is of amount

      3Cz   /dP²w          dP²w\
    - ---- ( ---- + [sigma]---- ),
      2h^3  \dPx²          dPy²/

  and there is a corresponding tension in direction y; the shearing
  stress consisting of traction parallel to y on planes x = const., and
  traction parallel to x on planes y = const., is of amount

    3C(1 - [sigma])z  dP²w
    ---------------- ------;
          2h^3       dPxdPy

  these tensions and shearing stresses are equivalent to two principal
  tensions, in the directions of the lines of curvature of the surface
  into which the middle plane is bent, and they give rise to the
  flexural couples.

  69. In the special example of a circular plate, of radius a, supported
  at the rim, and held bent by a uniform pressure p, the value of w at a
  point distant r from the axis is

    1  p             /5 + [sigma]       \
    -- -- (a² - r²) ( ----------- a² - r²),
    64 C             \1 + [sigma]       /

  and the most important of the stress components is the radial tension,
  of which the amount at any point is (3/32)(3 + [sigma])pz(a² - r)/h³;
  the maximum radial tension is about (1/3)(a/h)²p, and, when the
  thickness is small compared with the diameter, this is a large
  multiple of p.

70. _General Theorems._--Passing now from these questions of flexure and
torsion, we consider some results that can be deduced from the general
equations of equilibrium of an elastic solid body.

The form of the general expression for the potential energy (§ 27)
stored up in the strained body leads, by a general property of quadratic
functions, to a reciprocal theorem relating to the effects produced in
the body by two different systems of forces, viz.: The whole work done
by the forces of the first system, acting over the displacements
produced by the forces of the second system, is equal to the whole work
done by the forces of the second system, acting over the displacements
produced by the forces of the first system. By a suitable choice of the
second system of forces, the average values of the component stresses
and strains produced by given forces, considered as constituting the
first system, can be obtained, even when the distribution of the stress
and strain cannot be determined.

[Illustration: FIG. 29.]

  Taking for example the problem presented by an isotropic body of any
  form[4] pressed between two parallel planes distant l apart (fig. 29),
  and denoting the resultant pressure by p, we find that the diminution
  of volume -[delta]v is given by the equation

    -[delta]v = lp/3k,

  where k is the modulus of compression, equal to (1/3)E/(1 - 2[sigma]).
  Again, take the problem of the changes produced in a heavy body by
  different ways of supporting it; when the body is suspended from one
  or more points in a horizontal plane its volume is increased by

    [delta]v = Wh/3k,

  where W is the weight of the body, and h the depth of its centre of
  gravity below the plane; when the body is supported by upward
  vertical pressures at one or more points in a horizontal plane the
  volume is diminished by

    -[delta]v = Wh'/3k,

  where h' is the height of the centre of gravity above the plane; if
  the body is a cylinder, of length l and section A, standing with its
  base on a smooth horizontal plane, its length is shortened by an
  amount

    -[delta]l = Wl/2EA;

  if the same cylinder lies on the plane with its generators horizontal,
  its length is increased by an amount

    [delta]l = [sigma]Wh'/EA.



71. In recent years important results have been found by considering the
effects produced in an elastic solid by forces applied at isolated
points.

  Taking the case of a single force F applied at a point in the
  interior, we may show that the stress at a distance r from the point
  consists of

  (1) a radial pressure of amount

    2 - [sigma]   F   cos [theta]
    ----------- ----- -----------,
    1 - [sigma] 4[pi]     r²

  (2) tension in all directions at right angles to the radius of amount

     1 - 2[sigma]  F cos [theta]
    -------------- -------------,
    2(1 - [sigma])    4[pi]r²

  (3) shearing stress consisting of traction acting along the radius
  dr on the surface of the cone [theta] = const. and traction acting
  along the meridian d[theta] on the surface of the sphere r = const. of
  amount

     1 - 2[sigma]    F   sin [theta]
    -------------- ----- -----------,
    2(1 - [sigma]) 4[pi]     r²

  where [theta] is the angle between the radius vector r and the line of
  action of F. The line marked T in fig. 30 shows the direction of the
  tangential traction on the spherical surface.

  [Illustration: FIG. 30.]

  Thus the lines of stress are in and perpendicular to the meridian
  plane, and the direction of one of those in the meridian plane is
  inclined to the radius vector r at an angle

               /2 - 4[sigma]            \
    ½tan^(-1) ( ------------ tan [theta] ).
               \5 - 4[sigma]            /

  The corresponding displacement at any point is compounded of a radial
  displacement of amount

     1 + [sigma]     F    cos [theta]
    -------------- ------ -----------
    2(1 - [sigma]) 4[pi]E      r

  and a displacement parallel to the line of action of F of amount

    (3 - 4[sigma])(1 + [sigma])   F    1
    --------------------------- ------ --.
          2(1 - [sigma])        4[pi]E r

  The effects of forces applied at different points and in different
  directions can be obtained by summation, and the effect of
  continuously distributed forces can be obtained by integration.

72. The stress system considered in § 71 is equivalent, on the plane
through the origin at right angles to the line of action of F, to a
resultant pressure of magnitude ½F at the origin and a radial traction
of amount

   1 - 2[sigma]     F
  -------------- -------,
  2(1 - [sigma]) 4[pi]r²

and, by the application of this system of tractions to a solid bounded
by a plane, the displacement just described would be produced. There is
also another stress system for a solid so bounded which is equivalent,
on the same plane, to a resultant pressure at the origin, and a radial
traction proportional to 1/r², but these are in the ratio 2[pi]:r^(-2),
instead of being in the ratio 4[pi](1 - [sigma]) : (1 - 2[sigma])r^(-2).

[Illustration: FIG. 31.]

  The second stress system (see fig. 31) consists of:

  (1) radial pressure F'r^{-2},

  (2) tension in the meridian plane across the radius vector of amount

    F'r^(-2) cos [theta] /(1 + cos [theta]),

  (3) tension across the meridian plane of amount

    F'r^(-2)/(l + cos [theta]),

  (4) shearing stress as in § 71 of amount

    F'r^(-2) sin [theta]/(1 + cos [theta]),

  and the stress across the plane boundary consists of a resultant
  pressure of magnitude 2[pi]F' and a radial traction of amount
  F'r^(-2). If then we superpose the component stresses of the last
  section multiplied by 4(1 - [sigma])W/F, and the component stresses
  here written down multiplied by -(1 - 2[sigma])W/2[pi]F', the stress
  on the plane boundary will reduce to a single pressure W at the
  origin. We shall thus obtain the stress system at any point due to
  such a force applied at one point of the boundary.

  In the stress system thus arrived at the traction across any plane
  parallel to the boundary is directed away from the place where W is
  supported, and its amount is 3W cos²[theta]/2[pi]r². The corresponding
  displacement consists of

  (1) a horizontal displacement radially outwards from the vertical
  through the origin of amount

    W(1 + [sigma]) sin [theta]  /               1 - 2[sigma]  \
    -------------------------- ( cos [theta] - --------------- ),
             2[pi]Er            \              1 + cos [theta]/

  (2) a vertical displacement downwards of amount

    W(1 + [sigma])
    -------------- {2(1 - [sigma]) + cos²[theta]}.
       2[pi]Er

  The effects produced by a system of loads on a solid bounded by a
  plane can be deduced.

The results for a solid body bounded by an infinite plane may be
interpreted as giving the local effects of forces applied to a small
part of the surface of a body. The results show that pressure is
transmitted into a body from the boundary in such a way that the
traction at a point on a section parallel to the boundary is the same at
all points of any sphere which touches the boundary at the point of
pressure, and that its amount at any point is inversely proportional to
the square of the radius of this sphere, while its direction is that of
a line drawn from the point of pressure to the point at which the
traction is estimated. The transmission of force through a solid body
indicated by this result was strikingly demonstrated in an attempt that
was made to measure the lunar deflexion of gravity; it was found that
the weight of the observer on the floor of the laboratory produced a
disturbance of the instrument sufficient to disguise completely the
effect which the instrument had been designed to measure (see G.H.
Darwin, _The Tides and Kindred Phenomena in the Solar System_, London,
1898).

73. There is a corresponding theory of two-dimensional systems, that is
to say, systems in which either the displacement is parallel to a fixed
plane, or there is no traction across any plane of a system of parallel
planes. This theory shows that, when pressure is applied at a point of
the edge of a plate in any direction in the plane of the plate, the
stress developed in the plate consists exclusively of radial pressure
across any circle having the point of pressure as centre, and the
magnitude of this pressure is the same at all points of any circle which
touches the edge at the point of pressure, and its amount at any point
is inversely proportional to the radius of this circle. This result
leads to a number of interesting solutions of problems relating to plane
systems; among these may be mentioned the problem of a circular plate
strained by any forces applied at its edge.

74. The results stated in § 72 have been applied to give an account of
the nature of the actions concerned in the impact of two solid bodies.
The dissipation of energy involved in the impact is neglected, and the
resultant pressure between the bodies at any instant during the impact
is equal to the rate of destruction of momentum of either along the
normal to the plane of contact drawn towards the interior of the other.
It has been shown that in general the bodies come into contact over a
small area bounded by an ellipse, and remain in contact for a time which
varies inversely as the fifth root of the initial relative velocity.

  For equal spheres of the same material, with [sigma] = ¼, impinging
  directly with relative velocity v, the patches that come into contact
  are circles of radius

     /45[pi]\ ^(1/5)  /v \ ^(2/5)
    ( ------ )       ( -- )      r,
     \ 256  /         \V /

  where r is the radius of either, and V the velocity of longitudinal
  waves in a thin bar of the material. The duration of the impact is
  approximately

              /2025[pi]²\ ^(1/5)       r
    (2.9432) ( --------- )      --------------- .
              \   512   /       v^(1/5) V^(4/5)

  For two steel spheres of the size of the earth impinging with a
  velocity of 1 cm. per second the duration of the impact would be about
  twenty-seven hours. The fact that the duration of impact is, for
  moderate velocities, a considerable multiple of the time taken by a
  wave of compression to travel through either of two impinging bodies
  has been ascertained experimentally, and constitutes the reason for
  the adequacy of the statical theory here described.

75. _Spheres and Cylinders._--Simple results can be found for spherical
and cylindrical bodies strained by radial forces.

  For a sphere of radius a, and of homogeneous isotropic material of
  density [rho], strained by the mutual gravitation of its parts, the
  stress at a distance r from the centre consists of

  (1) uniform hydrostatic pressure of amount (1/10)g[rho]a(3 -
  [sigma])/(1 - [sigma]),

  (2) radial tension of amount (1/10)g[rho](r²/a)(3 - [sigma])/(1
  -[sigma]),

  (3) uniform tension at right angles to the radius vector of amount

    (1/10)g[rho](r²/a) (1 + 3[sigma])/(1 - [sigma]),

  where g is the value of gravity at the surface. The corresponding
  strains consist of

  (1) uniform contraction of all lines of the body of amount

    (1/30)k^(-1)g[rho]a(3 - [sigma])/(1 - [sigma]),

  (2) radial extension of amount (1/10)k^(-1)g[rho](r²/a)(1 +
  [sigma])/(1 - [sigma]),

  (3) extension in any direction at right angles to the radius vector of
  amount

    (1/30)k^(-1)g[rho](r²/a) (1 + [sigma])/(1 - [sigma]),

  where k is the modulus of compression. The volume is diminished by the
  fraction g[rho]a/5k of itself. The parts of the radii vectors within
  the sphere r = a{(3 - [sigma])/(3 + 3[sigma])}^½ are contracted, and
  the parts without this sphere are extended. The application of the
  above results to the state of the interior of the earth involves a
  neglect of the caution emphasized in § 40, viz. that the strain
  determined by the solution must be small if the solution is to be
  accepted. In a body of the size and mass of the earth, and having a
  resistance to compression and a rigidity equal to those of steel, the
  radial contraction at the centre, as given by the above solution,
  would be nearly 1/3, and the radial extension at the surface nearly
  1/6, and these fractions can by no means be regarded as "small."

  76. In a spherical shell of homogeneous isotropic material, of
  internal radius r1 and external radius r0, subjected to pressure p0 on
  the outer surface, and p1 on the inner surface, the stress at any
  point distant r from the centre consists of

                                                  p1r1³ - p0r0³
  (1) uniform tension in all directions of amount -------------,
                                                    r0³ - r1³

                                 p1 - p0   r0³ r1³
  (2) radial pressure of amount ---------  -------,
                                r0³ - r1³     r³

  (3) tension in all directions at right angles to the radius vector of
  amount

       p1 - p0  r0³ r1³
    ½ --------- -------.
      r0³ - r1³   r³

  The corresponding strains consist of

  (1) uniform extension of all lines of the body of amount

    1  p1r1³ - p0r0³
    -- -------------,
    3k   r0³ - r1³

                                   1   p1 - p0  r0³ r1³
  (2) radial contraction of amount -- --------- -------,
                                   2µ r0³ - r1³    r³

  (3) extension in all directions at right angles to the radius vector
  of amount

    1   p1 - p0  r0³ r1³
    -- --------- -------,
    4µ r0³ - r1³    r³

  where µ is the modulus of rigidity of the material, = ½E/(1 +
  [sigma]). The volume included between the two surfaces of the body is
  increased

                  p1r1³ - p0r0³
  by the fraction ------------- of itself, and the volume within the
                  k(r0³ - r1³)

  inner surface is increased by the fraction

    3(p1 - p0)    r0³      p1r1³ - p0r0³
    ---------- --------- + -------------
        4µ     r0³ - r1³   k(r0³ - r1³)

  of itself. For a shell subject only to internal pressure p the
  greatest extension is the extension at right angles to the radius at
  the inner surface, and its amount is

       pr1³    / 1   1  r0³ \
    --------- ( -- + -- ---  );
    r0³ - r1³  \3k   4µ r1³ /

  the greatest tension is the transverse tension at the inner surface,
  and its amount is p(½r0³ + r1³)/(r0³ - r1³).

  77. In the problem of a cylindrical shell under pressure a
  complication may arise from the effects of the ends; but when the ends
  are free from stress the solution is very simple. With notation
  similar to that in § 76 it can be shown that the stress at a distance
  r from the axis consists of

  (1) uniform tension in all directions at right angles to the axis of
  amount

    p1r1² - p0r0²
    -------------,
      r0² - r1²

                                 p1 - p0  r0² r1²
  (2) radial pressure of amount --------- -------,
                                r0² - r1²    r²

  (3) hoop tension numerically equal to this radial pressure.

  The corresponding strains consist of

  (1) uniform extension of all lines of the material at right angles to
  the axis of amount

    1 - [sigma] p1r1² - p0r0²
    ----------- -------------,
         E        r0² - r1²

  (2) radial contraction of amount

    1 + [sigma]  p1 - p0  r0² r1²
    ----------- --------- -------,
         E      r0² - r1²   r²

  (3) extension along the circular filaments numerically equal to this
  radial contraction,

  (4) uniform contraction of the longitudinal filaments of amount

    2[sigma] p1r1² - p0r0²
    -------- -------------.
       E       r0² - r1²

  For a shell subject only to internal pressure p the greatest extension
  is the circumferential extension at the inner surface, and its amount
  is

    p   /r0² + r1²          \
    -- ( --------- + [sigma] );
    E   \r0² - r1²          /

  the greatest tension is the hoop tension at the inner surface, and its
  amount is p(r0² + r1^²)/(r0² - r1²).

  78. When the ends of the tube, instead of being free, are closed by
  disks, so that the tube becomes a closed cylindrical vessel, the
  longitudinal extension is determined by the condition that the
  resultant longitudinal tension in the walls balances the resultant
  normal pressure on either end. This condition gives the value of the
  extension of the longitudinal filaments as

    (p1r1² - p0r0²)/3k(r0² - r1²),

  where k is the modulus of compression of the material. The result may
  be applied to the experimental determination of k, by measuring the
  increase of length of a tube subjected to internal pressure (A.
  Mallock, _Proc. R. Soc. London_, lxxiv., 1904, and C. Chree, _ibid._).

79. The results obtained in § 77 have been applied to gun construction;
we may consider that one cylinder is heated so as to slip over another
upon which it shrinks by cooling, so that the two form a single body in
a condition of initial stress.

  We take P as the measure of the pressure between the two, and p for
  the pressure within the inner cylinder by which the system is
  afterwards strained, and denote by r' the radius of the common
  surface. To obtain the stress at any point we superpose the

                                         r1² r0² - r²
  system consisting of radial pressure p --- --------- and hoop tension
                                         r²  r0² - r1²

     r1²  r0² + r²
   p --- ---------  upon a system which, for the outer cylinder, consists
     r²  r0² - r1²

                       r'²  r0² - r²
  of radial pressure P --- ---------
                       r²  r0² - r'²

                     r'²  r0² + r²
  and hoop tension P --- ---------, and for the inner cylinder consists
                     r²  r0² - r'²

                        r'²  r² - r1²                    r'²  r² + r1²
  of radial pressure  P --- --------- and hoop tension P --- ---------.
                        r²  r'² - r1²                    r²  r'² - r1²

  The hoop tension at the inner surface is less than it would be for a
  tube of equal thickness without initial stress in the ratio

        P     2r'²    r0² + r1²
    1 - -- ---------  --------- : 1.
        p  r0² + r1²  r'² - r1²

  This shows how the strength of the tube is increased by the initial
  stress. When the initial stress is produced by tightly wound wire, a
  similar gain of strength accrues.

80. In the problem of determining the distribution of stress and strain
in a circular cylinder, rotating about its axis, simple solutions have
been obtained which are sufficiently exact for the two special cases of
a thin disk and a long shaft.

  Suppose that a circular disk of radius a and thickness 2l, and of
  density [rho], rotates about its axis with angular velocity [omega],
  and consider the following systems of superposed stresses at any point
  distant r from the axis and z from the middle plane:

  (1) uniform tension in all directions at right angles to the axis of
  amount (1/8)[omega]²[rho]a²(3 + [sigma]),

  (2) radial pressure of amount (1/8)[omega]²[rho]r²(3 + [sigma]),

  (3) pressure along the circular filaments of amount
  (1/8)[omega]²[rho]r²(1 + 3[sigma]),

  (4) uniform tension in all directions at right angles to the axis of
  amount (1/6)[omega]²[rho](l²-3z²)[sigma](1 + [sigma])/(1 - [sigma]).

  The corresponding strains may be expressed as

  (1) uniform extension of all filaments at right angles to the axis of
  amount

    1 - [sigma]
    ----------- (1/8)[omega]²[rho]a²(3 + [sigma]),
         E

  (2) radial contraction of amount

    1 - [sigma]²
    ------------ (3/8)[omega]²[rho]r²,
         E

  (3) contraction along the circular filaments of amount

    1 - [sigma]²
    ------------ (1/8)[omega]²[rho]r²,
         E

  (4) extension of all filaments at right angles to the axis of amount

    (1/E)(1/6)[omega]²[rho][l² - (3_x)²][sigma](1+[sigma]),

  (5) contraction of the filaments normal to the plane of the disk of
  amount

    2[sigma]
    -------- (1/8)[omega]²[rho]a²(3 + [sigma])
       E

       [sigma]
     - ------- ½ [omega]²[rho]r²(1 + [sigma])
          E

       2[sigma]                                      (1 + [sigma])
     + -------- (1/6)[omega]²[rho](l^² - 3z²)[sigma] -------------.
          E                                          (1 - [sigma])

  The greatest extension is the circumferential extension near the
  centre, and its amount is

    (3 + [sigma])(1 - [sigma])                   [sigma](1 + [sigma])
    -------------------------- [omega]²[rho]a² + -------------------- [omega]²[rho]l².
                8E                                        6E

  [Illustration: Fig. 32.]

  The longitudinal contraction is required to make the plane faces of
  the disk free from pressure, and the terms in l and z enable us to
  avoid tangential traction on any cylindrical surface. The system of
  stresses and strains thus expressed satisfies all the conditions,
  except that there is a small radial tension on the bounding surface of
  amount per unit area (1/6)[omega]²[rho](l² - 3z²)[sigma](1 +
  [sigma])/(1 - [sigma]). The resultant of these tensions on any part of
  the edge of the disk vanishes, and the stress in question is very
  small in comparison with the other stresses involved when the disk is
  thin; we may conclude that, for a thin disk, the expressions given
  represent the actual condition at all points which are not very close
  to the edge (cf. § 55). The effect to the longitudinal contraction is
  that the plane faces become slightly concave (fig. 32).

  81. The corresponding solution for a disk with a circular axle-hole
  (radius b) will be obtained from that given in the last section by
  superposing the following system of additional stresses:

  (1) radial tension of amount (1/8)[omega]²[rho]b²(1 - a²/r²)(3 +
  [sigma]),

  (2) tension along the circular filaments of amount

    (1/8)[omega]²[rho]b²(1 + a²/r²)(3 + [sigma]).

  The corresponding additional strains are

  (1) radial contraction of amount
                 _                               _
    3 + [sigma] |              a²                 |
    ----------- | (1 + [sigma])-- - (1 - [sigma]) | [omega]²[rho]b²,
        8E      |_             r²                _|

  (2) extension along the circular filaments of amount
                 _                              _
    3 + [sigma] |             a²                 |
    ----------- |(1 + [sigma])-- + (1 - [sigma]) | [omega]²[rho]b².
        8E      |_            r²                _|

  (3) contraction of the filaments parallel to the axis of amount

    [sigma](3 + [sigma])
    -------------------- [omega]²[rho]b².
             4E

  Again, the greatest extension is the circumferential extension at the
  inner surface, and, when the hole is very small, its amount is nearly
  double what it would be for a complete disk.

  82. In the problem of the rotating shaft we have the following
  stress-system:

  (1) radial tension of amount

    (1/8)[omega]²[rho](a² - r²)(3 - 2[sigma])/(1-[sigma]),

  (2) circumferential tension of amount

    (1/8)[omega]²[rho]{(a²(3 - 2[sigma])/(1-[sigma])
      - r²(1 + 2[sigma])/(1 - [sigma])},

  (3) longitudinal tension of amount

    ¼[omega]²[rho](a² - 2r²)[sigma]/(1 - [sigma]).

  The resultant longitudinal tension at any normal section vanishes, and
  the radial tension vanishes at the bounding surface; and thus the
  expressions here given may be taken to represent the actual condition
  at all points which are not very close to the ends of the shaft. The
  contraction of the longitudinal filaments is uniform and equal to
  ½[omega]²[rho]a²[sigma]/E. The greatest extension in the rotating
  shaft is the circumferential extension close to the axis, and its
  amount is (1/8)[omega]²[rho]a²(3 - 5[sigma])/E(1 - [sigma]).

  The value of any theory of the strength of long rotating shafts
  founded on these formulae is diminished by the circumstance that at
  sufficiently high speeds the shaft may tend to take up a curved form,
  the straight form being unstable. The shaft is then said to _whirl_.
  This occurs when the period of rotation of the shaft is very nearly
  coincident with one of its periods of lateral vibration. The lowest
  speed at which whirling can take place in a shaft of length l, freely
  supported at its ends, is given by the formula

    [omega]²[rho] = ¼Ea²([pi]/l)^4.

  As in § 61, this formula should not be applied unless the length of
  the shaft is a considerable multiple of its diameter. It implies that
  whirling is to be expected whenever [omega] approaches this critical
  value.

83. When the forces acting upon a spherical or cylindrical body are not
radial, the problem becomes more complicated. In the case of the sphere
deformed by any forces it has been completely solved, and the solution
has been applied by Lord Kelvin and Sir G.H. Darwin to many interesting
questions of cosmical physics. The nature of the stress produced in the
interior of the earth by the weight of continents and mountains, the
spheroidal figure of a rotating solid planet, the rigidity of the earth,
are among the questions which have in this way been attacked. Darwin
concluded from his investigation that, to support the weight of the
existing continents and mountain ranges, the materials of which the
earth is composed must, at great depths (1600 kilometres), have at least
the strength of granite. Kelvin concluded from his investigation that
the actual heights of the tides in the existing oceans can be accounted
for only on the supposition that the interior of the earth is solid, and
of rigidity nearly as great as, if not greater than, that of steel.

  84. Some interesting problems relating to the strains produced in a
  cylinder of finite length by forces distributed symmetrically round
  the axis have been solved. The most important is that of a cylinder
  crushed between parallel planes in contact with its plane ends. The
  solution was applied to explain the discrepancies that have been
  observed in different tests of crushing strength according as the ends
  of the test specimen are or are not prevented from spreading. It was
  applied also to explain the fact that in such tests small conical
  pieces are sometimes cut out at the ends subjected to pressure.

85. _Vibrations and Waves._--When a solid body is struck, or otherwise
suddenly disturbed, it is thrown into a state of vibration. There always
exist dissipative forces which tend to destroy the vibratory motion, one
cause of the subsidence of the motion being the communication of energy
to surrounding bodies. When these dissipative forces are disregarded, it
is found that an elastic solid body is capable of vibrating in such a
way that the motion of any particle is simple harmonic motion, all the
particles completing their oscillations in the same period and being at
any instant in the same phase, and the displacement of any selected one
in any particular direction bearing a definite ratio to the displacement
of an assigned one in an assigned direction. When a body is moving in
this way it is said to be _vibrating in a normal mode_. For example,
when a tightly stretched string of negligible flexural rigidity, such as
a violin string may be taken to be, is fixed at the ends, and vibrates
transversely in a normal mode, the displacements of all the particles
have the same direction, and their magnitudes are proportional at any
instant to the ordinates of a curve of sines. Every body possesses an
infinite number of normal modes of vibration, and the _frequencies_ (or
numbers of vibrations per second) that belong to the different modes
form a sequence of increasing numbers. For the string, above referred
to, the fundamental tone and the various overtones form an harmonic
scale, that is to say, the frequencies of the normal modes of vibration
are proportional to the integers 1, 2, 3, .... In all these modes except
the first the string vibrates as if it were divided into a number of
equal pieces, each having fixed ends; this number is in each case the
integer defining the frequency. In general the normal modes of vibration
of a body are distinguished one from another by the number and situation
of the surfaces (or other _loci_) at which some characteristic
displacement or traction vanishes. The problem of determining the normal
modes and frequencies of free vibration of a body of definite size,
shape and constitution, is a mathematical problem of a similar character
to the problem of determining the state of stress in the body when
subjected to given forces. The bodies which have been most studied are
strings and thin bars, membranes, thin plates and shells, including
bells, spheres and cylinders. Most of the results are of special
importance in their bearing upon the theory of sound.

  86. The most complete success has attended the efforts of
  mathematicians to solve the problem of free vibrations for an
  isotropic sphere. It appears that the modes of vibration fall into two
  classes: one characterized by the absence of a radial component of
  displacement, and the other by the absence of a radial component of
  rotation (§ 14). In each class there is a doubly infinite number of
  modes. The displacement in any mode is determined in terms of a single
  spherical harmonic function, so that there are modes of each class
  corresponding to spherical harmonics of every integral degree; and for
  each degree there is an infinite number of modes, differing from one
  another in the number and position of the concentric spherical
  surfaces at which some characteristic displacement vanishes. The most
  interesting modes are those in which the sphere becomes slightly
  spheroidal, being alternately prolate and oblate during the course of
  a vibration; for these vibrations tend to be set up in a spherical
  planet by tide-generating forces. In a sphere of the size of the
  earth, supposed to be incompressible and as rigid as steel, the period
  of these vibrations is 66 minutes.

87. The theory of free vibrations has an important bearing upon the
question of the strength of structures subjected to sudden blows or
shocks. The stress and strain developed in a body by sudden applications
of force may exceed considerably those which would be produced by a
gradual application of the same forces. Hence there arises the general
question of _dynamical resistance_, or of the resistance of a body to
forces applied so quickly that the inertia of the body comes sensibly
into play. In regard to this question we have two chief theoretical
results. The first is that the strain produced by a force suddenly
applied may be as much as twice the statical strain, that is to say, as
the strain which would be produced by the same force when the body is
held in equilibrium under its action; the second is that the sudden
reversal of the force may produce a strain three times as great as the
statical strain. These results point to the importance of specially
strengthening the parts of any machine (e.g. screw propeller shafts)
which are subject to sudden applications or reversals of load. The
theoretical limits of twice, or three times, the statical strain are not
in general attained. For example, if a thin bar hanging vertically from
its upper end is suddenly loaded at its lower end with a weight equal to
its own weight, the greatest dynamical strain bears to the greatest
statical strain the ratio 1.63 : 1; when the attached weight is four
times the weight of the bar the ratio becomes 1.84 : 1. The method by
which the result just mentioned is reached has recently been applied to
the question of the breaking of winding ropes used in mines. It appeared
that, in order to bring the results into harmony with the observed
facts, the strain in the supports must be taken into account as well as
the strain in the rope (J. Perry, _Phil. Mag._, 1906 (vi.), vol. ii.).

88. The immediate effect of a blow or shock, locally applied to a body,
is the generation of a wave which travels through the body from the
locality first affected. The question of the propagation of waves
through an elastic solid body is historically of very great importance;
for the first really successful efforts to construct a theory of
elasticity (those of S.D. Poisson, A.L. Cauchy and G. Green) were
prompted, at least in part, by Fresnel's theory of the propagation of
light by transverse vibrations. For many years the luminiferous medium
was identified with the isotropic solid of the theory of elasticity.
Poisson showed that a disturbance communicated to the body gives rise to
two waves which are propagated through it with different velocities; and
Sir G.G. Stokes afterwards showed that the quicker wave is a wave of
irrotational dilatation, and the slower wave is a wave of rotational
distortion accompanied by no change of volume. The velocities of the two
waves in a solid of density [rho] are [root]{([lambda] + 2µ)/[rho]} and
[root](µ/[rho]), [lambda] and µ being the constants so denoted in § 26.
When the surface of the body is free from traction, the waves on
reaching the surface are reflected; and thus after a little time the
body would, if there were no dissipative forces, be in a very complex
state of motion due to multitudes of waves passing to and fro through
it. This state can be expressed as a state of vibration, in which the
motions belonging to the various normal modes (§ 85) are superposed,
each with an appropriate amplitude and phase. The waves of dilatation
and distortion do not, however, give rise to different modes of
vibration, as was at one time supposed, but any mode of vibration in
general involves both dilatation and rotation. There are exceptional
results for solids of revolution; such solids possess normal modes of
vibration which involve no dilatation. The existence of a boundary to
the solid body has another effect, besides reflexion, upon the
propagation of waves. Lord Rayleigh has shown that any disturbance
originating at the surface gives rise to waves which travel away over
the surface as well as to waves which travel through the interior; and
any internal disturbance, on reaching the surface, also gives rise to
such superficial waves. The velocity of the superficial waves is a
little less than that of the waves of distortion: 0.9554
[root](µ/[rho]) when the material is incompressible
0.9194[root](µ/[rho]) when the Poisson's ratio belonging to the material
is ¼.

89. These results have an application to the propagation of earthquake
shocks (see also EARTHQUAKE). An internal disturbance should, if the
earth can be regarded as solid, give rise to three wave-motions: two
propagated through the interior of the earth with different velocities,
and a third propagated over the surface. The results of seismographic
observations have independently led to the recognition of three phases
of the recorded vibrations: a set of "preliminary tremors" which are
received at different stations at such times as to show that they are
transmitted directly through the interior of the earth with a velocity
of about 10 km. per second, a second set of preliminary tremors which
are received at different stations at such times as to show that they
are transmitted directly through the earth with a velocity of about 5
km. per second, and a "main shock," or set of large vibrations, which
becomes sensible at different stations at such times as to show that a
wave is transmitted over the surface of the earth with a velocity of
about 3 km. per second. These results can be interpreted if we assume
that the earth is a solid body the greater part of which is practically
homogeneous, with high values for the rigidity and the resistance to
compression, while the superficial portions have lower values for these
quantities. The rigidity of the central portion would be about
(1.4)10^12 dynes per square cm., which is considerably greater than that
of steel, and the resistance to compression would be about (3.8)10^12
dynes per square cm. which is much greater than that of any known
material. The high value of the resistance to compression is not
surprising when account is taken of the great pressures, due to
gravitation, which must exist in the interior of the earth. The high
value of the rigidity can be regarded as a confirmation of Lord Kelvin's
estimate founded on tidal observations (§ 83).

90. _Strain produced by Heat._--The mathematical theory of elasticity as
at present developed takes no account of the strain which is produced in
a body by unequal heating. It appears to be impossible in the present
state of knowledge to form as in § 39 a system of differential equations
to determine both the stress and the temperature at any point of a solid
body the temperature of which is liable to variation. In the cases of
isothermal and adiabatic changes, that is to say, when the body is
slowly strained without variation of temperature, and also when the
changes are effected so rapidly that there is no gain or loss of heat by
any element, the internal energy of the body is sufficiently expressed
by the strain-energy-function (§§ 27, 30). Thus states of equilibrium
and of rapid vibration can be determined by the theory that has been
explained above. In regard to thermal effects we can obtain some
indications from general thermodynamic theory. The following passages
extracted from the article "Elasticity" contributed to the 9th edition
of the _Encyclopaedia Britannica_ by Sir W. Thomson (Lord Kelvin)
illustrate the nature of these indications:--"From thermodynamic theory
it is concluded that cold is produced whenever a solid is strained by
opposing, and heat when it is strained by yielding to, any elastic force
of its own, the strength of which would diminish if the temperature were
raised; but that, on the contrary, heat is produced when a solid is
strained against, and cold when it is strained by yielding to, any
elastic force of its own, the strength of which would increase if the
temperature were raised. When the strain is a condensation or
dilatation, uniform in all directions, a fluid may be included in the
statement. Hence the following propositions:--

"(1) A cubical compression of any elastic fluid or solid in an ordinary
condition causes an evolution of heat; but, on the contrary, a cubical
compression produces cold in any substance, solid or fluid, in such an
abnormal state that it would contract if heated while kept under
constant pressure. Water below its temperature (3.9° Cent.) of maximum
density is a familiar instance.

"(2) If a wire already twisted be suddenly twisted further, always,
however, within its limits of elasticity, cold will be produced; and if
it be allowed suddenly to untwist, heat will be evolved from itself
(besides heat generated externally by any work allowed to be wasted,
which it does in untwisting). It is assumed that the torsional rigidity
of the wire is diminished by an elevation of temperature, as the writer
of this article had found it to be for copper, iron, platinum and other
metals.

"(3) A spiral spring suddenly drawn out will become lower in
temperature, and will rise in temperature when suddenly allowed to draw
in. [This result has been experimentally verified by Joule
('Thermodynamic Properties of Solids,' _Phil. Trans._, 1858) and the
amount of the effect found to agree with that calculated, according to
the preceding thermodynamic theory, from the amount of the weakening of
the spring which he found by experiment.]

"(4) A bar or rod or wire of any substance with or without a weight hung
on it, or experiencing any degree of end thrust, to begin with, becomes
cooled if suddenly elongated by end pull or by diminution of end thrust,
and warmed if suddenly shortened by end thrust or by diminution of end
pull; except abnormal cases in which with constant end pull or end
thrust elevation of temperature produces shortening; in every such case
pull or diminished thrust produces elevation of temperature, thrust or
diminished pull lowering of temperature.

"(5) An india-rubber band suddenly drawn out (within its limits of
elasticity) becomes warmer; and when allowed to contract, it becomes
colder. Any one may easily verify this curious property by placing an
india-rubber band in slight contact with the edges of the lips, then
suddenly extending it--it becomes very perceptibly warmer: hold it for
some time stretched nearly to breaking, and then suddenly allow it to
shrink--it becomes quite startlingly colder, the cooling effect being
sensible not merely to the lips but to the fingers holding the band. The
first published statement of this curious observation is due to J. Gough
(_Mem. Lit. Phil. Soc. Manchester_, 2nd series, vol. i. p. 288), quoted
by Joule in his paper on 'Thermodynamic Properties of Solids' (cited
above). The thermodynamic conclusion from it is that an india-rubber
band, stretched by a constant weight of sufficient amount hung on it,
must, when heated, pull up the weight, and, when cooled, allow the
weight to descend: this Gough, independently of thermodynamic theory,
had found to be actually the case. The experiment any one can make with
the greatest ease by hanging a few pounds weight on a common
india-rubber band, and taking a red-hot coal in a pair of tongs, or a
red-hot poker, and moving it up and down close to the band. The way in
which the weight rises when the red-hot body is near, and falls when it
is removed, is quite startling. Joule experimented on the amount of
shrinking per degree of elevation of temperature, with different weights
hung on a band of vulcanized india-rubber, and found that they closely
agreed with the amounts calculated by Thomson's theory from the heating
effects of pull, and cooling effects of ceasing to pull, which he had
observed in the same piece of india-rubber."

91. _Initial Stress._--It has been pointed out above (§ 20) that the
"unstressed" state, which serves as a zero of reckoning for strains and
stresses is never actually attained, although the strain (measured from
this state), which exists in a body to be subjected to experiment, may
be very slight. This is the case when the "initial stress," or the
stress existing before the experiment, is small in comparison with the
stress developed during the experiment, and the limit of linear
elasticity (§ 32) is not exceeded. The existence of initial stress has
been correlated above with the existence of body forces such as the
force of gravity, but it is not necessarily dependent upon such forces.
A sheet of metal rolled into a cylinder, and soldered to maintain the
tubular shape, must be in a state of considerable initial stress quite
apart from the action of gravity. Initial stress is utilized in many
manufacturing processes, as, for example, in the construction of
ordnance, referred to in § 79, in the winding of golf balls by means of
india-rubber in a state of high tension (see the report of the case _The
Haskell Golf Ball Company_ v. _Hutchinson & Main_ in _The Times_ of
March 1, 1906). In the case of a body of ordinary dimensions it is such
internal stress as this which is especially meant by the phrase
"initial stress." Such a body, when in such a state of internal stress,
is sometimes described as "self-strained." It would be better described
as "self-stressed." The somewhat anomalous behaviour of cast iron has
been supposed to be due to the existence within the metal of initial
stress. As the metal cools, the outer layers cool more rapidly than the
inner, and thus the state of initial stress is produced. When cast iron
is tested for tensile strength, it shows at first no sensible range
either of perfect elasticity or of linear elasticity; but after it has
been loaded and unloaded several times its behaviour begins to be more
nearly like that of wrought iron or steel. The first tests probably
diminish the initial stress.

  92. From a mathematical point of view the existence of initial stress
  in a body which is "self-stressed" arises from the fact that the
  equations of equilibrium of a body free from body forces or surface
  tractions, viz. the equations of the type

    dPX_x   dPX_y   dPZ_x
    ----- + ----- + ----- = 0,
     dPx     dPy     dPz

  possess solutions which differ from zero. If, in fact, [phi]1, [phi]2,
  [phi]3 denote any arbitrary functions of x, y, z, the equations are
  satisfied by putting

          dP²[phi]3   dP²[phi]2               dP²[phi]1
    X_x = --------- + ---------, ..., Y_z = - ---------, ...;
             dPy²        dPz                    dPydPz

  and it is clear that the functions [phi]1, [phi]2, [phi]3 can be
  adjusted in an infinite number of ways so that the bounding surface of
  the body may be free from traction.

93. Initial stress due to body forces becomes most important in the case
of a gravitating planet. Within the earth the stress that arises from
the mutual gravitation of the parts is very great. If we assumed the
earth to be an elastic solid body with moduluses of elasticity no
greater than those of steel, the strain (measured from the unstressed
state) which would correspond to the stress would be much too great to
be calculated by the ordinary methods of the theory of elasticity (§
75). We require therefore some other method of taking account of the
initial stress. In many investigations, for example those of Lord Kelvin
and Sir G.H. Darwin referred to in § 83, the difficulty is turned by
assuming that the material may be treated as practically incompressible;
but such investigations are to some extent incomplete, so long as the
corrections due to a finite, even though high, resistance to compression
remain unknown. In other investigations, such as those relating to the
propagation of earthquake shocks and to gravitational instability, the
possibility of compression is an essential element of the problem. By
gravitational instability is meant the tendency of gravitating matter to
condense into nuclei when slightly disturbed from a state of uniform
diffusion; this tendency has been shown by J.H. Jeans (_Phil. Trans_. A.
201, 1903) to have exerted an important influence upon the course of
evolution of the solar system. For the treatment of such questions Lord
Rayleigh (_Proc. R. Soc. London_, A. 77, 1906) has advocated a method
which amounts to assuming that the initial stress is hydrostatic
pressure, and that the actual state of stress is to be obtained by
superposing upon this initial stress a stress related to the state of
strain (measured from the initial state) by the same formulae as hold
for an elastic solid body free from initial stress. The development of
this method is likely to lead to results of great interest.

  AUTHORITIES.--In regard to the analysis requisite to prove the results
  set forth above, reference may be made to A.E.H. Love, _Treatise on
  the Mathematical Theory of Elasticity_ (2nd ed., Cambridge, 1906),
  where citations of the original authorities will also be found. The
  following treatises may be mentioned: Navier, _Résumé des leçons sur
  l'application de la mécanique_ (3rd ed., with notes by Saint-Venant,
  Paris, 1864); G. Lamé, _Leçons sur la théorie mathématique de
  l'élasticité des corps solides_ (Paris, 1852); A. Clebsch, _Theorie
  der Elasticität fester Körper_ (Leipzig, 1862; French translation with
  notes by Saint-Venant, Paris, 1883); F. Neumann, _Vorlesungen über die
  Theorie der Elasticität_ (Leipzig, 1885); Thomson and Tait, _Natural
  Philosophy_ (Cambridge, 1879, 1883); Todhunter and Pearson, _History
  of the Elasticity and Strength of Materials_ (Cambridge, 1886-1893).
  The article "Elasticity" by Sir W. Thomson (Lord Kelvin) in 9th ed. of
  _Encyc. Brit_. (reprinted in his _Mathematical and Physical Papers_,
  iii., Cambridge, 1890) is especially valuable, not only for the
  exposition of the theory and its practical applications, but also for
  the tables of physical constants which are there given.
       (A. E. H. L.)


FOOTNOTES:

  [1] The sign of M is shown by the arrow-heads in fig. 19, for which,
    with y downwards,

         d²y
      EI --- + M = 0.
         dx²

  [2] The figure is drawn for a case where the bending moment has the
    same sign throughout.

  [3] M0 is taken to have, as it obviously has, the opposite sense to
    that shown in fig. 19.

  [4] The line joining the points of contact must be normal to the
    planes.



ELATERITE, also termed ELASTIC BITUMEN and MINERAL CAOUTCHOUC, a mineral
hydrocarbon, which occurs at Castleton in Derbyshire, in the lead mines
of Odin and elsewhere. It varies somewhat in consistency, being
sometimes soft, elastic and sticky; often closely resembling
india-rubber; and occasionally hard and brittle. It is usually dark
brown in colour and slightly translucent. A substance of similar
physical character is found in the Coorong district of South Australia,
and is hence termed coorongite, but Prof. Ralph Tate considers this to
be a vegetable product.



ELATERIUM, a drug consisting of a sediment deposited by the juice of the
fruit of _Ecballium Elaterium_, the squirting cucumber, a native of the
Mediterranean region. The plant, which is a member of the natural order
Cucurbitaceae, resembles the vegetable marrow in its growth. The fruit
resembles a small cucumber, and when ripe is highly turgid, and
separates almost at a touch from the fruit stalk. The end of the stalk
forms a stopper, on the removal of which the fluid contents of the
fruit, together with the seeds, are squirted through the aperture by the
sudden contraction of the wall of the fruit. To prepare the drug the
fruit is sliced lengthwise and slightly pressed; the greenish and
slightly turbid juice thus obtained is strained and set aside; and the
deposit of elaterium formed after a few hours is collected on a linen
filter, rapidly drained, and dried on porous tiles at a gentle heat.
Elaterium is met with in commerce in light, thin, friable, flat or
slightly incurved opaque cakes, of a greyish-green colour, bitter taste
and tea-like smell.

The drug is soluble in alcohol, but insoluble in water and ether. The
official dose is 1/10-½ grain, and the British pharmacopeia directs that
the drug is to contain from 20 to 25% of the active principle elaterinum
or elaterin. A resin in the natural product aids its action. Elaterin is
extracted from elaterium by chloroform and then precipitated by ether.
It has the formula C_20H_28O5. It forms colourless scales which have a
bitter taste, but it is highly inadvisable to taste either this
substance or elaterium. Its dose is 1/40-1/10 grain, and the British
pharmacopeia contains a useful preparation, the Pulvis Elaterini
Compositus, which contains one part of the active principle in forty.

The action of this drug resembles that of the saline aperients, but is
much more powerful. It is the most active hydragogue purgative known,
causing also much depression and violent griping. When injected
subcutaneously it is inert, as its action is entirely dependent upon its
admixture with the bile. The drug is undoubtedly valuable in cases of
dropsy and Bright's disease, and also in cases of cerebral haemorrhage,
threatened or present. It must not be used except in urgent cases, and
must invariably be employed with the utmost care, especially if the
state of the heart be unsatisfactory.



ELBA (Gr. [Greek: Aithalia]; Lat. _Ilva_), an island off the W. coast of
Italy, belonging to the province of Leghorn, from which it is 45 m. S.,
and 7 m. S.W. of Piombino, the nearest point of the mainland. Pop.
(1901) 25,043 (including Pianosa). It is about 19 m. long, 6½ m. broad,
and 140 sq. m. in area; and its highest point is 3340 ft. (Monte
Capanne). It forms, like Giglio and Monte Cristo, part of a sunken
mountain range extending towards Corsica and Sardinia.

The oldest rocks of Elba consist of schist and serpentine which in the
eastern part of the island are overlaid by beds containing Silurian and
Devonian fossils. The Permian may be represented, but the Trias is
absent, and in general the older Palaeozoic rocks are overlaid directly
by the Rhaetic and Lias. The Liassic beds are often metamorphosed and
the limestones contain garnet and wollastonite. The next geological
formation which is represented is the Eocene, consisting of nummulitic
limestone, sandstone and schist. The Miocene and Pliocene are absent.
The most remarkable feature in the geology of Elba is the extent of the
granitic and ophiolitic eruptions of the Tertiary period. Serpentines,
peridotites and diabases are interstratified with the Eocene deposits.
The granite, which is intruded through the Eocene beds, is associated
with a pegmatite containing tourmaline and cassiterite. The celebrated
iron ore of Elba is of Tertiary age and occurs indifferently in all the
older rocks. The deposits are superficial, resulting from the opening
out of veins at the surface, and consist chiefly of haematite. These
ores were worked by the ancients, but so inefficiently that their
spoil-heaps can be smelted again with profit. This process is now gone
through on the island itself. The granite was also quarried by the
Romans, but is not now much worked.

Parts of the island are fertile, and the cultivation of vines, and the
tunny and sardine fishery, also give employment to a part of the
population. The capital of the island is Portoferraio--pop. (1901)
5987--in the centre of the N. coast, enclosed by an amphitheatre of
lofty mountains, the slopes of which are covered with villas and
gardens. This is the best harbour, the ancient _Portus Argous_. The town
was built and fortified by Cosimo I. in 1548, who called it Cosmopolis.
Above the harbour, between the forts Stella and Falcone, is the palace
of Napoleon I., and 4 m. to the S.W. is his villa; while on the N. slope
of Monte Capanne is another of his country houses. The other villages in
the island are Campo nell' Elba, on the S. near the W. end, Marciana and
Marciana Marina on the N. of the island near the W. extremity, Porto
Longone, on the E. coast, with picturesque Spanish fortifications,
constructed in 1602 by Philip III.; Rio dell' Elba and Rio Marina, both
on the E. side of the island, in the mining district. At Le Grotte,
between Portoferraio and Rio dell' Elba, and at Capo Castello, on the
N.E. of the island, are ruins of Roman date.

Elba was famous for its mines in early times, and the smelting furnaces
gave it its Greek name of [Greek: A'thalia] ("soot island"). In Roman
times, and until 1900, however, owing to lack of fuel, the smelting was
done on the mainland. In 453 B.C. Elba was devastated by a Syracusan
squadron. From the 11th to the 14th century it belonged to Pisa, and in
1399 came under the dukes of Piombino. In 1548 it was ceded by them to
Cosimo I. of Florence. In 1596 Porto Longone was taken by Philip III. of
Spain, and retained until 1709, when it was ceded to Naples. In 1802 the
island was given to France by the peace of Amiens. On Napoleon's
deposition, the island was ceded to him with full sovereign rights, and
he resided there from the 5th of May 1814 to the 26th of February 1815.
After his fall it was restored to Tuscany, and passed with it to Italy
in 1860.

  See Sir R. Colt Hoare, _A Tour through the Island of Elba_ (London,
  1814).



ELBE (the _Albis_ of the Romans and the _Labe_ of the Czechs), a river
of Germany, which rises in Bohemia not far from the frontiers of
Silesia, on the southern side of the Riesengebirge, at an altitude of
about 4600 ft. Of the numerous small streams (Seifen or Flessen as they
are named in the district) whose confluent waters compose the infant
river, the most important are the Weisswasser, or White Water, and the
Elbseifen, which is formed in the same neighbourhood, but at a little
lower elevation. After plunging down the 140 ft. of the Elbfall, the
latter stream unites with the steep torrential Weisswasser at
Mädelstegbaude, at an altitude of 2230 ft., and thereafter the united
stream of the Elbe pursues a southerly course, emerging from the
mountain glens at Hohenelbe (1495 ft.), and continuing on at a soberer
pace to Pardubitz, where it turns sharply to the west, and at Kolin (730
ft.), some 27 m. farther on, bends gradually towards the north-west. A
little above Brandeis it picks up the Iser, which, like itself, comes
down from the Riesengebirge, and at Melnik it has its stream more than
doubled in volume by the Moldau, a river which winds northwards through
the heart of Bohemia in a sinuous, trough-like channel carved through
the plateaux. Some miles lower down, at Leitmeritz (433 ft.), the waters
of the Elbe are tinted by the reddish Eger, a stream which drains the
southern slopes of the Erzgebirge. Thus augmented, and swollen into a
stream 140 yds. wide, the Elbe carves a path through the basaltic mass
of the Mittelgebirge, churning its way through a deep, narrow rocky
gorge. Then the river winds through the fantastically sculptured
sandstone mountains of the "Saxon Switzerland," washing successively the
feet of the lofty Lilienstein (932 ft. above the Elbe), the scene of one
of Frederick the Great's military exploits in the Seven Years' War,
Königstein (797 ft. above the Elbe), where in times of war Saxony has
more than once stored her national purse for security, and the pinnacled
rocky wall of the Bastei, towering 650 ft. above the surface of the
stream. Shortly after crossing the Bohemian-Saxon frontier, and whilst
still struggling through the sandstone defiles, the stream assumes a
north-westerly direction, which on the whole it preserves right away to
the North Sea. At Pirna the Elbe leaves behind it the stress and turmoil
of the Saxon Switzerland, rolls through Dresden, with its noble river
terraces, and finally, beyond Meissen, enters on its long journey across
the North German plain, touching Torgau, Wittenberg, Magdeburg,
Wittenberge, Hamburg, Harburg and Altona on the way, and gathering into
itself the waters of the Mulde and Saale from the left, and those of the
Schwarze Elster, Havel and Elde from the right. Eight miles above
Hamburg the stream divides into the Norder (or Hamburg) Elbe and the
Süder (or Harburg) Elbe, which are linked together by several
cross-channels, and embrace in their arms the large island of
Wilhelmsburg and some smaller ones. But by the time the river reaches
Blankenese, 7 m. below Hamburg, all these anastomosing branches have
been reunited, and the Elbe, with a width of 4 to 9 m. between bank and
bank, travels on between the green marshes of Holstein and Hanover until
it becomes merged in the North Sea off Cuxhaven. At Kolin the width is
about 100 ft., at the mouth of the Moldau about 300, at Dresden 960, and
at Magdeburg over 1000. From Dresden to the sea the river has a total
fall of only 280 ft., although the distance is about 430 m. For the 75
m. between Hamburg and the sea the fall is only 3¼ ft. One consequence
of this is that the bed of the river just below Hamburg is obstructed by
a bar, and still lower down is choked with sandbanks, so that navigation
is confined to a relatively narrow channel down the middle of the
stream. But unremitting efforts have been made to maintain a sufficient
fairway up to Hamburg (q.v.). The tide advances as far as Geesthacht, a
little more than 100 m. from the sea. The river is navigable as far as
Melnik, that is, the confluence of the Moldau, a distance of 525 m., of
which 67 are in Bohemia. Its total length is 725 m., of which 190 are in
Bohemia, 77 in the kingdom of Saxony, and 350 in Prussia, the remaining
108 being in Hamburg and other states of Germany. The area of the
drainage basin is estimated at 56,000 sq. m.

_Navigation._--Since 1842, but more especially since 1871, improvements
have been made in the navigability of the Elbe by all the states which
border upon its banks. As a result of these labours there is now in the
Bohemian portion of the river a minimum depth of 2 ft. 8 in., whilst
from the Bohemian frontier down to Magdeburg the minimum depth is 3 ft.,
and from Magdeburg to Hamburg, 3 ft. 10 in. In 1896 and 1897 Prussia and
Hamburg signed covenants whereby two channels are to be kept open to a
depth of 9¾ ft., a width of 656 ft., and a length of 550 yds. between
Bunthaus and Ortkathen, just above the bifurcation of the Norder Elbe
and the Süder Elbe. In 1869 the maximum burden of the vessels which were
able to ply on the upper Elbe was 250 tons; but in 1899 it was increased
to 800 tons. The large towns through which the river flows have vied
with one another in building harbours, providing shipping accommodation,
and furnishing other facilities for the efficient navigation of the
Elbe. In this respect the greatest efforts have naturally been made by
Hamburg; but Magdeburg, Dresden, Meissen, Riesa, Tetschen, Aussig and
other places have all done their relative shares, Magdeburg, for
instance, providing a commercial harbour and a winter harbour. In spite,
however, of all that has been done, the Elbe remains subject to serious
inundations at periodic intervals. Among the worst floods were those of
the years 1774, 1799, 1815, 1830, 1845, 1862, 1890 and 1909. The growth
of traffic up and down the Elbe has of late years become very
considerable. A towing chain, laid in the bed of the river, extends from
Hamburg to Aussig, and by this means, as by paddle-tug haulage, large
barges are brought from the port of Hamburg into the heart of Bohemia.
The fleet of steamers and barges navigating the Elbe is in point of fact
greater than on any other German river. In addition to goods thus
conveyed, enormous quantities of timber are floated down the Elbe; the
weight of the rafts passing the station of Schandau on the Saxon
Bohemian frontier amounting in 1901 to 333,000 tons.

A vast amount of traffic is directed to Berlin, by means of the
Havel-Spree system of canals, to the Thuringian states and the Prussian
province of Saxony, to the kingdom of Saxony and Bohemia, and to the
various riverine states and provinces of the lower and middle Elbe. The
passenger traffic, which is in the hands of the Sächsisch-Böhmische
Dampfschifffahrtsgesellschaft is limited to Bohemia and Saxony, steamers
plying up and down the stream from Dresden to Melnik, occasionally
continuing the journey up the Moldau to Prague, and down the river as
far as Riesa, near the northern frontier of Saxony, and on the average
1½ million passengers are conveyed.

In 1877-1879, and again in 1888-1895, some 100 m. of canal were dug, 5
to 6½ ft. deep and of various widths, for the purpose of connecting the
Elbe, through the Havel and the Spree, with the system of the Oder. The
most noteworthy of these connexions are the Elbe Canal (14¼ m. long),
the Reek Canal (9½ m.), the Rüdersdorfer Gewässer (11½ m.), the
Rheinsberger Canal (11¼ m.), and the Sacrow-Paretzer Canal (10 m.),
besides which the Spree has been canalized for a distance of 28 m., and
the Elbe for a distance of 70 m. Since 1896 great improvements have been
made in the Moldau and the Bohemian Elbe, with the view of facilitating
communication between Prague and the middle of Bohemia generally on the
one hand, and the middle and lower reaches of the Elbe on the other. In
the year named a special commission was appointed for the regulation of
the Moldau and Elbe between Prague and Aussig, at a cost estimated at
about £1,000,000, of which sum two-thirds were to be borne by the
Austrian empire and one-third by the kingdom of Bohemia. The regulation
is effected by locks and movable dams, the latter so designed that in
times of flood or frost they can be dropped flat on the bottom of the
river. In 1901 the Austrian government laid before the Reichsrat a canal
bill, with proposals for works estimated to take twenty years to
complete, and including the construction of a canal between the Oder,
starting at Prerau, and the upper Elbe at Pardubitz, and for the
canalization of the Elbe from Pardubitz to Melnik (see AUSTRIA:
_Waterways_). In 1900 Lübeck was put into direct communication with the
Elbe at Lauenburg by the opening of the Elbe-Trave Canal, 42 m. in
length, and constructed at a cost of £1,177,700, of which the state of
Lübeck contributed £802,700, and the kingdom of Prussia £375,000. The
canal has been made 72 ft. wide at the bottom, 105 to 126 ft. wide at
the top, has a minimum depth of 8{1/6} ft., and is equipped with seven
locks, each 262½ ft. long and 39¼ ft. wide. It is thus able to
accommodate vessels up to 800 tons burden; and the passage from Lübeck
to Lauenburg occupies 18 to 21 hours. In the first year of its being
open (June 1900 to June 1901) a total of 115,000 tons passed through the
canal.[1] A gigantic project has also been put forward for providing
water communication between the Rhine and the Elbe, and so with the
Oder, through the heart of Germany. This scheme is known as the Midland
Canal. Another canal has been projected for connecting Kiel with the
Elbe by means of a canal trained through the Plön Lakes.

_Bridges._--The Elbe is crossed by numerous bridges, as at Königgrätz,
Pardubitz, Kolin, Leitmeritz, Tetschen, Schandau, Pirna, Dresden,
Meissen, Torgau, Wittenberg, Rosslau, Barby, Magdeburg, Rathenow,
Wittenberge, Dömitz, Lauenburg, and Hamburg and Harburg. At all these
places there are railway bridges, and nearly all, but more especially
those in Bohemia, Saxony and the middle course of the river--these last
on the main lines between Berlin and the west and south-west of the
empire--possess a greater or less strategic value. At Leitmeritz there
is an iron trellis bridge, 600 yds long. Dresden has four bridges, and
there is a fifth bridge at Loschwitz, about 3 m. above the city. Meissen
has a railway bridge, in addition to an old road bridge. Magdeburg is
one of the most important railway centres in northern Germany; and the
Elbe, besides being bridged--it divides there into three arms--several
times for vehicular traffic, is also spanned by two fine railway
bridges. At both Hamburg and Harburg, again, there are handsome railway
bridges, the one (1868-1873 and 1894) crossing the northern Elbe, and
the other (1900) the southern Elbe; and the former arm is also crossed
by a fine triple-arched bridge (1888) for vehicular traffic.

_Fish._--The river is well stocked with fish, both salt-water and
fresh-water species being found in its waters, and several varieties of
fresh-water fish in its tributaries. The kinds of greatest economic
value are sturgeon, shad, salmon, lampreys, eels, pike and whiting.

_Tolls._--In the days of the old German empire no fewer than thirty-five
different tolls were levied between Melnik and Hamburg, to say nothing
of the special dues and privileged exactions of various riparian owners
and political authorities. After these had been _de facto_, though not
_de jure_, in abeyance during the period of the Napoleonic wars, a
commission of the various Elbe states met and drew up a scheme for their
regulation, and the scheme, embodied in the Elbe Navigation Acts, came
into force in 1822. By this a definite number of tolls, at fixed rates,
was substituted for the often arbitrary tolls which had been exacted
previously. Still further relief was afforded in 1844 and in 1850, on
the latter occasion by the abolition of all tolls between Melnik and the
Saxon frontier. But the number of tolls was only reduced to one, levied
at Wittenberge, in 1863, about one year after Hanover was induced to
give up the Stade or Brunsbüttel toll in return for a compensation of
2,857,340 thalers. Finally, in 1870, 1,000,000 thalers were paid to
Mecklenburg and 85,000 thalers to Anhalt, which thereupon abandoned all
claims to levy tolls upon the Elbe shipping, and thus navigation on the
river became at last entirely free.

_History._--The Elbe cannot rival the Rhine in the picturesqueness of
the scenery it travels through, nor in the glamour which its romantic
and legendary associations exercise over the imagination. But it
possesses much to charm the eye in the deep glens of the Riesengebirge,
amid which its sources spring, and in the bizarre rock-carving of the
Saxon Switzerland. It has been indirectly or directly associated with
many stirring events in the history of the German peoples. In its lower
course, whatever is worthy of record clusters round the historical
vicissitudes of Hamburg--its early prominence as a missionary centre
(Ansgar) and as a bulwark against Slav and marauding Northman, its
commercial prosperity as a leading member of the Hanseatic League, and
its sufferings during the Napoleonic wars, especially at the hands of
the ruthless Davoût. The bridge over the river at Dessau recalls the hot
assaults of the _condottiere_ Ernst von Mansfeld in April 1626, and his
repulse by the crafty generalship of Wallenstein. But three years later
this imperious leader was checked by the heroic resistance of the
"Maiden" fortress of Magdeburg; though two years later still she lost
her reputation, and suffered unspeakable horrors at the hands of Tilly's
lawless and unlicensed soldiery. Mühlberg, just outside the Saxon
frontier, is the place where Charles V. asserted his imperial authority
over the Protestant elector of Saxony, John Frederick, the Magnanimous
or Unfortunate, in 1547. Dresden, Aussig and Leitmeritz are all
reminiscent of the fierce battles of the Hussite wars, and the last
named of the Thirty Years' War. But the chief historical associations of
the upper (i.e. the Saxon and Bohemian) Elbe are those which belong to
the Seven Years' War, and the struggle of the great Frederick of Prussia
against the power of Austria and her allies. At Pirna (and Lilienstein)
in 1756 he caught the entire Saxon army in his fowler's net, after
driving back at Lobositz the Austrian forces which were hastening to
their assistance; but only nine months later he lost his reputation for
"invincibility" by his crushing defeat at Kolin, where the great highway
from Vienna to Dresden crosses the Elbe. Not many miles distant, higher
up the stream, another decisive battle was fought between the same
national antagonists, but with a contrary result, on the memorable 3rd
of July 1866.

  See M. Buchheister, "Die Elbe u. der Hafen von Hamburg," in _Mitteil.
  d. Geog. Gesellsch. in Hamburg_ (1899), vol. xv. pp. 131-188; V. Kurs,
  "Die künstlichen Wasserstrassen des deutschen Reichs," in _Geog.
  Zeitschrift_ (1898), pp. 601-617; and (the official) _Der Elbstrom_
  (1900); B. Weissenborn, _Die Elbzölle und Elbstapelplätze im
  Mittelalter_ (Halle, 1900); Daniel, _Deutschland_; and A. Supan,
  _Wasserstrassen und Binnenschifffahrt_ (Berlin, 1902).


FOOTNOTE:

  [1] See _Der Bau des Elbe-Trave Canals und seine Vorgeschichte_
    (Lübeck, 1900).



ELBERFELD, a manufacturing town of Germany, in the Prussian Rhine
province, on the Wupper, and immediately west of and contiguous to
Barmen (q.v.). Pop. (1816) 21,710; (1840) 31,514; (1885) 109,218; (1905)
167,382. Elberfeld-Barmen, although administratively separate,
practically form a single whole. It winds, a continuous strip of houses
and factories, for 9 m. along the deep valley, on both banks of the
Wupper, which is crossed by numerous bridges, the engirdling hills
crowned with woods. Local intercommunication is provided by an electric
tramway line and a novel hanging railway--on the Langen mono-rail
system--suspended over the bed of the river, with frequent stations. In
the centre of the town are a number of irregular and narrow streets, and
the river, polluted by the refuse of dye-works and factories,
constitutes a constant eyesore. Yet within recent years great
alterations have been effected; in the newer quarters are several
handsome streets and public buildings; in the centre many insanitary
dwellings have been swept away, and their place occupied by imposing
blocks of shops and business premises, and a magnificent new town-hall,
erected in a dominant position. Among the most recent improvements must
be mentioned the Brausenwerther Platz, flanked by the theatre, the
public baths, and the railway station and administrative offices. There
are eleven Evangelical and five Roman Catholic churches (noticeable
among the latter the Suitbertuskirche), a synagogue, and chapels of
various other sects. Among other public buildings may be enumerated the
civic hall, the law courts and the old town-hall.

The town is particularly rich in educational, industrial, philanthropic
and religious institutions. The schools include the Gymnasium (founded
in 1592 by the Protestant community as a Latin school), the
Realgymnasium (founded in 1830, for "modern" subjects and Latin), the
Oberrealschule and Realschule (founded 1893, the latter wholly
"modern"), two girls' high schools, a girls' middle-class school, a
large number of popular schools, a mechanics' and polytechnic school, a
school of mechanics, an industrial drawing school, a commercial school,
and a school for the deaf and dumb. There are also a theatre, an
institute of music, a library, a museum, a zoological garden, and
numerous scientific societies. The town is the seat of the Berg Bible
Society. The majority of the inhabitants are Protestant, with a strong
tendency towards Pietism; but the Roman Catholics number upwards of
40,000, forming about one-fourth of the total population. The industries
of Elberfeld are on a scale of great magnitude. It is the chief centre
in Germany of the cotton, wool, silk and velvet manufactures, and of
upholstery, drapery and haberdashery of all descriptions, of printed
calicoes, of Turkey-red and other dyes, and of fine chemicals. Leather
and rubber goods, gold, silver and aluminium wares, machinery,
wall-paper, and stained glass are also among other of its staple
products. Commerce is lively and the exports to foreign countries are
very considerable. The railway system is well devised to meet the
requirements of its rapidly increasing trade. Two main lines of railway
traverse the valley; that on the south is the main line from
Aix-la-Chapelle, Cologne and Düsseldorf to central Germany and Berlin,
that on the north feeds the important towns of the Ruhr valley.

The surroundings of Elberfeld are attractive, and public grounds and
walks have been recently opened on the hills around with results
eminently beneficial to the health of the population.

In the 12th century the site of Elberfeld was occupied by the castle of
the lords of Elverfeld, feudatories of the archbishops of Cologne. The
fief passed later into the possession of the counts of Berg. The
industrial development of the place started with a colony of bleachers,
attracted by the clear waters of the Wupper, who in 1532 were granted
the exclusive privilege of bleaching yarn. It was not, however, until
1610 that Elberfeld was raised to the status of a town, and in 1640 was
surrounded with walls. In 1760 the manufacture of silk was introduced,
and dyeing with Turkey-red in 1780; but it was not till the end of the
century that its industries developed into importance under the
influence of Napoleon's continental system, which barred out British
competition. In 1815 Elberfeld was assigned by the congress of Vienna,
with the grand-duchy of Berg, to Prussia, and its prosperity rapidly
developed under the Prussian Zollverein.

  See Coutelle, _Elberfeld, topographisch-statistische Darstellung_
  (Elberfeld, 1853); Schell, _Geschichte der Stadt Elberfeld_ (1900); A.
  Shadwell, _Industrial Efficiency_ (London, 1906); and Jorde, _Führer
  durch Elberfeld und seine Umgebung_ (1902).



ELBEUF, a town of northern France in the department of Seine-Inférieure,
14 m. S.S.W. of Rouen by the western railway. Pop. (1906) 17,800.
Elbeuf, a town of wide, clean streets, with handsome houses and
factories, stands on the left bank of the Seine at the foot of hills
over which extends the forest of Elbeuf. A tribunal and chamber of
commerce, a board of trade-arbitrators, a lycée, a branch of the Bank of
France, a school of industry, a school of cloth manufacture and a museum
of natural history are among its institutions. The churches of St
Étienne and St Jean, both of the Renaissance period with later
additions, preserve stained glass of the 16th century. The
hôtel-de-ville and the Cercle du Commerce are the chief modern
buildings. The town with its suburbs, Orival, Caudebec-lès-Elbeuf, St
Aubin and St Pierre, is one of the principal and most ancient seats of
the woollen manufacture in France; more than half the inhabitants are
directly maintained by the staple industry and numbers more by the
auxiliary crafts. As a river-port it has a brisk trade in the produce of
the surrounding district as well as in the raw materials of its
manufactures, especially in wool from La Plata, Australia and Germany.
Two bridges, one of them a suspension-bridge, communicate with St Aubin
on the opposite bank of the Seine, and steamboats ply regularly to
Rouen.

Elbeuf was, in the 13th century, the centre of an important fief held by
the house of Harcourt, but its previous history goes back at least to
the early years of the Norman occupation, when it appears under the name
of Hollebof. It passed into the hands of the houses of Rieux and
Lorraine, and was raised to the rank of a duchy in the peerage of France
by Henry III. in favour of Charles of Lorraine (d. 1605), grandson of
Claude, duke of Guise, master of the hounds and master of the horse of
France. The last duke of Elbeuf was Charles Eugène of Lorraine, prince
de Lambesc, who distinguished himself in 1789 by his energy in
repressing risings of the people at Paris. He fought in the army of the
Bourbons, and later in the service of Austria, and died in 1825.



ELBING, a seaport town of Germany, in the kingdom of Prussia, 49 m. by
rail E.S.E. of Danzig, on the Elbing, a small river which flows into the
Frische Haff about 5 m. from the town, and is united with the Nogat or
eastern arm of the Vistula by means of the Kraffohl canal. Pop. (1905)
55,627. By the Elbing-Oberländischer canal, 110 m. long, constructed in
1845-1860, Lakes Geserich and Drewenz are connected with Lake Drausen,
and consequently with the port of Elbing. The old town was formerly
surrounded by fortifications, but of these only a few fragments remain.
There are several churches, among them the Marienkirche (dating from the
15th century and restored in 1887), a classical school (Gymnasium)
founded in 1536, a modern school (Realschule), a public library of over
28,000 volumes, and several charitable institutions. The town-hall
(1894) contains a historical museum.

Elbing is a place of rapidly growing industries. At the great Schichau
iron-works, which employ thousands of workmen, are built most of the
torpedo-boats and destroyers for the German navy, as well as larger
craft, locomotives and machinery. In addition to this there are at
Elbing important iron foundries, and manufactories of machinery, cigars,
lacquer and metal ware, flax and hemp yarn, cotton, linen, organs, &c.
There is a considerable trade also in agricultural produce.

The origin of Elbing was a colony of traders from Lübeck and Bremen,
which established itself under the protection of a castle of the
Teutonic Knights, built in 1237. In 1246 the town acquired "Lübeck
rights," i.e. the full autonomy conceded by the charter of the emperor
Frederick II. in 1226 (see LÜBECK), and it was early admitted to the
Hanseatic League. In 1454 the town repudiated the overlordship of the
Teutonic Order, and placed itself under the protection of the king of
Poland, becoming the seat of a Polish voivode. From this event dates a
decline in its prosperity, a decline hastened by the wars of the early
18th century. In 1698, and again in 1703, it was seized by the elector
of Brandenburg as security for a debt due to him by the Polish king. It
was taken and held to ransom by Charles XII. of Sweden, and in 1710 was
captured by the Russians. In 1772, when it fell to Prussia through the
first partition of Poland, it was utterly decayed.

  See Fuchs, _Gesch. der Stadt Elbing_ (Elbing, 1818-1852); Rhode, _Der
  Elbinger Kreis in topographischer, historischer, und statistischer
  Hinsicht_ (Danzig, 1871); Wernick, _Elbing_ (Elbing, 1888).



ELBOW, in anatomy, the articulation of the _humerus_, the bone of the
upper arm, and the _ulna_ and _radius_, the bones of the forearm (see
JOINTS). The word is thus applied to things which are like this joint in
shape, such as a sharp bend of a stream or river, an angle in a tube,
&c. The word is derived from the O. Eng. _elnboga_, a combination of
_eln_, the forearm, and _boga_, a bow or bend. This combination is
common to many Teutonic languages, cf. Ger. _Ellbogen_. _Eln_ still
survives in the name of a linear measure, the "ell," and is derived from
the O. Teut. _alina_, cognate with Lat. _ulna_ and Gr. [Greek: ôlenê],
the forearm. The use of the arm as a measure of length is illustrated by
the uses of _ulna_, in Latin, cubit, and fathom.



ELBURZ, or ALBURZ (from O. Pers. _Hara-bere-zaiti_, the "High
Mountain"), a great chain of mountains in northern Persia, separating
the Caspian depression from the Persian highlands, and extending without
any break for 650 m. from the western shore of the Caspian Sea to
north-eastern Khorasan. According to the direction, or strike, of its
principal ranges the Elburz may be divided into three sections: the
first 120 m. in length with a direction nearly N. to S., the second 240
m. in length with a direction N.W. to S.E., and the third 290 m. in
length striking S.W. to N.E. The first section, which is connected with
the system of the Caucasus, and begins west of Lenkoran in 39° N. and
45° E., is known as the Talish range and has several peaks 9000 to
10,000 ft. in height. It runs almost parallel to the western shore of
the Caspian, and west of Astara is only 10 or 12 m. distant from the
sea. At the point west of Resht, where the direction of the principal
range changes to one of N.W. to S.E., the second section of the Elburz
begins, and extends from there to beyond Mount Demavend, east of
Teheran. South of Resht this section is broken through at almost a right
angle by the Safid Rud (White river), and along it runs the principal
commercial road between the Caspian and inner Persia,
Resht-Kazvin-Teheran. The Elburz then splits into three principal ranges
running parallel to one another and connected at many places by
secondary ranges and spurs. Many peaks of the ranges in this section
have an altitude of 11,000 to 13,000 ft., and the elevation of the
passes leading over the ranges varies between 7000 and 10,000 ft. The
highest peaks are situated in the still unexplored district of Talikan,
N.W. of Teheran, and thence eastwards to beyond Mount Demavend. The part
of the Elburz immediately north of Teheran is known as the Kuh i Shimran
(mountain of Shimran, from the name of the Shimran district on its
southern slopes) and culminates in the Sar i Tochal (12,600 ft.). Beyond
it, and between the border of Talikan in the N.W. and Mount Demavend in
the N.E., are the ranges Azadbur, Kasil, Kachang, Kendevan, Shahzad,
Varzeh, Derbend i Sar and others, with elevations of 12,000 to 13,500
ft., while Demavend towers above them all with its altitude of 19,400
ft. The eastern foot of Demavend is washed by the river Herhaz (called
Lar river in its upper course), which there breaks through the Elburz in
a S.-N. direction in its course to the Caspian, past the city of Amol.
The third section of the Elburz, with its principal ranges striking S.W.
to N.E., has a length of about 290 m., and ends some distance beyond
Bujnurd in northern Khorasan, where it joins the Ala Dagh range, which
has a direction to the S.E., and, continuing with various appellations
to northern Afghanistan, unites with the Paropamisus. For about
two-thirds of its length--from its beginning to Khush Yailak--the third
section consists of three principal ranges connected by lateral ranges
and spurs. It also has many peaks over 10,000 ft. in height, and the
Nizva mountain on the southern border of the unexplored district of
Hazarjirib, north of Semnan, and the Shahkuh, between Shahrud and
Astarabad, have an elevation exceeding 13,000 ft. Beyond Khush Yailak
(meaning "pleasant summer quarters"), with an elevation of 10,000 ft.,
are the Kuh i Buhar (8000) and Kuh i Suluk (8000), which latter joins
the Ala Dagh (11,000).

The northern slopes of the Elburz and the lowlands which lie between
them and the Caspian, and together form the provinces of Gilan,
Mazandaran and Astarabad, are covered with dense forest and traversed by
hundreds (Persian writers say 1362) of perennial rivers and streams. The
breadth of the lowlands between the foot of the hills and the sea is
from 2 to 25 m., the greatest breadth being in the meridian of Resht in
Gilan, and in the districts of Amol, Sari and Barfurush in Mazandaran.
The inner slopes and ranges of the Elburz south of the principal
watershed, generally the central one of the three principal ranges which
are outside of the fertilizing influence of the moisture brought from
the sea, have little or no natural vegetation, and those farthest south
are, excepting a few stunted cypresses, completely arid and bare.

"North of the principal watershed forest trees and general verdure
refresh the eye. Gurgling water, strips of sward and tall forest trees,
backed by green hills, make a scene completely unlike the usual monotony
of Persian landscape. The forest scenery much resembles that of England,
with fine oaks and greensward. South of the watershed the whole aspect
of the landscape is as hideous and disappointing as scenery in
Afghanistan. Ridge after ridge of bare hill and curtain behind curtain
of serrated mountain, certainly sometimes of charming greys and blues,
but still all bare and naked, rugged and arid" ("Beresford Lovett,
_Proc. R.G.S._, Feb. 1883).

The higher ranges of the Elburz are snow-capped for the greater part of
the year, and some, which are not exposed to the refracted heat from the
arid districts of inner Persia, are rarely without snow. Water is
plentiful in the Elburz, and situated in well-watered valleys and gorges
are innumerable flourishing villages, embosomed in gardens and orchards,
with extensive cultivated fields and meadows, and at higher altitudes
small plateaus, under snow until March or April, afford cool camping
grounds to the nomads of the plains, and luxuriant grazing to their
sheep and cattle during the summer.     (A. H.-S.)



ELCHE, a town of eastern Spain, in the province of Alicante, on the
river Vinalapo. Pop. (1900) 27,308. Elche is the meeting-place of three
railways, from Novelda, Alicante and Murcia. It contains no building of
high architectural merit, except, perhaps, the collegiate church of
Santa Maria, with its lofty blue-tiled dome and fine west doorway. But
the costume and physiognomy of the inhabitants, the narrow streets and
flat-roofed, whitewashed houses, and more than all, the thousands of
palm-trees in its gardens and fields, give the place a strikingly
Oriental aspect, and render it unique among the cities of Spain. The
cultivation of the palm is indeed the principal occupation; and though
the dates are inferior to those of the Barbary States, upwards of 22,500
tons are annually exported. The blanched fronds are also sold in large
quantities for the processions of Palm Sunday, and after they have
received the blessing of the priest they are regarded throughout Spain
as certain defences against lightning. Other thriving local industries
include the manufacture of oil, soap, flour, leather, alcohol and
esparto grass rugs. The harbour of Elche is Santa Pola (pop. 4100),
situated 6 m. E.S.E., where the Vinalapo enters the Mediterranean, after
forming the wide lagoon known as the Albufera de Elche.

Elche is usually identified with the Iberian _Helike_, afterwards the
Roman colony of _Ilici_ or _Illici_. From the 8th century to the 13th it
was held by the Moors, who finally failed to recapture it from the
Spaniards in 1332.



ELCHINGEN, a village of Germany, in the kingdom of Bavaria, not far from
the Danube, 5 m. N.E. from Ulm. Here, on the 14th of October 1805, the
Austrians under Laudon were defeated by the French under Ney, who by
taking the bridge decided the day and gained for himself the title of
duke of Elchingen.



ELDAD BEN MAHLI, also surnamed had-Dani, Abu-Dani, David-had-Dani, or
the Danite, Jewish traveller, was the supposed author of a Jewish
travel-narrative of the 9th century A.D., which enjoyed great authority
in the middle ages, especially on the question of the Lost Ten Tribes.
Eldad first set out to visit his Hebrew brethren in Africa and Asia. His
vessel was wrecked, and he fell into the hands of cannibals; but he was
saved by his leanness, and by the opportune invasion of a neighbouring
tribe. After spending four years with his new captors, he was ransomed
by a fellow-countryman, a merchant of the tribe of Issachar. He then
(according to his highly fabulous narrative) visited the territory of
Issachar, in the mountains of Media and Persia; he also describes the
abodes of Zabulon, on the "other side" of the Paran Mountains, extending
to Armenia and the Euphrates; of Reuben, on another side of the same
mountains; of Ephraim and Half Manasseh, in Arabia, not far from Mecca;
and of Simeon and the other Half of Manasseh, in Chorazin, six months'
journey from Jerusalem. Dan, he declares, sooner than join in Jeroboam's
scheme of an Israelite war against Judah, had migrated to Cush, and
finally, with the help of Naphthali, Asher and Gad, had founded an
independent Jewish kingdom in the Gold Land of Havila, beyond Abyssinia.
The tribe of Levi had also been miraculously guided, from near Babylon,
to Havila, where they were enclosed and protected by the mystic river
Sambation or Sabbation, which on the Sabbath, though calm, was veiled in
impenetrable mist, while on other days it ran with a fierce
untraversable current of stones and sand.

Apart from these tales, we have the genuine Eldad, a celebrated Jewish
traveller and philologist; who flourished c. A.D. 830-890; to whom the
work above noticed is ascribed; who was a native either of S. Arabia,
Palestine or Media; who journeyed in Egypt, Mesopotamia, North Africa,
and Spain; who spent several years at Kairawan in Tunis; who died on a
visit to Cordova, and whose authority, as to the lost tribes, is
supported by a great Hebrew doctor of his own time, Zemah Gaon, the
rector of the Academy at Sura (A.D. 889-898). It is possible that a
certain relationship exists (as suggested by Epstein and supported by
D.H. Müller) between the famous apocryphal _Letter of Prester John_ (of
c. A.D. 1165) and the narrative of Eldad; but the affinity is not close.
Eldad is quoted as an authority on linguistic difficulties by the
leading medieval Jewish grammarians and lexicographers.

  The work ascribed to Eldad is in Hebrew, divided into six chapters,
  probably abbreviated from the original text. The first edition
  appeared at Mantua about 1480; the second at Constantinople in 1516;
  this was reprinted at Venice in 1544 and 1605, and at Jessnitz in
  1722. A Latin version by Gilb. Génébrard was published at Paris in
  1563, under the title of _Eldad Danius ... de Judaeis clausis eorumque
  in Aethiopia ... imperio_, and was afterwards incorporated in the
  translator's _Chronologia Hebraeorum_ of 1584; a German version
  appeared at Prague in 1695, and another at Jessnitz in 1723. In 1838
  E. Carmoly edited and translated a fuller recension which he had found
  in a MS. from the library of Eliezer Ben Hasan, forwarded to him by
  David Zabach of Morocco (see _Relation d'Eldad le Danite_, Paris,
  1838). Both forms are printed by Dr Jellinek in his _Bet-ha-Midrasch_,
  vols. ii. p. 102, &c., and iii. p. 6, &c. (Leipzig, 1853-1855). See
  also Bartolocci, _Bibliotheca magna Rabbinica_, i. 101-130; Fürst,
  _Bibliotheca Judaica_, i. 30, &c.; Hirsch Graetz, _Geschichte der
  Juden_ (3rd ed., Leipzig, 1895), v. 239-244; Rossi, _Dizionario degli
  Ebrei_; Steinschneider, _Cat. librorum Hebraeorum in bibliotheca
  Bodleiana_, cols. 923-925; Kitto's _Biblical Cyclopaedia_ (3rd
  edition, _sub nomine_); Abr. Epstein, _Eldad ha-Dani_ (Pressburg,
  1891); D.H. Müller, "Die Recensionen und Versionen des Eldad
  had-Dani," in _Denkschriften d. Wiener Akad._ (Phil.-Hist. Cl.), vol.
  xli. (1892), pp. 1-80.



ELDER (Gr. [Greek: presbuteros]), the name given at different times to a
ruler or officer in certain political and ecclesiastical systems of
government.

1. The office of elder is in its origin political and is a relic of the
old patriarchal system. The unit of primitive society is always the
family; the only tie that binds men together is that of kinship. "The
eldest male parent," to quote Sir Henry Maine,[1] "is absolutely
supreme in his household. His dominion extends to life and death and is
as unqualified over his children and their houses as over his slaves."
The tribe, which is a later development, is always an aggregate of
families or clans, not a collection of individuals. "The union of
several clans for common political action," as Robertson Smith says,
"was produced by the pressure of practical necessity, and always tended
towards dissolution when this practical pressure was withdrawn. The only
organization for common action was that the leading men of the clans
consulted together in time of need, and their influence led the masses
with them. Out of these conferences arose the senates of elders found in
the ancient states of Semitic and Aryan antiquity alike."[2] With the
development of civilization there came a time when age ceased to be an
indispensable condition of leadership. The old title was, however,
generally retained, e.g. the [Greek: gerontes] so often mentioned in
Homer, the [Greek: gerousia] of the Dorian states, the _senatus_ and the
_patres conscripti_ of Rome, the sheikh or elder of Arabia, the alderman
of an English borough, the seigneur (Lat. _senior_) of feudal France.

2. It was through the influence of Judaism that the originally political
office of elder passed over into the Christian Church and became
ecclesiastical. The Israelites inherited the office from their Semitic
ancestors (just as did the Moabites and the Midianites, of whose elders
we read in Numbers xxii. 7), and traces of it are found throughout their
history. Mention is made in Judges viii. 14 of the elders of Succoth
whom "Gideon taught with thorns of the wilderness and with briers." It
was to the elders of Israel in Egypt that Moses communicated the plan of
Yahweh for the redemption of the people (Exodus iii. 16). During the
sojourn in the wilderness the elders were the intermediaries between
Moses and the people, and it was out of the ranks of these elders that
Moses chose a council of seventy "to bear with him the burden of the
people" (Numbers xi. 16). The elders were the governors of the people
and the administrators of justice. There are frequent references to
their work in the latter capacity in the book of Deuteronomy, especially
in relation to the following crimes--the disobedience of sons; slander
against a wife; the refusal of levirate marriage; manslaughter; and
blood-revenge. Their powers were gradually curtailed by (a) the
development of the monarchy, to which of course they were in subjection,
and which became the court of appeal in questions of law;[3] (b) the
appointment of special judges, probably chosen from amongst the elders
themselves, though their appointment meant the loss of privilege to the
general body; (c) the rise of the priestly orders, which usurped many of
the prerogatives that originally belonged to the elders. But in spite of
the rise of new authorities, the elders still retained a large amount of
influence. We hear of them frequently in the Persian, Greek and Roman
periods. In the New Testament the members of the Sanhedrin in Jerusalem
are very frequently termed "elders" or [Greek: presbyteroi], and from
them the name was taken over by the Church.

3. The name "elder" was probably the first title bestowed upon the
officers of the Christian Church--since the word deacon does not occur
in connexion with the appointment of the Seven in Acts vi. Its universal
adoption is due not only to its currency amongst the Jews, but also to
the fact that it was frequently used as the title of magistrates in the
cities and villages of Asia Minor. For the history of the office of
elder in the early Church and the relation between elders and bishops
see PRESBYTER.

4. In modern times the use of the term is almost entirely confined to
the Presbyterian church, the officers of which are always called elders.
According to the Presbyterian theory of church government there are two
classes of elders--"teaching elders," or those specially set apart to
the pastoral office, and "ruling elders," who are laymen, chosen
generally by the congregation and set apart by ordination to be
associated with the pastor in the oversight and government of the
church. When the word is used without any qualification it is
understood to apply to the latter class alone. For an account of the
duties, qualifications and powers of elders in the Presbyterian Church
see PRESBYTERIANISM.

  See W.R. Smith, _History of the Semites_; H. Maine, _Ancient Law_; E.
  Schürer, _The Jewish People in the Time of Christ_; J. Wellhausen,
  _History of Israel and Judah_; G.A. Deissmann, _Bible Studies_, p.
  154.


FOOTNOTES:

  [1] _Ancient Law_, p. 126.

  [2] _Religion of the Semites_, p. 34.

  [3] There is a hint at this even in the Pentateuch, "every great
    matter they shall bring unto thee, but every small matter they shall
    judge themselves."



ELDER (O. Eng. _ellarn_; Ger. _Holunder_; Fr. _sureau_), the popular
designation of the deciduous shrubs and trees constituting the genus
_Sambucus_ of the natural order Caprifoliaceae. The Common Elder, _S.
nigra_, the bourtree of Scotland, is found in Europe, the north of
Africa, Western Asia, the Caucasus, and Southern Siberia; in sheltered
spots it attains a height of over 20 ft. The bark is smooth; the shoots
are stout and angular, and the leaves glabrous, pinnate, with oval or
elliptical leaflets. The flowers, which form dense flat-topped clusters
(corymbose cymes), with five main branches, have a cream-coloured,
gamopetalous, five-lobed corolla, five stamens, and three sessile
stigmas; the berries are purplish-black, globular and three- or
four-seeded, and ripen about September. The elder thrives best in moist,
well-drained situations, but can be grown in a great diversity of soils.
It grows readily from young shoots, which after a year are fit for
transplantation. It is found useful for making screen-fences in bleak,
exposed situations, and also as a shelter for other shrubs in the
outskirts of plantations. By clipping two or three times a year, it may
be made close and compact in growth. The young trees furnish a brittle
wood, containing much pith; the wood of old trees is white, hard and
close-grained, polishes well, and is employed for shoemakers' pegs,
combs, skewers, mathematical instruments and turned articles. Young
elder twigs deprived of pith have from very early times been in request
for making whistles, popguns and other toys.

The elder was known to the ancients for its medicinal properties, and in
England the inner bark was formerly administered as a cathartic. The
flowers (_sambuci flores_) contain a volatile oil, and serve for the
distillation of elder-flower water (_aqua sambuci_), used in
confectionery, perfumes and lotions. The leaves of the elder are
employed to impart a green colour to fat and oil (_unguentum sambuci
foliorum_ and _oleum viride_), and the berries for making wine, a common
adulterant of port. The leaves and bark emit a sickly odour, believed to
be repugnant to insects. Christopher Gullet (_Phil. Trans._, 1772, lxii.
p. 348) recommends that cabbages, turnips, wheat and fruit trees, to
preserve them from caterpillars, flies and blight, should be whipped
with twigs of young elder. According to German folklore, the hat must be
doffed in the presence of the elder-tree; and in certain of the English
midland counties a belief was once prevalent that the cross of Christ
was made from its wood, which should therefore never be used as fuel, or
treated with disrespect (see _Quart. Rev._ cxiv. 233). It was, however,
a common medieval tradition, alluded to by Ben Jonson, Shakespeare and
other writers, that the elder was the tree on which Judas hanged
himself; and on this account, probably, to be crowned with elder was in
olden times accounted a disgrace. In Cymbeline (act iv. s. 2) "the
stinking elder" is mentioned as a symbol of grief. In Denmark the tree
is supposed by the superstitious to be under the protection of the
"Elder-mother": its flowers may not be gathered without her leave; its
wood must not be employed for any household furniture; and a child
sleeping in an elder-wood cradle would certainly be strangled by the
Elder-mother.

Several varieties are known in cultivation: _aurea_, golden elder, has
golden-yellow leaves; _laciniata_, parsley-leaved elder, has the
leaflets cut into fine segments; _rotundifolia_ has rounded leaflets;
forms also occur with variegated white and yellow leaves, and
_virescens_ is a variety having white bark and green-coloured berries.
The scarlet-berried elder, _S. racemosa_, is the handsomest species of
the genus. It is a native of various parts of Europe, growing in Britain
to a height of over 15 ft., but often producing no fruit. The dwarf
elder or Danewort (supposed to have been introduced into Britain by the
Danes), _S. Ebulus_, a common European species, reaches a height of
about 6 ft. Its cyme is hairy, has three principal branches, and is
smaller than that of _S. nigra_; the flowers are white tipped with
pink. All parts of the plant are cathartic and emetic.



ELDON, JOHN SCOTT, 1st EARL OF (1751-1838), lord high chancellor of
England, was born at Newcastle on the 4th of June 1751. His grandfather,
William Scott of Sandgate, a suburb of Newcastle, was clerk to a
"fitter"--a sort of water-carrier and broker of coals. His father, whose
name also was William, began life as an apprentice to a fitter, in which
service he obtained the freedom of Newcastle, becoming a member of the
gild of Hoastmen (coal-fitters); later in life he became a principal in
the business, and attained a respectable position as a merchant in
Newcastle, accumulating property worth nearly £20,000.

John Scott was educated at the grammar school of his native town. He was
not remarkable at school for application to his studies, though his
wonderful memory enabled him to make good progress in them; he
frequently played truant and was whipped for it, robbed orchards, and
indulged in other questionable schoolboy freaks; nor did he always come
out of his scrapes with honour and a character for truthfulness. When he
had finished his education at the grammar school, his father thought of
apprenticing him to his own business, to which an elder brother Henry
had already devoted himself; and it was only through the interference of
his elder brother William (afterwards Lord Stowell, q.v.), who had
already obtained a fellowship at University College, Oxford, that it was
ultimately resolved that he should continue the prosecution of his
studies. Accordingly, in 1766, John Scott entered University College
with the view of taking holy orders and obtaining a college living. In
the year following he obtained a fellowship, graduated B.A. in 1770, and
in 1771 won the prize for the English essay, the only university prize
open in his time for general competition.

His wife was the eldest daughter of Aubone Surtees, a Newcastle banker.
The Surtees family objected to the match, and attempted to prevent it;
but a strong attachment had sprung up between them. On the 18th November
1772 Scott, with the aid of a ladder and an old friend, carried off the
lady from her father's house in the Sandhill, across the border to
Blackshiels, in Scotland, where they were married. The father of the
bridegroom objected not to his son's choice, but to the time he chose to
marry; for it was a blight on his son's prospects, depriving him of his
fellowship and his chance of church preferment. But while the bride's
family refused to hold intercourse with the pair, Mr Scott, like a
prudent man and an affectionate father, set himself to make the best of
a bad matter, and received them kindly, settling on his son £2000. John
returned with his wife to Oxford, and continued to hold his fellowship
for what is called the year of grace given after marriage, and added to
his income by acting as a private tutor. After a time Mr Surtees was
reconciled with his daughter, and made a liberal settlement on her.

John Scott's year of grace closed without any college living falling
vacant; and with his fellowship he gave up the church and turned to the
study of law. He became a student at the Middle Temple in January 1773.
In 1776 he was called to the bar, intending at first to establish
himself as an advocate in his native town, a scheme which his early
success led him to abandon, and he soon settled to the practice of his
profession in London, and on the northern circuit. In the autumn of the
year in which he was called to the bar his father died, leaving him a
legacy of £1000 over and above the £2000 previously settled on him.

In his second year at the bar his prospects began to brighten. His
brother William, who by this time held the Camden professorship of
ancient history, and enjoyed an extensive acquaintance with men of
eminence in London, was in a position materially to advance his
interests. Among his friends was the notorious Andrew Bowes of Gibside,
to the patronage of whose house the rise of the Scott family was largely
owing. Bowes having contested Newcastle and lost it, presented an
election petition against the return of his opponent. Young Scott was
retained as junior counsel in the case, and though he lost the petition
he did not fail to improve the opportunity which it afforded for
displaying his talents. This engagement, in the commencement of his
second year at the bar, and the dropping in of occasional fees, must
have raised his hopes; and he now abandoned the scheme of becoming a
provincial barrister. A year or two of dull drudgery and few fees
followed, and he began to be much depressed. But in 1780 we find his
prospects suddenly improved, by his appearance in the case of _Ackroyd_
v. _Smithson_, which became a leading case settling a rule of law; and
young Scott, having lost his point in the inferior court, insisted on
arguing it, on appeal, against the opinion of his clients, and carried
it before Lord Thurlow, whose favourable consideration he won by his
able argument. The same year Bowes again retained him in an election
petition; and in the year following Scott greatly increased his
reputation by his appearance as leading counsel in the Clitheroe
election petition. From this time his success was certain. In 1782 he
obtained a silk gown, and was so far cured of his early modesty that he
declined accepting the king's counselship if precedence over him were
given to his junior, Thomas (afterwards Lord) Erskine, though the latter
was the son of a peer and a most accomplished orator. He was now on the
high way to fortune. His health, which had hitherto been but
indifferent, strengthened with the demands made upon it; his talents,
his power of endurance, and his ambition all expanded together. He
enjoyed a considerable practice in the northern part of his circuit,
before parliamentary committees and at the chancery bar. By 1787 his
practice at the equity bar had so far increased that he was obliged to
give up the eastern half of his circuit (which embraced six counties)
and attend it only at Lancaster.

In 1782 he entered parliament for Lord Weymouth's close borough of
Weobley, which Lord Thurlow obtained for him without solicitation. In
parliament he gave a general and independent support to Pitt. His first
parliamentary speeches were directed against Fox's India Bill. They were
unsuccessful. In one he aimed at being brilliant; and becoming merely
laboured and pedantic, he was covered with ridicule by Sheridan, from
whom he received a lesson which he did not fail to turn to account. In
1788 he was appointed solicitor-general, and was knighted, and at the
close of this year he attracted attention by his speeches in support of
Pitt's resolutions on the state of the king (George III., who then
laboured under a mental malady) and the delegation of his authority. It
is said that he drew the Regency Bill, which was introduced in 1789. In
1793 Sir John Scott was promoted to the office of attorney-general, in
which it fell to him to conduct the memorable prosecutions for high
treason against British sympathizers with French republicanism,--amongst
others, against the celebrated Horne Tooke. These prosecutions, in most
cases, were no doubt instigated by Sir John Scott, and were the most
important proceedings in which he was ever professionally engaged. He
has left on record, in his _Anecdote Book_, a defence of his conduct in
regard to them. A full account of the principal trials, and of the
various legislative measures for repressing the expressions of popular
opinion for which he was more or less responsible, will be found in
Twiss's _Public and Private Life of the Lord Chancellor Eldon_, and in
the _Lives of the Lord Chancellors_, by Lord Campbell.

In 1799 the office of chief justice of the Court of Common Pleas falling
vacant, Sir John Scott's claim to it was not overlooked; and after
seventeen years' service in the Lower House, he entered the House of
Peers as Baron Eldon. In February 1801 the ministry of Pitt was
succeeded by that of Addington, and the chief justice now ascended the
woolsack. The chancellorship was given to him professedly on account of
his notorious anti-Catholic zeal. From the peace of Amiens (1802) till
1804 Lord Eldon appears to have interfered little in politics. In the
latter year we find him conducting the negotiations which resulted in
the dismissal of Addington and the recall of Pitt to office as prime
minister. Lord Eldon was continued in office as chancellor under Pitt;
but the new administration was of short duration, for on the 23rd of
January 1806 Pitt died, worn out with the anxieties of office, and his
ministry was succeeded by a coalition, under Lord Grenville. The death
of Fox, who became foreign secretary and leader of the House of Commons,
soon, however, broke up the Grenville administration; and in the spring
of 1807 Lord Eldon once more, under Lord Liverpool's administration,
returned to the woolsack, which, from that time, he continued to occupy
for about twenty years, swaying the cabinet, and being in all but name
prime minister of England. It was not till April 1827, when the
premiership, vacant through the paralysis of Lord Liverpool, fell to
Canning, the chief advocate of Roman Catholic emancipation, that Lord
Eldon, in the seventy-sixth year of his age, finally resigned the
chancellorship. When, after the two short administrations of Canning and
Goderich, it fell to the duke of Wellington to construct a cabinet, Lord
Eldon expected to be included, if not as chancellor, at least in some
important office, but he was overlooked, at which he was much chagrined.
Notwithstanding his frequent protests that he did not covet power, but
longed for retirement, we find him again, so late as 1835, within three
years of his death, in hopes of office under Peel. He spoke in
parliament for the last time in July 1834.

In 1821 Lord Eldon had been created Viscount Encombe and earl of Eldon
by George IV., whom he managed to conciliate, partly, no doubt, by
espousing his cause against his wife, whose advocate he had formerly
been, and partly through his reputation for zeal against the Roman
Catholics. In the same year his brother William, who from 1798 had
filled the office of judge of the High Court of Admiralty, was raised to
the peerage under the title of Lord Stowell.

Lord Eldon's wife, his dear "Bessy," his love for whom is a beautiful
feature in his life, died before him, on the 28th of June 1831. By
nature she was of simple character, and by habits acquired during the
early portion of her husband's career almost a recluse. Two of their
sons reached maturity--John, who died in 1805, and William Henry John,
who died unmarried in 1832. Lord Eldon himself survived almost all his
immediate relations. His brother William died in 1836. He himself died
in London on the 13th of January 1838, leaving behind him two daughters,
Lady Frances Bankes and Lady Elizabeth Repton, and a grandson John
(1805-1854), who succeeded him as second earl, the title subsequently
passing to the latter's son John (b. 1846).

Lord Eldon was no legislator--his one aim in politics was to keep in
office, and maintain things as he found them; and almost the only laws
he helped to pass were laws for popular coercion. For nearly forty years
he fought against every improvement in law, or in the
constitution--calling God to witness, on the smallest proposal of
reform, that he foresaw from it the downfall of his country. Without any
political principles, properly so called, and without interest in or
knowledge of foreign affairs, he maintained himself and his party in
power for an unprecedented period by his great tact, and in virtue of
his two great political properties--of zeal against every species of
reform, and zeal against the Roman Catholics. To pass from his political
to his judicial character is to shift to ground on which his greatness
is universally acknowledged. His judgments, which have received as much
praise for their accuracy as abuse for their clumsiness and uncouthness,
fill a small library. But though intimately acquainted with every nook
and cranny of the English law, he never carried his studies into foreign
fields, from which to enrich our legal literature; and it must be added
that against the excellence of his judgments, in too many cases, must be
set off the hardships, worse than injustice, that arose from his
protracted delays in pronouncing them. A consummate judge and the
narrowest of politicians, he was doubt on the bench, and promptness
itself in the political arena. For literature, as for art, he had no
feeling. What intervals of leisure he enjoyed from the cares of office
he filled up with newspapers and the gossip of old cronies. Nor were his
intimate associates men of refinement and taste; they were rather good
fellows who quietly enjoyed a good bottle and a joke; he uniformly
avoided encounters of wit with his equals. He is said to have been
parsimonious, and certainly he was quicker to receive than to
reciprocate hospitalities; but his mean establishment and mode of life
are explained by the retired habits of his wife, and her dislike of
company. His manners were very winning and courtly, and in the circle of
his immediate relatives he is said to have always been lovable and
beloved.

"In his person," says Lord Campbell, "Lord Eldon was about the middle
size, his figure light and athletic, his features regular and handsome,
his eye bright and full, his smile remarkably benevolent, and his whole
appearance prepossessing. The advance of years rather increased than
detracted from these personal advantages. As he sat on the
judgment-seat, 'the deep thought betrayed in his furrowed brow--the
large eyebrows, overhanging eyes that seemed to regard more what was
taking place within than around him--his calmness, that would have
assumed a character of sternness but for its perfect placidity--his
dignity, repose and venerable age, tended at once to win confidence and
to inspire respect' (Townsend). He had a voice both sweet and
deep-toned, and its effect was not injured by his Northumbrian burr,
which, though strong, was entirely free from harshness and vulgarity."

  AUTHORITIES.--Horace Twiss, _Life of Lord Chancellor Eldon_ (1844);
  W.E. Surtees, _Sketch of the Lives of Lords Stowell and Eldon_ (1846);
  Lord Campbell, _Lives of the Chancellors_; W.C. Townsend, _Lives of
  Twelve Eminent Judges_ (1846); _Greville Memoirs_.



EL DORADO (Span. "the gilded one"), a name applied, first, to the king
or chief priest of a South American tribe who was said to cover himself
with gold dust at a yearly religious festival held near Santa Fé de
Bogotá; next, to a legendary city called Manoa or Omoa; and lastly, to a
mythical country in which gold and precious stones were found in
fabulous abundance. The legend, which has never been traced to its
ultimate source, had many variants, especially as regards the situation
attributed to Manoa. It induced many Spanish explorers to lead
expeditions in search of treasure, but all failed. Among the most famous
were the expedition undertaken by Diego de Ordaz, whose lieutenant
Martinez claimed to have been rescued from shipwreck, conveyed inland,
and entertained at Omoa by "El Dorado" himself (1531); and the journeys
of Orellana (1540-1541), who passed down the Rio Napo to the valley of
the Amazon; that of Philip von Hutten (1541-1545), who led an exploring
party from Coro on the coast of Caracas; and of Gonzalo Ximenes de
Quesada (1569), who started from Santa Fé de Bogotá. Sir Walter Raleigh,
who resumed the search in 1595, described Manoa as a city on Lake Parimá
in Guiana. This lake was marked on English and other maps until its
existence was disproved by A. von Humboldt (1769-1859). Meanwhile the
name of El Dorado came to be used metaphorically of any place where
wealth could be rapidly acquired. It was given to a county in
California, and to towns and cities in various states. In literature
frequent allusion is made to the legend, perhaps the best-known
references being those in Milton's _Paradise Lost_ (vi. 411) and
Voltaire's _Candide_ (chs. 18, 19).

  See A.F.A. Bandelier, _The Gilded Man, El Dorado_ (New York, 1893).



ELDUAYEN, JOSÉ DE, 1st Marquis del Pazo de la Merced (1823-1898),
Spanish politician, was born in Madrid on the 22nd of June 1823. He was
educated in the capital, took the degree of civil engineer, and as such
directed important works in Asturias and Galicia, entered the Cortes in
1856 as deputy for Vigo, and sat in all the parliaments until 1867 as
member of the Union Liberal with Marshal O'Donnell. He attacked the
Miraflores cabinet in 1864, and became under-secretary of the home
office when Canovas was minister in 1865. He was made a councillor of
state in 1866, and in 1868 assisted the other members of the Union
Liberal in preparing the revolution. In the Cortes of 1872 he took much
part in financial debates. He accepted office as member of the last
Sagasta cabinet under King Amadeus. On the proclamation of the republic
Elduayen very earnestly co-operated in the Alphonsist conspiracy, and
endeavoured to induce the military and politicians to work together. He
went abroad to meet and accompany the prince after the _pronunciamiento_
of Marshal Campos, landed with him at Valencia, was made governor of
Madrid, a marquis, grand cross of Charles III., and minister for the
colonies in 1878. He accepted the portfolio of foreign affairs in the
Canovas cabinet from 1883 to 1885, and was made a life senator. He
always prided himself on having been one of the five members of the
Cortes of 1870 who voted for Alphonso XII. when that parliament elected
Amadeus of Savoy. He died at Madrid on the 24th of June 1898.



ELEANOR OF AQUITAINE (c. 1122-1204), wife of the English king Henry II.,
was the daughter and heiress of Duke William X. of Aquitaine, whom she
succeeded in April 1137. In accordance with arrangements made by her
father, she at once married Prince Louis, the heir to the French crown,
and a month later her husband became king of France under the title of
Louis VII. Eleanor bore Louis two daughters but no sons. This was
probably the reason why their marriage was annulled by mutual consent in
1151, but contemporary scandal-mongers attributed the separation to the
king's jealousy. It was alleged that, while accompanying her husband on
the Second Crusade (1146-1149), Eleanor had been unduly familiar with
her uncle, Raymond of Antioch. Chronology is against this hypothesis,
since Louis and she lived on good terms together for two years after the
Crusade. There is still less ground for the supposition that Henry of
Anjou, whom she married immediately after the divorce, had been her
lover before it. This second marriage, with a youth some years her
junior, was purely political. The duchy of Aquitaine required a strong
ruler, and the union with Anjou was eminently desirable. Louis, who had
hoped that Aquitaine would descend to his daughters, was mortified and
alarmed by the Angevin marriage; all the more so when Henry of Anjou
succeeded to the English crown in 1154. From this event dates the
beginning of the secular strife between England and France which runs
like a red thread through medieval history.

Eleanor bore to her second husband five sons and three daughters; John,
the youngest of their children, was born in 1167. But her relations with
Henry passed gradually through indifference to hatred. Henry was an
unfaithful husband, and Eleanor supported her sons in their great
rebellion of 1173. Throughout the latter years of the reign she was kept
in a sort of honourable confinement. It was during her captivity that
Henry formed his connexion with Rosamond Clifford, the Fair Rosamond of
romance. Eleanor, therefore, can hardly have been responsible for the
death of this rival, and the romance of the poisoned bowl appears to be
an invention of the next century.

Under the rule of Richard and John the queen became a political
personage of the highest importance. To both her sons the popularity
which she enjoyed in Aquitaine was most valuable. But in other
directions also she did good service. She helped to frustrate the
conspiracy with France which John concocted during Richard's captivity.
She afterwards reconciled the king and the prince, thus saving for John
the succession which he had forfeited by his misconduct. In 1199 she
crushed an Angevin rising in favour of John's nephew, Arthur of
Brittany. In 1201 she negotiated a marriage between her grand-daughter,
Blanche of Castile, and Louis of France, the grandson of her first
husband. It was through her staunch defence of Mirabeau in Poitou that
John got possession of his nephew's person. She died on the 1st of April
1204, and was buried at Fontevrault. Although a woman of strong passions
and great abilities she is, historically, less important as an
individual than as the heiress of Aquitaine, a part of which was,
through her second marriage, united to England for some four hundred
years.

  See the chronicles cited for the reigns of Henry II., Richard I. and
  John. Also Sir J.H. Ramsay, _Angevin Empire_ (London, 1903); K.
  Norgate, _England under the Angevin Kings_ (London, 1887); and A.
  Strickland, _Lives of the Queens of England_, vol. i. (1841).
       (H. W. C. D.)



ELEATIC SCHOOL, a Greek school of philosophy which came into existence
towards the end of the 6th century B.C., and ended with Melissus of
Samos (fl. c. 450 B.C.). It took its name from Elea, a Greek city of
lower Italy, the home of its chief exponents, Parmenides and Zeno. Its
foundation is often attributed to Xenophanes of Colophon, but, although
there is much in his speculations which formed part of the later Eleatic
doctrine, it is probably more correct to regard Parmenides as the
founder of the school. At all events, it was Parmenides who gave it its
fullest development. The main doctrines of the Eleatics were evolved in
opposition, on the one hand, to the physical theories of the early
physical philosophers who explained all existence in terms of primary
matter (see IONIAN SCHOOL), and, on the other hand, to the theory of
Heraclitus that all existence may be summed up as perpetual change. As
against these theories the Eleatics maintained that the true explanation
of things lies in the conception of a universal unity of being. The
senses with their changing and inconsistent reports cannot cognize this
unity; it is by thought alone that we can pass beyond the false
appearances of sense and arrive at the knowledge of being, at the
fundamental truth that "the All is One." There can be no creation, for
being cannot come from not-being; a thing cannot arise from that which
is different from it. The errors of common opinion arise to a great
extent from the ambiguous use of the verb "to be," which may imply
existence or be merely the copula which connects subject and predicate.

In these main contentions the Eleatic school achieved a real advance,
and paved the way to the modern conception of metaphysics. Xenophanes in
the middle of the 6th century had made the first great attack on the
crude mythology of early Greece, including in his onslaught the whole
anthropomorphic system enshrined in the poems of Homer and Hesiod. In
the hands of Parmenides this spirit of free thought developed on
metaphysical lines. Subsequently, whether from the fact that such bold
speculations were obnoxious to the general sense of propriety in Elea,
or from the inferiority of its leaders, the school degenerated into
verbal disputes as to the possibility of motion, and similar academic
trifling. The best work of the school was absorbed in the Platonic
metaphysic (see E. Caird, _Evolution of Theology in the Greek
Philosophers_, 1904).

  See further the articles on XENOPHANES; PARMENIDES; ZENO (of Elea);
  MELISSUS, with the works there quoted; also the histories of
  philosophy by Zeller, Gomperz, Windelband, &c.



ELECAMPANE (Med. Lat. _Enula Campana_), a perennial composite plant, the
_Inula Helenium_ of botanists, which is common in many parts of Britain,
and ranges throughout central and southern Europe, and in Asia as far
eastwards as the Himalayas. It is a rather rigid herb, the stem of which
attains a height of from 3 to 5 ft.; the leaves are large and toothed,
the lower ones stalked, the rest embracing the stem; the flowers are
yellow, 2 in. broad, and have many rays, each three-notched at the
extremity. The root is thick, branching and mucilaginous, and has a
warm, bitter taste and a camphoraceous odour. For medicinal purposes it
should be procured from plants not more than two or three years old.
Besides _inulin_, C_12H_20O_10, a body isomeric with starch, the root
contains _helenin_, C6H8O, a stearoptene, which may be prepared in white
acicular crystals, insoluble in water, but freely soluble in alcohol.
When freed from the accompanying inula-camphor by repeated
crystallization from alcohol, helenin melts at 110° C. By the ancients
the root was employed both as a medicine and as a condiment, and in
England it was formerly in great repute as an aromatic tonic and
stimulant of the secretory organs. "The fresh roots of elecampane
preserved with sugar, or made into a syrup or conserve," are recommended
by John Parkinson in his _Theatrum Botanicum_ as "very effectual to warm
a cold and windy stomack, and the pricking and stitches therein or in
the sides caused by the Spleene, and to helpe the cough, shortnesse of
breath, and wheesing in the Lungs." As a drug, however, the root is now
seldom resorted to except in veterinary practice, though it is
undoubtedly possessed of antiseptic properties. In France and
Switzerland it is used in the manufacture of absinthe.



ELECTION (from Lat. _eligere_, to pick out), the method by which a
choice or selection is made by a constituent body (the electors or
electorate) of some person to fill a certain office or dignity. The
procedure itself is called an election. Election, as a special form of
selection, is naturally a loose term covering many subjects; but except
in the theological sense (the doctrine of election), as employed by
Calvin and others, for the choice by God of His "elect," the legal sense
(see ELECTION, _in law_, below), and occasionally as a synonym for
personal choice (one's own "election"), it is confined to the selection
by the preponderating vote of some properly constituted body of electors
of one of two or more candidates, sometimes for admission only to some
private social position (as in a club), but more particularly in
connexion with public representative positions in political government.
It is thus distinguished from arbitrary methods of appointment, either
where the right of nominating rests in an individual, or where pure
chance (such as selection by lot) dictates the result. The part played
by different forms of election in history is alluded to in numerous
articles in this work, dealing with various countries and various
subjects. It is only necessary here to consider certain important
features in the elections, as ordinarily understood, namely, the
exercise of the right of voting for political and municipal offices in
the United Kingdom and America. See also the articles PARLIAMENT;
REPRESENTATION; VOTING; BALLOT, &c., and UNITED STATES: _Political
Institutions_. For practical details as to the conduct of political
elections in England reference must be made to the various text-books on
the subject; the candidate and his election agent require to be on their
guard against any false step which might invalidate his return.

_Law in the United Kingdom._--Considerable alterations have been made in
recent years in the law of Great Britain and Ireland relating to the
procedure at parliamentary and municipal elections, and to election
petitions.

As regards parliamentary elections (which may be either the "general
election," after a dissolution of parliament, or "by-elections," when
casual vacancies occur during its continuance), the most important of
the amending statutes is the Corrupt and Illegal Practices Act 1883.
This act, and the Parliamentary Elections Act 1868, as amended by it,
and other enactments dealing with corrupt practices, are temporary acts
requiring annual renewal. As regards municipal elections, the Corrupt
Practices (Municipal Elections) Act 1872 has been repealed by the
Municipal Corporations Act 1882 for England, and by the Local Government
(Ireland) Act 1898 for Ireland. The governing enactments for England are
now the Municipal Corporations Act 1882, part iv., and the Municipal
Elections (Corrupt and Illegal Practices) Act 1884, the latter annually
renewable. The provisions of these enactments have been applied with
necessary modifications to municipal and other local government
elections in Ireland by orders of the Irish Local Government Board made
under powers conferred by the Local Government (Ireland) Act 1898. In
Scotland the law regulating municipal and other local government
elections is now to be found in the Elections (Scotland) (Corrupt and
Illegal Practices) Act 1890.

The alterations in the law have been in the direction of greater
strictness in regard to the conduct of elections, and increased control
in the public interest over the proceedings on election petitions.
Various acts and payments which were previously lawful in the absence of
any corrupt bargain or motive are now altogether forbidden under the
name of "illegal practices" as distinguished from "corrupt practices."
Failure on the part of a parliamentary candidate or his election agent
to comply with the requirements of the law in any particular is
sufficient to invalidate the return (see the articles BRIBERY and
CORRUPT PRACTICES). Certain relaxations are, however, allowed in
consideration of the difficulty of absolutely avoiding all deviation
from the strict rules laid down. Thus, where the judges who try an
election petition report that there has been treating, undue influence,
or any illegal practice by the candidate or his election agent, but that
it was trivial, unimportant and of a limited character, and contrary to
the orders and without the sanction or connivance of the candidate or
his election agent, and that the candidate and his election agent took
all reasonable means for preventing corrupt and illegal practices, and
that the election was otherwise free from such practices on their part,
the election will not be avoided. The court has also the power to
relieve from the consequences of certain innocent contraventions of the
law caused by inadvertence or miscalculation.


  Election petitions.

The inquiry into a disputed parliamentary election was formerly
conducted before a committee of the House of Commons, chosen as nearly
as possible from both sides of the House for that particular business.
The decisions of these tribunals laboured under the suspicion of being
prompted by party feeling, and by an act of 1868 the jurisdiction was
finally transferred to judges of the High Court, notwithstanding the
general unwillingness of the bench to accept a class of business which
they feared might bring their integrity into dispute. Section 11 of the
act ordered, _inter alia_, that the trial of every election petition
shall be conducted before a _puisne judge_ of one of the common law
courts at Westminster and Dublin; that the said courts shall each select
a judge to be placed on the rota for the trial of election petitions;
that the said judges shall try petitions standing for trial according to
seniority or otherwise, as they may agree; that the trial shall take
place in the county or borough to which the petition refers, unless the
court should think it desirable to hold it elsewhere. The judge shall
determine "whether the member whose return is complained of, or any and
what other person, was duly returned and elected, or whether the
election was void," and shall certify his determination to the speaker.
When corrupt practices have been charged the judge shall also report (1)
whether any such practice has been committed by or with the knowledge or
consent of any candidate, and the nature thereof; (2) the names of
persons proved to have been guilty of any corrupt practice; and (3)
whether corrupt practices have extensively prevailed at the election.
Questions of law were to be referred to the decision of the court of
common pleas. On the abolition of that court by the Judicature Act 1873,
the jurisdiction was transferred to the common pleas division, and again
on the abolition of that division was transferred to the king's bench
division, in whom it is now vested. The rota of judges for the trial of
election petitions is also supplied by the king's bench division. The
trial now takes place before two judges instead of one; and, when
necessary, the number of judges on the rota may be increased. Both the
judges who try a petition are to sign the certificates to be made to the
speaker. If they differ as to the validity of a return, they are to
state such difference in their certificate, and the return is to be held
good; if they differ as to a report on any other matter, they are to
certify their difference and make no report on such matter. The director
of public prosecutions attends the trial personally or by
representative. It is his duty to watch the proceedings in the public
interest, to issue summonses to witnesses whose evidence is desired by
the court, and to prosecute before the election court or elsewhere those
persons whom he thinks to have been guilty of corrupt or illegal
practices at the election in question. If an application is made for
leave to withdraw a petition, copies of the affidavits in support are to
be delivered to him; and he is entitled to be heard and to call evidence
in opposition to such application. Witnesses are not excused from
answering criminating questions; but their evidence cannot be used
against them in any proceedings except criminal proceedings for perjury
in respect of that evidence. If a witness answers truly all questions
which he is required by the court to answer, he is entitled to receive a
certificate of indemnity, which will save him from all proceedings for
any offence under the Corrupt Practices Acts committed by him before the
date of the certificate at or in relation to the election, except
proceedings to enforce any incapacity incurred by such offence. An
application for leave to withdraw a petition must be supported by
affidavits from all the parties to the petition and their solicitors,
and by the election agents of all of the parties who were candidates at
the election. Each of these affidavits is to state that to the best of
the deponent's knowledge and belief there has been no agreement and no
terms or undertaking made or entered into as to the withdrawal, or, if
any agreement has been made, shall state its terms. The applicant and
his solicitor are also to state in their affidavits the grounds on which
the petition is sought to be withdrawn. If any person makes an agreement
for the withdrawal of a petition in consideration of a money payment, or
of the promise that the seat shall be vacated or another petition
withdrawn, or omits to state in his affidavit that he has made an
agreement, lawful or unlawful, for the withdrawal, he is guilty of an
indictable misdemeanour. The report of the judges to the speaker is to
contain particulars as to illegal practices similar to those previously
required as to corrupt practices; and they are to report further whether
any candidate has been guilty by his agents of an illegal practice, and
whether certificates of indemnity have been given to persons reported
guilty of corrupt or illegal practices.

The Corrupt Practices Acts apply, with necessary variations in details,
to parliamentary elections in Scotland and Ireland.

The amendments in the law as to municipal elections are generally
similar to those which have been made in parliamentary election law. The
procedure on trial of petitions is substantially the same, and wherever
no other provision is made by the acts or rules the procedure on the
trial of parliamentary election petitions is to be followed. Petitions
against municipal elections were dealt with in 35 & 36 Vict. c. 60. The
election judges appoint a number of barristers, not exceeding five, as
commissioners to try such petitions. No barrister can be appointed who
is of less than fifteen years' standing, or a member of parliament, or
holder of any office of profit (other than that of recorder) under the
crown; nor can any barrister try a petition in any borough in which he
is recorder or in which he resides, or which is included in his circuit.
The barrister sits without a jury. The provisions are generally similar
to those relating to parliamentary elections. The petition may allege
that the election was avoided as to the borough or ward on the ground of
general bribery, &c., or that the election of the person petitioned
against was avoided by corrupt practices, or by personal
disqualification, or that he had not the majority of lawful votes. The
commissioner who tries a petition sends to the High Court a certificate
of the result, together with reports as to corrupt and illegal
practices, &c., similar to those made to the speaker by the judges who
try a parliamentary election petition. The Municipal Elections (Corrupt
and Illegal Practices) Act 1884 applied to school board elections
subject to certain variations, and has been extended by the Local
Government Act 1888 to county council elections, and by the Local
Government Act 1894 to elections by parochial electors. The law in
Scotland is on the same lines, and extends to all non-parliamentary
elections, and, as has been stated, the English statutes have been
applied with adaptations to all municipal and local government elections
in Ireland.

_United States._--Elections are much more frequent in the United States
than they are in Great Britain, and they are also more complicated. The
terms of elective officers are shorter; and as there are also more
offices to be filled, the number of persons to be voted for is
necessarily much greater. In the year of a presidential election the
citizen may be called upon to vote at one time for all of the following:
(1) National candidates--president and vice-president (indirectly
through the electoral college) and members of the House of
Representatives; (2) state candidates--governor, members of the state
legislature, attorney-general, treasurer, &c.; (3) county
candidates--sheriff, county judges, district attorney, &c.; (4)
municipal or town candidates--mayor, aldermen, selectmen, &c. The number
of persons actually voted for may therefore be ten or a dozen, or it may
be many more. In addition, the citizen is often called upon to vote yea
or nay on questions such as amendments to the state constitutions,
granting of licences, and approval or disapproval of new municipal
undertakings. As there may be, and generally is, more than one candidate
for each office, and as all elections are now, and have been for many
years, conducted by ballot, the total number of names to appear on the
ballot may be one hundred or may be several hundred. These names are
arranged in different ways, according to the laws of the different
states. Under the Massachusetts law, which is considered the best by
reformers, the names of candidates for each office are arranged
alphabetically on a "blanket" ballot, as it is called from its size, and
the elector places a mark opposite the names of such candidates as he
may wish to vote for. Other states, New York for example, have the
blanket system, but the names of the candidates are arranged in party
columns. Still other states allow the grouping on one ballot of all the
candidates of a single party, and there would be therefore as many
separate ballots in such states as there were parties in the field.

The qualifications for voting, while varying in the different states in
details, are in their main features the same throughout the Union. A
residence in the state is required of from three months to two years.
Residence is also necessary, but for a shorter period, in the county,
city or town, or voting precinct. A few states require the payment of a
poll tax. Some require that the voter shall be able to read and
understand the Constitution. This latter qualification has been
introduced into several of the Southern states, partly at least to
disqualify the ignorant coloured voters. In all, or practically all, the
states idiots, convicts and the insane are disqualified; in some states
paupers; in some of the Western states the Chinese. In some states women
are allowed to vote on certain questions, or for the candidates for
certain offices, especially school officials; and in four of the Western
states women have the same rights of suffrage as men. The number of
those who are qualified to vote, but do not avail themselves of the
right, varies greatly in the different states and according to the
interest taken in the election. As a general rule, but subject to
exceptions, the national elections call out the largest number, the
state elections next, and the local elections the smallest number of
voters. In an exciting national election between 80 and 90% of the
qualified voters actually vote, a proportion considerably greater than
in Great Britain or Germany.

The tendency of recent years has been towards a decrease both in the
number and in the frequency of elections. A president and vice-president
are voted for every fourth year, in the years divisible by four, on the
first Tuesday following the first Monday of November. Members of the
national House of Representatives are chosen for two years on the
even-numbered years. State and local elections take place in accordance
with state laws, and may or may not be on the same day as the national
elections. Originally the rule was for the states to hold annual
elections; in fact, so strongly did the feeling prevail of the need in a
democratic country for frequent elections, that the maxim "where annual
elections end, tyranny begins," became a political proverb. But opinion
gradually changed even in the older or Eastern states, and in 1909
Massachusetts and Rhode Island were the only states in the Union holding
annual elections for governor and both houses of the state legislature.
In the Western states especially state officers are chosen for longer
terms--in the case of the governor often for four years--and the number
of elections has correspondingly decreased. Another cause of the
decrease in the number of elections is the growing practice of holding
all the elections of any year on one and the same day. Before the Civil
War Pennsylvania held its state elections several months before the
national elections. Ohio and Indiana, until 1885 and 1881 respectively,
held their state elections early in October. Maine, Vermont and Arkansas
keep to September. The selection of one day in the year for all
elections held in that year has resulted in a considerable decrease in
the total number.

Another tendency of recent years, but not so pronounced, is to hold
local elections in what is known as the "off" year; that is, on the
odd-numbered year, when no national election is held. The object of this
reform is to encourage independent voting. The average American citizen
is only too prone to carry his national political predilections into
local elections, and to vote for the local nominees of his party,
without regard to the question of fitness of candidates and the
fundamental difference of issues involved. This tendency to vote the
entire party ticket is the more pronounced because under the system of
voting in use in many of the states all the candidates of the party are
arranged on one ticket, and it is much easier to vote a straight or
unaltered ticket than to change or "scratch" it. Again, the voter,
especially the ignorant one, refrains from scratching his ticket, lest
in some way he should fail to comply with the technicalities of the law
and his vote be lost. On the other hand, if local elections are held on
the "off" or odd year, and there be no national or state candidates, the
voter feels much more free to select only those candidates whom he
considers best qualified for the various offices.

On the important question of the purity of elections it is difficult to
speak with precision. In many of the states, especially those with an
enlightened public spirit, such as most of the New England states and
many of the North-Western, the elections are fairly conducted, there
being no intimidation at all, little or no bribery, and an honest count.
It can safely be said that through the Union as a whole the tendency of
recent years has been decidedly towards greater honesty of elections.
This is owing to a number of causes: (1) The selection of a single day
for all elections, and the consequent immense number voting on that day.
Some years ago, when for instance the Ohio and Indiana elections were
held a few weeks before the general election, each party strained every
nerve to carry them, for the sake of prestige and the influence on other
states. In fact, presidential elections were often felt to turn on the
result in these early voting states, and the party managers were none
too scrupulous in the means employed to carry them. Bribery has
decreased in such states since the change of election day to that of the
rest of the country. (2) The enactment in most of the states of the
Australian or secret ballot (q.v.) laws. These have led to the secrecy
of the ballot, and hence to a greater or less extent have prevented
intimidation and bribery. (3) Educational or other such test, more
particularly in the Southern states, the object of which is to exclude
the coloured, and especially the ignorant coloured, voters from the
polls. In those southern states in which the coloured vote was large,
and still more in those in which it was the majority, it was felt among
the whites that intimidation or ballot-box stuffing was justified by the
necessity of white supremacy. With the elimination of the coloured vote
by educational or other tests the honesty of elections has increased.
(4) The enactment of new and more stringent registration laws. Under
these laws only those persons are allowed to vote whose names have been
placed on the rolls a certain number of days or months before election.
These rolls are open to public inspection, and the names may be
challenged at the polls, and "colonization" or repeating is therefore
almost impossible. (5) The reform of the civil service and the gradual
elimination of the vicious principle of "to the victors belong the
spoils." With the reform of the civil service elections become less a
scramble for office and more a contest of political or economic
principle. They bring into the field, therefore, a better class of
candidates. (6) The enactment in a number of states of various other
laws for the prevention of corrupt practices, for the publication of
campaign expenses, and for the prohibition of party workers from coming
within a certain specified distance of the polls. In the state of
Massachusetts, for instance, an act passed in 1892, and subsequently
amended, provides that political committees shall file a full statement,
duly sworn to, of all campaign expenditures made by them. The act
applies to all public elections except that of town officers, and also
covers nominations by caucuses and conventions as well. Apart from his
personal expenses such as postage, travelling expenses, &c., a candidate
is prohibited from spending anything himself to promote either his
nomination or his election, but he is allowed to contribute to the
treasury of the political committee. The law places no limit on the
amount that these committees may spend. The reform sought by the law is
thorough publicity, and not only are details of receipts and
expenditures to be published, but the names of contributors and the
amount of their contributions. In the state of New York the act which
seeks to prevent corrupt practices relies in like manner on the efficacy
of publicity, but it is less effective than the Massachusetts law in
that it provides simply for the filing by the candidates themselves of
sworn statements of their own expenses. There is nothing to prevent
their contributing to political committees, and the financial methods
and the amounts expended by such committees are not made public. But
behind all these causes that have led to more honest elections lies the
still greater one of a healthier public spirit. In the reaction
following the Civil War all reforms halted. In recent years, however, a
new and healthier interest has sprung up in things political; and one
result of this improved civic spirit is seen in the various laws for
purification of elections. It may now be safely affirmed that in the
majority of states the elections are honestly conducted; that
intimidation, bribery, stuffing of the ballot boxes or other forms of
corruption, when they exist, are owing in large measure to temporary or
local causes; and that the tendency of recent years has been towards a
decrease in all forms of corruption.

The expenses connected with elections, such as the renting and preparing
of the polling-places, the payment of the clerks and other officers who
conduct the elections and count the vote, are borne by the community. A
candidate therefore is not, as far as the law is concerned, liable to
any expense whatever. As a matter of fact he does commonly contribute to
the party treasury, though in the case of certain candidates,
particularly those for the presidency and for judicial offices,
financial contributions are not general. The amount of a candidate's
contribution varies greatly, according to the office sought, the state
in which he lives, and his private wealth. On one occasion, in a
district in New York, a candidate for Congress is credibly believed to
have spent at one election $50,000. On the other hand, in a
Congressional election in a certain district in Massachusetts, the only
expenditure of one of the candidates was for the two-cent stamp placed
on his letter of acceptance. No estimate of the average amount expended
can be made. It is, however, the conclusion of Mr Bryce, in his
_American Commonwealth_, that as a rule a seat in Congress costs the
candidate less than a seat for a county division in the House of
Commons. (See also BALLOT.)



ELECTION, in English law, the obligation imposed upon a party by courts
of equity to choose between two inconsistent or alternative rights or
claims in cases where there is a clear intention of the person from whom
he derives one that he should not enjoy both. Thus a testator died
seized of property in fee simple and in fee tail--he had two daughters,
and devised the fee simple property to one and the entailed property to
the other; the first one claimed to have her share of the entailed
property as coparcener and also to retain the benefit she took under the
will. It was held that she was put to her election whether she would
take under the will and renounce her claim to the entailed property or
take against the will, in which case she must renounce the benefits she
took under the will in so far as was necessary to compensate her sister.
As the essence of the doctrine is compensation, a person electing
against a document does not lose all his rights under it, but the court
will sequester so much only of the benefit intended for him as will
compensate the persons disappointed by his election. For the same reason
it is necessary that there should be a free and disposable fund passing
by the instrument from which compensation can be made in the event of
election against the will. If, therefore, a man having a special power
of appointment appoint the fund equally between two persons, one being
an object of the power and the other not an object, no question of
election arises, but the appointment to the person not an object is bad.

Election, though generally arising in cases of wills, may also arise in
the case of a deed. There is, however, a distinction to be observed. In
the case of a will a clear intention on the part of the testator that he
meant to dispose of property not his own must be shown, and parol
evidence is not admissible as to this. In the case of a deed, however,
no such intention need be shown, for if a deed confers a benefit and
imposes a liability on the same person he cannot be allowed to accept
the one and reject the other, but this must be distinguished from cases
where two separate gifts are given to a person, one beneficial and the
other onerous. In such a case no question of election arises and he may
take the one and reject the other, unless, indeed, there are words used
which make the one conditional on the acceptance of the other.

Election is either express, e.g. by deed, or implied; in the latter case
it is often a question of considerable difficulty whether there has in
fact been an election or not; each case must depend upon the particular
circumstances, but quite generally it may be said that the person who
has elected must have been capable of electing, aware of the existence
of the doctrine of election, and have had the opportunity of satisfying
himself of the relative value of the properties between which he has
elected. In the case of infants the court will sometimes elect after an
inquiry as to which course is the most advantageous, or if there is no
immediate urgency, will allow the matter to stand over till the infant
attains his majority. In the cases of married women and lunatics the
courts will exercise the right for them. It sometimes happens that the
parties have so dealt with the property that it would be inequitable to
disturb it; in such cases the court will not interfere in order to allow
of election.



ELECTORAL COMMISSION, in United States history, a commission created to
settle the disputed presidential election of 1876. In this election
Samuel J. Tilden, the Democratic candidate, received 184 uncontested
electoral votes, and Rutherford B. Hayes, the Republican candidate,
163.[1] The states of Florida, Louisiana, Oregon and South Carolina,
with a total of 22 votes, each sent in two sets of electoral ballots,[2]
and from each of these states except Oregon one set gave the whole vote
to Tilden and the other gave the whole vote to Hayes. From Oregon one
set of ballots gave the three electoral votes of the state to Hayes; the
other gave two votes to Hayes and one to Tilden.

The election of a president is a complex proceeding, the method being
indicated partly in the Constitution, and being partly left to Congress
and partly to the states. The manner of selecting the electors is left
to state law; the electoral ballots are sent to the president of the
Senate, who "shall, in the presence of the Senate and House of
Representatives, open all certificates, and the votes shall then be
counted." Concerning this provision many questions of vital importance
arose in 1876: Did the president of the Senate count the votes, the
houses being mere witnesses; or did the houses count them, the
president's duties being merely ministerial? Did counting imply the
determination of what should be counted, or was it a mere arithmetical
process; that is, did the Constitution itself afford a method of
settling disputed returns, or was this left to legislation by Congress?
Might Congress or an officer of the Senate go behind a state's
certificate and review the acts of its certifying officials? Might it go
further and examine into the choice of electors? And if it had such
powers, might it delegate them to a commission? As regards the procedure
of Congress, it seems that, although in early years the president of the
Senate not only performed or overlooked the electoral count but also
exercised discretion in some matters very important in 1876, Congress
early began to assert power, and, at least from 1821 onward, controlled
the count, claiming complete power. The fact, however, that the Senate
in 1876 was controlled by the Republicans and the House by the
Democrats, lessened the chances of any harmonious settlement of these
questions by Congress. The country seemed on the verge of civil war.
Hence it was that by an act of the 29th of January 1877, Congress
created the Electoral Commission to pass upon the contested returns,
giving it "the same powers, if any" possessed by itself in the premises,
the decisions to stand unless rejected by the two houses separately. The
commission was composed of five Democratic and five Republican
Congressmen, two justices of the Supreme Court of either party, and a
fifth justice chosen by these four. As its members of the commission the
Senate chose G.F. Edmunds of Vermont, O.P. Morton of Indiana, and F.T.
Frelinghuysen of New Jersey (Republicans); and A.G. Thurman of Ohio and
T.F. Bayard of Delaware (Democrats). The House chose Henry B. Payne of
Ohio, Eppa Hunton of Virginia, and Josiah G. Abbott of Massachusetts
(Democrats); and George F. Hoar of Massachusetts and James A. Garfield
of Ohio (Republicans). The Republican judges were William Strong and
Samuel F. Miller; the Democratic, Nathan Clifford and Stephen J. Field.
These four chose as the fifteenth member Justice Joseph P. Bradley, a
Republican but the only member not selected avowedly as a partisan. As
counsel for the Democratic candidate there appeared before the
commission at different times Charles O'Conor of New York, Jeremiah S.
Black of Pennsylvania, Lyman Trumbull of Illinois, R.T. Merrick of the
District of Columbia, Ashbel Green of New Jersey, Matthew H. Carpenter
of Wisconsin, George Hoadley of Ohio, and W.C. Whitney of New York. W.M.
Evarts and E.W. Stoughton of New York and Samuel Shellabarger and
Stanley Matthews of Ohio appeared regularly in behalf of Mr Hayes.

The popular vote seemed to indicate that Hayes had carried South
Carolina and Oregon, and Tilden Florida and Louisiana. It was evident,
however, that Hayes could secure the 185 votes necessary to elect only
by gaining every disputed ballot. As the choice of Republican electors
in Louisiana had been accomplished by the rejection of several thousand
Democratic votes by a Republican returning board, the Democrats insisted
that the commission should go behind the returns and correct injustice;
the Republicans declared that the state's action was final, and that to
go behind the returns would be invading its sovereignty. When this
matter came before the commission it virtually accepted the Republican
contention, ruling that it could not go behind the returns except on the
superficial issues of manifest fraud therein or the eligibility of
electors to their office under the Constitution; that is, it could not
investigate antecedents of fraud or misconduct of state officials in the
results certified. All vital questions were settled by the votes of
eight Republicans and seven Democrats; and as the Republican Senate
would never concur with the Democratic House in overriding the
decisions, all the disputed votes were awarded to Mr Hayes, who
therefore was declared elected.

The strictly partisan votes of the commission and the adoption by
prominent Democrats and Republicans, both within and without the
commission, of an attitude toward states-rights principles quite
inconsistent with party tenets and tendencies, have given rise to much
severe criticism. The Democrats and the country, however, quietly
accepted the decision. The judgments underlying it were two: (1) That
Congress rightly claimed the power to settle such contests within the
limits set; (2) that, as Justice Miller said regarding these limits, the
people had never at any time intended to give to Congress the power, by
naming the electors, to "decide who are to be the president and
vice-president of the United States."

There is no doubt that Mr Tilden was morally entitled to the presidency,
and the correction of the Louisiana frauds would certainly have given
satisfaction then and increasing satisfaction later, in the retrospect,
to the country. The commission might probably have corrected the frauds
without exceeding its Congressional precedents. Nevertheless, the
principles of its decisions must be recognized by all save
ultra-nationalists as truer to the spirit of the Constitution and
promising more for the good of the country than would have been the
principles necessary to a contrary decision.

By an act of the 3rd of February 1887 the electoral procedure is
regulated in great detail. Under this act determination by a state of
electoral disputes is conclusive, subject to certain formalities that
guarantee definite action and accurate certification. These formalities
constitute "regularity," and are in all cases judgable by Congress. When
Congress is forced by the lack or evident inconclusiveness of state
action, or by conflicting state action, to decide disputes, votes are
lost unless both houses concur.

  AUTHORITIES.--J.F. Rhodes, _History of the United States_, vol. 7,
  covering 1872-1877 (New York, 1906); P.L. Haworth, _The Hayes-Tilden
  disputed Presidential Election of 1876_ (Cleveland, 1906); J.W.
  Burgess, _Political Science Quarterly_, vol. 3 (1888), pp. 633-653,
  "The Law of the Electoral Count"; and for the sources. Senate
  Miscellaneous Document No. 5 (vol. 1), and House Miscel. Doc. No. 13
  (vol. 2), 44 Congress, 2 Session,--_Count of the Electoral Vote.
  Proceedings of Congress and Electoral Commission_,--the latter
  identical with _Congressional Record_, vol. 5, pt. 4, 44 Cong., 2
  Session; also about twenty volumes of evidence on the state elections
  involved. The volume called _The Presidential Counts_ (New York, 1877)
  was compiled by Mr. Tilden and his secretary.


FOOTNOTES:

  [1] The election of a vice-president was, of course, involved also.
    William A. Wheeler was the Republican candidate, and Thomas A.
    Hendricks the Democratic.

  [2] A second set of electoral ballots had also been sent in from
    Vermont, where Hayes had received a popular majority vote of 24,000.
    As these ballots had been transmitted in an irregular manner, the
    president of the Senate refused to receive them, and was sustained in
    this action by the upper House.



ELECTORS (Ger. _Kurfürsten_, from _Küren_, O.H.G. _kiosan_, choose,
elect, and _Fürst_, prince), a body of German princes, originally seven
in number, with whom rested the election of the German king, from the
13th until the beginning of the 19th century. The German kings, from the
time of Henry the Fowler (919-936) till the middle of the 13th century,
succeeded to their position partly by heredity, and partly by election.
Primitive Germanic practice had emphasized the element of heredity.
_Reges ex nobilitate sumunt_: the man whom a German tribe recognized as
its king must be in the line of hereditary descent from Woden; and
therefore the genealogical trees of early Teutonic kings (as, for
instance, in England those of the Kentish and West Saxon sovereigns) are
carefully constructed to prove that descent from the god which alone
will constitute a proper title for his descendants. Even from the first,
however, there had been some opening for election; for the principle of
primogeniture was not observed, and there might be several competing
candidates, all of the true Woden stock. One of these competing
candidates would have to be recognized (as the Anglo-Saxons said,
_geceosan_); and to this limited extent Teutonic kings may be termed
elective from the very first. In the other nations of western Europe
this element of election dwindled, and the principle of heredity alone
received legal recognition; in medieval Germany, on the contrary, the
principle of heredity, while still exercising an inevitable natural
force, sank formally into the background, and legal recognition was
finally given to the elective principle. _De facto_, therefore, the
principle of heredity exercises in Germany a great influence, an
influence never more striking than in the period which follows on the
formal recognition of the elective principle, when the Habsburgs (like
the Metelli at Rome) _fato imperatores fiunt: de jure_, each monarch
owes his accession simply and solely to the vote of an electoral
college.

This difference between the German monarchy and the other monarchies of
western Europe may be explained by various considerations. Not the least
important of these is what seems a pure accident. Whereas the Capetian
monarchs, during the three hundred years that followed on the election
of Hugh Capet in 987, always left an heir male, and an heir male of full
age, the German kings again and again, during the same period, either
left a minor to succeed to their throne, or left no issue at all. The
principle of heredity began to fail because there were no heirs. Again
the strength of tribal feeling in Germany made the monarchy into a
prize, which must not be the apanage of any single tribe, but must
circulate, as it were, from Franconian to Saxon, from Saxon to Bavarian,
from Bavarian to Franconian, from Franconian to Swabian; while the
growing power of the baronage, and its habit of erecting anti-kings to
emphasize its opposition to the crown (as, for instance, in the reign of
Henry IV.), coalesced with and gave new force to the action of tribal
feeling. Lastly, the fact that the German kings were also Roman emperors
finally and irretrievably consolidated the growing tendency towards the
elective principle. The principle of heredity had never held any great
sway under the ancient Roman Empire (see under EMPEROR); and the
medieval Empire, instituted as it was by the papacy, came definitely
under the influence of ecclesiastical prepossessions in favour of
election. The church had substituted for that descent from Woden, which
had elevated the old pagan kings to their thrones, the conception that
the monarch derived his crown from the choice of God, after the manner
of Saul; and the theoretical choice of God was readily turned into the
actual choice of the church, or, at any rate, of the general body of
churchmen. If an ordinary king is thus regarded by the church as
essentially elected, much more will the emperor, connected as he is with
the church as one of its officers, be held to be also elected; and as a
bishop is chosen by the chapter of his diocese, so, it will be thought,
must the emperor be chosen by some corresponding body in his empire.
Heredity might be tolerated in a mere matter of kingship: the precious
trust of imperial power could not be allowed to descend according to the
accidents of family succession. To Otto of Freising (_Gesta Frid._ ii.
1) it is already a point of right vindicated for itself by the
excellency of the Roman Empire, as a matter of singular prerogative,
that it should not descend _per sanguinis propaginem, sed per principum
electionem_.

The accessions of Conrad II. (see Wipo, _Vita Cuonradi_, c. 1-2), of
Lothair II. (see _Narratio de electione Lotharii_, M.G.H. _Scriptt._
xii. p. 510), of Conrad III. (see Otto of Freising, _Chronicon_, vii.
22) and of Frederick I. (see Otto of Freising, _Gesta Frid._ ii. 1) had
all been marked by an element, more or less pronounced, of election.
That element is perhaps most considerable in the case of Lothair, who
had no rights of heredity to urge. Here we read of ten princes being
selected from the princes of the various duchies, to whose choice the
rest promise to assent, and of these ten selecting three candidates, one
of whom, Lothair, is finally chosen (apparently by the whole assembly)
in a somewhat tumultuary fashion. In this case the electoral assembly
would seem to be, in the last resort, the whole diet of all the princes.
But a _de facto_ pre-eminence in the act of election is already, during
the 12th century, enjoyed by the three Rhenish archbishops, probably
because of the part they afterwards played at the coronation, and also
by the dukes of the great duchies--possibly because of the part they too
played, as vested for the time with the great offices of the household,
at the coronation feast.[1] Thus at the election of Lothair it is the
archbishop of Mainz who conducts the proceedings; and the election is
not held to be final until the duke of Bavaria has given his assent. The
fact is that, votes being weighed by quality as well as by quantity (see
DIET), the votes of the archbishops and dukes, which would first be
taken, would of themselves, if unanimous, decide the election. To
prevent tumultuary elections, it was well that the election should be
left exclusively with these great dignitaries; and this is what, by the
middle of the 13th century, had eventually been done.

The chaos of the interregnum from 1198 to 1212 showed the way for the
new departure; the chaos of the great interregnum (1250-1273) led to its
being finally taken. The decay of the great duchies, and the narrowing
of the class of princes into a close corporation, some of whose members
were the equals of the old dukes in power, introduced difficulties and
doubts into the practice of election which had been used in the 12th
century. The contested election of the interregnum of 1198-1212 brought
these difficulties and doubts into strong relief. The famous bull of
Innocent III. (_Venerabilem_), in which he decided for Otto IV. against
Philip of Swabia, on the ground that, though he had fewer votes than
Philip, he had a majority of the votes of those _ad quos principaliter
spectat electio_, made it almost imperative that there should be some
definition of these principal electors. The most famous attempt at such
a definition is that of the _Sachsenspiegel_, which was followed, or
combated, by many other writers in the first half of the 13th century.
Eventually the contested election of 1257 brought light and definition.
Here we find seven potentates acting--the same seven whom the Golden
Bull recognizes in 1356; and we find these seven described in an
official letter to the pope, as _principes vocem in hujusmodi electione
habentes, qui sunt septem numero_. The doctrine thus enunciated was at
once received. The pope acknowledged it in two bulls (1263); a cardinal,
in a commentary on the bull _Venerabilem_ of Innocent III., recognized
it about the same time; and the erection of statues of the seven
electors at Aix-la-Chapelle gave the doctrine a visible and outward
expression.

By the date of the election of Rudolph of Habsburg (1273) the seven
electors may be regarded as a definite body, with an acknowledged right.
But the definition and the acknowledgment were still imperfect. (1) The
composition of the electoral body was uncertain in two respects. The
duke of Bavaria claimed as his right the electoral vote of the king of
Bohemia; and the practice of _partitio_ in electoral families tended to
raise further difficulties about the exercise of the vote. The Golden
Bull of 1356 settled both these questions. Bohemia (of which Charles
IV., the author of the Golden Bull, was himself the king) was assigned
the electoral vote in preference to Bavaria; and a provision annexing
the electoral vote to a definite territory, declaring that territory
indivisible, and regulating its descent by the rule of primogeniture
instead of partition, swept away the old difficulties which the custom
of partition had raised. After 1356 the seven electors are regularly the
three Rhenish archbishops, Mainz, Cologne and Trier, and four lay
magnates, the palatine of the Rhine, the duke of Saxony, the margrave of
Brandenburg, and the king of Bohemia; the three former being vested with
the three archchancellorships, and the four latter with the four offices
of the royal household (see HOUSEHOLD). (2) The rights of the seven
electors, in their collective capacity as an electoral college, were a
matter of dispute with the papacy. The result of the election, whether
made, as at first, by the princes generally or, as after 1257, by the
seven electors exclusively, was in itself simply the creation of a
German king--an _electio in regem_. But since 962 the German king was
also, after coronation by the pope, Roman emperor. Therefore the
election had a double result: the man elected was not only _electus in
regem_, but also _promovendus ad imperium_. The difficulty was to define
the meaning of the term _promovendus_. Was the king elect _inevitably_
to become emperor? or did the _promotio_ only follow at the discretion
of the pope, if he thought the king elect fit for promotion? and if so,
to what extent, and according to what standard, did the pope judge of
such fitness? Innocent III. had already claimed, in the bull
_Venerabilem_, (1) that the electors derived their power of election, so
far as it made an emperor, from the Holy See (which had originally
"translated" the Empire from the East to the West), and (2) that the
papacy had a _jus et auctoritas examinandi personam electam in regem et
promovendam ad imperium_. The latter claim he had based on the fact that
he anointed, consecrated and crowned the emperor--in other words, that
he gave a spiritual office according to spiritual methods, which
entitled him to inquire into the fitness of the recipient of that
office, as a bishop inquires into the fitness of a candidate for
ordination. Innocent had put forward this claim as a ground for deciding
between competing candidates: Boniface VIII. pressed the claim against
Albert I. in 1298, even though his election was unanimous; while John
XXII. exercised it in its harshest form, when in 1324 he ex-communicated
Louis IV. for using the title and exerting the rights even of king
without previous papal confirmation. This action ultimately led to a
protest from the electors themselves, whose right of election would have
become practically meaningless, if such assumptions had been tolerated.
A meeting of the electors (_Kurverein_) at Rense in 1338 declared (and
the declaration was reaffirmed by a diet at Frankfort in the same year)
that _postquam aliquis eligitur in Imperatorem sive Regem ab Electoribus
Imperii concorditer, vel majori parte eorundem, statim ex sola electione
est Rex verus et Imperator Romanus censendus ... nec Papae sive Sedis
Apostolicae ... approbatione ... indiget_. The doctrine thus positively
affirmed at Rense is negatively reaffirmed in the Golden Bull, in which
a significant silence is maintained in regard to papal rights. But the
doctrine was not in practice followed: Sigismund himself did not venture
to dispense with papal approbation.

By the end of the 14th century the position of the electors, both
individually and as a corporate body, had become definite and precise.
Individually, they were distinguished from all other princes, as we have
seen, by the indivisibility of their territories and by the custom of
primogeniture which secured that indivisibility; and they were still
further distinguished by the fact that their person, like that of the
emperor himself, was protected by the law of treason, while their
territories were only subject to the jurisdiction of their own courts.
They were independent territorial sovereigns; and their position was at
once the envy and the ideal of the other princes of Germany. Such had
been the policy of Charles IV.; and thus had he, in the Golden Bull,
sought to magnify the seven electors, and himself as one of the seven,
in his capacity of king of Bohemia, even at the expense of the Empire,
and of himself in his capacity of emperor. Powerful as they were,
however, in their individual capacity, the electors showed themselves no
less powerful as a corporate body. As such a corporate body, they may be
considered from three different points of view, and as acting in three
different capacities. They are an electoral body, choosing each
successive emperor; they are one of the three colleges of the imperial
diet (see DIET); and they are also an electoral union
(_Kurfürstenverein_), acting as a separate and independent political
organ even after the election, and during the reign, of the monarch. It
was in this last capacity that they had met at Rense in 1338; and in the
same capacity they acted repeatedly during the 15th century. According
to the Golden Bull, such meetings were to be annual, and their
deliberations were to concern "the safety of the Empire and the world."
Annual they never were; but occasionally they became of great
importance. In 1424, during the attempt at reform occasioned by the
failure of German arms against the Hussites, the _Kurfürstenverein_
acted, or at least it claimed to act, as the predominant partner in a
duumvirate, in which the unsuccessful Sigismund was relegated to a
secondary position. During the long reign of Frederick III.--a reign in
which the interests of Austria were cherished, and the welfare of the
Empire neglected, by that apathetic yet tenacious emperor--the electors
once more attempted, in the year 1453, to erect a new central government
in place of the emperor, a government which, if not conducted by
themselves directly in their capacity of a _Kurfürstenverein_, should at
any rate be under their influence and control. So, they hoped, Germany
might be able to make head against that papal aggression, to which
Frederick had yielded, and to take a leading part in that crusade
against the Turks, which he had neglected. Like the previous attempt at
reform during the Hussite wars, the scheme came to nothing; the forces
of disunion in Germany were too strong for any central government,
whether monarchical and controlled by the emperor, or oligarchical and
controlled by the electors. But a final attempt, the most strenuous of
all, was made in the reign of Maximilian I., and under the influence of
Bertold, elector and archbishop of Mainz. The council of 1500, in which
the electors (with the exception of the king of Bohemia) were to have
sat, and which would have been under their control, represents the last
effective attempt at a real _Reichsregiment_. Inevitably, however, it
shipwrecked on the opposition of Maximilian; and though the attempt was
again made between 1521 and 1530, the idea of a real central government
under the control of the electors perished, and the development of local
administration by the circle took its place.

In the course of the 16th century a new right came to be exercised by
the electors. As an electoral body (that is to say, in the first of the
three capacities distinguished above), they claimed, at the election of
Charles V. in 1519 and at subsequent elections, to impose conditions on
the elected monarch, and to determine the terms on which he should
exercise his office in the course of his reign. This _Wahlcapitulation_,
similar to the _Pacta Conventa_ which limited the elected kings of
Poland, was left by the diet to the discretion of the electors, though
after the treaty of Westphalia an attempt was made, with some little
success,[2] to turn the capitulation into a matter of legislative
enactment by the diet. From this time onwards the only fact of
importance in the history of the electors is the change which took place
in the composition of their body during the 17th and 18th centuries.
From the Golden Bull to the treaty of Westphalia (1356-1648) the
composition of the electoral body had remained unchanged. In 1623,
however, in the course of the Thirty Years' War, the vote of the count
palatine of the Rhine had been transferred to the duke of Bavaria; and
at the treaty of Westphalia the vote, with the office of imperial butler
which it carried, was left to Bavaria, while an eighth vote, along with
the new office of imperial treasurer, was created for the count
palatine. In 1708 a ninth vote, along with the office of imperial
standard-bearer, was created for Hanover; while finally, in 1778, the
vote of Bavaria and the office of imperial butler returned to the counts
palatine, as heirs of the duchy, on the extinction of the ducal line,
while the new vote created for the Palatinate in 1648, with the office
of imperial treasurer, was transferred to Brunswick-Lüneburg (Hanover)
in lieu of the one which this house already held. In 1806, on the
dissolution of the Holy Roman Empire, the electors ceased to exist.

  LITERATURE.--T. Lindner, _Die deutschen Königswahlen und die
  Entstehung des Kurfürstentums_ (1893), and _Der Hergang bei den
  deutschen Königswahlen_ (1899); R. Kirchhöfer, _Zur Entstehung des
  Kurkollegiums_ (1893); W. Maurenbrecher, _Geschichte der deutschen
  Königswahlen_ (1889); and G. Blondel, _Étude sur Frédéric II_, p. 27
  sqq. See also J. Bryce, _Holy Roman Empire_ (edition of 1904), c. ix.;
  and R. Schröder, _Lehrbuch der deutschen Rechtsgeschichte_, pp.
  471-481 and 819-820.     (E. Br.)


FOOTNOTES:

  [1] This is the view of the _Sachsenspiegel_, and also of Albert of
    Stade (quoted in Schröder, p. 476, n. 27): "Palatinus eligit, quia
    dapifer est; dux Saxoniae, quia marescalcus," &c. Schröder points out
    (p. 479, n. 45) that "participation in the coronation feast is an
    express recognition of the king"; and those who are to discharge
    their office in the one must have had a prominent voice in the other.

  [2] See Schröder's _Lehrbuch der deutschen Rechtsgeschichte_, p. 820.



ELECTRA ([Greek: Elektra]), "the bright one," in Greek mythology. (1)
One of the seven Pleiades, daughter of Atlas and Pleïone. She is closely
connected with the old constellation worship and the religion of
Samothrace, the chief seat of the Cabeiri (q.v.), where she was
generally supposed to dwell. By Zeus she was the mother of Dardanus,
Iasion (or Eëtion), and Harmonia; but in the Italian tradition, which
represented Italy as the original home of the Trojans, Dardanus was her
son by a king of Italy named Corythus. After her amour with Zeus,
Electra fled to the Palladium as a suppliant, but Athena, enraged that
it had been touched by one who was no longer a maiden, flung Electra and
the image from heaven to earth, where it was found by Ilus, and taken by
him to Ilium; according to another tradition, Electra herself took it to
Ilium, and gave it to her son Dardanus (Schol. Eurip. _Phoen._ 1136). In
her grief at the destruction of the city she plucked out her hair and
was changed into a comet; in another version Electra and her six sisters
had been placed among the stars as the Pleiades, and the star which she
represented lost its brilliancy after the fall of Troy. Electra's
connexion with Samothrace (where she was also called Electryone and
Strategis) is shown by the localization of the carrying off of her
reputed daughter Harmonia by Cadmus, and by the fact that, according to
Athenicon (the author of a work on Samothrace quoted by the scholiast on
Apollonius Rhodius i. 917), the Cabeiri were Dardanus and Iasion. The
gate Electra at Thebes and the fabulous island Electris were said to
have been called after her (Apollodorus iii. 10. 12; Servius on _Aen._
iii. 167, vii. 207, x. 272, _Georg._ i. 138).

(2) Daughter of Agamemnon and Clytaemnestra, sister of Orestes and
Iphigeneia. She does not appear in Homer, although according to Xanthus
(regarded by some as a fictitious personage), to whom Stesichorus was
indebted for much in his _Oresteia_, she was identical with the Homeric
Laodice, and was called Electra because she remained so long unmarried
([Greek: 'A-lektra]). She was said to have played an important part in
the poem of Stesichorus, and subsequently became a favourite figure in
tragedy. After the murder of her father on his return from Troy by her
mother and Aegisthus, she saved the life of her brother Orestes by
sending him out of the country to Strophius, king of Phanote in Phocis,
who had him brought up with his own son Pylades. Electra, cruelly
ill-treated by Clytaemnestra and her paramour, never loses hope that her
brother will return to avenge his father. When grown up, Orestes, in
response to frequent messages from his sister, secretly repairs with
Pylades to Argos, where he pretends to be a messenger from Strophius
bringing the news of the death of Orestes. Being admitted to the palace,
he slays both Aegisthus and Clytaemnestra. According to another story
(Hyginus, _Fab._ 122), Electra, having received a false report that
Orestes and Pylades had been sacrificed to Artemis in Tauris, went to
consult the oracle at Delphi. In the meantime Aletes, the son of
Aegisthus, seized the throne of Mycenae. Her arrival at Delphi coincided
with that of Orestes and Iphigeneia. The same messenger, who had already
communicated the false report of the death of Orestes, informed her that
he had been slain by Iphigeneia. Electra in her rage seized a burning
brand from the altar, intending to blind her sister; but at the critical
moment Orestes appeared, recognition took place, and the brother and
sister returned to Mycenae. Aletes was slain by Orestes, and Electra
became the wife of Pylades. The story of Electra is the subject of the
_Choëphori_ of Aeschylus, the _Electra_ of Sophocles and the _Electra_
of Euripides. It is in the Sophoclean play that Electra is most
prominent.

  There are many variations in the treatment of the legend, for which,
  as also for a discussion of the modern plays on the subject by
  Voltaire and Alfieri, see Jebb's Introduction to his edition of the
  _Electra_ of Sophocles.



ELECTRICAL (or ELECTROSTATIC) MACHINE, a machine operating by manual or
other power for transforming mechanical work into electric energy in the
form of electrostatic charges of opposite sign delivered to separate
conductors. Electrostatic machines are of two kinds: (1) Frictional, and
(2) Influence machines.

[Illustration: FIG. 1.--Ramsden's electrical machine.]

_Frictional Machines._--A primitive form of frictional electrical
machine was constructed about 1663 by Otto von Guericke (1602-1686). It
consisted of a globe of sulphur fixed on an axis and rotated by a winch,
and it was electrically excited by the friction of warm hands held
against it. Sir Isaac Newton appears to have been the first to use a
glass globe instead of sulphur (_Optics_, 8th Query). F. Hawksbee in
1709 also used a revolving glass globe. A metal chain resting on the
globe served to collect the charge. Later G.M. Bose (1710-1761), of
Wittenberg, added the prime conductor, an insulated tube or cylinder
supported on silk strings, and J.H. Winkler (1703-1770), professor of
physics at Leipzig, substituted a leather cushion for the hand. Andreas
Gordon (1712-1751) of Erfurt, a Scotch Benedictine monk, first used a
glass cylinder in place of a sphere. Jesse Ramsden (1735-1800) in 1768
constructed his well-known form of plate electrical machine (fig. 1). A
glass plate fixed to a wooden or metal shaft is rotated by a winch. It
passes between two rubbers made of leather, and is partly covered with
two silk aprons which extend over quadrants of its surface. Just below
the places where the aprons terminate, the glass is embraced by two
insulated metal forks having the sharp points projecting towards the
glass, but not quite touching it. The glass is excited positively by
friction with the rubbers, and the charge is drawn off by the action of
the points which, when acted upon inductively, discharge negative
electricity against it. The insulated conductor to which the points are
connected therefore becomes positively electrified. The cushions must be
connected to earth to remove the negative electricity which accumulates
on them. It was found that the machine acted better if the rubbers were
covered with bisulphide of tin or with F. von Kienmayer's amalgam,
consisting of one part of zinc, one of tin and two of mercury. The
cushions were greased and the amalgam in a state of powder spread over
them. Edward Nairne's electrical machine (1787) consisted of a glass
cylinder with two insulated conductors, called prime conductors, on
glass legs placed near it. One of these carried the leather exacting
cushions and the other the collecting metal points, a silk apron
extending over the cylinder from the cushion almost to the points. The
rubber was smeared with amalgam. The function of the apron is to prevent
the escape of electrification from the glass during its passage from the
rubber to the collecting points. Nairne's machine could give either
positive or negative electricity, the first named being collected from
the prime conductor carrying the collecting points and the second from
the prime conductor carrying the cushion.

[Illustration: FIG. 2.]

_Influence Machines._--Frictional machines are, however, now quite
superseded by the second class of instrument mentioned above, namely,
influence machines. These operate by electrostatic induction and convert
mechanical work into electrostatic energy by the aid of a small initial
charge which is continually being replenished or reinforced. The general
principle of all the machines described below will be best understood by
considering a simple ideal case. Imagine two Leyden jars with large
brass knobs, A and B, to stand on the ground (fig. 2). Let one jar be
initially charged with positive electricity on its inner coating and the
other with negative, and let both have their outsides connected to
earth. Imagine two insulated balls A' and B' so held that A' is near A
and B' is near B. Then the positive charge on A induces two charges on
A', viz.: a negative on the side nearest and a positive on the side most
removed. Likewise the negative charge on B induces a positive charge on
the side of B' nearest to it and repels negative electricity to the far
side. Next let the balls A' and B' be connected together for a moment by
a wire N called a neutralizing conductor which is subsequently removed.
Then A' will be left negatively electrified and B' will be left
positively electrified. Suppose that A' and B' are then made to change
places. To do this we shall have to exert energy to remove A' against
the attraction of A and B' against the attraction of B. Finally let A'
be brought in contact with B and B' with A. The ball A' will give up its
charge of negative electricity to the Leyden jar B, and the ball B' will
give up its positive charge to the Leyden jar A. This transfer will take
place because the inner coatings of the Leyden jars have greater
capacity with respect to the earth than the balls. Hence the charges of
the jars will be increased. The balls A' and B' are then practically
discharged, and the above cycle of operations may be repeated. Hence,
however small may be the initial charges of the Leyden jars, by a
principle of accumulation resembling that of compound interest, they can
be increased as above shown to any degree. If this series of operations
be made to depend upon the continuous rotation of a winch or handle, the
arrangement constitutes an electrostatic influence machine. The
principle therefore somewhat resembles that of the self-exciting dynamo.


  Bennet's Doubler.

The first suggestion for a machine of the above kind seems to have grown
out of the invention of Volta's electrophorus. Abraham Bennet, the
inventor of the gold leaf electroscope, described a doubler or machine
for multiplying electric charges (_Phil. Trans._, 1787).

  The principle of this apparatus may be explained thus. Let A and C be
  two fixed disks, and B a disk which can be brought at will within a
  very short distance of either A or C. Let us suppose all the plates to
  be equal, and let the capacities of A and C in presence of B be each
  equal to p, and the coefficient of induction between A and B, or C and
  B, be q. Let us also suppose that the plates A and C are so distant
  from each other that there is no mutual influence, and that p' is the
  capacity of one of the disks when it stands alone. A small charge Q is
  communicated to A, and A is insulated, and B, uninsulated, is brought
  up to it; the charge on B will be--(q/p)Q. B is now uninsulated and
  brought to face C, which is uninsulated; the charge on C will be
  (q/p)²Q. C is now insulated and connected with A, which is always
  insulated. B is then brought to face A and uninsulated, so that the
  charge on A becomes rQ, where

           p      /    q²\
    r = -------- ( 1 + -- ).
        (p + p')  \    p²/

  A is now disconnected from C, and here the first operation ends. It is
  obvious that at the end of n such operations the charge on A will be
  r^_(n)Q, so that the charge goes on increasing in geometrical
  progression. If the distance between the disks could be made
  infinitely small each time, then the multiplier r would be 2, and the
  charge would be doubled each time. Hence the name of the apparatus.

[Illustration: FIG. 3.--Nicholson's Revolving Doubler.]


  Nicholson's doubler.

Erasmus Darwin, B. Wilson, G.C. Bohnenberger and J.C.E. Peclet devised
various modifications of Bennet's instrument (see S.P. Thompson, "The
Influence Machine from 1788 to 1888," _Journ. Soc. Tel. Eng._, 1888, 17,
p. 569). Bennet's doubler appears to have given a suggestion to William
Nicholson (_Phil. Trans._, 1788, p. 403) of "an instrument which by
turning a winch produced the two states of electricity without friction
or communication with the earth." This "revolving doubler," according to
the description of Professor S.P. Thompson (_loc. cit._), consists of
two fixed plates of brass A and C (fig. 3), each two inches in diameter
and separately supported on insulating arms in the same plane, so that a
third revolving plate B may pass very near them without touching. A
brass ball D two inches in diameter is fixed on the end of the axis that
carries the plate B, and is loaded within at one side, so as to act as a
counterpoise to the revolving plate B. The axis P N is made of varnished
glass, and so are the axes that join the three plates with the brass
axis N O. The axis N O passes through the brass piece M, which stands on
an insulating pillar of glass, and supports the plates A and C. At one
extremity of this axis is the ball D, and the other is connected with a
rod of glass, N P, upon which is fixed the handle L, and also the piece
G H, which is separately insulated. The pins E, F rise out of the back
of the fixed plates A and C, at unequal distances from the axis. The
piece K is parallel to G H, and both of them are furnished at their ends
with small pieces of flexible wire that they may touch the pins E, F in
certain points of their revolution. From the brass piece M there stands
out a pin I, to touch against a small flexible wire or spring which
projects sideways from the rotating plate B when it comes opposite A.
The wires are so adjusted by bending that B, at the moment when it is
opposite A, communicates with the ball D, and A communicates with C
through GH; and half a revolution later C, when B comes opposite to it,
communicates with the ball D through the contact of K with F. In all
other positions A, B, C and D are completely disconnected from each
other. Nicholson thus described the operation of his machine:--

  "When the plates A and B are opposite each other, the two fixed plates
  A and C may be considered as one mass, and the revolving plate B,
  together with the ball D, will constitute another mass. All the
  experiments yet made concur to prove that these two masses will not
  possess the same electric state.... The redundant electricities in the
  masses under consideration will be unequally distributed; the plate A
  will have about ninety-nine parts, and the plate C one; and, for the
  same reason, the revolving plate B will have ninety-nine parts of the
  opposite electricity, and the ball D one. The rotation, by destroying
  the contacts, preserves this unequal distribution, and carries B from
  A to C at the same time that the tail K connects the ball with the
  plate C. In this situation, the electricity in B acts upon that in C,
  and produces the contrary state, by virtue of the communication
  between C and the ball; which last must therefore acquire an
  electricity of the same kind with that of the revolving plate. But the
  rotation again destroys the contact and restores B to its first
  situation opposite A. Here, if we attend to the effect of the whole
  revolution, we shall find that the electric states of the respective
  masses have been greatly increased; for the ninety-nine parts in A and
  B remain, and the one part of electricity in C has been increased so
  as nearly to compensate ninety-nine parts of the opposite electricity
  in the revolving plate B, while the communication produced an opposite
  mutation in the electricity of the ball. A second rotation will, of
  course, produce a proportional augmentation of these increased
  quantities; and a continuance of turning will soon bring the
  intensities to their maximum, which is limited by an explosion between
  the plates" (_Phil. Trans._, 1788, p. 405).

[Illustration: FIG. 4.--Belli's Doubler.]


  Belli's doubler.

Nicholson described also another apparatus, the "spinning condenser,"
which worked on the same principle. Bennet and Nicholson were followed
by T. Cavallo, John Read, Bohnenberger, C.B. Désormes and J.N.P.
Hachette and others in the invention of various forms of rotating
doubler. A simple and typical form of doubler, devised in 1831 by G.
Belli (fig. 4), consisted of two curved metal plates between which
revolved a pair of balls carried on an insulating stem. Following the
nomenclature usual in connexion with dynamos we may speak of the
conductors which carry the initial charges as the field plates, and of
the moving conductors on which are induced the charges which are
subsequently added to those on the field plates, as the carriers. The
wire which connects two armature plates for a moment is the neutralizing
conductor. The two curved metal plates constitute the field plates and
must have original charges imparted to them of opposite sign. The
rotating balls are the carriers, and are connected together for a moment
by a wire when in a position to be acted upon inductively by the field
plates, thus acquiring charges of opposite sign. The moment after they
are separated again. The rotation continuing the ball thus negatively
charged is made to give up this charge to that negatively electrified
field plate, and the ball positively charged its charge to the
positively electrified field plate, by touching little contact springs.
In this manner the field plates accumulate charges of opposite sign.

[Illustration: FIG. 5.--Varley's Machine.]


  Varley's machine.

Modern types of influence machine may be said to date from 1860 when
C.F. Varley patented a type of influence machine which has been the
parent of numerous subsequent forms (_Brit. Pat. Spec._ No. 206 of
1860). In it the field plates were sheets of tin-foil attached to a
glass plate (fig. 5). In front of them a disk of ebonite or glass,
having carriers of metal fixed to its edge, was rotated by a winch. In
the course of their rotation two diametrically opposite carriers touched
against the ends of a neutralizing conductor so as to form for a moment
one conductor, and the moment afterwards these two carriers were
insulated, one carrying away a positive charge and the other a negative.
Continuing their rotation, the positively charged carrier gave up its
positive charge by touching a little knob attached to the positive field
plate, and similarly for the negative charge carrier. In this way the
charges on the field plates were continually replenished and reinforced.
Varley also constructed a multiple form of influence machine having six
rotating disks, each having a number of carriers and rotating between
field plates. With this apparatus he obtained sparks 6 in. long, the
initial source of electrification being a single Daniell cell.


  Toepler machine.

Varley was followed by A.J.I. Toepler, who in 1865 constructed an
influence machine consisting of two disks fixed on the same shaft and
rotating in the same direction. Each disk carried two strips of tin-foil
extending nearly over a semi-circle, and there were two field plates,
one behind each disk; one of the plates was positively and the other
negatively electrified. The carriers which were touched under the
influence of the positive field plate passed on and gave up a portion of
their negative charge to increase that of the negative field plate; in
the same way the carriers which were touched under the influence of the
negative field plate sent a part of their charge to augment that of the
positive field plate. In this apparatus one of the charging rods
communicated with one of the field plates, but the other with the
neutralizing brush opposite to the other field plate. Hence one of the
field plates would always remain charged when a spark was taken at the
transmitting terminals.

[Illustration: FIG. 6.--Holtz's Machine.]


  Holtz machine.

Between 1864 and 1880, W.T.B. Holtz constructed and described a large
number of influence machines which were for a long time considered the
most advanced development of this type of electrostatic machine. In one
form the Holtz machine consisted of a glass disk mounted on a horizontal
axis F (fig. 6) which could be made to rotate at a considerable speed by
a multiplying gear, part of which is seen at X. Close behind this disk
was fixed another vertical disk of glass in which were cut two windows
B, B. On the side of the fixed disk next the rotating disk were pasted
two sectors of paper A, A, with short blunt points attached to them
which projected out into the windows on the side away from the rotating
disk. On the other side of the rotating disk were placed two metal combs
C, C, which consisted of sharp points set in metal rods and were each
connected to one of a pair of discharge balls E, D, the distance between
which could be varied. To start the machine the balls were brought in
contact, one of the paper armatures electrified, say, with positive
electricity, and the disk set in motion. Thereupon very shortly a
hissing sound was heard and the machine became harder to turn as if the
disk were moving through a resisting medium. After that the discharge
balls might be separated a little and a continuous series of sparks or
brush discharges would take place between them. If two Leyden jars L, L
were hung upon the conductors which supported the combs, with their
outer coatings put in connexion with one another by M, a series of
strong spark discharges passed between the discharge balls. The action
of the machine is as follows: Suppose one paper armature to be charged
positively, it acts by induction on the right hand comb, causing
negative electricity to issue from the comb points upon the glass
revolving disk; at the same time the positive electricity passes through
the closed discharge circuit to the left comb and issues from its teeth
upon the part of the glass disk at the opposite end of the diameter.
This positive electricity electrifies the left paper armature by
induction, positive electricity issuing from the blunt point upon the
side farthest from the rotating disk. The charges thus deposited on the
glass disk are carried round so that the upper half is electrified
negatively on both sides and the lower half positively on both sides,
the sign of the electrification being reversed as the disk passes
between the combs and the armature by discharges issuing from them
respectively. If it were not for leakage in various ways, the
electrification would go on everywhere increasing, but in practice a
stationary state is soon attained. Holtz's machine is very uncertain in
its action in a moist climate, and has generally to be enclosed in a
chamber in which the air is kept artificially dry.


  Voss's machine.

Robert Voss, a Berlin instrument maker, in 1880 devised a form of
machine in which he claimed that the principles of Toepler and Holtz
were combined. On a rotating glass or ebonite disk were placed carriers
of tin-foil or metal buttons against which neutralizing brushes touched.
This armature plate revolved in front of a field plate carrying two
pieces of tin-foil backed up by larger pieces of varnished paper. The
studs on the armature plate were charged inductively by being connected
for a moment by a neutralizing wire as they passed in front of the field
plates, and then gave up their charges partly to renew the field charges
and partly to collecting combs connected to discharge balls. In general
design and construction, the manner of moving the rotating plate and in
the use of the two Leyden jars in connexion with the discharge balls,
Voss borrowed his ideas from Holtz.


  Wimshurst machine.

All the above described machines, however, have been thrown into the
shade by the invention of a greatly improved type of influence machine
first constructed by James Wimshurst about 1878. Two glass disks are
mounted on two shafts in such a manner that, by means of two belts and
pulleys worked from a winch shaft, the disks can be rotated rapidly in
opposite directions close to each other (fig. 7). These glass disks
carry on them a certain number (not less than 16 or 20) tin-foil
carriers which may or may not have brass buttons upon them. The glass
plates are well varnished, and the carriers are placed on the outer
sides of the two glass plates. As therefore the disks revolve, these
carriers travel in opposite directions, coming at intervals in
opposition to each other. Each upright bearing carrying the shafts of
the revolving disks also carries a neutralizing conductor or wire ending
in a little brush of gilt thread. The neutralizing conductors for each
disk are placed at right angles to each other. In addition there are
collecting combs which occupy an intermediate position and have sharp
points projecting inwards, and coming near to but not touching the
carriers. These combs on opposite sides are connected respectively to
the inner coatings of two Leyden jars whose outer coatings are in
connexion with one another.

[Illustration: FIG. 7.--Wimshurst's Machine.]

The operation of the machine is as follows: Let us suppose that one of
the studs on the back plate is positively electrified and one at the
opposite end of a diameter is negatively electrified, and that at that
moment two corresponding studs on the front plate passing opposite to
these back studs are momentarily connected together by the neutralizing
wire belonging to the front plate. The positive stud on the back plate
will act inductively on the front stud and charge it negatively, and
similarly for the other stud, and as the rotation continues these
charged studs will pass round and give up most of their charge through
the combs to the Leyden jars. The moment, however, a pair of studs on
the front plate are charged, they act as field plates to studs on the
back plate which are passing at the moment, provided these last are
connected by the back neutralizing wire. After a few revolutions of the
disks half the studs on the front plate at any moment are charged
negatively and half positively and the same on the back plate, the
neutralizing wires forming the boundary between the positively and
negatively charged studs. The diagram in fig. 8, taken by permission
from S.P. Thompson's paper (_loc. cit._), represents a view of the
distribution of these charges on the front and back plates respectively.
It will be seen that each stud is in turn both a field plate and a
carrier having a charge induced on it, and then passing on in turn
induces further charges on other studs. Wimshurst constructed numerous
very powerful machines of this type, some of them with multiple plates,
which operate in almost any climate, and rarely fail to charge
themselves and deliver a torrent of sparks between the discharge balls
whenever the winch is turned. He also devised an alternating current
electrical machine in which the discharge balls were alternately
positive and negative. Large Wimshurst multiple plate influence machines
are often used instead of induction coils for exciting Röntgen ray tubes
in medical work. They give very steady illumination on fluorescent
screens.

[Illustration: FIG. 8.--Action of the Wimshurst Machine.]

In 1900 it was found by F. Tudsbury that if an influence machine is
enclosed in a metallic chamber containing compressed air, or better,
carbon dioxide, the insulating properties of compressed gases enable a
greatly improved effect to be obtained owing to the diminution of the
leakage across the plates and from the supports. Hence sparks can be
obtained of more than double the length at ordinary atmospheric
pressure. In one case a machine with plates 8 in. in diameter which
could give sparks 2.5 in. at ordinary pressure gave sparks of 5, 7, and
8 in. as the pressure was raised to 15, 30 and 45 lb. above the normal
atmosphere.

[Illustration: FIG. 9.--Lord Kelvin's Replenisher.

  C, C, Metal carriers fixed to ebonite cross-arm.
  F, F, Brass field-plates or conductors.
  a, a, Receiving springs.
  n, n, Connecting springs or neutralizing brushes.]

The action of Lord Kelvin's replenisher (fig. 9) used by him in
connexion with his electrometers for maintaining their charge, closely
resembles that of Belli's doubler and will be understood from fig. 9.
Lord Kelvin also devised an influence machine, commonly called a "mouse
mill," for electrifying the ink in connexion with his siphon recorder.
It was an electrostatic and electromagnetic machine combined, driven by
an electric current and producing in turn electrostatic charges of
electricity. In connexion with this subject mention must also be made of
the water dropping influence machine of the same inventor.[1]

The action and efficiency of influence machines have been investigated
by F. Rossetti, A. Righi and F.W.G. Kohlrausch. The electromotive force
is practically constant no matter what the velocity of the disks, but
according to some observers the internal resistance decreases as the
velocity increases. Kohlrausch, using a Holtz machine with a plate 16
in. in diameter, found that the current given by it could only
electrolyse acidulated water in 40 hours sufficient to liberate one
cubic centimetre of mixed gases. E.E.N. Mascart, A. Roiti, and E.
Bouchotte have also examined the efficiency and current producing power
of influence machines.

  BIBLIOGRAPHY.--In addition to S.P. Thompson's valuable paper on
  influence machines (to which this article is much indebted) and other
  references given, see J. Clerk Maxwell, _Treatise on Electricity and
  Magnetism_ (2nd ed., Oxford, 1881), vol. i. p. 294; J.D. Everett,
  _Electricity_ (expansion of part iii. of Deschanel's _Natural
  Philosophy_) (London, 1901), ch. iv. p. 20; A. Winkelmann, _Handbuch
  der Physik_ (Breslau, 1905), vol. iv. pp. 50-58 (contains a large
  number of references to original papers); J. Gray, _Electrical
  Influence Machines, their Development and Modern Forms_ (London,
  1903).     (J. A. F.)


FOOTNOTE:

  [1] See Lord Kelvin, _Reprint of Papers on Electrostatics and
    Magnetism_ (1872); "Electrophoric Apparatus and Illustrations of
    Voltaic Theory," p. 319; "On Electric Machines Founded on Induction
    and Convection," p. 330; "The Reciprocal Electrophorus," p. 337.



ELECTRIC EEL (_Gymnotus electricus_), a member of the family of fishes
known as _Gymnotidae_. In spite of their external similarity the
_Gymnotidae_ have nothing to do with the eels (_Anguilla_). They
resemble the latter in the elongation of the body, the large number of
vertebrae (240 in _Gymnotus_), and the absence of pelvic fins; but they
differ in all the more important characters of internal structure. They
are in fact allied to the carps or _Cyprinidae_ and the cat-fishes or
_Siluridae_. In common with these two families and the _Characinidae_ of
Africa and South America, the _Gymnotidae_ possess the peculiar
structures called _ossicula auditus_ or Weberian ossicles. These are a
chain of small bones belonging to the first four vertebrae, which are
much modified, and connecting the air-bladder with the auditory organs.
Such an agreement in the structure of so complicated and specialized an
apparatus can only be the result of a community of descent of the
families possessing it. Accordingly these families are now placed
together in a distinct sub-order, the Ostariophysi. The _Gymnotidae_ are
strongly modified and degraded _Characinidae_. In them the dorsal and
caudal fins are very rudimentary or absent, and the anal is very long,
extending from the anus, which is under the head or throat, to the end
of the body.

_Gymnotus_ is the only genus of the family which possesses electric
organs. These extend the whole length of the tail, which is four-fifths
of the body. They are modifications of the lateral muscles and are
supplied with numerous branches of the spinal nerves. They consist of
longitudinal columns, each composed of an immense number of "electric
plates." The posterior end of the organ is positive, the anterior
negative, and the current passes from the tail to the head. The maximum
shock is given when the head and tail of the _Gymnotus_ are in contact
with different points in the surface of some other animal. _Gymnotus
electricus_ attains a length of 3 ft. and the thickness of a man's
thigh, and frequents the marshes of Brazil and the Guianas, where it is
regarded with terror, owing to the formidable electrical apparatus with
which it is provided. When this natural battery is discharged in a
favourable position, it is sufficiently powerful to stun the largest
animal; and according to A. von Humboldt, it has been found necessary to
change the line of certain roads passing through the pools frequented by
the electric eels. These fish are eaten by the Indians, who, before
attempting to capture them, seek to exhaust their electrical power by
driving horses into the ponds. By repeated discharges upon these they
gradually expend this marvellous force; after which, being defenceless,
they become timid, and approach the edge for shelter, when they fall an
easy prey to the harpoon. It is only after long rest and abundance of
food that the fish is able to resume the use of its subtle weapon.
Humboldt's description of this method of capturing the fish has not,
however, been verified by recent travellers.



ELECTRICITY. This article is devoted to a general sketch of the history
of the development of electrical knowledge on both the theoretical and
the practical sides. The two great branches of electrical theory which
concern the phenomena of electricity at rest, or "frictional" or
"static" electricity, and of electricity in motion, or electric
currents, are treated in two separate articles, ELECTROSTATICS and
ELECTROKINETICS. The phenomena attendant on the passage of electricity
through solids, through liquids and through gases, are described in the
article CONDUCTION, ELECTRIC, and also ELECTROLYSIS, and the propagation
of electrical vibrations in ELECTRIC WAVES. The interconnexion of
magnetism (which has an article to itself) and electricity is discussed
in ELECTROMAGNETISM, and these manifestations in nature in ATMOSPHERIC
ELECTRICITY; AURORA POLARIS and MAGNETISM, TERRESTRIAL. The general
principles of electrical engineering will be found in ELECTRICITY
SUPPLY, and further details respecting the generation and use of
electrical power are given in such articles as DYNAMO; MOTORS, ELECTRIC;
TRANSFORMERS; ACCUMULATOR; POWER TRANSMISSION: _Electric_; TRACTION;
LIGHTING: _Electric_; ELECTROCHEMISTRY and ELECTROMETALLURGY. The
principles of telegraphy (land, submarine and wireless) and of telephony
are discussed in the articles TELEGRAPH and TELEPHONE, and various
electrical instruments are treated in separate articles such as
AMPEREMETER; ELECTROMETER; GALVANOMETER; VOLTMETER; WHEATSTONE'S BRIDGE;
POTENTIOMETER; METER, ELECTRIC; ELECTROPHORUS; LEYDEN JAR; &c.

The term "electricity" is applied to denote the physical agency which
exhibits itself by effects of attraction and repulsion when particular
substances are rubbed or heated, also in certain chemical and
physiological actions and in connexion with moving magnets and metallic
circuits. The name is derived from the word _electrica_, first used by
William Gilbert (1544-1603) in his epoch-making treatise _De magnete,
magneticisque corporibus, et de magno magnete tellure_, published in
1600,[1] to denote substances which possess a similar property to amber
(= _electrum_, from [Greek: êlektron]) of attracting light objects when
rubbed. Hence the phenomena came to be collectively called electrical, a
term first used by William Barlowe, archdeacon of Salisbury, in 1618,
and the study of them, electrical science.


_Historical Sketch._

Gilbert was the first to conduct systematic scientific experiments on
electrical phenomena. Prior to his date the scanty knowledge possessed
by the ancients and enjoyed in the middle ages began and ended with
facts said to have been familiar to Thales of Miletus (600 B.C.) and
mentioned by Theophrastus (321 B.C.) and Pliny (A.D. 70), namely, that
amber, jet and one or two other substances possessed the power, when
rubbed, of attracting fragments of straw, leaves or feathers. Starting
with careful and accurate observations on facts concerning the
mysterious properties of amber and the lodestone, Gilbert laid the
foundations of modern electric and magnetic science on the true
experimental and inductive basis. The subsequent history of electricity
may be divided into four well-marked periods. The first extends from the
date of publication of Gilbert's great treatise in 1600 to the invention
by Volta of the voltaic pile and the first production of the electric
current in 1799. The second dates from Volta's discovery to the
discovery by Faraday in 1831 of the induction of electric currents and
the creation of currents by the motion of conductors in magnetic fields,
which initiated the era of modern electrotechnics. The third covers the
period between 1831 and Clerk Maxwell's enunciation of the
electromagnetic theory of light in 1865 and the invention of the
self-exciting dynamo, which marks another great epoch in the development
of the subject; and the fourth comprises the modern development of
electric theory and of absolute quantitative measurements, and above
all, of the applications of this knowledge in electrical engineering. We
shall sketch briefly the historical progress during these various
stages, and also the growth of electrical theories of electricity during
that time.

FIRST PERIOD.--Gilbert was probably led to study the phenomena of the
attraction of iron by the lodestone in consequence of his conversion to
the Copernican theory of the earth's motion, and thence proceeded to
study the attractions produced by amber. An account of his electrical
discoveries is given in the _De magnete_, lib. ii. cap. 2.[2] He
invented the _versorium_ or electrical needle and proved that
innumerable bodies he called _electrica_, when rubbed, can attract the
needle of the versorium (see ELECTROSCOPE). Robert Boyle added many new
facts and gave an account of them in his book, _The Origin of
Electricity_. He showed that the attraction between the rubbed body and
the test object is mutual. Otto von Guericke (1602-1686) constructed the
first electrical machine with a revolving ball of sulphur (see
ELECTRICAL MACHINE), and noticed that light objects were repelled after
being attracted by excited electrics. Sir Isaac Newton substituted a
ball of glass for sulphur in the electrical machine and made other not
unimportant additions to electrical knowledge. Francis Hawksbee (d.
1713) published in his book _Physico-Mechanical Experiments_ (1709), and
in several Memoirs in the _Phil. Trans._ about 1707, the results of his
electrical inquiries. He showed that light was produced when mercury was
shaken up in a glass tube exhausted of its air. Dr Wall observed the
spark and crackling sound when warm amber was rubbed, and compared them
with thunder and lightning (_Phil. Trans._, 1708, 26, p. 69). Stephen
Gray (1696-1736) noticed in 1720 that electricity could be excited by
the friction of hair, silk, wool, paper and other bodies. In 1729 Gray
made the important discovery that some bodies were conductors and others
non-conductors of electricity. In conjunction with his friend Granville
Wheeler (d. 1770), he conveyed the electricity from rubbed glass, a
distance of 886 ft., along a string supported on silk threads (_Phil.
Trans._, 1735-1736, 39, pp. 16, 166 and 400). Jean Théophile Desaguliers
(1683-1744) announced soon after that electrics were non-conductors, and
conductors were non-electrics. C.F. de C. du Fay (1699-1739) made the
great discovery that electricity is of two kinds, vitreous and resinous
(_Phil. Trans._, 1733, 38, p. 263), the first being produced when glass,
crystal, &c. are rubbed with silk, and the second when resin, amber,
silk or paper, &c. are excited by friction with flannel. He also
discovered that a body charged with positive or negative electricity
repels a body free to move when the latter is charged with electricity
of like sign, but attracts it if it is charged with electricity of
opposite sign, i.e. positive repels positive and negative repels
negative, but positive attracts negative. It is to du Fay also that we
owe the abolition of the distinction between electrics and
non-electrics. He showed that all substances could be electrified by
friction, but that to electrify conductors they must be insulated or
supported on non-conductors. Various improvements were made in the
electrical machine, and thereby experimentalists were provided with the
means of generating strong electrification; C.F. Ludolff (1707-1763) of
Berlin in 1744 succeeded in igniting ether with the electric spark
(_Phil. Trans._, 1744, 43, p. 167).

  For a very full list of the papers and works of these early electrical
  philosophers, the reader is referred to the bibliography on
  Electricity in Dr Thomas Young's _Natural Philosophy_, vol. ii. p.
  415.

In 1745 the important invention of the Leyden jar or condenser was made
by E.G. von Kleist of Kammin, and almost simultaneously by Cunaeus and
Pieter van Musschenbroek (1692-1761) of Leiden (see LEYDEN JAR). Sir
William Watson (1715-1787) in England first observed the flash of light
when a Leyden jar is discharged, and he and Dr John Bevis (1695-1771)
suggested coating the jar inside and outside with tinfoil. Watson
carried out elaborate experiments to discover how far the electric
discharge of the jar could be conveyed along metallic wires and was able
to accomplish it for a distance of 2 m., making the important
observation that the electricity appeared to be transmitted
instantaneously.

_Franklin's Researches._--Benjamin Franklin (1706-1790) was one of the
great pioneers of electrical science, and made the ever-memorable
experimental identification of lightning and electric spark. He argued
that electricity is not created by friction, but merely collected from
its state of diffusion through other matter by which it is attracted. He
asserted that the glass globe, when rubbed, attracted the electrical
fire, and took it from the rubber, the same globe being disposed, when
the friction ceases, to give out its electricity to any body which has
less. In the case of the charged Leyden jar, he asserted that the inner
coating of tinfoil had received more than its ordinary quantity of
electricity, and was therefore electrified positively, or plus, while
the outer coating of tinfoil having had its ordinary quantity of
electricity diminished, was electrified negatively, or minus. Hence the
cause of the shock and spark when the jar is discharged, or when the
superabundant or plus electricity of the inside is transferred by a
conducting body to the defective or minus electricity of the outside.
This theory of the Leyden phial Franklin supported very ingeniously by
showing that the outside and the inside coating possessed electricities
of opposite sign, and that, in charging it, exactly as much electricity
is added on one side as is subtracted from the other. The abundant
discharge of electricity by points was observed by Franklin is his
earliest experiments, and also the power of points to conduct it
copiously from an electrified body. Hence he was furnished with a simple
method of collecting electricity from other bodies, and he was enabled
to perform those remarkable experiments which are chiefly connected with
his name. Hawksbee, Wall and J.A. Nollet (1700-1770) had successively
suggested the identity of lightning and the electric spark, and of
thunder and the snap of the spark. Previously to the year 1750, Franklin
drew up a statement, in which he showed that all the general phenomena
and effects which were produced by electricity had their counterparts in
lightning. After waiting some time for the erection of a spire at
Philadelphia, by means of which he hoped to bring down the electricity
of a thunderstorm, he conceived the idea of sending up a kite among
thunder-clouds. With this view he made a small cross of two small light
strips of cedar, the arms being sufficiently long to reach to the four
corners of a large thin silk handkerchief when extended. The corners of
the handkerchief were tied to the extremities of the cross, and when the
body of the kite was thus formed, a tail, loop and string were added to
it. The body was made of silk to enable it to bear the violence and wet
of a thunderstorm. A very sharp pointed wire was fixed at the top of the
upright stick of the cross, so as to rise a foot or more above the wood.
A silk ribbon was tied to the end of the twine next the hand, and a key
suspended at the junction of the twine and silk. In company with his
son, Franklin raised the kite like a common one, in the first
thunderstorm, which happened in the month of June 1752. To keep the silk
ribbon dry, he stood within a door, taking care that the twine did not
touch the frame of the door; and when the thunder-clouds came over the
kite he watched the state of the string. A cloud passed without any
electrical indications, and he began to despair of success. At last,
however, he saw the loose filaments of the twine standing out every way,
and he found them to be attracted by the approach of his finger. The
suspended key gave a spark on the application of his knuckle, and when
the string had become wet with the rain the electricity became abundant.
A Leyden jar was charged at the key, and by the electric fire thus
obtained spirits were inflamed, and many other experiments performed
which had been formerly made by excited electrics. In subsequent trials
with another apparatus, he found that the clouds were sometimes
positively and sometimes negatively electrified, and so demonstrated the
perfect identity of lightning and electricity. Having thus succeeded in
drawing the electric fire from the clouds, Franklin conceived the idea
of protecting buildings from lightning by erecting on their highest
parts pointed iron wires or conductors communicating with the ground.
The electricity of a hovering or a passing cloud would thus be carried
off slowly and silently; and if the cloud was highly charged, the
lightning would strike in preference the elevated conductors.[3] The
most important of Franklin's electrical writings are his _Experiments
and Observations on Electricity made at Philadelphia_, 1751-1754; his
_Letters on Electricity_; and various memoirs and letters in the _Phil.
Trans._ from 1756 to 1760.

About the same time that Franklin was making his kite experiment in
America, T.F. Dalibard (1703-1779) and others in France had erected a
long iron rod at Marli, and obtained results agreeing with those of
Franklin. Similar investigations were pursued by many others, among whom
Father G.B. Beccaria (1716-1781) deserves especial mention. John Canton
(1718-1772) made the important contribution to knowledge that
electricity of either sign could be produced on nearly any body by
friction with appropriate substances, and that a rod of glass roughened
on one half was excited negatively in the rough part and positively in
the smooth part by friction with the same rubber. Canton first suggested
the use of an amalgam of mercury and tin for use with glass cylinder
electrical machines to improve their action. His most important
discovery, however, was that of electrostatic induction, the fact that
one electrified body can produce charges of electricity upon another
insulated body, and that when this last is touched it is left
electrified with a charge of opposite sign to that of the inducing
charge (_Phil. Trans._, 1753-1754). We shall make mention lower down of
Canton's contributions to electrical theory. Robert Symmer (d. 1763)
showed that quite small differences determined the sign of the
electrification that was generated by the friction of two bodies one
against the other. Thus wearing a black and a white silk stocking one
over the other, he found they were electrified oppositely when rubbed
and drawn off, and that such a rubbed silk stocking when deposited in a
Leyden jar gave up its electrification to the jar (_Phil. Trans._,
1759). Ebenezer Kinnersley (1711-1778) of Philadelphia made useful
observations on the elongation and fusion of iron wires by electrical
discharges (_Phil. Trans._, 1763). A contemporary of Canton and
co-discoverer with him of the facts of electrostatic induction was the
Swede, Johann Karl Wilcke (1732-1796), then resident in Germany, who in
1762 published an account of experiments in which a metal plate held
above the upper surface of a glass table was subjected to the action of
a charge on an electrified metal plate held below the glass (_Kon.
Schwedische Akad. Abhandl._, 1762, 24, p. 213).

_Pyro-electricity._--The subject of pyro-electricity, or the power
possessed by some minerals of becoming electrified when merely heated,
and of exhibiting positive and negative electricity, now began to
attract notice. It is possible that the _lyncurium_ of the ancients,
which according to Theophrastus attracted light bodies, was tourmaline,
a mineral found in Ceylon, which had been christened by the Dutch with
the name of _aschentrikker_, or the attractor of ashes. In 1717 Louis
Lémery exhibited to the Paris Academy of Sciences a stone from Ceylon
which attracted light bodies; and Linnaeus in mentioning his experiments
gives the stone the name of _lapis electricus_. Giovanni Caraffa, duca
di Noja (1715-1768), was led in 1758 to purchase some of the stones
called tourmaline in Holland, and, assisted by L.J.M. Daubenton and
Michel Adanson, he made a series of experiments with them, a description
of which he gave in a letter to G.L.L. Buffon in 1759. The subject,
however, had already engaged the attention of the German philosopher,
F.U.T. Aepinus, who published an account of them in 1756. Hitherto
nothing had been said respecting the necessity of heat to excite the
tourmaline; but it was shown by Aepinus that a temperature between 99½°
and 212° Fahr. was requisite for the development of its attractive
powers. Benjamin Wilson (_Phil. Trans._, 1763, &c.), J. Priestley, and
Canton continued the investigation, but it was reserved for the Abbé
Haüy to throw a clear light on this curious branch of the science
(_Traité de minéralogie_, 1801). He found that the electricity of the
tourmaline decreased rapidly from the summits or poles towards the
middle of the crystal, where it was imperceptible; and he discovered
that if a tourmaline is broken into any number of fragments, each
fragment, when excited, has two opposite poles. Haüy discovered the same
property in the Siberian and Brazilian topaz, borate of magnesia,
mesotype, prehnite, sphene and calamine. He also found that the polarity
which minerals receive from heat has a relation to the secondary forms
of their crystals--the tourmaline, for example, having its resinous pole
at the summit of the crystal which has three faces. In the other
pyro-electric crystals above mentioned, Haüy detected the same deviation
from the rules of symmetry in their secondary crystals which occurs in
tourmaline. C.P. Brard (1788-1838) discovered that pyro-electricity was
a property of axinite; and it was afterwards detected in other minerals.
In repeating and extending the experiments of Haüy much later, Sir David
Brewster discovered that various artificial salts were pyro-electric,
and he mentions the tartrates of potash and soda and tartaric acid as
exhibiting this property in a very strong degree. He also made many
experiments with the tourmaline when cut into thin slices, and reduced
to the finest powder, in which state each particle preserved its
pyro-electricity; and he showed that scolezite and mesolite, even when
deprived of their water of crystallization and reduced to powder, retain
their property of becoming electrical by heat. When this white powder is
heated and stirred about by any substance whatever, it collects in
masses like new-fallen snow, and adheres to the body with which it is
stirred.

  For Sir David Brewster's work on pyro-electricity, see _Trans. Roy.
  Soc. Edin._, 1845, also _Phil. Mag._, Dec. 1847. The reader will also
  find a full discussion on the subject in the _Treatise on
  Electricity_, by A. de la Rive, translated by C.V. Walker (London,
  1856), vol. ii. part v. ch. i.

_Animal electricity._--The observation that certain animals could give
shocks resembling the shock of a Leyden jar induced a closer examination
of these powers. The ancients were acquainted with the benumbing power
of the torpedo-fish, but it was not till 1676 that modern naturalists
had their attention again drawn to the fact. E. Bancroft was the first
person who distinctly suspected that the effects of the torpedo were
electrical. In 1773 John Walsh (d. 1795) and Jan Ingenhousz (1730-1799)
proved by many curious experiments that the shock of the torpedo was an
electrical one (_Phil. Trans._, 1773-1775); and John Hunter (id. 1773,
1775) examined and described the anatomical structure of its electrical
organs. A. von Humboldt and Gay-Lussac (_Ann. Chim._, 1805), and Etienne
Geoffroy Saint-Hilaire (_Gilb. Ann._, 1803) pursued the subject with
success; and Henry Cavendish (_Phil. Trans._, 1776) constructed an
artificial torpedo, by which he imitated the actions of the living
animal. The subject was also investigated (_Phil. Trans._, 1812, 1817)
by Dr T.J. Todd (1789-1840), Sir Humphry Davy (id. 1829), John Davy (id.
1832, 1834, 1841) and Faraday (_Exp. Res._, vol. ii.). The power of
giving electric shocks has been discovered also in the _Gymnotus
electricus_ (electric eel), the _Malapterurus electricus_, the
_Trichiurus electricus_, and the _Tetraodon electricus_. The most
interesting and the best known of these singular fishes is the
_Gymnotus_ or Surinam eel. Humboldt gives a very graphic account of the
combats which are carried on in South America between the gymnoti and
the wild horses in the vicinity of Calabozo.

_Cavendish's Researches._--The work of Henry Cavendish (1731-1810)
entitles him to a high place in the list of electrical investigators. A
considerable part of Cavendish's work was rescued from oblivion in 1879
and placed in an easily accessible form by Professor Clerk Maxwell, who
edited the original manuscripts in the possession of the duke of
Devonshire.[4] Amongst Cavendish's important contributions were his
exact measurements of electrical capacity. The leading idea which
distinguishes his work from that of his predecessors was his use of the
phrase "degree of electrification" with a clear scientific definition
which shows it to be equivalent in meaning to the modern term "electric
potential." Cavendish compared the capacity of different bodies with
those of conducting spheres of known diameter and states these
capacities in "globular inches," a globular inch being the capacity of a
sphere 1 in. in diameter. Hence his measurements are all directly
comparable with modern electrostatic measurements in which the unit of
capacity is that of a sphere 1 centimetre in radius. Cavendish measured
the capacity of disks and condensers of various forms, and proved that
the capacity of a Leyden pane is proportional to the surface of the
tinfoil and inversely as the thickness of the glass. In connexion with
this subject he anticipated one of Faraday's greatest discoveries,
namely, the effect of the dielectric or insulator upon the capacity of a
condenser formed with it, in other words, made the discovery of specific
inductive capacity (see _Electrical Researches_, p. 183). He made many
measurements of the electric conductivity of different solids and
liquids, by comparing the intensity of the electric shock taken through
his body and various conductors. He seems in this way to have educated
in himself a very precise "electrical sense," making use of his own
nervous system as a kind of physiological galvanometer. One of the most
important investigations he made in this way was to find out, as he
expressed it, "what power of the velocity the resistance is proportional
to." Cavendish meant by the term "velocity" what we now call the
current, and by "resistance" the electromotive force which maintains the
current. By various experiments with liquids in tubes he found this
power was nearly unity. This result thus obtained by Cavendish in
January 1781, that the current varies in direct proportion to the
electromotive force, was really an anticipation of the fundamental law
of electric flow, discovered independently by G.S. Ohm in 1827, and
since known as Ohm's Law. Cavendish also enunciated in 1776 all the laws
of division of electric current between circuits in parallel, although
they are generally supposed to have been first given by Sir C.
Wheatstone. Another of his great investigations was the determination of
the law according to which electric force varies with the distance.
Starting from the fact that if an electrified globe, placed within two
hemispheres which fit over it without touching, is brought in contact
with these hemispheres, it gives up the whole of its charge to them--in
other words, that the charge on an electrified body is wholly on the
surface--he was able to deduce by most ingenious reasoning the law that
electric force varies inversely as the square of the distance. The
accuracy of his measurement, by which he established within 2% the above
law, was only limited by the sensibility, or rather insensibility, of
the pith ball electrometer, which was his only means of detecting the
electric charge.[5] In the accuracy of his quantitative measurements and
the range of his researches and his combination of mathematical and
physical knowledge, Cavendish may not inaptly be described as the Kelvin
of the 18th century. Nothing but his curious indifference to the
publication of his work prevented him from securing earlier recognition
for it.

_Coulomb's Work._--Contemporary with Cavendish was C.A. Coulomb
(1736-1806), who in France addressed himself to the same kind of exact
quantitative work as Cavendish in England. Coulomb has made his name for
ever famous by his invention and application of his torsion balance to
the experimental verification of the fundamental law of electric
attraction, in which, however, he was anticipated by Cavendish, namely,
that the force of attraction between two small electrified spherical
bodies varies as the product of their charges and inversely as the
square of the distance of their centres. Coulomb's work received better
publication than Cavendish's at the time of its accomplishment, and
provided a basis on which mathematicians could operate. Accordingly the
close of the 18th century drew into the arena of electrical
investigation on its mathematical side P.S. Laplace, J.B. Biot, and
above all, S.D. Poisson. Adopting the hypothesis of two fluids, Coulomb
investigated experimentally and theoretically the distribution of
electricity on the surface of bodies by means of his proof plane. He
determined the law of distribution between two conducting bodies in
contact; and measured with his proof plane the density of the
electricity at different points of two spheres in contact, and
enunciated an important law. He ascertained the distribution of
electricity among several spheres (whether equal or unequal) placed in
contact in a straight line; and he measured the distribution of
electricity on the surface of a cylinder, and its distribution between
a sphere and cylinder of different lengths but of the same diameter. His
experiments on the dissipation of electricity possess also a high value.
He found that the momentary dissipation was proportional to the degree
of electrification at the time, and that, when the charge was moderate,
its dissipation was not altered in bodies of different kinds or shapes.
The temperature and pressure of the atmosphere did not produce any
sensible change; but he concluded that the dissipation was nearly
proportional to the cube of the quantity of moisture in the air.[6] In
examining the dissipation which takes place along imperfectly insulating
substances, he found that a thread of gum-lac was the most perfect of
all insulators; that it insulated ten times as well as a dry silk
thread; and that a silk thread covered with fine sealing-wax insulated
as powerfully as gum-lac when it had four times its length. He found
also that the dissipation of electricity along insulators was chiefly
owing to adhering moisture, but in some measure also to a slight
conducting power. For his memoirs see _Mém. de math. et phys. de l'acad.
de sc._, 1785, &c.

SECOND PERIOD.--We now enter upon the second period of electrical
research inaugurated by the epoch-making discovery of Alessandro Volta
(1745-1827). L. Galvani had made in 1790 his historic observations on
the muscular contraction produced in the bodies of recently killed frogs
when an electrical machine was being worked in the same room, and
described them in 1791 (_De viribus electricitatis in motu musculari
commentarius_, Bologna, 1791). Volta followed up these observations with
rare philosophic insight and experimental skill. He showed that all
conductors liquid and solid might be divided into two classes which he
called respectively conductors of the first and of the second class, the
first embracing metals and carbon in its conducting form, and the second
class, water, aqueous solutions of various kinds, and generally those
now called electrolytes. In the case of conductors of the first class he
proved by the use of the condensing electroscope, aided probably by some
form of multiplier or doubler, that a difference of potential (see
ELECTROSTATICS) was created by the mere contact of two such conductors,
one of them being positively electrified and the other negatively. Volta
showed, however, that if a series of bodies of the first class, such as
disks of various metals, are placed in contact, the potential difference
between the first and the last is just the same as if they are
immediately in contact. There is no accumulation of potential. If,
however, pairs of metallic disks, made, say, of zinc and copper, are
alternated with disks of cloth wetted with a conductor of the second
class, such, for instance, as dilute acid or any electrolyte, then the
effect of the feeble potential difference between one pair of copper and
zinc disks is added to that of the potential difference between the next
pair, and thus by a sufficiently long series of pairs any required
difference of potential can be accumulated.

_The Voltaic Pile._--This led him about 1799 to devise his famous
voltaic pile consisting of disks of copper and zinc or other metals with
wet cloth placed between the pairs. Numerous examples of Volta's
original piles at one time existed in Italy, and were collected together
for an exhibition held at Como in 1899, but were unfortunately destroyed
by a disastrous fire on the 8th of July 1899. Volta's description of his
pile was communicated in a letter to Sir Joseph Banks, president of the
Royal Society of London, on the 20th of March 1800, and was printed in
the _Phil. Trans._, vol. 90, pt. 1, p. 405. It was then found that when
the end plates of Volta's pile were connected to an electroscope the
leaves diverged either with positive or negative electricity. Volta also
gave his pile another form, the _couronne des tasses_ (crown of cups),
in which connected strips of copper and zinc were used to bridge between
cups of water or dilute acid. Volta then proved that all metals could be
arranged in an electromotive series such that each became positive when
placed in contact with the one next below it in the series. The origin
of the electromotive force in the pile has been much discussed, and
Volta's discoveries gave rise to one of the historic controversies of
science. Volta maintained that the mere contact of metals was sufficient
to produce the electrical difference of the end plates of the pile. The
discovery that chemical action was involved in the process led to the
advancement of the chemical theory of the pile and this was strengthened
by the growing insight into the principle of the conservation of energy.
In 1851 Lord Kelvin (Sir W. Thomson), by the use of his then
newly-invented electrometer, was able to confirm Volta's observations on
contact electricity by irrefutable evidence, but the contact theory of
the voltaic pile was then placed on a basis consistent with the
principle of the conservation of energy. A.A. de la Rive and Faraday
were ardent supporters of the chemical theory of the pile, and even at
the present time opinions of physicists can hardly be said to be in
entire accordance as to the source of the electromotive force in a
voltaic couple or pile.[7]

Improvements in the form of the voltaic pile were almost immediately
made by W. Cruickshank (1745-1800), Dr W.H. Wollaston and Sir H. Davy,
and these, together with other eminent continental chemists, such as
A.F. de Fourcroy, L.J. Thénard and J.W. Ritter (1776-1810), ardently
prosecuted research with the new instrument. One of the first
discoveries made with it was its power to electrolyse or chemically
decompose certain solutions. William Nicholson (1753-1815) and Sir
Anthony Carlisle (1768-1840) in 1800 constructed a pile of silver and
zinc plates, and placing the terminal wires in water noticed the
evolution from these wires of bubbles of gas, which they proved to be
oxygen and hydrogen. These two gases, as Cavendish and James Watt had
shown in 1784, were actually the constituents of water. From that date
it was clearly recognized that a fresh implement of great power had been
given to the chemist. Large voltaic piles were then constructed by
Andrew Crosse (1784-1855) and Sir H. Davy, and improvements initiated by
Wollaston and Robert Hare (1781-1858) of Philadelphia. In 1806 Davy
communicated to the Royal Society of London a celebrated paper on some
"Chemical Agencies of Electricity," and after providing himself at the
Royal Institution of London with a battery of several hundred cells, he
announced in 1807 his great discovery of the electrolytic decomposition
of the alkalis, potash and soda, obtaining therefrom the metals
potassium and sodium. In July 1808 Davy laid a request before the
managers of the Royal Institution that they would set on foot a
subscription for the purchase of a specially large voltaic battery; as a
result he was provided with one of 2000 pairs of plates, and the first
experiment performed with it was the production of the electric arc
light between carbon poles. Davy followed up his initial work with a
long and brilliant series of electrochemical investigations described
for the most part in the _Phil. Trans._ of the Royal Society.

_Magnetic Action of Electric Current._--Noticing an analogy between the
polarity of the voltaic pile and that of the magnet, philosophers had
long been anxious to discover a relation between the two, but twenty
years elapsed after the invention of the pile before Hans Christian
Oersted (1777-1851), professor of natural philosophy in the university
of Copenhagen, made in 1819 the discovery which has immortalized his
name. In the _Annals of Philosophy_ (1820, 16, p. 273) is to be found an
English translation of Oersted's original Latin essay (entitled
"Experiments on the Effect of a Current of Electricity on the Magnetic
Needle"), dated the 21st of July 1820, describing his discovery. In it
Oersted describes the action he considers is taking place around the
conductor joining the extremities of the pile; he speaks of it as the
electric conflict, and says: "It is sufficiently evident that the
electric conflict is not confined to the conductor, but is dispersed
pretty widely in the circumjacent space. We may likewise conclude that
this conflict performs circles round the wire, for without this
condition it seems impossible that one part of the wire when placed
below the magnetic needle should drive its pole to the east, and when
placed above it, to the west." Oersted's important discovery was the
fact that when a wire joining the end plates of a voltaic pile is held
near a pivoted magnet or compass needle, the latter is deflected and
places itself more or less transversely to the wire, the direction
depending upon whether the wire is above or below the needle, and on the
manner in which the copper or zinc ends of the pile are connected to it.
It is clear, moreover, that Oersted clearly recognized the existence of
what is now called the magnetic field round the conductor. This
discovery of Oersted, like that of Volta, stimulated philosophical
investigation in a high degree.

_Electrodynamics._--On the 2nd of October 1820, A.M. Ampère presented to
the French Academy of Sciences an important memoir,[8] in which he
summed up the results of his own and D.F.J. Arago's previous
investigations in the new science of electromagnetism, and crowned that
labour by the announcement of his great discovery of the dynamical
action between conductors conveying the electric currents. Ampère in
this paper gave an account of his discovery that conductors conveying
electric currents exercise a mutual attraction or repulsion on one
another, currents flowing in the same direction in parallel conductors
attracting, and those in opposite directions repelling. Respecting this
achievement when developed in its experimental and mathematical
completeness, Clerk Maxwell says that it was "perfect in form and
unassailable in accuracy." By a series of well-chosen experiments Ampère
established the laws of this mutual action, and not only explained
observed facts by a brilliant train of mathematical analysis, but
predicted others subsequently experimentally realized. These
investigations led him to the announcement of the fundamental law of
action between elements of current, or currents in infinitely short
lengths of linear conductors, upon one another at a distance; summed up
in compact expression this law states that the action is proportional to
the product of the current strengths of the two elements, and the
lengths of the two elements, and inversely proportional to the square of
the distance between the two elements, and also directly proportional to
a function of the angles which the line joining the elements makes with
the directions of the two elements respectively. Nothing is more
remarkable in the history of discovery than the manner in which Ampère
seized upon the right clue which enabled him to disentangle the
complicated phenomena of electrodynamics and to deduce them all as a
consequence of one simple fundamental law, which occupies in
electrodynamics the position of the Newtonian law of gravitation in
physical astronomy.

In 1821 Michael Faraday (1791-1867), who was destined later on to do so
much for the science of electricity, discovered electromagnetic
rotation, having succeeded in causing a wire conveying a voltaic current
to rotate continuously round the pole of a permanent magnet.[9] This
experiment was repeated in a variety of forms by A.A. De la Rive, Peter
Barlow (1776-1862), William Ritchie (1790-1837), William Sturgeon
(1783-1850), and others; and Davy (_Phil. Trans._, 1823) showed that
when two wires connected with the pole of a battery were dipped into a
cup of mercury placed on the pole of a powerful magnet, the fluid
rotated in opposite directions about the two electrodes.

_Electromagnetism._--In 1820 Arago (_Ann. Chim. Phys._, 1820, 15, p. 94)
and Davy (_Annals of Philosophy_, 1821) discovered independently the
power of the electric current to magnetize iron and steel. Félix Savary
(1797-1841) made some very curious observations in 1827 on the
magnetization of steel needles placed at different distances from a wire
conveying the discharge of a Leyden jar (_Ann. Chim. Phys._, 1827, 34).
W. Sturgeon in 1824 wound a copper wire round a bar of iron bent in the
shape of a horseshoe, and passing a voltaic current through the wire
showed that the iron became powerfully magnetized as long as the
connexion with the pile was maintained (_Trans. Soc. Arts_, 1825). These
researches gave us the electromagnet, almost as potent an instrument of
research and invention as the pile itself (see ELECTROMAGNETISM).

Ampère had already previously shown that a spiral conductor or solenoid
when traversed by an electric current possesses magnetic polarity, and
that two such solenoids act upon one another when traversed by electric
currents as if they were magnets. Joseph Henry, in the United States,
first suggested the construction of what were then called intensity
electromagnets, by winding upon a horseshoe-shaped piece of soft iron
many superimposed windings of copper wire, insulated by covering it with
silk or cotton, and then sending through the coils the current from a
voltaic battery. The dependence of the intensity of magnetization on the
strength of the current was subsequently investigated (_Pogg. Ann.
Phys._, 1839, 47) by H.F.E. Lenz (1804-1865) and M.H. von Jacobi
(1801-1874). J.P. Joule found that magnetization did not increase
proportionately with the current, but reached a maximum (_Sturgeon's
Annals of Electricity_, 1839, 4). Further investigations on this subject
were carried on subsequently by W.E. Weber (1804-1891), J.H.J. Müller
(1809-1875), C.J. Dub (1817-1873), G.H. Wiedemann (1826-1899), and
others, and in modern times by H.A. Rowland (1848-1901), Shelford
Bidwell (b. 1848), John Hopkinson (1849-1898), J.A. Ewing (b. 1855) and
many others. Electric magnets of great power were soon constructed in
this manner by Sturgeon, Joule, Henry, Faraday and Brewster. Oersted's
discovery in 1819 was indeed epoch-making in the degree to which it
stimulated other research. It led at once to the construction of the
galvanometer as a means of detecting and measuring the electric current
in a conductor. In 1820 J.S.C. Schweigger (1779-1857) with his
"multiplier" made an advance upon Oersted's discovery, by winding the
wire conveying the electric current many times round the pivoted
magnetic needle and thus increasing the deflection; and L. Nobili
(1784-1835) in 1825 conceived the ingenious idea of neutralizing the
directive effect of the earth's magnetism by employing a pair of
magnetized steel needles fixed to one axis, but with their magnetic
poles pointing in opposite directions. Hence followed the astatic
multiplying galvanometer.

_Electrodynamic Rotation._--The study of the relation between the magnet
and the circuit conveying an electric current then led Arago to the
discovery of the "magnetism of rotation." He found that a vibrating
magnetic compass needle came to rest sooner when placed over a plate of
copper than otherwise, and also that a plate of copper rotating under a
suspended magnet tended to drag the magnet in the same direction. The
matter was investigated by Charles Babbage, Sir J.F.W. Herschel, Peter
Barlow and others, but did not receive a final explanation until after
the discovery of electromagnetic induction by Faraday in 1831. Ampère's
investigations had led electricians to see that the force acting upon a
magnetic pole due to a current in a neighbouring conductor was such as
to tend to cause the pole to travel round the conductor. Much ingenuity
had, however, to be expended before a method was found of exhibiting
such a rotation. Faraday first succeeded by the simple but ingenious
device of using a light magnetic needle tethered flexibly to the bottom
of a cup containing mercury so that one pole of the magnet was just
above the surface of the mercury. On bringing down on to the mercury
surface a wire conveying an electric current, and allowing the current
to pass through the mercury and out at the bottom, the magnetic pole at
once began to rotate round the wire (_Exper. Res._, 1822, 2, p. 148).
Faraday and others then discovered, as already mentioned, means to make
the conductor conveying the current rotate round a magnetic pole, and
Ampère showed that a magnet could be made to rotate on its own axis when
a current was passed through it. The difficulty in this case consisted
in discovering means by which the current could be passed through one
half of the magnet without passing it through the other half. This,
however, was overcome by sending the current out at the centre of the
magnet by means of a short length of wire dipping into an annular groove
containing mercury. Barlow, Sturgeon and others then showed that a
copper disk could be made to rotate between the poles of a horseshoe
magnet when a current was passed through the disk from the centre to the
circumference, the disk being rendered at the same time freely movable
by making a contact with the circumference by means of a mercury trough.
These experiments furnished the first elementary forms of electric
motor, since it was then seen that rotatory motion could be produced in
masses of metal by the mutual action of conductors conveying electric
current and magnetic fields. By his discovery of thermo-electricity in
1822 (_Pogg. Ann. Phys._, 6), T.J. Seebeck (1770-1831) opened up a new
region of research (see THERMOELECTRICITY). James Cumming (1777-1861) in
1823 (_Annals of Philosophy_, 1823) found that the thermo-electric
series varied with the temperature, and J.C.A. Peltier (1785-1845) in
1834 discovered that a current passed across the junction of two metals
either generated or absorbed heat.

_Ohm's Law._--In 1827 Dr G.S. Ohm (1787-1854) rendered a great service
to electrical science by his mathematical investigation of the voltaic
circuit, and publication of his paper, _Die galvanische Kette
mathematisch bearbeitet_. Before his time, ideas on the measurable
quantities with which we are concerned in an electric circuit were
extremely vague. Ohm introduced the clear idea of current strength as an
effect produced by electromotive force acting as a cause in a circuit
having resistance as its quality, and showed that the current was
directly proportional to the electromotive force and inversely as the
resistance. Ohm's law, as it is called, was based upon an analogy with
the flow of heat in a circuit, discussed by Fourier. Ohm introduced the
definite conception of the distribution along the circuit of
"electroscopic force" or tension (_Spannung_), corresponding to the
modern term potential. Ohm verified his law by the aid of
thermo-electric piles as sources of electromotive force, and Davy,
C.S.M. Pouillet (1791-1868), A.C. Becquerel (1788-1878), G.T. Fechner
(1801-1887), R.H.A. Kohlrausch (1809-1858) and others laboured at its
confirmation. In more recent times, 1876, it was rigorously tested by G.
Chrystal (b. 1851) at Clerk Maxwell's instigation (see _Brit. Assoc.
Report_, 1876, p. 36), and although at its original enunciation its
meaning was not at first fully apprehended, it soon took its place as
the expression of the fundamental law of electrokinetics.

_Induction of Electric Currents._--In 1831 Faraday began the
investigations on electromagnetic induction which proved more fertile in
far-reaching practical consequences than any of those which even his
genius gave to the world. These advances all centre round his supreme
discovery of the induction of electric currents. Fully familiar with the
fact that an electric charge upon one conductor could produce a charge
of opposite sign upon a neighbouring conductor, Faraday asked himself
whether an electric current passing through a conductor could not in any
like manner induce an electric current in some neighbouring conductor.
His first experiments on this subject were made in the month of November
1825, but it was not until the 29th of August 1831 that he attained
success. On that date he had provided himself with an iron ring, over
which he had wound two coils of insulated copper wire. One of these
coils was connected with the voltaic battery and the other with the
galvanometer. He found that at the moment the current in the battery
circuit was started or stopped, transitory currents appeared in the
galvanometer circuit in opposite directions. In ten days of brilliant
investigation, guided by clear insight from the very first into the
meaning of the phenomena concerned, he established experimentally the
fact that a current may be induced in a conducting circuit simply by the
variation in a magnetic field, the lines of force of which are linked
with that circuit. The whole of Faraday's investigations on this
subject can be summed up in the single statement that if a conducting
circuit is placed in a magnetic field, and if either by variation of the
field or by movement or variation of the form of the circuit the total
magnetic flux linked with the circuit is varied, an electromotive force
is set up in that circuit which at any instant is measured by the rate
at which the total flux linked with the circuit is changing.

Amongst the memorable achievements of the ten days which Faraday devoted
to this investigation was the discovery that a current could be induced
in a conducting wire simply by moving it in the neighbourhood of a
magnet. One form which this experiment took was that of rotating a
copper disk between the poles of a powerful electric magnet. He then
found that a conductor, the ends of which were connected respectively
with the centre and edge of the disk, was traversed by an electric
current. This important fact laid the foundation for all subsequent
inventions which finally led to the production of electromagnetic or
dynamo-electric machines.

THIRD PERIOD.--With this supremely important discovery of Faraday's we
enter upon the third period of electrical research, in which that
philosopher himself was the leading figure. He not only collected the
facts concerning electromagnetic induction so industriously that nothing
of importance remained for future discovery, and embraced them all in
one law of exquisite simplicity, but he introduced his famous conception
of lines of force which changed entirely the mode of regarding
electrical phenomena. The French mathematicians, Coulomb, Biot, Poisson
and Ampère, had been content to accept the fact that electric charges or
currents in conductors could exert forces on other charges or conductors
at a distance without inquiring into the means by which this action at a
distance was produced. Faraday's mind, however, revolted against this
notion; he felt intuitively that these distance actions must be the
result of unseen operations in the interposed medium. Accordingly when
he sprinkled iron filings on a card held over a magnet and revealed the
curvilinear system of lines of force (see MAGNETISM), he regarded these
fragments of iron as simple indicators of a physical state in the space
already in existence round the magnet. To him a magnet was not simply a
bar of steel; it was the core and origin of a system of lines of
magnetic force attached to it and moving with it. Similarly he came to
see an electrified body as a centre of a system of lines of
electrostatic force. All the space round magnets, currents and electric
charges was therefore to Faraday the seat of corresponding lines of
magnetic or electric force. He proved by systematic experiments that the
electromotive forces set up in conductors by their motions in magnetic
fields or by the induction of other currents in the field were due to
the secondary conductor _cutting_ lines of magnetic force. He invented
the term "electrotonic state" to signify the total magnetic flux due to
a conductor conveying a current, which was linked with any secondary
circuit in the field or even with itself.

_Faraday's Researches._--Space compels us to limit our account of the
scientific work done by Faraday in the succeeding twenty years, in
elucidating electrical phenomena and adding to the knowledge thereon, to
the very briefest mention. We must refer the reader for further
information to his monumental work entitled _Experimental Researches on
Electricity_, in three volumes, reprinted from the _Phil. Trans._
between 1831 and 1851. Faraday divided these researches into various
series. The 1st and 2nd concern the discovery of magneto-electric
induction already mentioned. The 3rd series (1833) he devoted to
discussion of the identity of electricity derived from various sources,
frictional, voltaic, animal and thermal, and he proved by rigorous
experiments the identity and similarity in properties of the electricity
generated by these various methods. The 5th series (1833) is occupied
with his electrochemical researches. In the 7th series (1834) he defines
a number of new terms, such as electrolyte, electrolysis, anode and
cathode, &c., in connexion with electrolytic phenomena, which were
immediately adopted into the vocabulary of science. His most important
contribution at this date was the invention of the voltameter and his
enunciation of the laws of electrolysis. The voltameter provided a means
of measuring quantity of electricity, and in the hands of Faraday and
his successors became an appliance of fundamental importance. The 8th
series is occupied with a discussion of the theory of the voltaic pile,
in which Faraday accumulates evidence to prove that the source of the
energy of the pile must be chemical. He returns also to this subject in
the 16th series. In the 9th series (1834) he announced the discovery of
the important property of electric conductors, since called their
self-induction or inductance, a discovery in which, however, he was
anticipated by Joseph Henry in the United States. The 11th series (1837)
deals with electrostatic induction and the statement of the important
fact of the specific inductive capacity of insulators or dielectrics.
This discovery was made in November 1837 when Faraday had no knowledge
of Cavendish's previous researches into this matter. The 19th series
(1845) contains an account of his brilliant discovery of the rotation of
the plane of polarized light by transparent dielectrics placed in a
magnetic field, a relation which established for the first time a
practical connexion between the phenomena of electricity and light. The
20th series (1845) contains an account of his researches on the
universal action of magnetism and diamagnetic bodies. The 22nd series
(1848) is occupied with the discussion of magneto-crystallic force and
the abnormal behaviour of various crystals in a magnetic field. In the
25th series (1850) he made known his discovery of the magnetic character
of oxygen gas, and the important principle that the terms paramagnetic
and diamagnetic are relative. In the 26th series (1850) he returned to a
discussion of magnetic lines of force, and illuminated the whole subject
of the magnetic circuit by his transcendent insight into the intricate
phenomena concerned. In 1855 he brought these researches to a conclusion
by a general article on magnetic philosophy, having placed the whole
subject of magnetism and electromagnetism on an entirely novel and solid
basis. In addition to this he provided the means for studying the
phenomena not only qualitatively, but also quantitatively, by the
profoundly ingenious instruments he invented for that purpose.

_Electrical Measurement._--Faraday's ideas thus pressed upon
electricians the necessity for the quantitative measurement of
electrical phenomena.[10] It has been already mentioned that Schweigger
invented in 1820 the "multiplier," and Nobili in 1825 the astatic
galvanometer. C.S.M. Pouillet in 1837 contributed the sine and tangent
compass, and W.E. Weber effected great improvements in them and in the
construction and use of galvanometers. In 1849 H. von Helmholtz devised
a tangent galvanometer with two coils. The measurement of electric
resistance then engaged the attention of electricians. By his Memoirs in
the _Phil. Trans._ in 1843, Sir Charles Wheatstone gave a great impulse
to this study. He invented the rheostat and improved the resistance
balance, invented by S.H. Christie (1784-1865) in 1833, and subsequently
called the Wheatstone Bridge. (See his _Scientific Papers_, published by
the Physical Society of London, p. 129.) Weber about this date invented
the electrodynamometer, and applied the mirror and scale method of
reading deflections, and in co-operation with C.F. Gauss introduced a
system of absolute measurement of electric and magnetic phenomena. In
1846 Weber proceeded with improved apparatus to test Ampère's laws of
electrodynamics. In 1845 H.G. Grassmann (1809-1877) published (_Pogg.
Ann._ vol. 64) his "Neue Theorie der Electrodynamik," in which he gave
an elementary law differing from that of Ampère but leading to the same
results for closed circuits. In the same year F.E. Neumann published
another law. In 1846 Weber announced his famous hypothesis concerning
the connexion of electrostatic and electrodynamic phenomena. The work of
Neumann and Weber had been stimulated by that of H.F.E. Lenz
(1804-1865), whose researches (_Pogg. Ann._, 1834, 31; 1835, 34) among
other results led him to the statement of the law by means of which the
direction of the induced current can be predicted from the theory of
Ampère, the rule being that the direction of the induced current is
always such that its electrodynamic action tends to oppose the motion
which produces it.

Neumann in 1845 did for electromagnetic induction what Ampère did for
electrodynamics, basing his researches upon the experimental laws of
Lenz. He discovered a function, which has been called the potential of
one circuit on another, from which he deduced a theory of induction
completely in accordance with experiment. Weber at the same time deduced
the mathematical laws of induction from his elementary law of electrical
action, and with his improved instruments arrived at accurate
verifications of the law of induction, which by this time had been
developed mathematically by Neumann and himself. In 1849 G.R. Kirchhoff
determined experimentally in a certain case the absolute value of the
current induced by one circuit in another, and in the same year Erik
Edland (1819-1888) made a series of careful experiments on the induction
of electric currents which further established received theories. These
labours laid the foundation on which was subsequently erected a complete
system for the absolute measurement of electric and magnetic quantities,
referring them all to the fundamental units of mass, length and time.
Helmholtz gave at the same time a mathematical theory of induced
currents and a valuable series of experiments in support of them (_Pogg.
Ann._, 1851). This great investigator and luminous expositor just before
that time had published his celebrated essay, _Die Erhaltung der Kraft_
("The Conservation of Energy"), which brought to a focus ideas which had
been accumulating in consequence of the work of J.P. Joule, J.R. von
Mayer and others, on the transformation of various forms of physical
energy, and in particular the mechanical equivalent of heat. Helmholtz
brought to bear upon the subject not only the most profound mathematical
attainments, but immense experimental skill, and his work in connexion
with this subject is classical.

_Lord Kelvin's Work._--About 1842 Lord Kelvin (then William Thomson)
began that long career of theoretical and practical discovery and
invention in electrical science which revolutionized every department of
pure and applied electricity. His early contributions to electrostatics
and electrometry are to be found described in his _Reprint of Papers on
Electrostatics and Magnetism_ (1872), and his later work in his
collected _Mathematical and Physical Papers_. By his studies in
electrostatics, his elegant method of electrical images, his development
of the theory of potential and application of the principle of
conservation of energy, as well as by his inventions in connexion with
electrometry, he laid the foundations of our modern knowledge of
electrostatics. His work on the electrodynamic qualities of metals,
thermo-electricity, and his contributions to galvanometry, were not less
massive and profound. From 1842 onwards to the end of the 19th century,
he was one of the great master workers in the field of electrical
discovery and research.[11] In 1853 he published a paper "On Transient
Electric Currents" (_Phil. Mag._, 1853 [4], 5, p. 393), in which he
applied the principle of the conservation of energy to the discharge of
a Leyden jar. He added definiteness to the idea of the self-induction or
inductance of an electric circuit, and gave a mathematical expression
for the current flowing out of a Leyden jar during its discharge. He
confirmed an opinion already previously expressed by Helmholtz and by
Henry, that in some circumstances this discharge is oscillatory in
nature, consisting of an alternating electric current of high frequency.
These theoretical predictions were confirmed and others, subsequently,
by the work of B.W. Feddersen (b. 1832), C.A. Paalzow (b. 1823), and it
was then seen that the familiar phenomena of the discharge of a Leyden
jar provided the means of generating electric oscillations of very high
frequency.

_Telegraphy._--Turning to practical applications of electricity, we may
note that electric telegraphy took its rise in 1820, beginning with a
suggestion of Ampère immediately after Oersted's discovery. It was
established by the work of Weber and Gauss at Göttingen in 1836, and
that of C.A. Steinheil (1801-1870) of Munich, Sir W.F. Cooke (1806-1879)
and Sir C. Wheatstone in England, Joseph Henry and S.F.B. Morse
(1791-1872) in the United States in 1837. In 1845 submarine telegraphy
was inaugurated by the laying of an insulated conductor across the
English Channel by the brothers Brett, and their temporary success was
followed by the laying in 1851 of a permanent Dover-Calais cable by T.R.
Crampton. In 1856 the project for an Atlantic submarine cable took shape
and the Atlantic Telegraph Company was formed with a capital of
£350,000, with Sir Charles Bright as engineer-in-chief and E.O.W.
Whitehouse as electrician. The phenomena connected with the propagation
of electric signals by underground insulated wires had already engaged
the attention of Faraday in 1854, who pointed out the Leyden-jar-like
action of an insulated subterranean wire. Scientific and practical
questions connected with the possibility of laying an Atlantic submarine
cable then began to be discussed, and Lord Kelvin was foremost in
developing true scientific knowledge on this subject, and in the
invention of appliances for utilizing it. One of his earliest and most
useful contributions (in 1858) was the invention of the mirror
galvanometer. Abandoning the long and somewhat heavy magnetic needles
that had been used up to that date in galvanometers, he attached to the
back of a very small mirror made of microscopic glass a fragment of
magnetized watch-spring, and suspended the mirror and needle by means of
a cocoon fibre in the centre of a coil of insulated wire. By this simple
device he provided a means of measuring small electric currents far in
advance of anything yet accomplished, and this instrument proved not
only most useful in pure scientific researches, but at the same time was
of the utmost value in connexion with submarine telegraphy. The history
of the initial failures and final success in laying the Atlantic cable
has been well told by Mr. Charles Bright (see _The Story of the Atlantic
Cable_, London, 1903).[12] The first cable laid in 1857 broke on the
11th of August during laying. The second attempt in 1858 was successful,
but the cable completed on the 5th of August 1858 broke down on the 20th
of October 1858, after 732 messages had passed through it. The third
cable laid in 1865 was lost on the 2nd of August 1865, but in 1866 a
final success was attained and the 1865 cable also recovered and
completed. Lord Kelvin's mirror galvanometer was first used in receiving
signals through the short-lived 1858 cable. In 1867 he invented his
beautiful siphon-recorder for receiving and recording the signals
through long cables. Later, in conjunction with Prof. Fleeming Jenkin,
he devised his automatic curb sender, an appliance for sending signals
by means of punched telegraphic paper tape. Lord Kelvin's contributions
to the science of exact electric measurement[13] were enormous. His
ampere-balances, voltmeters and electrometers, and double bridge, are
elsewhere described in detail (see AMPEREMETER; ELECTROMETER, and
WHEATSTONE'S BRIDGE).

_Dynamo._--The work of Faraday from 1831 to 1851 stimulated and
originated an immense mass of scientific research, but at the same time
practical inventors had not been slow to perceive that it was capable of
purely technical application. Faraday's copper disk rotated between the
poles of a magnet, and producing thereby an electric current, became the
parent of innumerable machines in which mechanical energy was directly
converted into the energy of electric currents. Of these machines,
originally called magneto-electric machines, one of the first was
devised in 1832 by H. Pixii. It consisted of a fixed horseshoe armature
wound over with insulated copper wire in front of which revolved about a
vertical axis a horseshoe magnet. Pixii, who invented the split tube
commutator for converting the alternating current so produced into a
continuous current in the external circuit, was followed by J. Saxton,
E.M. Clarke, and many others in the development of the above-described
magneto-electric machine. In 1857 E.W. Siemens effected a great
improvement by inventing a shuttle armature and improving the shape of
the field magnet. Subsequently similar machines with electromagnets were
introduced by Henry Wilde (b. 1833), Siemens, Wheatstone, W. Ladd and
others, and the principle of self-excitation was suggested by Wilde,
C.F. Varley (1828-1883), Siemens and Wheatstone (see DYNAMO). These
machines about 1866 and 1867 began to be constructed on a commercial
scale and were employed in the production of the electric light. The
discovery of electric-current induction also led to the production of
the induction coil (q.v.), improved and brought to its present
perfection by W. Sturgeon, E.R. Ritchie, N.J. Callan, H.D. Rühmkorff
(1803-1877), A.H.L. Fizeau, and more recently by A. Apps and modern
inventors. About the same time Fizeau and J.B.L. Foucault devoted
attention to the invention of automatic apparatus for the production of
Davy's electric arc (see LIGHTING: _ELECTRIC_), and these appliances in
conjunction with magneto-electric machines were soon employed in
lighthouse work. With the advent of large magneto-electric machines the
era of electrotechnics was fairly entered, and this period, which may be
said to terminate about 1867 to 1869, was consummated by the theoretical
work of Clerk Maxwell.

_Maxwell's Researches._--James Clerk Maxwell (1831-1879) entered on his
electrical studies with a desire to ascertain if the ideas of Faraday,
so different from those of Poisson and the French mathematicians, could
be made the foundation of a mathematical method and brought under the
power of analysis.[14] Maxwell started with the conception that all
electric and magnetic phenomena are due to effects taking place in the
dielectric or in the ether if the space be vacuous. The phenomena of
light had compelled physicists to postulate a space-filling medium, to
which the name ether had been given, and Henry and Faraday had long
previously suggested the idea of an electromagnetic medium. The
vibrations of this medium constitute the agency called light. Maxwell
saw that it was unphilosophical to assume a multiplicity of ethers or
media until it had been proved that one would not fulfil all the
requirements. He formulated the conception, therefore, of electric
charge as consisting in a displacement taking place in the dielectric or
electromagnetic medium (see ELECTROSTATICS). Maxwell never committed
himself to a precise definition of the physical nature of electric
displacement, but considered it as defining that which Faraday had
called the polarization in the insulator, or, what is equivalent, the
number of lines of electrostatic force passing normally through a unit
of area in the dielectric. A second fundamental conception of Maxwell
was that the electric displacement whilst it is changing is in effect an
electric current, and creates, therefore, magnetic force. The total
current at any point in a dielectric must be considered as made up of
two parts: first, the true conduction current, if it exists; and second,
the rate of change of dielectric displacement. The fundamental fact
connecting electric currents and magnetic fields is that the line
integral of magnetic force taken once round a conductor conveying an
electric current is equal to 4 [pi]-times the surface integral of the
current density, or to 4 [pi]-times the total current flowing through
the closed line round which the integral is taken (see ELECTROKINETICS).
A second relation connecting magnetic and electric force is based upon
Faraday's fundamental law of induction, that the rate of change of the
total magnetic flux linked with a conductor is a measure of the
electromotive force created in it (see ELECTROKINETICS). Maxwell also
introduced in this connexion the notion of the vector potential.
Coupling together these ideas he was finally enabled to prove that the
propagation of electric and magnetic force takes place through space
with a certain velocity determined by the dielectric constant and the
magnetic permeability of the medium. To take a simple instance, if we
consider an electric current as flowing in a conductor it is, as Oersted
discovered, surrounded by closed lines of magnetic force. If we imagine
the current in the conductor to be instantaneously reversed in
direction, the magnetic force surrounding it would not be instantly
reversed everywhere in direction, but the reversal would be propagated
outwards through space with a certain velocity which Maxwell showed was
inversely as the square root of the product of the magnetic permeability
and the dielectric constant or specific inductive capacity of the
medium.

These great results were announced by him for the first time in a paper
presented in 1864 to the Royal Society of London and printed in the
_Phil. Trans._ for 1865, entitled "A Dynamical Theory of the
Electromagnetic Field." Maxwell showed in this paper that the velocity
of propagation of an electromagnetic impulse through space could also be
determined by certain experimental methods which consisted in measuring
the same electric quantity, capacity, resistance or potential in two
ways. W.E. Weber had already laid the foundations of the absolute system
of electric and magnetic measurement, and proved that a quantity of
electricity could be measured either by the force it exercises upon
another static or stationary quantity of electricity, or magnetically by
the force this quantity of electricity exercises upon a magnetic pole
when flowing through a neighbouring conductor. The two systems of
measurement were called respectively the electrostatic and the
electromagnetic systems (see UNITS, PHYSICAL). Maxwell suggested new
methods for the determination of this ratio of the electrostatic to the
electromagnetic units, and by experiments of great ingenuity was able to
show that this ratio, which is also that of the velocity of the
propagation of an electromagnetic impulse through space, is identical
with that of light. This great fact once ascertained, it became clear
that the notion that electric phenomena are affections of the
luminiferous ether was no longer a mere speculation but a scientific
theory capable of verification. An immediate deduction from Maxwell's
theory was that in transparent dielectrics, the dielectric constant or
specific inductive capacity should be numerically equal to the square of
the refractive index for very long electric waves. At the time when
Maxwell developed his theory the dielectric constants of only a few
transparent insulators were known and these were for the most part
measured with steady or unidirectional electromotive force. The only
refractive indices which had been measured were the optical refractive
indices of a number of transparent substances. Maxwell made a comparison
between the optical refractive index and the dielectric constant of
paraffin wax, and the approximation between the numerical values of the
square of the first and that of the last was sufficient to show that
there was a basis for further work. Maxwell's electric and magnetic
ideas were gathered together in a great mathematical treatise on
electricity and magnetism which was published in 1873.[15] This book
stimulated in a most remarkable degree theoretical and practical
research into the phenomena of electricity and magnetism. Experimental
methods were devised for the further exact measurements of the
electromagnetic velocity and numerous determinations of the dielectric
constants of various solids, liquids and gases, and comparisons of these
with the corresponding optical refractive indices were conducted. This
early work indicated that whilst there were a number of cases in which
the square of optical refractive index for long waves and the
dielectric constant of the same substance were sufficiently close to
afford an apparent confirmation of Maxwell's theory, yet in other cases
there were considerable divergencies. L. Boltzmann (1844-1907) made a
large number of determinations for solids and for gases, and the
dielectric constants of many solid and liquid substances were determined
by N.N. Schiller (b. 1848), P.A. Silow (b. 1850), J. Hopkinson and
others. The accumulating determinations of the numerical value of the
electromagnetic velocity (v) from the earliest made by Lord Kelvin (Sir
W. Thomson) with the aid of King and M^cKichan, or those of Clerk
Maxwell, W.E. Ayrton and J. Perry, to more recent ones by J.J. Thomson,
F. Himstedt, H.A. Rowland, E.B. Rosa, J.S.H. Pellat and H.A. Abraham,
showed it to be very close to the best determinations of the velocity of
light (see UNITS, PHYSICAL). On the other hand, the divergence in some
cases between the square of the optical refractive index and the
dielectric constant was very marked. Hence although Maxwell's theory of
electrical action when first propounded found many adherents in Great
Britain, it did not so much dominate opinion on the continent of Europe.

FOURTH PERIOD.--With the publication of Clerk Maxwell's treatise in
1873, we enter fully upon the fourth and modern period of electrical
research. On the technical side the invention of a new form of armature
for dynamo electric machines by Z.T. Gramme (1826-1901) inaugurated a
departure from which we may date modern electrical engineering. It will
be convenient to deal with technical development first.

_Technical Development._--As far back as 1841 large magneto-electric
machines driven by steam power had been constructed, and in 1856 F.H.
Holmes had made a magneto machine with multiple permanent magnets which
was installed in 1862 in Dungeness lighthouse. Further progress was made
in 1867 when H. Wilde introduced the use of electromagnets for the field
magnets. In 1860 Dr Antonio Pacinotti invented what is now called the
toothed ring winding for armatures and described it in an Italian
journal, but it attracted little notice until reinvented in 1870 by
Gramme. In this new form of bobbin, the armature consisted of a ring of
iron wire wound over with an endless coil of wire and connected to a
commutator consisting of copper bars insulated from one another. Gramme
dynamos were then soon made on the self-exciting principle. In 1873 at
Vienna the fact was discovered that a dynamo machine of the Gramme type
could also act as an electric motor and was set in rotation when a
current was passed into it from another similar machine. Henceforth the
electric transmission of power came within the possibilities of
engineering.

_Electric Lighting._--In 1876, Paul Jablochkov (1847-1894), a Russian
officer, passing through Paris, invented his famous electric candle,
consisting of two rods of carbon placed side by side and separated from
one another by an insulating material. This invention in conjunction
with an alternating current dynamo provided a new and simple form of
electric arc lighting. Two years afterwards C.F. Brush, in the United
States, produced another efficient form of dynamo and electric arc lamp
suitable for working in series (see LIGHTING: _Electric_), and these
inventions of Brush and Jablochkov inaugurated commercial arc lighting.
The so-called subdivision of electric light by incandescent lighting
lamps then engaged attention. E.A. King in 1845 and W.E. Staite in 1848
had made incandescent electric lamps of an elementary form, and T.A.
Edison in 1878 again attacked the problem of producing light by the
incandescence of platinum. It had by that time become clear that the
most suitable material for an incandescent lamp was carbon contained in
a good vacuum, and St G. Lane Fox and Sir J.W. Swan in England, and T.A.
Edison in the United States, were engaged in struggling with the
difficulties of producing a suitable carbon incandescence electric lamp.
Edison constructed in 1879 a successful lamp of this type consisting of
a vessel wholly of glass containing a carbon filament made by
carbonizing paper or some other carbonizable material, the vessel being
exhausted and the current led into the filament through platinum wires.
In 1879 and 1880, Edison in the United States, and Swan in conjunction
with C.H. Stearn in England, succeeded in completely solving the
practical problems. From and after that date incandescent electric
lighting became commercially possible, and was brought to public notice
chiefly by an electrical exhibition held at the Crystal Palace, near
London, in 1882. Edison, moreover, as well as Lane-Fox, had realized the
idea of a public electric supply station, and the former proceeded to
establish in Pearl Street, New York, in 1881, the first public electric
supply station. A similar station in England was opened in the basement
of a house in Holborn Viaduct, London, in March 1882. Edison, with
copious ingenuity, devised electric meters, electric mains, lamp
fittings and generators complete for the purpose. In 1881 C.A. Faure
made an important improvement in the lead secondary battery which G.
Planté (1834-1889) had invented in 1859, and storage batteries then
began to be developed as commercial appliances by Faure, Swan, J.S.
Sellon and many others (see ACCUMULATOR). In 1882, numerous electric
lighting companies were formed for the conduct of public and private
lighting, but an electric lighting act passed in that year greatly
hindered commercial progress in Great Britain. Nevertheless the delay
was utilized in the completion of inventions necessary for the safe and
economical distribution of electric current for the purpose of electric
lighting.

_Telephone._--Going back a few years we find the technical applications
of electrical invention had developed themselves in other directions.
Alexander Graham Bell in 1876 invented the speaking telephone (q.v.),
and Edison and Elisha Gray in the United States followed almost
immediately with other telephonic inventions for electrically
transmitting speech. About the same time D.E. Hughes in England invented
the microphone. In 1879 telephone exchanges began to be developed in the
United States, Great Britain and other countries.

_Electric Power._--Following on the discovery in 1873 of the reversible
action of the dynamo and its use as a motor, efforts began to be made to
apply this knowledge to transmission of power, and S.D. Field, T.A.
Edison, Leo Daft, E.M. Bentley and W.H. Knight, F.J. Sprague, C.J. Van
Depoele and others between 1880 and 1884 were the pioneers of electric
traction. One of the earliest electric tram cars was exhibited by E.W.
and W. Siemens in Paris in 1881. In 1883 Lucien Gaulard, following a
line of thought opened by Jablochkov, proposed to employ high pressure
alternating currents for electric distributions over wide areas by means
of transformers. His ideas were improved by Carl Zipernowsky and O.T.
Bláthy in Hungary and by S.Z. de Ferranti in England, and the
alternating current transformer (see TRANSFORMERS) came into existence.
Polyphase alternators were first exhibited at the Frankfort electrical
exhibition in 1891, developed as a consequence of scientific researches
by Galileo Ferraris (1847-1897), Nikola Tesla, M.O. von
Dolivo-Dobrowolsky and C.E.L. Brown, and long distance transmission of
electrical power by polyphase electrical currents (see POWER
TRANSMISSION: _Electric_) was exhibited in operation at Frankfort in
1891. Meanwhile the early continuous current dynamos devised by Gramme,
Siemens and others had been vastly improved in scientific principle and
practical construction by the labours of Siemens, J. Hopkinson, R.E.B.
Crompton, Elihu Thomson, Rudolf Eickemeyer, Thomas Parker and others,
and the theory of the action of the dynamo had been closely studied by
J. and E. Hopkinson, G. Kapp, S.P. Thompson, C.P. Steinmetz and J.
Swinburne, and great improvements made in the alternating current dynamo
by W.M. Mordey, S.Z. de Ferranti and Messrs Ganz of Budapest. Thus in
twenty years from the invention of the Gramme dynamo, electrical
engineering had developed from small beginnings into a vast industry.
The amendment, in 1888, of the Electric Lighting Act of 1882, before
long caused a huge development of public electric lighting in Great
Britain. By the end of the 19th century every large city in Europe and
in North and South America was provided with a public electric supply
for the purposes of electric lighting. The various improvements in
electric illuminants, such as the Nernst oxide lamp, the tantalum and
osmium incandescent lamps, and improved forms of arc lamp, enclosed,
inverted and flame arcs, are described under LIGHTING: _Electric_.

Between 1890 and 1900, electric traction advanced rapidly in the United
States of America but more slowly in England. In 1902 the success of
deep tube electric railways in Great Britain was assured, and in 1904
main line railways began to abandon, at least experimentally, the steam
locomotive and substitute for it the electric transmission of power.
Long distance electrical transmission had been before that time
exemplified in the great scheme of utilizing the falls of Niagara. The
first projects were discussed in 1891 and 1892 and completed practically
some ten years later. In this scheme large turbines were placed at the
bottom of hydraulic fall tubes 150 ft. deep, the turbines being coupled
by long shafts with 5000 H.P. alternating current dynamos on the
surface. By these electric current was generated and transmitted to
towns and factories around, being sent overhead as far as Buffalo, a
distance of 18 m. At the end of the 19th century electrochemical
industries began to be developed which depended on the possession of
cheap electric energy. The production of aluminium in Switzerland and
Scotland, carborundum and calcium carbide in the United States, and soda
by the Castner-Kellner process, began to be conducted on an immense
scale. The early work of Sir W. Siemens on the electric furnace was
continued and greatly extended by Henri Moissan and others on its
scientific side, and electrochemistry took its place as one of the most
promising departments of technical research and invention. It was
stimulated and assisted by improvements in the construction of large
dynamos and increased knowledge concerning the control of powerful
electric currents.

In the early part of the 20th century the distribution in bulk of
electric energy for power purposes in Great Britain began to assume
important proportions. It was seen to be uneconomical for each city and
town to manufacture its own supply since, owing to the intermittent
nature of the demand for current for lighting, the price had to be kept
up to 4d. and 6d. per unit. It was found that by the manufacture in
bulk, even by steam engines, at primary centres the cost could be
considerably reduced, and in numerous districts in England large power
stations began to be erected between 1903 and 1905 for the supply of
current for power purposes. This involved almost a revolution in the
nature of the tools used, and in the methods of working, and may
ultimately even greatly affect the factory system and the concentration
of population in large towns which was brought about in the early part
of the 19th century by the invention of the steam engine.


_Development of Electric Theory._

Turning now to the theory of electricity, we may note the equally
remarkable progress made in 300 years in scientific insight into the
nature of the agency which has so recast the face of human society.
There is no need to dwell upon the early crude theories of the action of
amber and lodestone. In a true scientific sense no hypothesis was
possible, because few facts had been accumulated. The discoveries of
Stephen Gray and C.F. de C. du Fay on the conductivity of some bodies
for the electric agency and the dual character of electrification gave
rise to the first notions of electricity as an imponderable fluid, or
non-gravitative subtile matter, of a more refined and penetrating kind
than ordinary liquids and gases. Its duplex character, and the fact that
the electricity produced by rubbing glass and vitreous substances was
different from that produced by rubbing sealing-wax and resinous
substances, seemed to necessitate the assumption of two kinds of
electric fluid; hence there arose the conception of _positive_ and
_negative_ electricity, and the two-fluid theory came into existence.

_Single-fluid Theory._--The study of the phenomena of the Leyden jar and
of the fact that the inside and outside coatings possessed opposite
electricities, so that in charging the jar as much positive electricity
is added to one side as negative to the other, led Franklin about 1750
to suggest a modification called the single fluid theory, in which the
two states of electrification were regarded as not the results of two
entirely different fluids but of the addition or subtraction of one
electric fluid from matter, so that positive electrification was to be
looked upon as the result of increase or addition of something to
ordinary matter and negative as a subtraction. The positive and negative
electrifications of the two coatings of the Leyden jar were therefore to
be regarded as the result of a transformation of something called
electricity from one coating to the other, by which process a certain
measurable quantity became so much less on one side by the same amount
by which it became more on the other. A modification of this single
fluid theory was put forward by F.U.T. Aepinus which was explained and
illustrated in his _Tentamen theoriae electricitatis et magnetismi_,
published in St Petersburg in 1759. This theory was founded on the
following principles:--(1) the particles of the electric fluid repel
each other with a force decreasing as the distance increases; (2) the
particles of the electric fluid attract the atoms of all bodies and are
attracted by them with a force obeying the same law; (3) the electric
fluid exists in the pores of all bodies, and while it moves without any
obstruction in conductors such as metals, water, &c., it moves with
extreme difficulty in so-called non-conductors such as glass, resin,
&c.; (4) electrical phenomena are produced either by the transference of
the electric fluid of a body containing more to one containing less, or
from its attraction and repulsion when no transference takes place.
Electric attractions and repulsions were, however, regarded as
differential actions in which the mutual repulsion of the particles of
electricity operated, so to speak, in antagonism to the mutual
attraction of particles of matter for one another and of particles of
electricity for matter. Independently of Aepinus, Henry Cavendish put
forward a single-fluid theory of electricity (_Phil. Trans._, 1771, 61,
p. 584), in which he considered it in more precise detail.

_Two-fluid Theory._--In the elucidation of electrical phenomena,
however, towards the end of the 18th century, a modification of the
two-fluid theory seems to have been generally preferred. The notion then
formed of the nature of electrification was something as follows:--All
bodies were assumed to contain a certain quantity of a so-called neutral
fluid made up of equal quantities of positive and negative electricity,
which when in this state of combination neutralized one another's
properties. The neutral fluid could, however, be divided up or separated
into its two constituents, and these could be accumulated on separate
conductors or non-conductors. This view followed from the discovery of
the facts of electric induction of J. Canton (1753, 1754). When, for
instance, a positively electrified body was found to induce upon another
insulated conductor a charge of negative electricity on the side nearest
to it, and a charge of positive electricity on the side farthest from
it, this was explained by saying that the particles of each of the two
electric fluids repelled one another but attracted those of the positive
fluid. Hence the operation of the positive charge upon the neutral fluid
was to draw towards the positive the negative constituent of the neutral
charge and repel to the distant parts of the conductor the positive
constituent.

C.A. Coulomb experimentally proved that the law of attraction and
repulsion of simple electrified bodies was that the force between them
varied inversely as the square of the distance and thus gave
mathematical definiteness to the two-fluid hypothesis. It was then
assumed that each of the two constituents of the neutral fluid had an
atomic structure and that the so-called particles of one of the electric
fluids, say positive, repelled similar particles with a force varying
inversely as a square of the distance and attracted those of the
opposite fluid according to the same law. This fact and hypothesis
brought electrical phenomena within the domain of mathematical analysis
and, as already mentioned, Laplace, Biot, Poisson, G.A.A. Plana
(1781-1846), and later Robert Murphy (1806-1843), made them the subject
of their investigations on the mode in which electricity distributes
itself on conductors when in equilibrium.

_Faraday's Views._--The two-fluid theory may be said to have held the
field until the time when Faraday began his researches on electricity.
After he had educated himself by the study of the phenomena of lines of
magnetic force in his discoveries on electromagnetic induction, he
applied the same conception to electrostatic phenomena, and thus created
the notion of lines of electrostatic force and of the important function
of the dielectric or non-conductor in sustaining them. Faraday's notion
as to the nature of electrification, therefore, about the middle of the
19th century came to be something as follows:--He considered that the
so-called charge of electricity on a conductor was in reality nothing on
the conductor or in the conductor itself, but consisted in a state of
strain or polarization, or a physical change of some kind in the
particles of the dielectric surrounding the conductor, and that it was
this physical state in the dielectric which constituted electrification.
Since Faraday was well aware that even a good vacuum can act as a
dielectric, he recognized that the state he called dielectric
polarization could not be wholly dependent upon the presence of
gravitative matter, but that there must be an electromagnetic medium of
a supermaterial nature. In the 13th series of his _Experimental
Researches on Electricity_ he discussed the relation of a vacuum to
electricity. Furthermore his electrochemical investigations, and
particularly his discovery of the important law of electrolysis, that
the movement of a certain quantity of electricity through an electrolyte
is always accompanied by the transfer of a certain definite quantity of
matter from one electrode to another and the liberation at these
electrodes of an equivalent weight of the ions, gave foundation for the
idea of a definite atomic charge of electricity. In fact, long
previously to Faraday's electrochemical researches, Sir H. Davy and J.J.
Berzelius early in the 19th century had advanced the hypothesis that
chemical combination was due to electric attractions between the
electric charges carried by chemical atoms. The notion, however, that
electricity is atomic in structure was definitely put forward by Hermann
von Helmholtz in a well-known Faraday lecture. Helmholtz says: "If we
accept the hypothesis that elementary substances are composed of atoms,
we cannot well avoid concluding that electricity also is divided into
elementary portions which behave like atoms of electricity."[16] Clerk
Maxwell had already used in 1873 the phrase, "a molecule of
electricity."[17] Towards the end of the third quarter of the 19th
century it therefore became clear that electricity, whatever be its
nature, was associated with atoms of matter in the form of exact
multiples of an indivisible minimum electric charge which may be
considered to be "Nature's unit of electricity." This ultimate unit of
electric quantity Professor Johnstone Stoney called an _electron_.[18]
The formulation of electrical theory as far as regards operations in
space free from matter was immensely assisted by Maxwell's mathematical
theory. Oliver Heaviside after 1880 rendered much assistance by reducing
Maxwell's mathematical analysis to more compact form and by introducing
greater precision into terminology (see his _Electrical Papers_, 1892).
This is perhaps the place to refer also to the great services of Lord
Rayleigh to electrical science. Succeeding Maxwell as Cavendish
professor of physics at Cambridge in 1880, he soon devoted himself
especially to the exact redetermination of the practical electrical
units in absolute measure. He followed up the early work of the British
Association Committee on electrical units by a fresh determination of
the ohm in absolute measure, and in conjunction with other work on the
electrochemical equivalent of silver and the absolute electromotive
force of the Clark cell may be said to have placed exact electrical
measurement on a new basis. He also made great additions to the theory
of alternating electric currents, and provided fresh appliances for
other electrical measurements (see his _Collected Scientific Papers_,
Cambridge, 1900).

_Electro-optics._--For a long time Faraday's observation on the rotation
of the plane of polarized light by heavy glass in a magnetic field
remained an isolated fact in electro-optics. Then M.E. Verdet
(1824-1860) made a study of the subject and discovered that a solution
of ferric perchloride in methyl alcohol rotated the plane of
polarization in an opposite direction to heavy glass (_Ann. Chim.
Phys._, 1854, 41, p. 370; 1855, 43, p. 37; _Com. Rend._, 1854, 39, p.
548). Later A.A.E.E. Kundt prepared metallic films of iron, nickel and
cobalt, and obtained powerful negative optical rotation with them
(_Wied. Ann._, 1884, 23, p. 228; 1886, 27, p. 191). John Kerr
(1824-1907) discovered that a similar effect was produced when plane
polarized light was reflected from the pole of a powerful magnet (_Phil.
Mag._, 1877, [5], 3, p. 321, and 1878, 5, p. 161). Lord Kelvin showed
that Faraday's discovery demonstrated that some form of rotation was
taking place along lines of magnetic force when passing through a
medium.[19] Many observers have given attention to the exact
determination of Verdet's constant of rotation for standard substances,
e.g. Lord Rayleigh for carbon bisulphide,[20] and Sir W.H. Perkin for an
immense range of inorganic and organic bodies.[21] Kerr also discovered
that when certain homogeneous dielectrics were submitted to electric
strain, they became birefringent (_Phil. Mag._, 1875, 50, pp. 337 and
446). The theory of electro-optics received great attention from Kelvin,
Maxwell, Rayleigh, G.F. Fitzgerald, A. Righi and P.K.L. Drude, and
experimental contributions from innumerable workers, such as F.T.
Trouton, O.J. Lodge and J.L. Howard, and many others.

_Electric Waves._--In the decade 1880-1890, the most important advance
in electrical physics was, however, that which originated with the
astonishing researches of Heinrich Rudolf Hertz (1857-1894). This
illustrious investigator was stimulated, by a certain problem brought to
his notice by H. von Helmholtz, to undertake investigations which had
for their object a demonstration of the truth of Maxwell's principle
that a variation in electric displacement was in fact an electric
current and had magnetic effects. It is impossible to describe here the
details of these elaborate experiments; the reader must be referred to
Hertz's own papers, or the English translation of them by Prof. D.E.
Jones. Hertz's great discovery was an experimental realization of a
suggestion made by G.F. Fitzgerald (1851-1901) in 1883 as to a method of
producing electric waves in space. He invented for this purpose a
radiator consisting of two metal rods placed in one line, their inner
ends being provided with poles nearly touching and their outer ends with
metal plates. Such an arrangement constitutes in effect a condenser, and
when the two plates respectively are connected to the secondary
terminals of an induction coil in operation, the plates are rapidly and
alternately charged, and discharged across the spark gap with electrical
oscillations (see ELECTROKINETICS). Hertz then devised a wave detecting
apparatus called a resonator. This in its simplest form consisted of a
ring of wire nearly closed terminating in spark balls very close
together, adjustable as to distance by a micrometer screw. He found that
when the resonator was placed in certain positions with regard to the
oscillator, small sparks were seen between the micrometer balls, and
when the oscillator was placed at one end of a room having a sheet of
zinc fixed against the wall at the other end, symmetrical positions
could be found in the room at which, when the resonator was there
placed, either no sparks or else very bright sparks occurred at the
poles. These effects, as Hertz showed, indicated the establishment of
stationary electric waves in space and the propagation of electric and
magnetic force through space with a finite velocity. The other
additional phenomena he observed finally contributed an all but
conclusive proof of the truth of Maxwell's views. By profoundly
ingenious methods Hertz showed that these invisible electric waves could
be reflected and refracted like waves of light by mirrors and prisms,
and that familiar experiments in optics could be repeated with electric
waves which could not affect the eye. Hence there arose a new science of
electro-optics, and in all parts of Europe and the United States
innumerable investigators took possession of the novel field of research
with the greatest delight. O.J. Lodge,[22] A. Righi,[23] J.H.
Poincaré,[24] V.F.K. Bjerknes, P.K.L. Drude, J.J. Thomson,[25] John
Trowbridge, Max Abraham, and many others, contributed to its
elucidation.

In 1892, E. Branly of Paris devised an appliance for detecting these
waves which subsequently proved to be of immense importance. He
discovered that they had the power of affecting the electric
conductivity of materials when in a state of powder, the majority of
metallic filings increasing in conductivity. Lodge devised a similar
arrangement called a coherer, and E. Rutherford invented a magnetic
detector depending on the power of electric oscillations to demagnetize
iron or steel. The sum total of all these contributions to electrical
knowledge had the effect of establishing Maxwell's principles on a firm
basis, but they also led to technical inventions of the very greatest
utility. In 1896 G. Marconi applied a modified and improved form of
Branly's wave detector in conjunction with a novel form of radiator for
the telegraphic transmission of intelligence through space without
wires, and he and others developed this new form of telegraphy with the
greatest rapidity and success into a startling and most useful means of
communicating through space electrically without connecting wires.

_Electrolysis._--The study of the transfer of electricity through
liquids had meanwhile received much attention. The general facts and
laws of electrolysis (q.v.) were determined experimentally by Davy and
Faraday and confirmed by the researches of J.F. Daniell, R.W. Bunsen and
Helmholtz. The modern theory of electrolysis grew up under the hands of
R.J.E. Clausius, A.W. Williamson and F.W.G. Kohlrausch, and received a
great impetus from the work of Svante Arrhenius, J.H. Van't Hoff, W.
Ostwald, H.W. Nernst and many others. The theory of the ionization of
salts in solution has raised much discussion amongst chemists, but the
general fact is certain that electricity only moves through liquids in
association with matter, and simultaneously involves chemical
dissociation of molecular groups.

_Discharge through Gases._--Many eminent physicists had an instinctive
feeling that the study of the passage of electricity through gases would
shed much light on the intrinsic nature of electricity. Faraday devoted
to a careful examination of the phenomena the XIII^th series of his
_Experimental Researches_, and among the older workers in this field
must be particularly mentioned J. Plücker, J.W. Hittorf, A.A. de la
Rive, J.P. Gassiot, C.F. Varley, and W. Spottiswoode and J. Fletcher
Moulton. It has long been known that air and other gases at the pressure
of the atmosphere were very perfect insulators, but that when they were
rarefied and contained in glass tubes with platinum electrodes sealed
through the glass, electricity could be passed through them under
sufficient electromotive force and produced a luminous appearance known
as the electric glow discharge. The so-called vacuum tubes constructed
by H. Geissler (1815-1879) containing air, carbonic acid, hydrogen, &c.,
under a pressure of one or two millimetres, exhibit beautiful
appearances when traversed by the high tension current produced by the
secondary circuit of an induction coil. Faraday discovered the existence
of a dark space round the negative electrode which is usually known as
the "Faraday dark space." De la Rive added much to our knowledge of the
subject, and J. Plücker and his disciple J.W. Hittorf examined the
phenomena exhibited in so-called high vacua, that is, in exceedingly
rarefied gases. C.F. Varley discovered the interesting fact that no
current could be sent through the rarefied gas unless a certain minimum
potential difference of the electrodes was excited. Sir William Crookes
took up in 1872 the study of electric discharge through high vacua,
having been led to it by his researches on the radiometer. The
particular details of the phenomena observed will be found described in
the article CONDUCTION, ELECTRIC (§ III.). The main fact discovered by
researches of Plücker, Hittorf and Crookes was that in a vacuum tube
containing extremely rarefied air or other gas, a luminous discharge
takes place from the negative electrode which proceeds in lines normal
to the surface of the negative electrode and renders phosphorescent both
the glass envelope and other objects placed in the vacuum tube when it
falls upon them. Hittorf made in 1869 the discovery that solid objects
could cast shadows or intercept this cathode discharge. The cathode
discharge henceforth engaged the attention of many physicists. Varley
had advanced tentatively the hypothesis that it consisted in an actual
projection of electrified matter from the cathode, and Crookes was led
by his researches in 1870, 1871 and 1872 to embrace and confirm this
hypothesis in a modified form and announce the existence of a fourth
state of matter, which he called radiant matter, demonstrating by many
beautiful and convincing experiments that there was an actual projection
of material substance of some kind possessing inertia from the surface
of the cathode. German physicists such as E. Goldstein were inclined to
take another view. Sir J.J. Thomson, the successor of Maxwell and Lord
Rayleigh in the Cavendish chair of physics in the university of
Cambridge, began about the year 1899 a remarkable series of
investigations on the cathode discharge, which finally enabled him to
make a measurement of the ratio of the electric charge to the mass of
the particles of matter projected from the cathode, and to show that
this electric charge was identical with the atomic electric charge
carried by a hydrogen ion in the act of electrolysis, but that the mass
of the cathode particles, or "corpuscles" as he called them, was far
less, viz. about 1/2000th part of the mass of a hydrogen atom.[26] The
subject was pursued by Thomson and the Cambridge physicists with great
mathematical and experimental ability, and finally the conclusion was
reached that in a high vacuum tube the electric charge is carried by
particles which have a mass only a fraction, as above mentioned, of that
of the hydrogen atom, but which carry a charge equal to the unit
electric charge of the hydrogen ion as found by electrochemical
researches.[27] P.E.A. Lenard made in 1894 (_Wied. Ann. Phys._, 51, p.
225) the discovery that these cathode particles or corpuscles could pass
through a window of thin sheet aluminium placed in the wall of the
vacuum tube and give rise to a class of radiation called the Lenard
rays. W.C. Röntgen of Munich made in 1896 his remarkable discovery of
the so-called X or Röntgen rays, a class of radiation produced by the
impact of the cathode particles against an impervious metallic screen or
anticathode placed in the vacuum tube. The study of Röntgen rays was
ardently pursued by the principal physicists in Europe during the years
1897 and 1898 and subsequently. The principal property of these Röntgen
rays which attracted public attention was their power of passing through
many solid bodies and affecting a photographic plate. Hence some
substances were opaque to them and others transparent. The astonishing
feat of photographing the bones of the living animal within the tissues
soon rendered the Röntgen rays indispensable in surgery and directed an
army of investigators to their study.

_Radioactivity._--One outcome of all this was the discovery by H.
Becquerel in 1896 that minerals containing uranium, and particularly the
mineral known as pitchblende, had the power of affecting sensitive
photographic plates enclosed in a black paper envelope when the mineral
was placed on the outside, as well as of discharging a charged
electroscope (_Com. Rend._, 1896, 122, p. 420). This research opened a
way of approach to the phenomena of radioactivity, and the history of
the steps by which P. Curie and Madame Curie were finally led to the
discovery of radium is one of the most fascinating chapters in the
history of science. The study of radium and radioactivity (see
RADIOACTIVITY) led before long to the further remarkable knowledge that
these so-called radioactive materials project into surrounding space
particles or corpuscles, some of which are identical with those
projected from the cathode in a high vacuum tube, together with others
of a different nature. The study of radioactivity was pursued with great
ability not only by the Curies and A. Debierne, who associated himself
with them, in France, but by E. Rutherford and F. Soddy in Canada, and
by J.J. Thomson, Sir William Crookes, Sir William Ramsay and others in
England.

_Electronic Theory._--The final outcome of these investigations was the
hypothesis that Thomson's corpuscles or particles composing the cathode
discharge in a high vacuum tube must be looked upon as the ultimate
constituent of what we call negative electricity; in other words, they
are atoms of negative electricity, possessing, however, inertia, and
these negative electrons are components at any rate of the chemical
atom. Each electron is a point-charge of negative electricity equal to
3.9×10^{-10} of an electrostatic unit or to 1.3×10^{-20} of an
electromagnetic unit, and the ratio of its charge to its mass is nearly
2×10^7 using E.M. units. For the hydrogen atom the ratio of charge to
mass as deduced from electrolysis is about 10^4. Hence the mass of an
electron is 1/2000th of that of a hydrogen atom. No one has yet been
able to isolate positive electrons, or to give a complete demonstration
that the whole inertia of matter is only electric inertia due to what
may be called the inductance of the electrons. Prof. Sir J. Larmor
developed in a series of very able papers (_Phil. Trans._, 1894, 185;
1895, 186; 1897, 190), and subsequently in his book _Aether and Matter_
(1900), a remarkable hypothesis of the structure of the electron or
corpuscle, which he regards as simply a strain centre in the aether or
electromagnetic medium, a chemical atom being a collection of positive
and negative electrons or strain centres in stable orbital motion round
their common centre of mass (see AETHER). J.J. Thomson also developed
this hypothesis in a profoundly interesting manner, and we may therefore
summarize very briefly the views held on the nature of electricity and
matter at the beginning of the 20th century by saying that the term
electricity had come to be regarded, in part at least, as a collective
name for electrons, which in turn must be considered as constituents of
the chemical atom, furthermore as centres of certain lines of
self-locked and permanent strain existing in the universal aether or
electromagnetic medium. Atoms of matter are composed of congeries of
electrons and the inertia of matter is probably therefore only the
inertia of the electromagnetic medium.[28] Electric waves are produced
wherever electrons are accelerated or retarded, that is, whenever the
velocity of an electron is changed or accelerated positively or
negatively. In every solid body there is a continual atomic
dissociation, the result of which is that mixed up with the atoms of
chemical matter composing them we have a greater or less percentage of
free electrons. The operation called an electric current consists in a
diffusion or movement of these electrons through matter, and this is
controlled by laws of diffusion which are similar to those of the
diffusion of liquids or gases. Electromotive force is due to a
difference in the density of the electronic population in different or
identical conducting bodies, and whilst the electrons can move freely
through so-called conductors their motion is much more hindered or
restricted in non-conductors. Electric charge consists, therefore, in an
excess or deficit of negative electrons in a body. In the hands of H.A.
Lorentz, P.K.L. Drude, J. J, Thomson, J. Larmor and many others, the
electronic hypothesis of matter and of electricity has been developed in
great detail and may be said to represent the outcome of modern
researches upon electrical phenomena.

The reader may be referred for an admirable summary of the theories of
electricity prior to the advent of the electronic hypothesis to J.J.
Thomson's "Report on Electrical Theories" (_Brit. Assoc. Report_, 1885),
in which he divides electrical theories enunciated during the 19th
century into four classes, and summarizes the opinions and theories of
A.M. Ampère, H.G. Grassman, C.F. Gauss, W.E. Weber, G.F.B. Riemann,
R.J.E. Clausius, F.E. Neumann and H. von Helmholtz.

  BIBLIOGRAPHY.--M. Faraday, _Experimental Researches in Electricity_ (3
  vols., London, 1839, 1844, 1855); A.A. De la Rive, _Treatise on
  Electricity_ (3 vols., London, 1853, 1858); J. Clerk Maxwell, _A
  Treatise on Electricity and Magnetism_ (2 vols., 3rd ed., 1892); id.,
  _Scientific Papers_ (2 vols., edited by Sir W.J. Niven, Cambridge,
  1890); H.M. Noad, _A Manual of Electricity_ (2 vols., London, 1855,
  1857); J.J. Thomson, _Recent Researches in Electricity and Magnetism_
  (Oxford, 1893); id., _Conduction of Electricity through Gases_
  (Cambridge, 1903); id., _Electricity and Matter_ (London, 1904); O.
  Heaviside, _Electromagnetic Theory_ (London, 1893); O.J. Lodge,
  _Modern Views of Electricity_ (London, 1889); E. Mascart and J.
  Joubert, _A Treatise on Electricity and Magnetism_, English trans. by
  E. Atkinson (2 vols., London, 1883); Park Benjamin, _The Intellectual
  Rise in Electricity_ (London, 1895); G.C. Foster and A.W. Porter,
  _Electricity and Magnetism_ (London, 1903); A. Gray, _A Treatise on
  Magnetism and Electricity_ (London, 1898); H.W. Watson and S.H.
  Burbury, _The Mathematical Theory of Electricity and Magnetism_ (2
  vols., 1885); Lord Kelvin (Sir William Thomson), _Mathematical and
  Physical Papers_ (3 vols., Cambridge, 1882); Lord Rayleigh,
  _Scientific Papers_ (4 vols., Cambridge, 1903); A. Winkelmann,
  _Handbuch der Physik_, vols. iii. and iv. (Breslau, 1903 and 1905; a
  mine of wealth for references to original papers on electricity and
  magnetism from the earliest date up to modern times). For particular
  information on the modern Electronic theory the reader may consult W.
  Kaufmann, "The Developments of the Electron Idea." _Physikalische
  Zeitschrift_ (1st of Oct. 1901), or _The Electrician_ (1901), 48, p.
  95; H.A. Lorentz, _The Theory of Electrons_ (1909); E.E. Fournier
  d'Albe, _The Electron Theory_ (London, 1906); H. Abraham and P.
  Langevin, _Ions, Electrons, Corpuscles_ (Paris, 1905); J.A. Fleming,
  "The Electronic Theory of Electricity," _Popular Science Monthly_ (May
  1902); Sir Oliver J. Lodge, _Electrons, or the Nature and Properties
  of Negative Electricity_ (London, 1907).     (J. A. F.)


FOOTNOTES:

  [1] Gilbert's work, _On the Magnet, Magnetic Bodies and the Great
    Magnet, the Earth_, has been translated from the rare folio Latin
    edition of 1600, but otherwise reproduced in its original form by the
    chief members of the Gilbert Club of England, with a series of
    valuable notes by Prof. S.P. Thompson (London, 1900). See also _The
    Electrician_, February 21, 1902.

  [2] See _The Intellectual Rise in Electricity_, ch. x., by Park
    Benjamin (London, 1895).

  [3] See Sir Oliver Lodge, "Lightning, Lightning Conductors and
    Lightning Protectors," _Journ. Inst. Elec. Eng._ (1889), 18, p. 386,
    and the discussion on the subject in the same volume; also the book
    by the same author on _Lightning Conductors and Lightning Guards_
    (London, 1892).

  [4] _The Electrical Researches of the Hon. Henry Cavendish
    1771-1781_, edited from the original manuscripts by J. Clerk Maxwell,
    F.R.S. (Cambridge, 1879).

  [5] In 1878 Clerk Maxwell repeated Cavendish's experiments with
    improved apparatus and the employment of a Kelvin quadrant
    electrometer as a means of detecting the absence of charge on the
    inner conductor after it had been connected to the outer case, and
    was thus able to show that if the law of electric attraction varies
    inversely as the nth power of the distance, then the exponent n must
    have a value of 2±{1/21600}. See Cavendish's _Electrical Researches_,
    p. 419.

  [6] Modern researches have shown that the loss of charge is in fact
    dependent upon the ionization of the air, and that, provided the
    atmospheric moisture is prevented from condensing on the insulating
    supports, water vapour in the air does not _per se_ bestow on it
    conductance for electricity.

  [7] Faraday discussed the chemical theory of the pile and arguments
    in support of it in the 8th and 16th series of his _Experimental
    Researches on Electricity_. De la Rive reviews the subject in his
    large _Treatise on Electricity and Magnetism_, vol. ii. ch. iii. The
    writer made a contribution to the discussion in 1874 in a paper on
    "The Contact Theory of the Galvanic Cell," _Phil. Mag._, 1874, 47, p.
    401. Sir Oliver Lodge reviewed the whole position in a paper in 1885,
    "On the Seat of the Electromotive Force in a Voltaic Cell," _Journ.
    Inst. Elec. Eng._, 1885, 14, p. 186.

  [8] "Mémoire sur la théorie mathématique des phénomènes
    électrodynamiques," _Mémoires de l'institut_, 1820, 6; see also _Ann.
    de Chim._, 1820, 15.

  [9] See M. Faraday, "On some new Electro-Magnetical Motions and on
    the Theory of Magnetism," _Quarterly Journal of Science_, 1822, 12,
    p. 74; or _Experimental Researches on Electricity_, vol. ii. p. 127.

  [10] Amongst the most important of Faraday's quantitative researches
    must be included the ingenious and convincing proofs he provided that
    the production of any quantity of electricity of one sign is always
    accompanied by the production of an equal quantity of electricity of
    the opposite sign. See _Experimental Researches on Electricity_, vol.
    i. § 1177.

  [11] In this connexion the work of George Green (1793-1841) must not
    be forgotten. Green's _Essay on the Application of Mathematical
    Analysis to the Theories of Electricity and Magnetism_, published in
    1828, contains the first exposition of the theory of potential. An
    important theorem contained in it is known as Green's theorem, and is
    of great value.

  [12] See also his _Submarine Telegraphs_ (London, 1898).

  [13] The quantitative study of electrical phenomena has been
    enormously assisted by the establishment of the absolute system of
    electrical measurement due originally to Gauss and Weber. The British
    Association for the advancement of science appointed in 1861 a
    committee on electrical units, which made its first report in 1862
    and has existed ever since. In this work Lord Kelvin took a leading
    part. The popularization of the system was greatly assisted by the
    publication by Prof. J.D. Everett of _The C.G.S. System of Units_
    (London, 1891).

  [14] The first paper in which Maxwell began to translate Faraday's
    conceptions into mathematical language was "On Faraday's Lines of
    Force," read to the Cambridge Philosophical Society on the 10th of
    December 1855 and the 11th of February 1856. See Maxwell's _Collected
    Scientific Papers_, i. 155.

  [15] _A Treatise on Electricity and Magnetism_ (2 vols.), by James
    Clerk Maxwell, sometime professor of experimental physics in the
    university of Cambridge. A second edition was edited by Sir W.D.
    Niven in 1881 and a third by Prof. Sir J.J. Thomson in 1891.

  [16] H. von Helmholtz, "On the Modern Development of Faraday's
    Conception of Electricity," _Journ. Chem. Soc._, 1881, 39, p. 277.

  [17] See Maxwell's _Electricity and Magnetism_, vol. i. p. 350 (2nd
    ed., 1881).

  [18] "On the Physical Units of Nature," _Phil. Mag._, 1881, [5], 11,
    p. 381. Also _Trans. Roy. Soc._ (Dublin, 1891), 4, p. 583.

  [19] See Sir W. Thomson, _Proc. Roy. Soc. Lond._, 1856, 8, p. 152; or
    Maxwell, _Elect. and Mag._, vol. ii. p. 831.

  [20] See Lord Rayleigh, _Proc. Roy. Soc. Lond._, 1884, 37, p. 146;
    Gordon, _Phil. Trans._, 1877, 167, p. 1; H. Becquerel, _Ann. Chim.
    Phys._, 1882, [3], 27, p. 312.

  [21] Perkin's Papers are to be found in the _Journ. Chem. Soc.
    Lond._, 1884, p. 421; 1886, p. 177; 1888, p. 561; 1889, p. 680; 1891,
    p. 981; 1892, p. 800; 1893, p. 75.

  [22] _The Work of Hertz_ (London, 1894).

  [23] _L'Ottica delle oscillazioni elettriche_ (Bologna, 1897).

  [24] _Les Oscillations électriques_ (Paris, 1894).

  [25] _Recent Researches in Electricity and Magnetism_ (Oxford, 1892).

  [26] See J.J. Thomson, _Proc. Roy. Inst. Lond._, 1897, 15, p. 419;
   also _Phil. Mag._, 1899, [5], 48, p. 547.

  [27] Later results show that the mass of a hydrogen atom is not far
    from 1.3 × 10^-24 gramme and that the unit atomic charge or natural
    unit of electricity is 1.3 × 10^-20 of an electromagnetic C.G.S.
    unit. The mass of the electron or corpuscle is 7.0 × 10^-28 gramme
    and its diameter is 3 × 10^-13 centimetre. The diameter of a chemical
    atom is of the order of 10^-7 centimetre.

    See H.A. Lorentz, "The Electron Theory," _Elektrotechnische
    Zeitschrift_, 1905, 26, p. 584; or _Science Abstracts_, 1905, 8, A,
    p. 603.

  [28] See J.J. Thomson, _Electricity and Matter_ (London, 1904).



ELECTRICITY SUPPLY. I. _General Principles._--The improvements made in
the dynamo and electric motor between 1870 and 1880 and also in the
details of the arc and incandescent electric lamp towards the close of
that decade, induced engineers to turn their attention to the question
of the private and public supply of electric current for the purpose of
lighting and power. T.A. Edison[1] and St G. Lane Fox[2] were among the
first to see the possibilities and advantages of public electric supply,
and to devise plans for its practical establishment. If a supply of
electric current has to be furnished to a building the option exists in
many cases of drawing from a public supply or of generating it by a
private plant.

_Private Plants._--In spite of a great amount of ingenuity devoted to
the development of the primary battery and the thermopile, no means of
generation of large currents can compete in economy with the dynamo.
Hence a private electric generating plant involves the erection of a
dynamo which may be driven either by a steam, gas or oil engine, or by
power obtained by means of a turbine from a low or high fall of water.
It may be either directly coupled to the motor, or driven by a belt; and
it may be either a continuous-current machine or an alternator, and if
the latter, either single-phase or polyphase. The convenience of being
able to employ storage batteries in connexion with a private-supply
system is so great that unless power has to be transmitted long
distances, the invariable rule is to employ a continuous-current dynamo.
Where space is valuable this is always coupled direct to the motor; and
if a steam-engine is employed, an enclosed engine is most cleanly and
compact. Where coal or heating gas is available, a gas-engine is
exceedingly convenient, since it requires little attention. Where coal
gas is not available, a Dowson gas-producer can be employed. The
oil-engine has been so improved that it is extensively used in
combination with a direct-coupled or belt-driven dynamo and thus forms a
favourite and easily-managed plant for private electric lighting. Lead
storage cells, however, as at present made, when charged by a
steam-driven dynamo deteriorate less rapidly than when an oil-engine is
employed, the reason being that the charging current is more irregular
in the latter case, since the single cylinder oil-engine only makes an
impulse every other revolution. In connexion with the generator, it is
almost the invariable custom to put down a secondary battery of storage
cells, to enable the supply to be given after the engine has stopped.
This is necessary, not only as a security for the continuity of supply,
but because otherwise the costs of labour in running the engine night
and day become excessive. The storage battery gives its supply
automatically, but the dynamo and engine require incessant skilled
attendance. If the building to be lighted is at some distance from the
engine-house the battery should be placed in the basement of the
building, and underground or overhead conductors, to convey the charging
current, brought to it from the dynamo.

It is usual, in the case of electric lighting installations, to reckon
all lamps in their equivalent number of 8 candle power (c.p.)
incandescent lamps. In lighting a private house or building, the first
thing to be done is to settle the total number of incandescent lamps and
their size, whether 32 c.p., 16 c.p. or 8 c.p. Lamps of 5 c.p. can be
used with advantage in small bedrooms and passages. Each candle-power in
the case of a carbon filament lamp can be taken as equivalent to 3.5
watts, or the 8 c.p. lamp as equal to 30 watts, the 16 c.p. lamp to 60
watts, and so on. In the case of metallic filament lamps about 1.0 or
1.25 watts. Hence if the equivalent of 100 carbon filament 8 c.p. lamps
is required in a building the maximum electric power-supply available
must be 3000 watts or 3 kilowatts. The next matter to consider is the
pressure of supply. If the battery can be in a position near the
building to be lighted, it is best to use 100-volt incandescent lamps
and enclosed arc lamps, which can be worked singly off the 100-volt
circuit. If, however, the lamps are scattered over a wide area, or in
separate buildings somewhat far apart, as in a college or hospital, it
may be better to select 200 volts as the supply pressure. Arc lamps can
then be worked three in series with added resistance. The third step is
to select the size of the dynamo unit and the amount of spare plant. It
is desirable that there should be at least three dynamos, two of which
are capable of taking the whole of the full load, the third being
reserved to replace either of the others when required. The total power
to be absorbed by the lamps and motors (if any) being given, together
with an allowance for extensions, the size of the dynamos can be
settled, and the power of the engines required to drive them determined.
A good rule to follow is that the indicated horse-power (I.H.P.) of the
engine should be double the dynamo full-load output in kilowatts; that
is to say, for a 10-kilowatt dynamo an engine should be capable of
giving 20 indicated (not nominal) H.P. From the I.H.P. of the engine, if
a steam engine, the size of the boiler required for steam production
becomes known. For small plants it is safe to reckon that, including
water waste, boiler capacity should be provided equal to evaporating 40
lb. of water per hour for every I.H.P. of the engine. The locomotive
boiler is a convenient form; but where large amounts of steam are
required, some modification of the Lancashire boiler or the water-tube
boiler is generally adopted. In settling the electromotive force of the
dynamo to be employed, attention must be paid to the question of
charging secondary cells, if these are used. If a secondary battery is
employed in connexion with 100-volt lamps, it is usual to put in 53 or
54 cells. The electromotive force of these cells varies between 2.2 and
1.8 volts as they discharge; hence the above number of cells is
sufficient for maintaining the necessary electromotive force. For
charging, however, it is necessary to provide 2.5 volts per cell, and
the dynamo must therefore have an electromotive force of 135 volts,
_plus_ any voltage required to overcome the fall of potential in the
cable connecting the dynamo with the secondary battery. Supposing this
to be 10 volts, it is safe to install dynamos having an electromotive
force of 150 volts, since by means of resistance in the field circuits
this electromotive force can be lowered to 110 or 115 if it is required
at any time to dispense with the battery. The size of the secondary cell
will be determined by the nature of the supply to be given after the
dynamos have been stopped. It is usual to provide sufficient storage
capacity to run all the lamps for three or four hours without assistance
from the dynamo.

  As an example taken from actual practice, the following figures give
  the capacity of the plant put down to supply 500 8 c.p. lamps in a
  hospital. The dynamos were 15-unit machines, having a full-load
  capacity of 100 amperes at 150 volts, each coupled direct to an engine
  of 25 H.P.; and a double plant of this description was supplied from
  two steel locomotive boilers, each capable of evaporating 800 lb. of
  water per hour. One dynamo during the day was used for charging the
  storage battery of 54 cells; and at night the discharge from the
  cells, together with the current from one of the dynamos, supplied the
  lamps until the heaviest part of the load had been taken; after that
  the current was drawn from the batteries alone. In working such a
  plant it is necessary to have the means of varying the electromotive
  force of the dynamo as the charging of the cells proceeds. When they
  are nearly exhausted, their electromotive force is less than 2 volts;
  but as the charging proceeds, a counter-electromotive force is
  gradually built up, and the engineer-in-charge has to raise the
  voltage of the dynamo in order to maintain a constant charging
  current. This is effected by having the dynamos designed to give
  normally the highest E.M.F. required, and then inserting resistance in
  their field circuits to reduce it as may be necessary. The space and
  attendance required for an oil-engine plant are much less than for a
  steam-engine.

_Public Supply._--The methods at present in successful operation for
public electric supply fall into two broad divisions:--(1)
continuous-current systems and (2) alternating-current systems.
Continuous-current systems are either low- or high-pressure. In the
former the current is generated by dynamos at some pressure less than
500 volts, generally about 460 volts, and is supplied to users at half
this pressure by means of a three-wire system (see below) of
distribution, with or without the addition of storage batteries.


  Low-pressure continuous supply.

The general arrangements of a low-pressure continuous-current town
supply station are as follows:--If steam is the motive power selected,
it is generated under all the best conditions of economy by a battery of
boilers, and supplied to engines which are now almost invariably coupled
direct, each to its own dynamo, on one common bedplate; a multipolar
dynamo is most usually employed, coupled direct to an enclosed engine.
Parsons or Curtis steam turbines (see STEAM-ENGINE) are frequently
selected, since experience has shown that the costs of oil and
attendance are far less for this type than for the reciprocating engine,
whilst the floor space and, therefore, the building cost are greatly
reduced. In choosing the size of unit to be adopted, the engineer has
need of considerable experience and discretion, and also a full
knowledge of the nature of the public demand for electric current. The
rule is to choose as large units as possible, consistent with security,
because they are proportionately more economical than small ones. The
over-all efficiency of a steam dynamo--that is, the ratio between the
electrical power output, reckoned say in kilowatts, and the I.H.P. of
the engine, reckoned in the same units--is a number which falls rapidly
as the load decreases, but at full load may reach some such value as 80
or 85%. It is common to specify the efficiency, as above defined, which
must be attained by the plant at full-load, and also the efficiencies at
quarter- and half-load which must be reached or exceeded. Hence in the
selection of the size of the units the engineer is guided by the
consideration that whatever units are in use shall be as nearly as
possible fully loaded. If the demand on the station is chiefly for
electric lighting, it varies during the hours of the day and night with
tolerable regularity. If the output of the station, either in amperes or
watts, is represented by the ordinates of a curve, the abscissae of
which represent the hours of the day, this load diagram for a supply
station with lighting load only, is a curve such as is shown in fig. 1,
having a high peak somewhere between 6 and 8 P.M. The area enclosed by
this load-diagram compared with the area of the circumscribing rectangle
is called the _load-factor_ of the station. This varies from day to day
during the year, but on the average for a simple lighting load is not
generally above 10 or 12%, and may be lower. Thus the total output from
the station is only some 10% on an average of that which it would be if
the supply were at all times equal to the maximum demand. Roughly
speaking, therefore, the total output of an electric supply station,
furnishing current chiefly for electric lighting, is at best equal to
about two hours' supply during the day at full load. Hence during the
greater part of the twenty-four hours a large part of the plant is lying
idle. It is usual to provide certain small sets of steam dynamos, called
the daylight machines, for supplying the demand during the day and later
part of the evening, the remainder of the machines being called into
requisition only for a short time. Provision must be made for sufficient
reserve of plant, so that the breakdown of one or more sets will not
cripple the output of the station.

[Illustration: FIG. 1.]

[Illustration: FIG. 2.]


  Three-wire system.

Assuming current to be supplied at about 460 volts by different and
separate steam dynamos, Dy1, Dy2 (fig. 2), the machines are connected
through proper amperemeters and voltmeters with _omnibus bars_, O1, O2,
O3, on a main switchboard, so that any dynamo can be put in connexion or
removed. The switchboard is generally divided into three parts--one
panel for the connexions of the positive feeders, F1, with the positive
terminals of the generators; one for the negative feeders, F3, and
negative generator terminals; while from the third (or middle-wire
panel) proceed an equal number of middle-wire feeders, F2. These sets of
conductors are led out into the district to be supplied with current,
and are there connected into a distributing system, consisting of three
separate insulated conductors, D1, D2, D3, respectively called the
positive, middle and negative distributing mains. The lamps in the
houses, H1, H2, &c., are connected between the middle and negative, and
the middle and positive, mains by smaller supply and service wires. As
far as possible the numbers of lamps installed on the two sides of the
system are kept equal; but since it is not possible to control the
consumption of current, it becomes necessary to provide at the station
two small dynamos called the _balancing machines_, B1, B2, connected
respectively between the middle and positive and the middle and negative
omnibus bars. These machines may have their shafts connected together,
or they may be driven by separate steam dynamos; their function is to
supply the difference in the total current circulating through the whole
of the lamps respectively on the two opposite sides of the middle wire.
If storage batteries are employed in the station, it is usual to install
two complete batteries, S1, S2, which are placed in a separate battery
room and connected between the middle omnibus bar and the two outer
omnibus bars. The extra electromotive force required to charge these
batteries is supplied by two small dynamos b1, b2, called _boosters_. It
is not unusual to join together the two balancing dynamos and the two
boosters on one common bedplate, the shafts being coupled and in line,
and to employ the balancing machines as electromotors to drive the
boosters as required. By the use of _reversible boosters_, such as those
made by the Lancashire Dynamo & Motor Company under the patents of
Turnbull & M^cLeod, having four field windings on the booster magnets
(see _The Electrician_, 1904, p. 303), it is possible to adjust the
relative duty of the dynamos and battery so that the load on the supply
dynamos is always constant. Under these conditions the main engines can
be worked all the time at their maximum steam economy and a smaller
engine plant employed. If the load in the station rises above the fixed
amount, the batteries discharge in parallel with the station dynamos; if
it falls below, the batteries are charged and the station dynamos take
the external load.

[Illustration: From _The Electrician_.

FIGS. 3 and 4.--Low-pressure Supply Station.]


  Generating stations.

The general arrangements of a low-pressure supply station are shown in
figs. 3 and 4. It consists of a boiler-house containing a bank of
boilers, either Lancashire or Babcock & Wilcox being generally used (see
BOILER), which furnish steam to the engines and dynamos, provision
being made by duplicate steam-pipes or a ring main so that the failure
of a single engine or dynamo does not cripple the whole supply. The
furnace gases are taken through an economizer (generally Green's) so
that they give up their heat to the cold feed water. If condensing water
is available the engines are worked condensing, and this is an essential
condition of economy when steam turbines are employed. Hence, either a
condensing water pond or a cooling tower has to be provided to cool the
condensing water and enable it to be used over and over again.
Preferably the station should be situated near a river or canal and a
railway siding. The steam dynamos are generally arranged in an
engine-room so as to be overlooked from a switchboard gallery (fig. 3),
from which all the control is carried out. The boiler furnaces are
usually stoked by automatic stokers. Owing to the relatively small load
factor (say 8 or 10%) of a station giving electric supply for lighting
only, the object of every station engineer is to cultivate a demand for
electric current for power during the day-time by encouraging the use of
electric motors for lifts and other purposes, but above all to create a
demand for traction purposes. Hence most urban stations now supply
current not only for electric lighting but for running the town tramway
system, and this traction load being chiefly a daylight load serves to
keep the plant employed and remunerative. It is usual to furnish a
continuous current supply for traction at 500 or 600 volts, although
some station engineers are advocating the use of higher voltages. In
those stations which supply current for traction, but which have a
widely scattered lighting load, _double current_ dynamos are often
employed, furnishing from one and the same armature a continuous current
for traction purposes, and an alternating current for lighting purposes.


  High-pressure continuous supply.

In some places a high voltage system of electric supply by continuous
current is adopted. In this case the current is generated at a pressure
of 1000 or 2000 volts, and transmitted from the generating station by
conductors, called high-pressure feeders, to certain sub-centres or
transformer centres, which are either buildings above ground or cellars
or excavations under the ground. In these transformer centres are placed
machines, called _continuous-current transformers_, which transform the
electric energy and create a secondary electric current at a lower
pressure, perhaps 100 or 150 volts, to be supplied by distributing mains
to users (see TRANSFORMERS). From these sub-centres insulated conductors
are run back to the generating station, by which the engineer can start
or stop the continuous-current rotatory transformers, and at the same
time inform himself as to their proper action and the electromotive
force at the secondary terminals. This system was first put in practice
in Oxford, England, and hence has been sometimes called by British
engineers "the Oxford system." It is now in operation in a number of
places in England, such as Wolverhampton, Walsall, and Shoreditch in
London. It has the advantage that in connexion with the low-pressure
distributing system secondary batteries can be employed, so that a
storage of electric energy is effected. Further, continuous-current arc
lamps can be worked in series off the high-pressure mains, that is to
say, sets of 20 to 40 arc lamps can be operated for the purpose of
street lighting by means of the high-pressure continuous current.


  Alternating supply.

The alternating current systems in operation at the present time are the
_single-phase_ system, with distributing transformers or transformer
sub-centres, and the _polyphase_ systems, in which the alternating
current is transformed down into an alternating current of low pressure,
or, by means of rotatory transformers, into a continuous current. The
general arrangement of a _single-phase_ alternating-current system is as
follows: The generating station contains a number of alternators, A1 A2
(fig. 5), producing single-phase alternating current, either at 1000,
2000, or sometimes, as at Deptford and other places, 10,000 volts. This
current is distributed from the station either at the pressure at which
it is generated, or after being transformed up to a higher pressure by
the transformer T. The alternators are sometimes worked in parallel,
that is to say, all furnish their current to two common omnibus bars on
a high-pressure switchboard, and each is switched into circuit at the
moment when it is brought into step with the other machines, as shown by
some form of _phase-indicator_. In some cases, instead of the
high-pressure feeders starting from omnibus bars, each alternator works
independently and the feeders are grouped together on the various
alternators as required. A number of high-pressure feeders are carried
from the main switchboard to various transformer sub-centres or else run
throughout the district to which current is to be furnished. If the
system laid down is the transformer sub-centre system, then at each of
these sub-centres is placed a battery of alternating-current
transformers, T1 T2 T3, having their primary circuits all joined in
parallel to the terminals of the high-pressure feeders, and their
secondary circuits all joined in parallel on a distributing main,
suitable switches and cut-outs being interposed. The pressure of the
current is then transformed down by these transformers to the required
supply pressure. The secondary circuits of these transformers are
generally provided with three terminals, so as to supply the
low-pressure side on a three-wire system. It is not advisable to connect
together directly the secondary circuits of all the different
sub-centres, because then a fault or short circuit on one secondary
system affects all the others. In banking together transformers in this
manner in a sub-station it is necessary to take care that the
transformation ratio and secondary drop (see TRANSFORMERS) are exactly
the same, otherwise one transformer will take more than its full share
of the load and will become overheated. The transformer sub-station
system can only be adopted where the area of supply is tolerably
compact. Where the consumers lie scattered over a large area, it is
necessary to carry the high-pressure mains throughout the area, and to
place a separate transformer or transformers in each building. From a
financial point of view, this "house-to-house system" of
alternating-current supply, generally speaking, is less satisfactory in
results than the transformer sub-centre system. In the latter some of
the transformers can be switched off, either by hand or by automatic
apparatus, during the time when the load is light, and then no power is
expended in magnetizing their cores. But with the house-to-house system
the whole of the transformers continually remain connected with the
high-pressure circuits; hence in the case of supply stations which have
only an ordinary electric lighting load, and therefore a load-factor not
above 10%, the efficiency of distribution is considerably diminished.

[Illustration: FIG. 5.]

The single-phase alternating-current system is defective in that it
cannot be readily combined with secondary batteries for the storage of
electric energy. Hence in many places preference is now given to the
_polyphase system_. In such a system a polyphase alternating current,
either two- or three-phase, is transmitted from the generating station
at a pressure of 5000 to 10,000 volts, or sometimes higher, and at
various sub-stations is transformed down, first by static transformers
into an alternating current of lower pressure, say 500 volts, and then
by means of rotatory transformers into a continuous current of 500
volts or lower for use for lighting or traction.

In the case of large cities such as London, New York, Chicago, Berlin
and Paris the use of small supply stations situated in the interior of
the city has gradually given way to the establishment of large supply
stations outside the area; in these alternating current is generated on
the single or polyphase system at a high voltage and transmitted by
underground cables to sub-stations in the city, at which it is
transformed down for distribution for private and public electric
lighting and for urban electric traction.

Owing to the high relative cost of electric power when generated in
small amounts and the great advantages of generating it in proximity to
coal mines and waterfalls, the supply of electric power in bulk to small
towns and manufacturing districts has become a great feature in modern
electrical engineering. In Great Britain, where there is little useful
water power but abundance of coal, electric supply stations for supply
in bulk have been built in the coal-producing districts of South Wales,
the Midlands, the Clyde valley and Yorkshire. In these cases the current
is a polyphase current generated at a high voltage, 5000 to 10,000
volts, and sometimes raised again in pressure to 20,000 or 40,000 volts
and transmitted by overhead lines to the districts to be supplied. It is
there reduced in voltage by transformers and employed as an alternating
current, or is used to drive polyphase motors coupled to direct current
generators to reproduce the power in continuous current form. It is then
distributed for local lighting, street or railway traction, driving
motors, and metallurgical or electrochemical applications. Experience
has shown that it is quite feasible to distribute in all directions for
25 miles round a high-pressure generating station, which thus supplies
an area of nearly 2000 sq. m. At such stations, employing large turbine
engines and alternators, electric power may be generated at a works cost
of 0.375d. per kilowatt (K.W.), the coal cost being less than 0.125d.
per K.W., and the selling price to large load-factor users not more than
0.5d. per K.W. The average price of supply from the local generating
stations in towns and cities is from 3d. to 4d. per unit, electric
energy for power and heating being charged at a lower rate than that for
lighting only.


  Conductors.

We have next to consider the structure and the arrangement of the
conductors employed to convey the currents from their place of creation
to that of utilization. The conductors themselves for the most part
consist of copper having a conductivity of not less than 98% according
to Matthiessen's standard. They are distinguished as (1) _External
conductors_, which are a part of the public supply and belong to the
corporation or company supplying the electricity; (2) _Internal
conductors_, or house wiring, forming a part of the structure of the
house or building supplied and usually the property of its owner.


  External conductors.

The external conductors may be overhead or underground. _Overhead_
conductors may consist of bare stranded copper cables carried on
porcelain insulators mounted on stout iron or wooden poles. If the
current is a high-pressure one, these insulators must be carefully
tested, and are preferably of the pattern known as oil insulators. In
and near towns it is necessary to employ insulated overhead conductors,
generally india-rubber-covered stranded copper cables, suspended by
leather loops from steel bearer wires which take the weight. The British
Board of Trade have issued elaborate rules for the construction of
overhead lines to transmit large electric currents. Where telephone and
telegraph wires pass over such overhead electric lighting wires, they
have to be protected from falling on the latter by means of guard wires.

By far the largest part, however, of the external electric distribution
is now carried out by _underground conductors_, which are either bare or
insulated. Bare copper conductors may be carried underground in culverts
or chases, air being in this case the insulating material, as in the
overhead system. A culvert and covered chase is constructed under the
road or side-walk, and properly shaped oak crossbars are placed in it
carrying glass or porcelain insulators, on which stranded copper
cables, or, preferably, copper strips placed edgeways, are stretched and
supported. The advantages of this method of construction are cheapness
and the ease with which connexions can be made with service-lines for
house supply; the disadvantages are the somewhat large space in which
coal-gas leaking out of gas-pipes can accumulate, and the difficulty of
keeping the culverts at all times free from rain-water. Moisture has a
tendency to collect on the negative insulators, and hence to make a dead
earth on the negative side of the main; while unless the culverts are
well ventilated, explosions from mixtures of coal-gas and air are liable
to occur. Insulated cables are insulated either with a material which is
in itself waterproof, or with one which is only waterproof in so far as
it is enclosed in a waterproof tube, e.g. of lead. Gutta-percha and
india-rubber are examples of materials of the former kind. Gutta-percha,
although practically everlasting when in darkness and laid under water,
as in the case of submarine cables, has not been found satisfactory for
use with large systems of electric distribution, although much employed
for telephone and telegraph work. Insulated underground external
conductors are of three types:--(a) _Insulated Cables drawn into
Pipes._--In this system of distribution cast-iron or stoneware pipes, or
special stoneware conduits, or conduits made of a material called
bitumen concrete, are first laid underground in the street. These
contain a number of holes or "ways," and at intervals drawing-in boxes
are placed which consist of a brick or cast-iron box having a
water-tight lid, by means of which access is gained to a certain section
of the conduit. Wires are used to draw in the cables, which are covered
with either india-rubber or lead, the copper being insulated by means of
paper, impregnated jute, or other similar material. The advantages of a
drawing-in system are that spare ways can be left when the conduits are
put in, so that at a future time fresh cables can be added without
breaking up the roadway. (b) _Cables in Bitumen._--One of the earliest
systems of distribution employed by T.A. Edison consisted in fixing two
segment-shaped copper conductors in a steel tube, the interspace between
the conductors and the tube being filled in with a bitumen compound. A
later plan is to lay down an iron trough, in which the cables are
supported by wooden bearers at proper distances, and fill in the whole
with natural bitumen. This system has been carried out extensively by
the Callendar Cable Company. Occasionally concentric lead-covered and
armoured cables are laid in this way, and then form an expensive but
highly efficient form of insulated conductor. In selecting a system of
distribution regard must be paid to the nature of the soil in which the
cables are laid. Lead is easily attacked by soft water, although under
some conditions it is apparently exceedingly durable, and an atmosphere
containing coal-gas is injurious to india-rubber. (c) _Armoured
Cables._--In a very extensively used system of distribution armoured
cables are employed. In this case the copper conductors, two, three or
more in number, may be twisted together or arranged concentrically, and
insulated by means of specially prepared jute or paper insulation,
overlaid with a continuous tube of lead. Over the lead, but separated by
a hemp covering, is put a steel armour consisting of two layers of steel
strip, wound in opposite directions and kept in place by an external
covering. Such a cable can be laid directly in the ground without any
preparation other than the excavation of a simple trench, junction-boxes
being inserted at intervals to allow of branch cables being taken off.
The armoured cable used is generally of the concentric pattern (fig. 6).
It consists of a stranded copper cable composed of a number of wires
twisted together and overlaid with an insulating material. Outside this
a tubular arrangement of copper wires and a second layer of insulation,
and finally a protective covering of lead and steel wires or armour are
placed. In some cases three concentric cylindrical conductors are formed
by twisting wires or copper strips with insulating material between. In
others two or three cables of stranded copper are embedded in insulating
material and included in a lead sheath. This last type of cable is
usually called a _two-_ or _three-core_ pattern cable (fig. 7).

[Illustration: FIG. 6.--Armoured Concentric Cable (Section).

  IC, Inner conductor.
  OC, Outer conductor.
  I, Insulation.
  L, Lead sheath.
  S, Steel armour.
  H, Hemp covering.]

[Illustration: FIG. 7.--Triple Conductor Armoured Cable (Section).

  C, Copper conductor.
  I, Insulation.
  L, Lead sheath.
  H, Hemp covering.
  S, Steel armour.]

The arrangement and nature of the external conductors depends on the
system of electric supply in which they are used. In the case of
continuous-current supply for incandescent electric lighting and motive
power in small units, when the external conductors are laid down on the
three-wire system, each main or branch cable in the street consists of a
set of three conductors called the positive, middle and negative. Of
these triple conductors some run from the supply station to various
points in the area of supply without being tapped, and are called the
_feeders_; others, called the _distributing mains_, are used for making
connexions with the service lines of the consumers, one service line, as
already explained, being connected to the middle conductor, and the
other to either the positive or the negative one. Since the middle
conductor serves to convey only the difference between the currents
being used on the two sides of the system, it is smaller in section than
the positive and negative ones. In laying out the system great judgment
has to be exercised as to the selection of the points of attachment of
the feeders to the distributing mains, the object being to keep a
constant electric pressure or voltage between the two service-lines in
all the houses independently of the varying demand for current. Legally
the suppliers are under regulations to keep the supply voltage constant
within 4% either way above or below the standard pressure. As a matter
of fact very few stations do maintain such good regulation. Hence a
considerable variation in the light given by the incandescent lamps is
observed, since the candle-power of carbon glow lamps varies as the
fifth or sixth power of the voltage of supply, i.e. a variation of only
2% in the supply pressure affects the resulting candle-power of the
lamps to the extent of 10 or 12%. This variation is, however, less in
the case of metallic filament lamps (see LIGHTING: _Electric_). In the
service-lines are inserted the meters for measuring the electric energy
supplied to the customer (see METER, ELECTRIC).


  Interior wiring.

In the interior of houses and buildings the conductors generally consist
of india-rubber-covered cables laid in wood casing. The copper wire must
be tinned and then covered, first with a layer of unvulcanized pure
india-rubber, then with a layer of vulcanized rubber, and lastly with
one or more layers of protective cotton twist or tape. No conductor of
this character employed for interior house-wiring should have a smaller
insulation resistance than 300 megohms per mile when tested with a
pressure of 600 volts after soaking 24 hours in water. The wood casing
should, if placed in damp positions or under plaster, be well varnished
with waterproof varnish. As far as possible all joints in the run of the
cable should be avoided by the use of the so-called looping-in system,
and after the wiring is complete, careful tests for insulation should be
made. The Institution of Electrical Engineers of Great Britain have
drawn up rules to be followed in interior house-wiring, and the
principal Fire Insurance offices, following the lead of the Phoenix Fire
Office, of London, have made regulations which, if followed, are a
safeguard against bad workmanship and resulting possibility of damage by
fire. Where fires having an electric origin have taken place, they have
invariably been traced to some breach of these rules. Opinions differ,
however, as to the value and security of this method of laying interior
conductors in buildings, and two or three alternative systems have been
much employed. In one of these, called the _interior conduit_ system,
highly insulating waterproof and practically fireproof tubes or conduits
replace the wooden casing; these, being either of plain insulating
material, or covered with brass or steel armour, may be placed under
plaster or against walls. They are connected by bends or joint-boxes.
The insulated wires being drawn into them, any short circuit or heating
of the wire cannot give rise to a fire, as it can only take place in the
interior of a non-inflammable tube. A third system of electric light
wiring is the safety concentric system, in which concentric conductors
are used. The inner one, which is well insulated, consists of a
copper-stranded cable. The outer may be a galvanized iron strand, a
copper tape or braid, or a brass tube, and is therefore necessarily
connected with the earth. A fourth system consists in the employment of
twin insulated wires twisted together and sheathed with a lead tube; the
conductor thus formed can be fastened by staples against walls, or laid
under plaster or floors.

The general arrangement for distributing current to the different
portions of a building for the purpose of electric lighting is to run up
one or more rising mains, from which branches are taken off to
distributing boxes on each floor, and from these boxes to carry various
branch circuits to the lamps. At the distributing boxes are collected
the cut-outs and switches controlling the various circuits. When
alternating currents are employed, it is usual to select as a type of
conductor either twin-twisted conductor or concentric; and the
employment of these types of cable, rather than two separate cables, is
essential in any case where there are telephone or telegraph wires in
proximity, for otherwise the alternating current would create inductive
disturbances in the telephone circuit. The house-wiring also comprises
the details of _switches_ for controlling the lamps, _cut-outs_ or fuses
for preventing an excess of current passing, and fixtures or supports
for lamps often of an ornamental character. For the details of these,
special treatises on electric interior wiring must be consulted.

  For further information the reader may be referred to the following
  books:--C.H. Wordingham, _Central Electrical Stations_ (London, 1901);
  A. Gay and C.Y. Yeaman, _Central Station Electricity Supply_ (London,
  1906); S.P. Thompson, _Dynamo Electric Machinery_ (2 vols., London,
  1905); E. Tremlett Carter and T. Davies, _Motive Power and Gearing_
  (London, 1906); W.C. Clinton, _Electric Wiring_ (2nd ed., London,
  1906); W. Perren Maycock, _Electric Wiring, Fitting, Switches and
  Lamps_ (London, 1899); D. Salomons, _Electric Light Installations_
  (London, 1894); Stuart A. Russell, _Electric Light Cables_ (London,
  1901); F.A.C. Perrine, _Conductors for Electrical Distribution_
  (London, 1903); E. Rosenberg, W.W. Haldane Gee and C. Kinzbrunner,
  _Electrical Engineering_ (London, 1903); E.C. Metcalfe, _Practical
  Electric Wiring for Lighting Installations_ (London, 1905); F.C.
  Raphael, _The Wireman's Pocket Book_ (London, 1903).     (J. A. F.)


  History.

II. _Commercial Aspects._--To enable the public supply enterprises
referred to in the foregoing section to be carried out in England,
statutory powers became necessary to break up the streets. In the early
days a few small stations were established for the supply of electricity
within "block" buildings, or by means of overhead wires within
restricted areas, but the limitations proved uneconomical and the
installations were for the most part merged into larger undertakings
sanctioned by parliamentary powers. In the year 1879 the British
government had its attention directed for the first time to electric
lighting as a possible subject for legislation, and the consideration of
the then existing state of electric lighting was referred to a select
committee of the House of Commons. No legislative action, however, was
taken at that time. In fact the invention of the incandescent lamp was
incomplete--Edison's British master-patent was only filed in Great
Britain in November 1879. In 1881 and 1882 electrical exhibitions were
held in Paris and at the Crystal Palace, London, where the improved
electric incandescent lamp was brought before the general public. In
1882 parliament passed the first Electric Lighting Act, and considerable
speculation ensued. The aggregate capital of the companies registered in
1882-1883 to carry out the public supply of electricity in the United
Kingdom amounted to £15,000,000, but the onerous conditions of the act
deterred investors from proceeding with the enterprise. Not one of the
sixty-two provisional orders granted to companies in 1883 under the act
was carried out. In 1884 the Board of Trade received only four
applications for provisional orders, and during the subsequent four
years only one order was granted. Capitalists declined to go on with a
business which if successful could be taken away from them by local
authorities at the end of twenty-one years upon terms of paying only the
then value of the plant, lands and buildings, without regard to past or
future profits, goodwill or other considerations. The electrical
industry in Great Britain ripened at a time when public opinion was
averse to the creation of further monopolies, the general belief being
that railway, water and gas companies had in the past received valuable
concessions on terms which did not sufficiently safeguard the interests
of the community. The great development of industries by means of
private enterprise in the early part of the 19th century produced a
reaction which in the latter part of the century had the effect of
discouraging the creation by private enterprise of undertakings
partaking of the nature of monopolies; and at the same time efforts were
made to strengthen local and municipal institutions by investing them
with wider functions. There were no fixed principles governing the
relations between the state or municipal authorities and commercial
companies rendering monopoly services. The new conditions imposed on
private enterprise for the purpose of safeguarding the interests of the
public were very tentative, and a former permanent secretary of the
Board of Trade has stated that the efforts made by parliament in these
directions have sometimes proved injurious alike to the public and to
investors. One of these tentative measures was the Tramways Act 1870,
and twelve years later it was followed by the first Electric Lighting
Act.

It was several years before parliament recognized the harm that had been
done by the passing of the Electric Lighting Act 1882. A select
committee of the House of Lords sat in 1886 to consider the question of
reform, and as a result the Electric Lighting Act 1888 was passed. This
amending act altered the period of purchase from twenty-one to forty-two
years, but the terms of purchase were not materially altered in favour
of investors. The act, while stipulating for the consent of local
authorities to the granting of provisional orders, gives the Board of
Trade power in exceptional cases to dispense with the consent, but this
power has been used very sparingly. The right of vetoing an undertaking,
conferred on local authorities by the Electric Lighting Acts and also by
the Tramways Act 1870, has frequently been made use of to exact unduly
onerous conditions from promoters, and has been the subject of complaint
for years. Although, in the opinion of ministers of the Crown, the
exercise of the veto by local authorities has on several occasions led
to considerable scandals, no government has so far been able, owing to
the very great power possessed by local authorities, to modify the law
in this respect. After 1888 electric lighting went ahead in Great
Britain for the first time, although other countries where legislation
was different had long previously enjoyed its benefits. The developments
proceeded along three well-defined lines. In London, where none of the
gas undertakings was in the hands of local authorities, many of the
districts were allotted to companies, and competition was permitted
between two and sometimes three companies. In the provinces the cities
and larger towns were held by the municipalities, while the smaller
towns, in cases where consents could be obtained, were left to the
enterprise of companies. Where consents could not be obtained these
towns were for some time left without supply.

  Some statistics showing the position of the electricity supply
  business respectively in 1896 and 1906 are interesting as indicating
  the progress made and as a means of comparison between these two
  periods of the state of the industry as a whole. In 1896 thirty-eight
  companies were at work with an aggregate capital of about £6,000,000,
  and thirty-three municipalities with electric lighting loans of nearly
  £2,000,000. The figures for 1906, ten years later, show that 187
  electricity supply companies were in operation with a total investment
  of close on £32,000,000, and 277 municipalities with loans amounting
  to close on £36,000,000. The average return on the capital invested in
  the companies at the later period was 5.1% per annum. In 1896 the
  average capital expenditure was about £100 per kilowatt of plant
  installed; and £50 per kilowatt was regarded as a very low record. For
  1906 the average capital expenditure per kilowatt installed was about
  £81. The main divisions of the average expenditure are:--

                             1896.   1906.
    Land and buildings       22.3%   17.8%
    Plant and machinery      36.7    36.5
    Mains                    32.2    35.5
    Meters and instruments    4.6     5.7
    Provisional orders, &c.   3.2     2.8

  The load connected, expressed in equivalents of eight candle-power
  lamps, was 2,000,000 in 1896 and 24,000,000 in 1906. About one-third
  of this load would be for power purposes and about two-thirds for
  lighting. The Board of Trade units sold were 30,200,000 in 1896 and
  533,600,000 in 1906, and the average prices per unit obtained were
  5.7d. and 2.7d. respectively, or a revenue of £717,250 in 1896 and
  over £6,000,000 in 1906. The working expenses per Board of Trade unit
  sold, excluding depreciation, sinking fund and interest were as
  follows:--

                                   1896.    1906.
    Generation and distribution    2.81d.   .99d.
    Rent, rates and taxes           .35     .14
    Management                      .81     .18
    Sundries                        .10     .02
                                   ------  ------
                 Total             4.07d.  1.33d.

  In 1896 the greatest output at one station was about 5½ million units,
  while in 1906 the station at Manchester had the largest output of over
  40 million units.

  The capacity of the plants installed in the United Kingdom in 1906
  was:--

                               K.W.
    Continuous current         417,000     / Provinces    333,000
                                           \ London        84,000
    Alternating current        132,000     / Provinces     83,000
                                           \ London        49,000
    Continuous current and \
      alternating current   >  480,000     / Provinces    366,000
      combined             /               \ London       114,000
                             ---------
                             1,029,000 k.w.


  Economics.

The economics of electric lighting were at first assumed to be similar
to those of gas lighting. Experience, however, soon proved that there
were important differences, one being that gas may be stored in
gasometers without appreciable loss and the work of production carried
on steadily without reference to fluctuations of demand. Electricity
cannot be economically stored to the same extent, and for the most part
it has to be used as it is generated. The demand for electric light is
practically confined to the hours between sunset and midnight, and it
rises sharply to a "peak" during this period. Consequently the
generating station has to be equipped with plant of sufficient capacity
to cope with the maximum load, although the peak does not persist for
many minutes--a condition which is very uneconomical both as regards
capital expenditure and working costs (see LIGHTING: _Electric_). In
order to obviate the unproductiveness of the generating plant during the
greater part of the day, electricity supply undertakings sought to
develop the "daylight" load. This they did by supplying electricity for
traction purposes, but more particularly for industrial power purposes.
The difficulties in the way of this line of development, however, were
that electric power could not be supplied cheaply enough to compete with
steam, hydraulic, gas and other forms of power, unless it was generated
on a very large scale, and this large demand could not be developed
within the restricted areas for which provisional orders were granted
and under the restrictive conditions of these orders in regard to
situation of power-house and other matters.

The leading factors which make for economy in electricity supply are the
magnitude of the output, the load factor, and the diversity factor,
also the situation of the power house, the means of distribution, and
the provision of suitable, trustworthy and efficient plant. These
factors become more favourable the larger the area and the greater and
more varied the demand to be supplied. Generally speaking, as the output
increases so the cost per unit diminishes, but the ratio (called the
load factor) which the output during any given period bears to the
_maximum_ possible output during the same period has a very important
influence on costs. The ideal condition would be when a power station is
working at its normal _maximum_ output continuously night and day. This
would give a load-factor of 100%, and represents the ultimate ideal
towards which the electrical engineer strives by increasing the area of
his operations and consequently also the load and the variety of the
overlapping demands. It is only by combining a large number of demands
which fluctuate at different times--that is by achieving a high
diversity factor--that the supplier of electricity can hope to approach
the ideal of continuous and steady output. Owing to the dovetailing of
miscellaneous demands the actual demand on a power station at any moment
is never anything like the aggregate of all the maximum demands. One
large station would require a plant of 36,000 k.w. capacity if all the
demands came upon the station simultaneously, but the maximum demand on
the generating plant is only 15,000 kilowatts. The difference between
these two figures may be taken to represent the economy effected by
combining a large number of demands on one station. In short, the
keynote of progress in cheap electricity is increased and diversified
demand combined with concentration of load. The average load-factor of
all the British electricity stations in 1907 was 14.5%--a figure which
tends to improve.


  Power companies.

Several electric power supply companies have been established in the
United Kingdom to give practical effect to these principles. The
Electric Lighting Acts, however, do not provide for the establishment of
large power companies, and special acts of parliament have had to be
promoted to authorize these undertakings. In 1898 several bills were
introduced in parliament for these purposes. They were referred to a
joint committee of both Houses of Parliament presided over by Lord
Cross. The committee concluded that, where sufficient public advantages
are shown, powers should be given for the supply of electricity over
areas including the districts of several local authorities and involving
the use of exceptional plant; that the usual conditions of purchase of
the undertakings by the local authorities did not apply to such
undertakings; that the period of forty-two years was "none too long" a
tenure; and that the terms of purchase should be reconsidered. With
regard to the provision of the Electric Lighting Acts which requires
that the consent of the local authority should be obtained as a
condition precedent to the granting of a provisional order, the
committee was of opinion that the local authority should be entitled to
be heard by the Board of Trade, but should not have the power of veto.
No general legislation took place as a result of these recommendations,
but the undermentioned special acts constituting power supply companies
were passed.

In 1902 the president of the Board of Trade stated that a bill had been
drafted which he thought "would go far to meet all the reasonable
objections that had been urged against the present powers by the local
authorities." In 1904 the government introduced the Supply of
Electricity Bill, which provided for the removal of some of the minor
anomalies in the law relating to electricity. The bill passed through
all its stages in the House of Lords but was not proceeded with in the
House of Commons. In 1905 the bill was again presented to parliament but
allowed to lie on the table. In the words of the president of the Board
of Trade, there was "difficulty of dealing with this question so long as
local authorities took so strong a view as to the power which ought to
be reserved to them in connexion with this enterprise." In the official
language of the council of the Institution of Electrical Engineers, the
development of electrical science in the United Kingdom is in a backward
condition as compared with other countries in respect of the practical
application to the industrial and social requirements of the nation,
notwithstanding that Englishmen have been among the first in inventive
genius. The cause of such backwardness is largely due to the conditions
under which the electrical industry has been carried on in the country,
and especially to the restrictive character of the legislation governing
the initiation and development of electrical power and traction
undertakings, and to the powers of obstruction granted to local
authorities. Eventually The Electric Lighting Act 1909 was passed. This
Act provides:--(1) for the granting of provisional orders authorizing
any local authority or company to supply electricity in bulk; (2) for
the exercise of electric lighting powers by local authorities jointly
under provisional order; (3) for the supply of electricity to railways,
canals and tramways outside the area of supply with the consent of the
Board of Trade; (4) for the compulsory acquisition of land for
generating stations by provisional order; (5) for the exemption of
agreements for the supply of electricity from stamp duty; and (6) for
the amendment of regulations relating to July notices, revision of
maximum price, certification of meters, transfer of powers of
undertakers, auditors' reports, and other matters.

The first of the Power Bills was promoted in 1898, under which it was
proposed to erect a large generating station in the Midlands from which
an area of about two thousand square miles would be supplied. Vigorous
opposition was organized against the bill by the local authorities and
it did not pass. The bill was revived in 1899, but was finally crushed.
In 1900 and following years several power bills were successfully
promoted, and the following are the areas over which the powers of these
acts extend:

In Scotland, (1) the Clyde Valley, (2) the county of Fife, (3) the
districts described as "Scottish Central," comprising Linlithgow,
Clackmannan, and portions of Dumbarton and Stirling, and (4) the
Lothians, which include portions of Midlothian, East Lothian, Peebles
and Lanark.

In England there are companies operating in (1) Northumberland, (2)
Durham county, (3) Lancashire, (4) South Wales and Carmarthenshire, (5)
Derbyshire and Nottinghamshire, (6) Leicestershire and Warwickshire, (7)
Yorkshire, (8) Shropshire, Worcestershire and Staffordshire, (9)
Somerset, (10) Kent, (11) Cornwall, (12) portions of Gloucestershire,
(13) North Wales, (14) North Staffordshire, Derbyshire, Denbighshire and
Flintshire, (15) West Cumberland, (16) the Cleveland district, (17) the
North Metropolitan district, and (18) the West Metropolitan area. An
undertaking which may be included in this category, although it is not a
Power Act company, is the Midland Electric Corporation in South
Staffordshire. The systems of generation and distribution are generally
10,000 or 11,000 volts three-phase alternating current.

The powers conferred by these acts were much restricted as a result of
opposition offered to them. In many cases the larger towns were cut out
of the areas of supply altogether, but the general rule was that the
power company was prohibited from supplying direct to a power consumer
in the area of an authorized distributor without the consent of the
latter, subject to appeal to the Board of Trade. Even this restricted
power of direct supply was not embodied in all the acts, the power of
taking supply in bulk being left only to certain authorized distributors
and to authorized users such as railways and tramways. Owing chiefly to
the exclusion of large towns and industrial centres from their areas,
these power supply companies did not all prove as successful as was
expected.

In the case of one of the power companies which has been in a favourable
position for the development of its business, the theoretical
conclusions in regard to the economy of large production above stated
have been amply demonstrated in practice. In 1901, when this company was
emerging from the stage of a simple electric lighting company, the total
costs per unit were 1.05d. with an output of about 2½ million units per
annum. In 1905 the output rose to over 30 million units mostly for power
and traction purposes, and the costs fell to 0.56d. per unit.

An interesting phase of the power supply question has arisen in London.
Under the general acts it was stipulated that the power-house should be
erected within the area of supply, and amalgamation of undertakings was
prohibited. After less than a decade of development several of the
companies in London found themselves obliged to make considerable
additions to their generating plants. But their existing buildings were
full to their utmost capacity, and the difficulties of generating
cheaply on crowded sites had increased instead of diminished during the
interval. Several of the companies had to promote special acts of
parliament to obtain relief, but the idea of a general combination was
not considered to be within the range of practical politics until 1905,
when the Administrative County of London Electric Power Bill was
introduced. Compared with other large cities, the consumption of
electricity in London is small. The output of electricity in New York
for all purposes is 971 million units per annum or 282 units per head of
population. The output of electricity in London is only 42 units per
head per annum. There are in London twelve local authorities and
fourteen companies carrying on electricity supply undertakings. The
capital expenditure is £3,127,000 by the local authorities and
£12,530,000 by the companies, and their aggregate capacity of plant is
165,000 k.w. The total output is about 160,000,000 units per annum, the
total revenue is over £2,000,000, and the gross profit before providing
for interest and sinking fund charges is £1,158,000. The general average
cost of production is 1.55d. per unit, and the average price per unit
sold is 3.16d., but some of the undertakers have already supplied
electricity to large power consumers at below 1d. per unit. By
generating on a large scale for a wide variety of demands the promoters
of the new scheme calculated to be able to offer electrical energy in
bulk to electricity supply companies and local authorities at prices
substantially below their costs of production at separate stations, and
also to provide them and power users with electricity at rates which
would compete with other forms of power. The authorized capital was
fixed at £6,666,000, and the initial outlay on the first plant of 90,000
k.w., mains, &c., was estimated at £2,000,000. The costs of generation
were estimated at 0.15d. per unit, and the total cost at 0.52d. per unit
sold. The output by the year 1911 was estimated at 133,500,000 units at
an average selling price of 0.7d. per unit, to be reduced to 0.55d. by
1916 when the output was estimated at 600,000,000 units. The bill
underwent a searching examination before the House of Lords committee
and was passed in an amended form. At the second reading in the House of
Commons a strong effort was made to throw it out, but it was allowed to
go to committee on the condition--contrary to the general
recommendations of the parliamentary committee of 1898--that a purchase
clause would be inserted; but amendments were proposed to such an extent
that the bill was not reported for third reading until the eve of the
prorogation of parliament. In the following year (1906) the
Administrative Company's bill was again introduced in parliament, but
the London County Council, which had previously adopted an attitude both
hostile and negative, also brought forward a similar bill. Among other
schemes, one known as the Additional Electric Power Supply Bill was to
authorize the transmission of current from St Neots in Hunts. This bill
was rejected by the House of Commons because the promoters declined to
give precedence to the bill of the London County Council. The latter
bill was referred to a hybrid committee with instructions to consider
the whole question of London power supply, but it was ultimately
rejected. The same result attended a second bill which was promoted by
the London County Council in 1907. The question was settled by the
London Electric Supply Act 1908, which constitutes the London County
Council the purchasing authority (in the place of the local authorities)
for the electric supply companies in London. This Act also enabled the
Companies and other authorized undertakers to enter into agreements for
the exchange of current and the linking-up of stations.


  Legislation and regulations.

The general supply of electricity is governed primarily by the two acts
of parliament passed in 1882 and 1888, which apply to the whole of the
United Kingdom. Until 1899 the other statutory provisions relating to
electricity supply were incorporated in provisional orders granted by
the Board of Trade and confirmed by parliament in respect of each
undertaking, but in that year an Electric Lighting Clauses Act was
passed by which the clauses previously inserted in each order were
standardized. Under these acts the Board of Trade made rules with
respect to applications for licences and provisional orders, and
regulations for the protection of the public, and of the electric lines
and works of the post office, and others, and also drew up a model form
for provisional orders.

Until the passing of the Electric Lighting Acts, wires could be placed
wherever permission for doing so could be obtained, but persons breaking
up streets even with the consent of the local authority were liable to
indictment for nuisance. With regard to overhead wires crossing the
streets, the local authorities had no greater power than any member of
the public, but a road authority having power to make a contract for
lighting the road could authorize others to erect poles and wires for
the purpose. A property owner, however, was able to prevent wires from
being taken over his property. The act of 1888 made all electric lines
or other works for the supply of electricity, not entirely enclosed
within buildings or premises in the same occupation, subject to
regulations of the Board of Trade. The postmaster-general may also
impose conditions for the protection of the post office. Urban
authorities, the London County Council, and some other corporations have
now powers to make by-laws for prevention of obstruction from posts and
overhead wires for telegraph, telephone, lighting or signalling
purposes; and electric lighting stations are now subject to the
provisions of the Factory Acts.

Parliamentary powers to supply electricity can now be obtained by (A)
Special Act, (B) Licence, or (C) Provisional order.

A. _Special Act._--Prior to the report of Lord Cross's joint committee
of 1898 (referred to above), only one special act was passed. The
provisions of the Electric Power Acts passed subsequently are not
uniform, but the following are some of the usual provisions:--

The company shall not supply electricity for lighting purposes except to
authorized undertakers, provided that the energy supplied to any person
for power may be used for lighting any premises on which the power is
utilized. The company shall not supply energy (except to authorized
undertakers) in any area which forms part of the area of supply of any
authorized distributors without their consent, such consent not to be
unreasonably withheld. The company is bound to supply authorized
undertakers upon receiving notice and upon the applicants agreeing to
pay for at least seven years an amount sufficient to yield 20% on the
outlay (excluding generating plant or wires already installed). Other
persons to whom the company is authorized to supply may require it upon
terms to be settled, if not agreed, by the Board of Trade. Dividends are
usually restricted to 8%, with a provision that the rate may be
increased upon the average price charged being reduced. The maximum
charges are usually limited to 3d. per unit for any quantity up to 400
hours' supply, and 2d. per unit beyond. No preference is to be shown
between consumers in like circumstances. Many provisions of the general
Electric Lighting Acts are excluded from these special acts, in
particular the clause giving the local authority the right to purchase
the undertaking compulsorily.

B. _Licence._--The only advantages of proceeding by licence are that it
can be expeditiously obtained and does not require confirmation by
parliament; but some of the provisions usually inserted in provisional
orders would be _ultra vires_ in a licence, and the Electric Lighting
Clauses Act 1899 does not extend to licences. The term of a licence does
not exceed seven years, but is renewable. The consent of the local
authority is necessary even to an application for a licence. None of the
licences that have been granted is now in force.

C. _Provisional Order._--An intending applicant for a provisional order
must serve notice of his intention on every local authority within the
proposed area of supply on or before the 1st of July prior to the
session in which application is to be made to the Board of Trade. This
provision has given rise to much complaint, as it gives the local
authorities a long time for bargaining and enables them to supersede
the company's application by themselves applying for provisional orders.
The Board of Trade generally give preference to the applications of
local authorities.

In 1905 the Board of Trade issued a memorandum stating that, in view of
the revocation of a large number of provisional orders which had been
obtained by local authorities, or in regard to which local authorities
had entered into agreements with companies for carrying the orders into
effect (which agreements were in many cases _ultra vires_ or at least of
doubtful validity), it appeared undesirable that a local authority
should apply for a provisional order without having a definite intention
of exercising the powers, and that in future the Board of Trade would
not grant an order to a local authority unless the board were satisfied
that the powers would be exercised within a specified period.

Every undertaking authorized by provisional order is subject to the
provision of the general act entitling the local authority to purchase
compulsorily at the end of forty-two years (or shorter period), or after
the expiration of every subsequent period of ten years (unless varied by
agreement between the parties with the consent of the Board of Trade),
so much of the undertaking as is within the jurisdiction of the
purchasing authority upon the terms of paying the then value of all
lands, buildings, works, materials and plant, suitable to and used for
the purposes of the undertaking; provided that the value of such lands,
&c., shall be deemed to be their fair market value at the time of
purchase, due regard being had to the nature and then condition and
state of repair thereof, and to the circumstance that they are in such
positions as to be ready for immediate working, and to the suitability
of the same to the purposes of the undertaking, and where a part only of
the undertaking is purchased, to any loss occasioned by severance, but
without any addition in respect of compulsory purchase or of goodwill,
or of any profits which may or might have been or be made from the
undertaking or any similar consideration. Subject to this right of
purchase by the local authority, a provisional order (but not a licence)
may be for such period as the Board of Trade may think proper, but so
far no limit has been imposed, and unless purchased by a local authority
the powers are held in perpetuity. No monopoly is granted to
undertakers, and since 1889 the policy of the Board of Trade has been to
sanction two undertakings in the same metropolitan area, preferably
using different systems, but to discourage competing schemes within the
same area in the provinces. Undertakers must within two years lay mains
in certain specified streets. After the first eighteen months they may
be required to lay mains in other streets upon conditions specified in
the order, and any owner or occupier of premises within 50 yds. of a
distributing main may require the undertakers to give a supply to his
premises; but the consumer must pay the cost of the lines laid upon his
property and of so much outside as exceeds 60 ft. from the main, and he
must also contract for two and in some cases for three years' supply.
But undertakers are prohibited in making agreements for supply from
showing any undue preference. The maximum price in London is 13s. 4d.
per quarter for any quantity up to 20 units, and beyond that 8d. per
unit, but 11s. 8d. per quarter up to 20 units and 7d. per unit beyond is
the more general maximum. The "Bermondsey clause" requires the
undertakers (local authority) so to fix their charges (not exceeding the
specified maximum) that the revenue shall not be less than the
expenditure.

There is no statutory obligation on municipalities to provide for
depreciation of electricity supply undertakings, but after providing for
all expenses, interest on loans, and sinking fund instalments, the local
authority may create a reserve fund until it amounts, with interest, to
one-tenth of the aggregate capital expenditure. Any deficiency when not
met out of reserve is payable out of the local rates.

The principle on which the Local Government Board sanctions municipal
loans for electric lighting undertakings is that the period of the loan
shall not exceed the life of the works, and that future ratepayers shall
not be unduly burdened. The periods of the loans vary from ten years for
accumulators and arc lamps to sixty years for lands. Within the county
of London the loans raised by the metropolitan borough councils for
electrical purposes are sanctioned by the London County Council, and
that body allows a minimum period of twenty years for repayment. Up to
1904-1905, 245 loans had been granted by the council amounting in the
aggregate to £4,045,067.


  Standardization.

In 1901 the Institution of Civil Engineers appointed a committee to
consider the advisability of standardizing various kinds of iron and
steel sections. Subsequently the original reference was enlarged, and in
1902 the Institution of Electrical Engineers was invited to co-operate.
The treasury, as well as railway companies, manufacturers and others,
have made grants to defray the expenses. The committee on electrical
plant has ten sub-committees. In August 1904 an interim report was
issued by the sub-committee on generators, motors and transformers,
dealing with pressures and frequencies, rating of generators and motors,
direct-current generators, alternating-current generators, and motors.

In 1903 the specification for British standard tramway rails and
fish-plates was issued, and in 1904 a standard specification for tubular
tramway poles was issued. A sectional committee was formed in 1904 to
correspond with foreign countries with regard to the formation of an
electrical international commission to study the question of an
international standardization of nomenclature and ratings of electrical
apparatus and machinery.


  The electrical industry.

The electrical manufacturing branch, which is closely related to the
electricity supply and other operating departments of the electrical
industry, only dates from about 1880. Since that time it has undergone
many vicissitudes. It began with the manufacture of small arc lighting
equipments for railway stations, streets and public buildings. When the
incandescent lamp became a commercial article, ship-lighting sets and
installations for theatres and mansions constituted the major portion of
the electrical work. The next step was the organization of
house-to-house distribution of electricity from small "central
stations," ultimately leading to the comprehensive public supply in
large towns, which involved the manufacture of generating and
distributing plants of considerable magnitude and complexity. With the
advent of electric traction about 1896, special machinery had to be
produced, and at a later stage the manufacturer had to solve problems in
connexion with bulk supply in large areas and for power purposes. Each
of these main departments involved changes in ancillary manufactures,
such as cables, switches, transformers, meters, &c., so that the
electrical manufacturing industry has been in a constant state of
transition. At the beginning of the period referred to Germany and
America were following the lead of England in theoretical developments,
and for some time Germany obtained electrical machinery from England.
Now scarcely any electrical apparatus is exported to Germany, and
considerable imports are received by England from that country and
America. The explanation is to be found mainly in the fact that the
adverse legislation of 1882 had the effect of restricting enterprise,
and while British manufacturers were compulsorily inert during periods
of impeded growth of the two most important branches of the
industry--electric lighting and traction--manufacturers in America and
on the continent of Europe, who were in many ways encouraged by their
governments, devoted their resources to the establishment of factories
and electrical undertakings, and to the development of efficient selling
organizations at home and abroad. When after the amendment of the
adverse legislation in 1888 a demand for electrical machinery arose in
England, the foreign manufacturers were fully organized for trade on a
large scale, and were further aided by fiscal conditions to undersell
English manufacturers, not only in neutral markets, but even in their
own country. Successful manufacture on a large scale is possible only by
standardizing the methods of production. English manufacturers were not
able to standardize because they had not the necessary output. There had
been no repetitive demand, and there was no production on a large scale.
Foreign manufacturers, however, were able to standardize by reason of
the large uniform demand which existed for their manufactures.
Statistics are available showing the extent to which the growth of the
electrical manufacturing industry in Great Britain was delayed. Nearly
twenty years after the inception of the industry there were only
twenty-four manufacturing companies registered in the United Kingdom,
having an aggregate subscribed capital of under £7,000,000. But in 1907
there were 292 companies with over £42,000,000 subscribed capital. The
cable and incandescent lamp sections show that when the British
manufacturers are allowed opportunities they are not slow to take
advantage of them. The cable-making branch was established under the
more encouraging conditions of the telegraph industry, and the lamp
industry was in the early days protected by patents. Other departments
not susceptible to foreign competition on account of freightage, such as
the manufacture of storage batteries and rolling stock, are also fairly
prosperous. In departments where special circumstances offer a prospect
of success, the technical skill, commercial enterprise and general
efficiency of British manufacturers manifest themselves by positive
progress and not merely by the continuance of a struggle against adverse
conditions. The normal posture of the British manufacturer of electrical
machinery has been described as one of desperate defence of his home
trade; that of the foreign manufacturer as one of vigorous attack upon
British and other open markets. In considering the position of English
manufacturers as compared with their foreign rivals, some regard should
be had to the patent laws. One condition of a grant of a patent in most
foreign countries is that the patent shall be worked in those countries
within a specified period. But a foreign inventor was until 1907 able to
secure patent protection in Great Britain without any obligation to
manufacture there. The effect of this was to encourage the manufacture
of patented apparatus in foreign countries, and to stimulate their
exportation to Great Britain in competition with British products. With
regard to the electrochemical industry the progress which has been
achieved by other nations, notably Germany, is very marvellous by
comparison with the advance made by England, but to state the reasons
why this industry has had such extraordinary development in Germany,
notwithstanding that many of the fundamental inventions were made in
England, would require a statement of the marked differences in the
methods by which industrial progress is promoted in the two countries.

There has been very little solidarity among those interested in the
commercial development of electricity, and except for the discussion of
scientific subjects there has been very little organization with the
object of protecting and promoting common interests. (E. GA.)


FOOTNOTES:

  [1] British Patent Specification, No. 5306 of 1878, and No. 602 of
    1880.

  [2] Ibid. No. 3988 of 1878.



ELECTRIC WAVES. § 1. Clerk Maxwell proved that on his theory
electromagnetic disturbances are propagated as a wave motion through the
dielectric, while Lord Kelvin in 1853 (_Phil. Mag._ [4] 5, p. 393)
proved from electromagnetic theory that the discharge of a condenser is
oscillatory, a result which Feddersen (_Pogg. Ann._ 103, p. 69, &c.)
verified by a beautiful series of experiments. The oscillating discharge
of a condenser had been inferred by Henry as long ago as 1842 from his
experiments on the magnetization produced in needles by the discharge of
a condenser. From these two results it follows that electric waves must
be passing through the dielectric surrounding a condenser in the act of
discharging, but it was not until 1887 that the existence of such waves
was demonstrated by direct experiment. This great step was made by Hertz
(_Wied. Ann._ 34, pp. 155, 551, 609; _Ausbreitung der elektrischen
Kraft_, Leipzig, 1892), whose experiments on this subject form one of
the greatest contributions ever made to experimental physics. The
difficulty which had stood in the way of the observations of these waves
was the absence of any method of detecting electrical and magnetic
forces, reversed some millions of times per second, and only lasting for
an exceedingly short time. This was removed by Hertz, who showed that
such forces would produce small sparks between pieces of metal very
nearly in contact, and that these sparks were sufficiently regular to be
used to detect electric waves and to investigate their properties. Other
and more delicate methods have subsequently been discovered, but the
results obtained by Hertz with his detector were of such signal
importance, that we shall begin our account of experiments on these
waves by a description of some of Hertz's more fundamental experiments.

[Illustration: FIG. 1.]

[Illustration: FIG. 2.]

To produce the waves Hertz used two forms of vibrator. The first is
represented in fig. 1. A and B are two zinc plates about 40 cm. square;
to these brass rods, C, D, each about 30 cm. long, are soldered,
terminating in brass balls E and F. To get good results it is necessary
that these balls should be very brightly polished, and as they get
roughened by the sparks which pass between them it is necessary to
repolish them at short intervals; they should be shaded from light and
from sparks, or other source of ultra-violet light. In order to excite
the waves, C and D are connected to the two poles of an induction coil;
sparks cross the air-gap which becomes a conductor, and the charges on
the plates oscillate backwards and forwards like the charges on the
coatings of a Leyden jar when it is short-circuited. The object of
polishing the balls and screening off light is to get a sudden and sharp
discharge; if the balls are rough there will be sharp points from which
the charge will gradually leak, and the discharge will not be abrupt
enough to start electrical vibrations, as these have an exceedingly
short period. From the open form of this vibrator we should expect the
radiation to be very large and the rate of decay of the amplitude very
rapid. Bjerknes (_Wied. Ann._ 44, p. 74) found that the amplitude fell
to 1/e of the original value, after a time 4T where T was the period of
the electrical vibrations. Thus after a few vibrations the amplitude
becomes inappreciable. To detect the waves produced by this vibrator
Hertz used a piece of copper wire bent into a circle, the ends being
furnished with two balls, or a ball and a point connected by a screw, so
that the distance between them admitted of very fine adjustment. The
radius of the circle for use with the vibrator just described was 35
cm., and was so chosen that the free period of the detector might be the
same as that of the vibrator, and the effects in it increased by
resonance. It is evident, however, that with a primary system as greatly
damped as the vibrator used by Hertz, we could not expect very marked
resonance effects, and as a matter of fact the accurate timing of
vibrator and detector in this case is not very important. With
electrical vibrators which can maintain a large number of vibrations,
resonance effects are very striking, as is beautifully shown by the
following experiment due to Lodge (_Nature_, 41, p. 368), whose
researches have greatly advanced our knowledge of electric waves. A and
C (fig. 2) are two Leyden jars, whose inner and outer coatings are
connected by wires, B and D, bent so as to include a considerable area.
There is an air-break in the circuit connecting the inside and outside
of one of the jars, A, and electrical oscillations are started in A by
joining the inside and outside with the terminals of a coil or
electrical machine. The circuit in the jar C is provided with a sliding
piece, F, by means of which the self-induction of the discharging
circuit, and, therefore, the time of an electrical oscillation of the
jar, can be adjusted. The inside and outside of this jar are put almost,
but not quite, into electrical contact by means of a piece of tin-foil,
E, bent over the lip of the jar. The jars are placed face to face so
that the circuits B and D are parallel to each other, and approximately
at right angles to the line joining their centres. When the electrical
machine is in action sparks pass across the air-break in the circuit in
A, and by moving the slider F it is possible to find one position for it
in which sparks pass from the inside to the outside of C across the
tin-foil, while when the slider is moved a short distance on either side
of this position the sparks cease.

Hertz found that when he held his detector in the neighbourhood of the
vibrator minute sparks passed between the balls. These sparks were not
stopped when a large plate of non-conducting substance, such as the wall
of a room, was interposed between the vibrator and detector, but a large
plate of very thin metal stopped them completely.

To illustrate the analogy between electric waves and waves of light
Hertz found another form of apparatus more convenient. The vibrator
consisted of two equal brass cylinders, 12 cm. long and 3 cm. in
diameter, placed with their axes coincident, and in the focal line of a
large zinc parabolic mirror about 2 m. high, with a focal length of 12.5
cm. The ends of the cylinders nearest each other, between which the
sparks passed, were carefully polished. The detector, which was placed
in the focal line of an equal parabolic mirror, consisted of two lengths
of wire, each having a straight piece about 50 cm. long and a curved
piece about 15 cm. long bent round at right angles so as to pass through
the back of the mirror. The ends which came through the mirror were
connected with a spark micrometer, the sparks being observed from behind
the mirror. The mirrors are shown, in fig. 3.

[Illustration: FIG. 3.]

§ 2. _Reflection and Refraction._--To show the reflection of the waves
Hertz placed the mirrors side by side, so that their openings looked in
the same direction, and their axes converged at a point about 3 m. from
the mirrors. No sparks were then observed in the detector when the
vibrator was in action. When, however, a large zinc plate about 2 m.
square was placed at right angles to the line bisecting the angle
between the axes of the mirrors sparks became visible, but disappeared
again when the metal plate was twisted through an angle of about 15° to
either side. This experiment showed that electric waves are reflected,
and that, approximately at any rate, the angle of incidence is equal to
the angle of reflection. To show refraction Hertz used a large prism
made of hard pitch, about 1.5 m. high, with a slant side of 1.2 m. and
an angle of 30°. When the waves from the vibrator passed through this
the sparks in the detector were not excited when the axes of the two
mirrors were parallel, but appeared when the axis of the mirror
containing the detector made a certain angle with the axis of that
containing the vibrator. When the system was adjusted for minimum
deviation the sparks were most vigorous when the angle between the axes
of the mirrors was 22°. This corresponds to an index of refraction of
1.69.

§ 3. _Analogy to a Plate of Tourmaline._--If a screen be made by winding
wire round a large rectangular framework, so that the turns of the wire
are parallel to one pair of sides of the frame, and if this screen be
interposed between the parabolic mirrors when placed so as to face each
other, there will be no sparks in the detector when the turns of the
wire are parallel to the focal lines of the mirror; but if the frame is
turned through a right angle so that the wires are perpendicular to the
focal lines of the mirror the sparks will recommence. If the framework
is substituted for the metal plate in the experiment on the reflection
of electric waves, sparks will appear in the detector when the wires are
parallel to the focal lines of the mirrors, and will disappear when the
wires are at right angles to these lines. Thus the framework reflects
but does not transmit the waves when the electric force in them is
parallel to the wires, while it transmits but does not reflect waves in
which the electric force is at right angles to the wires. The wire
framework behaves towards the electric waves exactly as a plate of
tourmaline does to waves of light. Du Bois and Rubens (_Wied. Ann._ 49,
p. 593), by using a framework wound with very fine wire placed very
close together, have succeeded in polarizing waves of radiant heat,
whose wave length, although longer than that of ordinary light, is very
small compared with that of electric waves.

§ 4. _Angle of Polarization._--When light polarized at right angles to
the plane of incidence falls on a refracting substance at an angle
tan^{-1}µ, where µ is the refractive index of the substance, all the
light is refracted and none reflected; whereas when light is polarized
in the plane of incidence, some of the light is always reflected
whatever the angle of incidence. Trouton (_Nature_, 39, p. 391) showed
that similar effects take place with electric waves. From a paraffin
wall 3 ft. thick, reflection always took place when the electric force
in the incident wave was at right angles to the plane of incidence,
whereas at a certain angle of incidence there was no reflection when the
vibrator was turned, so that the electric force was in the plane of
incidence. This shows that on the electromagnetic theory of light the
electric force is at right angles to the plane of polarization.

[Illustration: FIG. 4.]

§ 5. _Stationary Electrical Vibrations._--Hertz (_Wied. Ann._ 34, p.
609) made his experiments on these in a large room about 15 m. long. The
vibrator, which was of the type first described, was placed at one end
of the room, its plates being parallel to the wall, at the other end a
piece of sheet zinc about 4 m. by 2 m. was placed vertically against the
wall. The detector--the circular ring previously described--was held so
that its plane was parallel to the metal plates of the vibrator, its
centre on the line at right angles to the metal plate bisecting at right
angles the spark gap of the vibrator, and with the spark gap of the
detector parallel to that of the vibrator. The following effects were
observed when the detector was moved about. When it was close up to the
zinc plate there were no sparks, but they began to pass feebly as soon
as it was moved forward a little way from the plate, and increased
rapidly in brightness until it was about 1.8 m. from the plate, when
they attained their maximum. When its distance was still further
increased they diminished in brightness, and vanished again at a
distance of about 4 m. from the plate. When the distance was still
further increased they reappeared, attained another maximum, and so on.
They thus exhibited a remarkable periodicity similar to that which
occurs when stationary vibrations are produced by the interference of
direct waves with those reflected from a surface placed at right angles
to the direction of propagation. Similar periodic alterations in the
spark were observed by Hertz when the waves, instead of passing freely
through the air and being reflected by a metal plate at the end of the
room, were led along wires, as in the arrangement shown in fig. 4. L and
K are metal plates placed parallel to the plates of the vibrator, long
parallel wires being attached to act as guides to the waves which were
reflected from the isolated end. (Hertz used only one plate and one
wire, but the double set of plates and wires introduced by Sarasin and
De la Rive make the results more definite.) In this case the detector is
best placed so that its plane is at right angles to the wires, while the
air space is parallel to the plane containing the wires. The sparks
instead of vanishing when the detector is at the far end of the wire are
a maximum in this position, but wax and wane periodically as the
detector is moved along the wires. The most obvious interpretation of
these experiments was the one given by Hertz--that there was
interference between the direct waves given out by the vibrator and
those reflected either from the plate or from the ends of the wire, this
interference giving rise to stationary waves. The places where the
electric force was a maximum were the places where the sparks were
brightest, and the places where the electric force was zero were the
places where the sparks vanished. On this explanation the distance
between two consecutive places where the sparks vanished would be half
the wave length of the waves given out by the vibrator.

Some very interesting experiments made by Sarasin and De la Rive
(_Comptes rendus_, 115, p. 489) showed that this explanation could not
be the true one, since by using detectors of different sizes they found
that the distance between two consecutive places where the sparks
vanished depended mainly upon the size of the detector, and very little
upon that of the vibrator. With small detectors they found the distance
small, with large detectors, large; in fact it is directly proportional
to the diameter of the detector. We can see that this result is a
consequence of the large damping of the oscillations of the vibrator and
the very small damping of those of the detector. Bjerknes showed that
the time taken for the amplitude of the vibrations of the vibrator to
sink to 1/e of their original value was only 4T, while for the detector
it was 500T', when T and T' are respectively the times of vibration of
the vibrator and the detector. The rapid decay of the oscillations of
the vibrator will stifle the interference between the direct and the
reflected wave, as the amplitude of the direct wave will, since it is
emitted later, be much smaller than that of the reflected one, and not
able to annul its effects completely; while the well-maintained
vibrations of the detector will interfere and produce the effects
observed by Sarasin and De la Rive. To see this let us consider the
extreme case in which the oscillations of the vibrator are absolutely
dead-beat. Here an impulse, starting from the vibrator on its way to the
reflector, strikes against the detector and sets it in vibration; it
then travels up to the plate and is reflected, the electric force in the
impulse being reversed by reflection. After reflection the impulse again
strikes the detector, which is still vibrating from the effects of the
first impact; if the phase of this vibration is such that the reflected
impulse tends to produce a current round the detector in the same
direction as that which is circulating from the effects of the first
impact, the sparks will be increased, but if the reflected impulse tends
to produce a current in the opposite direction the sparks will be
diminished. Since the electric force is reversed by reflection, the
greatest increase in the sparks will take place when the impulse finds,
on its return, the detector in the opposite phase to that in which it
left it; that is, if the time which has elapsed between the departure
and return of the impulse is equal to an odd multiple of half the time
of vibration of the detector. If d is the distance of the detector from
the reflector when the sparks are brightest, and V the velocity of
propagation of electromagnetic disturbance, then 2d/V = (2n + 1)(T'/2);
where n is an integer and T' the time of vibration of the detector, the
distance between two spark maxima will be VT'/2, and the places where
the sparks are a minimum will be midway between the maxima. Sarasin and
De la Rive found that when the same detector was used the distance
between two spark maxima was the same with the waves through air
reflected from a metal plate and with those guided by wires and
reflected from the free ends of the wire, the inference being that the
velocity of waves along wires is the same as that through the air. This
result, which follows from Maxwell's theory, when the wires are not too
fine, had been questioned by Hertz on account of some of his
experiments on wires.

§ 6. _Detectors._--The use of a detector with a period of vibration of
its own thus tends to make the experiments more complicated, and many
other forms of detector have been employed by subsequent experimenters.
For example, in place of the sparks in air the luminous discharge
through a rarefied gas has been used by Dragoumis, Lecher (who used
tubes without electrodes laid across the wires in an arrangement
resembling that shown in fig. 7) and Arons. A tube containing neon at a
low pressure is especially suitable for this purpose. Zehnder (_Wied.
Ann._ 47, p. 777) used an exhausted tube to which an external
electromotive force almost but not quite sufficient of itself to produce
a discharge was applied; here the additional electromotive force due to
the waves was sufficient to start the discharge. Detectors depending on
the heat produced by the rapidly alternating currents have been used by
Paalzow and Rubens, Rubens and Ritter, and I. Klemencic. Rubens measured
the heat produced by a bolometer arrangement, and Klemencic used a
thermo-electric method for the same purpose; in consequence of the great
increase in the sensitiveness of galvanometers these methods are now
very frequently resorted to. Boltzmann used an electroscope as a
detector. The spark gap consisted of a ball and a point, the ball being
connected with the electroscope and the point with a battery of 200 dry
cells. When the spark passed the cells charged up the electroscope.
Ritter utilized the contraction of a frog's leg as a detector, Lucas and
Garrett the explosion produced by the sparks in an explosive mixture of
hydrogen and oxygen; while Bjerknes and Franke used the mechanical
attraction between oppositely charged conductors. If the two sides of
the spark gap are connected with the two pairs of quadrants of a very
delicate electrometer, the needle of which is connected with one pair of
quadrants, there will be a deflection of the electrometer when the
detector is struck by electric waves. A very efficient detector is that
invented by E. Rutherford (_Trans. Roy. Soc._ A. 1897, 189, p. 1); it
consists of a bundle of fine iron wires magnetized to saturation and
placed inside a small magnetizing coil, through which the electric waves
cause rapidly alternating currents to pass which demagnetize the soft
iron. If the instrument is used to detect waves in air, long straight
wires are attached to the ends of the demagnetizing coil to collect the
energy from the field; to investigate waves in wires it is sufficient to
make a loop or two in the wire and place the magnetized piece of iron
inside it. The amount of demagnetization which can be observed by the
change in the deflection of a magnetometer placed near the iron,
measures the intensity of the electric waves, and very accurate
determinations can be made with ease with this apparatus. It is also
very delicate, though in this respect it does not equal the detector to
be next described, the coherer; Rutherford got indications in 1895 when
the vibrator was ¾ of a mile away from the detector, and where the waves
had to traverse a thickly populated part of Cambridge. It can also be
used to measure the coefficient of damping of the electric waves, for
since the wire is initially magnetized to saturation, if the direction
of the current when it first begins to flow in the magnetizing coil is
such as to tend to increase the magnetization of the wire, it will
produce no effect, and it will not be until the current is reversed that
the wire will lose some of its magnetization. The effect then gives the
measure of the intensity half a period after the commencement of the
waves. If the wire is put in the coil the opposite way, i.e. so that the
magnetic force due to the current begins at once to demagnetize the
wire, the demagnetization gives a measure of the initial intensity of
the waves. Comparing this result with that obtained when the wires were
reversed, we get the coefficient of damping. A very convenient detector
of electric waves is the one discovered almost simultaneously by
Fessenden (_Electrotech. Zeits._, 1903, 24, p. 586) and Schlömilch
(_ibid._ p. 959). This consists of an electrolytic cell in which one of
the electrodes is an exceedingly fine point. The electromotive force in
the circuit is small, and there is large polarization in the circuit
with only a small current. When the circuit is struck by electric waves
there is an increase in the currents due to the depolarization of the
circuit. If a galvanometer is in the circuit, the increased deflection
of the instrument will indicate the presence of the waves.

§ 7. _Coherers._--The most sensitive detector of electric waves is the
"coherer," although for metrical work it is not so suitable as that just
described. It depends upon the fact discovered by Branly (_Comptes
rendus_, 111, p. 785; 112, p. 90) that the resistance between loose
metallic contacts, such as a pile of iron turnings, diminishes when they
are struck by an electric wave. One of the forms made by Lodge (_The
Work of Hertz and some of his Successors_, 1894) on this principle
consists simply of a glass tube containing iron turnings, in contact
with which are wires led into opposite ends of the tube. The arrangement
is placed in series with a galvanometer (one of the simplest kind will
do) and a battery; when the iron turnings are struck by electric waves
their resistance is diminished and the deflection of the galvanometer is
increased. Thus the deflection of the galvanometer can be used to
indicate the arrival of electric waves. The tube must be tapped between
each experiment, and the deflection of the galvanometer brought back to
about its original value. This detector is marvellously delicate, but
not metrical, the change produced in the resistance depending upon so
many things besides the intensity of the waves that the magnitude of the
galvanometer deflection is to some extent a matter of chance. Instead of
the iron turnings we may use two iron wires, one resting on the other;
the resistance of this contact will be altered by the incidence of the
waves. To get greater regularity Bose uses, instead of the iron
turnings, spiral springs, which are pushed against each other by means
of a screw until the most sensitive state is attained. The sensitiveness
of the coherer depends on the electromotive force put in the
galvanometer circuit. Very sensitive ones can be made by using springs
of very fine silver wire coated electrolytically with nickel. Though the
impact of electric waves generally produces a diminution of resistance
with these loose contacts, yet there are exceptions to the rule. Thus
Branly showed that with lead peroxide, PbO2, there is an increase in
resistance. Aschkinass proved the same to be true with copper sulphide,
CuS; and Bose showed that with potassium there is an increase of
resistance and great power of self-recovery of the original resistance
after the waves have ceased. Several theories of this action have been
proposed. Branly (_Lumière électrique_, 40, p. 511) thought that the
small sparks which certainly pass between adjacent portions of metal
clear away layers of oxide or some other kind of non-conducting film,
and in this way improve the contact. It would seem that if this theory
is true the films must be of a much more refined kind than layers of
oxide or dirt, for the coherer effect has been observed with clean
non-oxidizable metals. Lodge explains the effect by supposing that the
heat produced by the sparks fuses adjacent portions of metal into
contact and hence diminishes the resistance; it is from this view of the
action that the name coherer is applied to the detector. Auerbeck
thought that the effect was a mechanical one due to the electrostatic
attractions between the various small pieces of metal. It is probable
that some or all of these causes are at work in some cases, but the
effects of potassium make us hesitate to accept any of them as the
complete explanation. Blanc (_Ann. chim. phys._, 1905, [8] 6, p. 5), as
the result of a long series of experiments, came to the conclusion that
coherence is due to pressure. He regarded the outer layers as different
from the mass of the metal and having a much greater specific
resistance. He supposed that when two pieces of metal are pressed
together the molecules diffuse across the surface, modifying the surface
layers and increasing their conductivity.

  § 8. _Generators of Electric Waves._--Bose (_Phil. Mag._ 43, p. 55)
  designed an instrument which generates electric waves with a length of
  not more than a centimetre or so, and therefore allows their
  properties to be demonstrated with apparatus of moderate dimensions.
  The waves are excited by sparking between two platinum beads carried
  by jointed electrodes; a platinum sphere is placed between the beads,
  and the distance between the beads and the sphere can be adjusted by
  bending the electrodes. The diameter of the sphere is 8 mm., and the
  wave length of the shortest electrical waves generated is said to be
  about 6 mm. The beads are connected with the terminals of a small
  induction coil, which, with the battery to work it and the sparking
  arrangement, are enclosed in a metal box, the radiation passing out
  through a metal tube opposite to the spark gap. The ordinary vibrating
  break of the coil is not used, a single spark made by making and
  breaking the circuit by means of a button outside the box being
  employed instead. The detector is one of the spiral spring coherers
  previously described; it is shielded from external disturbance by
  being enclosed in a metal box provided with a funnel-shaped opening to
  admit the radiation. The wires leading from the coherers to the
  galvanometer are also surrounded by metal tubes to protect them from
  stray radiation. The radiating apparatus and the receiver are mounted
  on stands sliding in an optical bench. If a parallel beam of radiation
  is required, a cylindrical lens of ebonite or sulphur is mounted in a
  tube fitting on to the radiator tube and stopped by a guide when the
  spark is at the principal focal line of the lens. For experiments
  requiring angular measurements a spectrometer circle is mounted on one
  of the sliding stands, the receiver being carried on a radial arm and
  pointing to the centre of the circle. The arrangement is represented
  in fig. 5.

  [Illustration: FIG. 5.]

  With this apparatus the laws of reflection, refraction and
  polarization can readily be verified, and also the double refraction
  of crystals, and of bodies possessing a fibrous or laminated structure
  such as jute or books. (The double refraction of electric waves seems
  first to have been observed by Righi, and other researches on this
  subject have been made by Garbasso and Mack.) Bose showed the rotation
  of the plane of polarization by means of pieces of twisted jute rope;
  if the pieces were arranged so that their twists were all in one
  direction and placed in the path of the radiation, they rotated the
  plane of polarization in a direction depending upon the direction of
  twist; if they were mixed so that there were as many twisted in one
  direction as the other, there was no rotation.

  [Illustration: FIG. 6.]

  A series of experiments showing the complete analogy between electric
  and light waves is described by Righi in his book _L'Ottica delle
  oscillazioni elettriche_. Righi's exciter, which is especially
  convenient when large statical electric machines are used instead of
  induction coils, is shown in fig. 6. E and F are balls connected with
  the terminals of the machine, and AB and CD are conductors insulated
  from each other, the ends B, C, between which the sparks pass, being
  immersed in vaseline oil. The period of the vibrations given out by
  the system is adjusted by means of metal plates M and N attached to AB
  and CD. When the waves are produced by induction coils or by
  electrical machines the intervals between the emission of different
  sets of waves occupy by far the largest part of the time. Simon
  (_Wied. Ann._, 1898, 64, p. 293; _Phys. Zeit._, 1901, 2, p. 253),
  Duddell (_Electrician_, 1900, 46, p. 269) and Poulsen (_Electrotech.
  Zeits._, 1906, 27, p. 1070) reduced these intervals very considerably
  by using the electric arc to excite the waves, and in this way
  produced electrical waves possessing great energy. In these methods
  the terminals between which the arc is passing are connected through
  coils with self-induction L to the plates of a condenser of capacity
  C. The arc is not steady, but is continually varying. This is
  especially the case when it passes through hydrogen. These variations
  excite vibrations with a period 2[pi][root](LC) in the circuit
  containing the capacity of the self-induction. By this method Duddell
  produced waves with a frequency of 40,000. Poulsen, who cooled the
  terminals of the arc, produced waves with a frequency of 1,000,000,
  while Stechodro (_Ann. der Phys._ 27, p. 225) claims to have produced
  waves with three hundred times this frequency, i.e. having a wave
  length of about a metre. When the self-induction and capacity are
  large so that the frequency comes within the limits of the frequency
  of audible notes, the system gives out a musical note, and the
  arrangement is often referred to as the singing arc.

  [Illustration: FIG. 7.]

  [Illustration: FIG. 8.]

  § _9. Waves in Wires._--Many problems on electric waves along wires
  can readily be investigated by a method due to Lecher (_Wied. Ann._
  41, p. 850), and known as Lecher's bridge, which furnishes us with a
  means of dealing with waves of a definite and determinable
  wave-length. In this arrangement (fig. 7) two large plates A and B
  are, as in Hertz's exciter, connected with the terminals of an
  induction coil; opposite these and insulated from them are two smaller
  plates D, E, to which long parallel wires DFH, EGJ are attached. These
  wires are bridged across by a wire LM, and their farther ends H, J,
  may be insulated, or connected together, or with the plates of a
  condenser. To detect the waves in the circuit beyond the bridge,
  Lecher used an exhausted tube placed across the wires, and Rubens a
  bolometer, but Rutherford's detector is the most convenient and
  accurate. If this detector is placed in a fixed position at the end of
  the circuit, it is found that the deflections of this detector depend
  greatly upon the position of the bridge LM, rising rapidly to a
  maximum for some positions, and falling rapidly away when the bridge
  is displaced. As the bridge is moved from the coil end towards the
  detector the deflections show periodic variations, such as are
  represented in fig. 8 when the ordinates represent the deflections of
  the detector and the abscissae the distance of the bridge from the
  ends D, E. The maximum deflections of the detector correspond to the
  positions in which the two circuits DFLMGE, HLMJ (in which the
  vibrations are but slightly damped) are in resonance. For since the
  self-induction and resistance of the bridge LM is very small compared
  with that of the circuit beyond, it follows from the theory of
  circuits in parallel that only a small part of the current will in
  general flow round the longer circuit; it is only when the two
  circuits DFLMGE, HLMJ are in resonance that a considerable current
  will flow round the latter. Hence when we get a maximum effect in the
  detector we know that the waves we are dealing with are those
  corresponding to the free periods of the system HLMJ, so that if we
  know the free periods of this circuit we know the wave length of the
  electric waves under consideration. Thus if the ends of the wires H, J
  are free and have no capacity, the current along them must vanish at H
  and J, which must be in opposite electric condition. Hence half the
  wave length must be an odd submultiple of the length of the circuit
  HLMJ. If H and J are connected together the wave length must be a
  submultiple of the length of this circuit. When the capacity at the
  ends is appreciable the wave length of the circuit is determined by a
  somewhat complex expression. To facilitate the determination of the
  wave length in such cases, Lecher introduced a second bridge L'M', and
  moved this about until the deflection of the detector was a maximum;
  when this occurs the wave length is one of those corresponding to the
  closed circuit LMM'L', and must therefore be a submultiple of the
  length of the circuit. Lecher showed that if instead of using a single
  wire LM to form the bridge, he used two parallel wires PQ, LM, placed
  close together, the currents in the further circuit were hardly
  appreciably diminished when the main wires were cut between PL and QM.
  Blondlot used a modification of this apparatus better suited for the
  production of short waves. In his form (fig. 9) the exciter consists
  of two semicircular arms connected with the terminals of an induction
  coil, and the long wires, instead of being connected with the small
  plates, form a circuit round the exciter.

  As an example of the use of Lecher's arrangement, we may quote Drude's
  application of the method to find the specific induction capacity of
  dielectrics under electric oscillations of varying frequency. In this
  application the ends of the wire are connected to the plates of a
  condenser, the space between whose plates can be filled with the
  liquid whose specific inductive capacity is required, and the bridge
  is moved until the detector at the end of the circuit gives the
  maximum deflection. Then if [lambda] is the wave length of the waves,
  [lambda] is the wave length of one of the free vibrations of the
  system HLMJ; hence if C is the capacity of the condenser at the end in
  electrostatic measure we have

         2[pi]l
    cot --------
        [lambda]    C
    ------------ = ---
       2[pi]l      C'l
      --------
      [lambda]

  where l is the distance of the condenser from the bridge and C' is the
  capacity of unit length of the wire. In the condenser part of the
  lines of force will pass through air and part through the dielectric;
  hence C will be of the form C0+KC1 where K is the specific inductive
  capacity of the dielectric. Hence if l is the distance of maximum
  deflection when the dielectric is replaced by air, l' when filled with
  a dielectric whose specific inductive capacity is known to be K', and
  l" the distance when filled with the dielectric whose specific
  inductive capacity is required, we easily see that--

         2[pi]l        2[pi]l'
    cot -------- - cot --------
        [lambda]       [lambda]   1 - K'
    --------------------------- = ------
         2[pi]l        2[pi]l"    1 - K
    cot -------- - cot --------
        [lambda]       [lambda]

  an equation by means of which K can be determined. It was in this way
  that Drude investigated the specific inductive capacity with varying
  frequency, and found a falling off in the specific inductive capacity
  with increase of frequency when the dielectrics contained the radicle
  OH. In another method used by him the wires were led through long
  tanks filled with the liquid whose specific inductive capacity was
  required; the velocity of propagation of the electric waves along the
  wires in the tank being the same as the velocity of propagation of an
  electromagnetic disturbance through the liquid filling the tank, if we
  find the wave length of the waves along the wires in the tank, due to
  a vibration of a given frequency, and compare this with the wave
  lengths corresponding to the same frequency when the wires are
  surrounded by air, we obtain the velocity of propagation of
  electromagnetic disturbance through the fluid, and hence the specific
  inductive capacity of the fluid.

  [Illustration: FIG. 9.]

  § 10. _Velocity of Propagation of Electromagnetic Effects through
  Air._--The experiments of Sarasin and De la Rive already described
  (see § 5) have shown that, as theory requires, the velocity of
  propagation of electric effects through air is the same as along
  wires. The same result had been arrived at by J.J. Thomson, although
  from the method he used greater differences between the velocities
  might have escaped detection than was possible by Sarasin and De la
  Rive's method. The velocity of waves along wires has been directly
  determined by Blondlot by two different methods. In the first the
  detector consisted of two parallel plates about 6 cm. in diameter
  placed a fraction of a millimetre apart, and forming a condenser whose
  capacity C was determined in electromagnetic measure by Maxwell's
  method. The plates were connected by a rectangular circuit whose
  self-induction L was calculated from the dimensions of the rectangle
  and the size of the wire. The time of vibration T is equal to
  2[pi][root](LC). (The wave length corresponding to this time is long
  compared with the length of the circuit, so that the use of this
  formula is legitimate.) This detector is placed between two parallel
  wires, and the waves produced by the exciter are reflected from a
  movable bridge. When this bridge is placed just beyond the detector
  vigorous sparks are observed, but as the bridge is pushed away a place
  is reached where the sparks disappear; this place is distance
  2/[lambda] from the detector, when [lambda] is the wave length of the
  vibration given out by the detector. The sparks again disappear when
  the distance of the bridge from the detector is 3[lambda]/4. Thus by
  measuring the distance between two consecutive positions of the bridge
  at which the sparks disappear [lambda] can be determined, and v, the
  velocity of propagation, is equal to [lambda]/T. As the means of a
  number of experiments Blondlot found v to be 3.02 × 10^10 cm./sec.,
  which, within the errors of experiment, is equal to 3 × 10^10
  cm./sec., the velocity of light. A second method used by Blondlot, and
  one which does not involve the calculation of the period, is as
  follows:--A and A' (fig. 10) are two equal Leyden jars coated inside
  and outside with tin-foil. The outer coatings form two separate rings
  a, a1; a', a'1, and the inner coatings are connected with the poles of
  the induction coil by means of the metal pieces b, b'. The sharply
  pointed conductors p and p', the points of which are about ½ mm.
  apart, are connected with the rings of the tin-foil a and a', and two
  long copper wires pca1, p'c'a'1, 1029 cm. long, connect these points
  with the other rings a1, a1'. The rings aa', a1a1', are connected by
  wet strings so as to charge up the jars. When a spark passes between b
  and b', a spark at once passes between pp', and this is followed by
  another spark when the waves travelling by the paths a1cp, a'1c'p'
  reach p and p'. The time between the passage of these sparks, which is
  the time taken by the waves to travel 1029 cm., was observed by means
  of a rotating mirror, and the velocity measured in 15 experiments
  varied between 2.92 × 10^10 and 3.03 × 10^10 cm./sec., thus agreeing
  well with that deduced by the preceding method. Other determinations
  of the velocity of electromagnetic propagation have been made by Lodge
  and Glazebrook, and by Saunders.

  [Illustration: FIG. 10.]

  On Maxwell's electromagnetic theory the velocity of propagation of
  electromagnetic disturbances should equal the velocity of light, and
  also the ratio of the electromagnetic unit of electricity to the
  electrostatic unit. A large number of determinations of this ratio
  have been made:--

        Observer.            Date.    Ratio 10^10×.
    Klemencic                1884    3.019 cm./sec.
    Himstedt                 1888    3.009 cm./sec.
    Rowland                  1889    2.9815 cm./sec.
    Rosa                     1889    2.9993 cm./sec.
    J.J. Thomson and Searle  1890    2.9955 cm./sec.
    Webster                  1891    2.987 cm./sec.
    Pellat                   1891    3.009 cm./sec.
    Abraham                  1892    2.992 cm./sec.
    Hurmuzescu               1895    3.002 cm./sec.
    Rosa                     1908    2.9963 cm./sec.

  The mean of these determinations is 3.001 × 10^10 cm./sec., while the
  mean of the last five determinations of the velocity of light in air
  is given by Himstedt as 3.002 × 10^10 cm./sec. From these experiments
  we conclude that the velocity of propagation of an electromagnetic
  disturbance is equal to the velocity of light, and to the velocity
  required by Maxwell's theory.

  In experimenting with electromagnetic waves it is in general more
  difficult to measure the period of the oscillations than their wave
  length. Rutherford used a method by which the period of the vibration
  can easily be determined; it is based upon the theory of the
  distribution of alternating currents in two circuits ACB, ADB in
  parallel. If A and B are respectively the maximum currents in the
  circuits ACB, ADB, then

    A           / S² + (N - M)²p² \
    -- = [root](  ---------------  )
    B           \ R² + (L - M)²p² /

  when R and S are the resistances, L and N the coefficients of
  self-induction of the circuits ACB, ADB respectively, M the
  coefficient of mutual induction between the circuits, and p the
  frequency of the currents. Rutherford detectors were placed in the two
  circuits, and the circuits adjusted until they showed that A = B; when
  this is the case

               R² - S²
    p² = -------------------.
         N² - L² - 2M(N - L)

  If we make one of the circuits, ADB, consist of a short length of a
  high liquid resistance, so that S is large and N small, and the
  other circuit ACB of a low metallic resistance bent to have
  considerable self-induction, the preceding equation becomes
  approximately p = S/L, so that when S and L are known p is readily
  determined.     (J. J. T.)



ELECTROCHEMISTRY. The present article deals with processes that involve
the electrolysis of aqueous solutions, whilst those in which electricity
is used in the manufacture of chemical products at furnace temperatures
are treated under ELECTROMETALLURGY, although, strictly speaking, in
some cases (e.g. calcium carbide and phosphorus manufacture) they are
not truly metallurgical in character. For the theory and elemental laws
of electro-deposition see ELECTROLYSIS; and for the construction and use
of electric generators see DYNAMO and BATTERY: _Electric_. The
importance of the subject may be gauged by the fact that all the
aluminium, magnesium, sodium, potassium, calcium carbide, carborundum
and artificial graphite, now placed on the market, is made by electrical
processes, and that the use of such processes for the refining of copper
and silver, and in the manufacture of phosphorus, potassium chlorate and
bleach, already pressing very heavily on the older non-electrical
systems, is every year extending. The convenience also with which the
energy of waterfalls can be converted into electric energy has led to
the introduction of chemical industries into countries and districts
where, owing to the absence of coal, they were previously unknown.
Norway and Switzerland have become important producers of chemicals, and
pastoral districts such as those in which Niagara or Foyers are situated
manufacturing centres. In this way the development of the
electrochemical industry is in a marked degree altering the distribution
of trade throughout the world.

_Electrolytic Refining of Metals._--The principle usually followed in
the electrolytic refining of metals is to cast the impure metal into
plates, which are exposed as anodes in a suitable solvent, commonly a
salt of the metal under treatment. On passing a current of electricity,
of which the volume and pressure are adjusted to the conditions of the
electrolyte and electrodes, the anode slowly dissolves, leaving the
insoluble impurities in the form of a sponge, if the proportion be
considerable, but otherwise as a mud or slime which becomes detached
from the anode surface and must be prevented from coming into contact
with the cathode. The metal to be refined passing into solution is
concurrently deposited at the cathode. Soluble impurities which are more
electro-negative than the metal under treatment must, if present, be
removed by a preliminary process, and the voltage and other conditions
must be so selected that none of the more electro-positive metals are
co-deposited with the metal to be refined. From these and other
considerations it is obvious that (1) the electrolyte must be such as
will freely dissolve the metal to be refined; (2) the electrolyte must
be able to dissolve the major portion of the anode, otherwise the mass
of insoluble matter on the outer layer will prevent access of
electrolyte to the core, which will thus escape refining; (3) the
electrolyte should, if possible, be incapable of dissolving metals more
electro-negative than that to be refined; (4) the proportion of soluble
electro-positive impurities must not be excessive, or these substances
will accumulate too rapidly in the solution and necessitate its frequent
purification; (5) the current density must be so adjusted to the
strength of the solution and to other conditions that no relatively
electro-positive metal is deposited, and that the cathode deposit is
physically suitable for subsequent treatment; (6) the current density
should be as high as is consistent with the production of a pure and
sound deposit, without undue expense of voltage, so that the operation
may be rapid and the "turnover" large; (7) the electrolyte should be as
good a conductor of electricity as possible, and should not, ordinarily,
be altered chemically by exposure to air; and (8) the use of porous
partitions should be avoided, as they increase the resistance and
usually require frequent renewal. For details of the practical methods
see GOLD; SILVER; COPPER and headings for other metals.

_Electrolytic Manufacture of Chemical Products._--When an aqueous
solution of the salt of an alkali metal is electrolysed, the metal
reacts with the water, as is well known, forming caustic alkali, which
dissolves in the solution, and hydrogen, which comes off as a gas. So
early as 1851 a patent was taken out by Cooke for the production of
caustic alkali without the use of a separate current, by immersing iron
and copper plates on opposite sides of a porous (biscuit-ware) partition
in a suitable cell, containing a solution of the salt to be
electrolysed, at 21°-65° C. (70°-150° F.). The solution of the iron
anode was intended to afford the necessary energy. In the same year
another patent was granted to C. Watt for a similar process, involving
the employment of an externally generated current. When an alkaline
chloride, say sodium chloride, is electrolysed with one electrode
immersed in a porous cell, while caustic soda is formed at the cathode,
chlorine is deposited at the anode. If the latter be insoluble, the gas
diffuses into the solution and, when this becomes saturated, escapes
into the air. If, however, no porous division be used to prevent the
intermingling by diffusion of the anode and cathode solutions, a
complicated set of subsidiary reactions takes place. The chlorine reacts
with the caustic soda, forming sodium hypochlorite, and this in turn,
with an excess of chlorine and at higher temperatures, becomes for the
most part converted into chlorate, whilst any simultaneous electrolysis
of a hydroxide or water and a chloride (so that hydroxyl and chlorine
are simultaneously liberated at the anode) also produces oxygen-chlorine
compounds direct. At the same time, the diffusion of these compounds
into contact with the cathode leads to a partial reduction to chloride,
by the removal of combined oxygen by the instrumentality of the hydrogen
there evolved. In proportion as the original chloride is thus
reproduced, the efficiency of the process is of course diminished. It is
obvious that, with suitable methods and apparatus, the electrolysis of
alkaline chlorides may be made to yield chlorine, hypochlorites
(bleaching liquors), chlorates or caustic alkali, but that great care
must be exercised if any of these products is to be obtained pure and
with economy. Many patents have been taken out in this branch of
electrochemistry, but it is to be remarked that that granted to C. Watt
traversed the whole of the ground. In his process a current was passed
through a tank divided into two or three cells by porous partitions,
hoods and tubes were arranged to carry off chlorine and hydrogen
respectively, and the whole was heated to 120° F. by a steam jacket when
caustic alkali was being made. Hypochlorites were made, at ordinary
temperatures, and chlorates at higher temperatures, in a cell without a
partition in which the cathode was placed horizontally immediately above
the anode, to favour the mixing of the ascending chlorine with the
descending caustic solution.

  The relation between the composition of the electrolyte and the
  various conditions of current-density, temperature and the like has
  been studied by F. Oettel (_Zeitschrift f. Elektrochem._, 1894, vol.
  i. pp. 354 and 474) in connexion with the production of hypochlorites
  and chlorates in tanks without diaphragms, by C. Häussermann and W.
  Naschold (_Chemiker Zeitung_, 1894, vol. xviii. p. 857) for their
  production in cells with porous diaphragms, and by F. Haber and S.
  Grinberg (_Zeitschrift f. anorgan. Chem._, 1898, vol. xvi. pp. 198,
  329, 438) in connexion with the electrolysis of hydrochloric acid.
  Oettel, using a 20% solution of potassium chloride, obtained the best
  yield of hypochlorite with a high current-density, but as soon as 1¼%
  of bleaching chlorine (as hypochlorite) was present, the formation of
  chlorate commenced. The yield was at best very low as compared with
  that theoretically possible. The best yield of chlorate was obtained
  when from 1 to 4% of caustic potash was present. With high
  current-density, heating the solution tended to increase the
  proportion of chlorate to hypochlorite, but as the proportion of water
  decomposed is then higher, the amount of chlorine produced must be
  less and the total chlorine efficiency lower. He also traced a
  connexion between alkalinity, temperature and current-density, and
  showed that these conditions should be mutually adjusted. With a
  current-density of 130 to 140 amperes per sq. ft., at 3 volts, passing
  between platinum electrodes, he attained to a current-efficiency of
  52%, and each (British) electrical horse-power hour was equivalent to
  a production of 1378.5 grains of potassium chlorate. In other words,
  each pound of chlorate would require an expenditure of nearly 5.1
  e.h.p. hours. One of the earliest of the more modern processes was
  that of E. Hermite, which consisted in the production of
  bleach-liquors by the electrolysis (according to the 1st edition of
  the 1884 patent) of magnesium or calcium chloride between platinum
  anodes carried in wooden frames, and zinc cathodes. The solution,
  containing hypochlorites and chlorates, was then applied to the
  bleaching of linen, paper-pulp or the like, the solution being used
  over and over again. Many modifications have been patented by Hermite,
  that of 1895 specifying the use of platinum gauze anodes, held in
  ebonite or other frames. Rotating zinc cathodes were used, with
  scrapers to prevent the accumulation of a layer of insoluble magnesium
  compounds, which would otherwise increase the electrical resistance
  beyond reasonable limits. The same inventor has patented the
  application of electrolysed chlorides to the purification of starch by
  the oxidation of less stable organic bodies, to the bleaching of oils,
  and to the purification of coal gas, spirit and other substances. His
  system for the disinfection of sewage and similar matter by the
  electrolysis of chlorides, or of sea-water, has been tried, but for
  the most part abandoned on the score of expense. Reference may be made
  to papers written in the early days of the process by C.F. Cross and
  E.J. Bevan (_Journ. Soc. Chem. Industry_, 1887, vol. vi. p. 170, and
  1888, vol. vii. p. 292), and to later papers by P. Schoop
  (_Zeitschrift f. Elektrochem._, 1895, vol. ii. pp. 68, 88, 107, 209,
  289).

  E. Kellner, who in 1886 patented the use of cathode (caustic soda) and
  anode (chlorine) liquors in the manufacture of cellulose from
  wood-fibre, and has since evolved many similar processes, has produced
  an apparatus that has been largely used. It consists of a stoneware
  tank with a thin sheet of platinum-iridium alloy at either end forming
  the primary electrodes, and between them a number of glass plates
  reaching nearly to the bottom, each having a platinum gauze sheet on
  either side; the two sheets belonging to each plate are in metallic
  connexion, but insulated from all the others, and form intermediary or
  bi-polar electrodes. A 10-12% solution of sodium chloride is caused to
  flow upwards through the apparatus and to overflow into troughs, by
  which it is conveyed (if necessary through a cooling apparatus) back
  to the circulating pump. Such a plant has been reported as giving
  0.229 gallon of a liquor containing 1% of available chlorine per
  kilowatt hour, or 0.171 gallon per e.h.p. hour. Kellner has also
  patented a "bleaching-block," as he terms it, consisting of a frame
  carrying parallel plates similar in principle to those last described.
  The block is immersed in the solution to be bleached, and may be
  lifted in or out as required. O. Knöfler and Gebauer have also a
  system of bi-polar electrodes, mounted in a frame in appearance
  resembling a filter-press.

_Other Electrochemical Processes._--It is obvious that electrolytic
iodine and bromine, and oxygen compounds of these elements, may be
produced by methods similar to those applied to chlorides (see ALKALI
MANUFACTURE and CHLORATES), and Kellner and others have patented
processes with this end in view. _Hydrogen_ and _oxygen_ may also be
produced electrolytically as gases, and their respective reducing and
oxidizing powers at the moment of deposition on the electrode are
frequently used in the laboratory, and to some extent industrially,
chiefly in the field of organic chemistry. Similarly, the formation of
organic halogen products may be effected by electrolytic chlorine, as,
for example, in the production of _chloral_ by the gradual introduction
of alcohol into an anode cell in which the electrolyte is a strong
solution of potassium chloride. Again, anode reactions, such as are
observed in the electrolysis of the fatty acids, may be utilized, as,
for example, when the radical CH3CO2--deposited at the anode in the
electrolysis of acetic acid--is dissociated, two of the groups react to
give one molecule of _ethane_, C2H6, and two of carbon dioxide. This,
which has long been recognized as a class-reaction, is obviously capable
of endless variation. Many electrolytic methods have been proposed for
the purification of _sugar_; in some of them soluble anodes are used for
a few minutes in weak alkaline solutions, so that the caustic alkali
from the cathode reaction may precipitate chemically the hydroxide of
the anode metal dissolved in the liquid, the precipitate carrying with
it mechanically some of the impurities present, and thus clarifying the
solution. In others the current is applied for a longer time to the
original sugar-solution with insoluble (e.g. carbon) anodes. F. Peters
has found that with these methods the best results are obtained when
ozone is employed in addition to electrolytic oxygen. Use has been made
of electrolysis in _tanning_ operations, the current being passed
through the tan-liquors containing the hides. The current, by
endosmosis, favours the passage of the solution into the hide-substance,
and at the same time appears to assist the chemical combinations there
occurring; hence a great reduction in the time required for the
completion of the process. Many patents have been taken out in this
direction, one of the best known being that of Groth, experimented upon
by S. Rideal and A.P. Trotter (_Journ. Soc. Chem. Indust._, 1891, vol.
x. p. 425), who employed copper anodes, 4 sq. ft. in area, with
current-densities of 0.375 to 1 (ranging in some cases to 7.5) ampere
per sq. ft., the best results being obtained with the smaller
current-densities. Electrochemical processes are often indirectly used,
as for example in the Villon process (_Elec. Rev._, New York, 1899, vol.
xxxv. p. 375) applied in Russia to the manufacture of alcohol, by a
series of chemical reactions starting from the production of acetylene
by the action of water upon calcium carbide. The production of _ozone_
in small quantities during electrolysis, and by the so-called silent
discharge, has long been known, and the Siemens induction tube has been
developed for use industrially. The Siemens and Halske ozonizer, in form
somewhat resembling the old laboratory instrument, is largely used in
Germany; working with an alternating current transformed up to 6500
volts, it has been found to give 280 grains or more of ozone per e.h.p.
hour. E. Andreoli (whose first British ozone patent was No. 17,426 of
1891) uses flat aluminium plates and points, and working with an
alternating current of 3000 volts is said to have obtained 1440 grains
per e.h.p. hour. Yarnold's process, using corrugated glass plates coated
on one side with gold or other metal leaf, is stated to have yielded as
much as 2700 grains per e.h.p. hour. The ozone so prepared has numerous
uses, as, for example, in bleaching oils, waxes, fabrics, &c.,
sterilizing drinking-water, maturing wines, cleansing foul beer-casks,
oxidizing oil, and in the manufacture of vanillin.

  For further information the following books, among others, may be
  consulted:--Haber, _Grundriss der technischen Elektrochemie_ (München,
  1898); Borchers and M'Millan, _Electric Smelting and Refining_
  (London, 1904); E.D. Peters, _Principles of Copper Smelting_ (New
  York, 1907); F. Peters, _Angewandte Elektrochemie_, vols. ii. and iii.
  (Leipzig, 1900); Gore, _The Art of Electrolytic Separation of Metals_
  (London, 1890); Blount, _Practical Electro-Chemistry_ (London, 1906);
  G. Langbein, _Vollständiges Handbuch der galvanischen
  Metall-Niederschläge_ (Leipzig, 1903), Eng. trans. by W.T. Brannt
  (1909); A. Watt, _Electro-Plating and Electro-Refining of Metals_
  (London, 1902); W.H. Wahl, _Practical Guide to the Gold and Silver
  Electroplater, &c._ (Philadelphia, 1883); Wilson, _Stereotyping and
  Electrotyping_ (London); Lunge, _Sulphuric Acid and Alkali_, vol. iii.
  (London, 1909). Also papers in various technical periodicals. The
  industrial aspect is treated in a Gartside Report, _Some
  Electro-Chemical Centres_ (Manchester, 1908), by J.N. Pring.
       (W. G. M.)



ELECTROCUTION (an anomalous derivative from "electro-execution"; syn.
"electrothanasia"), the popular name, invented in America, for the
infliction of the death penalty on criminals (see CAPITAL PUNISHMENT) by
passing through the body of the condemned a sufficient current of
electricity to cause death. The method was first adopted by the state of
New York, a law making this method obligatory having been passed and
approved by the governor on the 4th of June 1888. The law provides that
there shall be present, in addition to the warden, two physicians,
twelve reputable citizens of full age, seven deputy sheriffs, and such
ministers, priests or clergymen, not exceeding two, as the criminal may
request. A post-mortem examination of the body of the convict is
required, and the body, unless claimed by relatives, is interred in the
prison cemetery with a sufficient quantity of quicklime to consume it.
The law became effective in New York on the 1st of January 1889. The
first criminal to be executed by electricity was William Kemmler, on the
6th of August 1890, at Auburn prison. The validity of the New York law
had previously been attacked in regard to this case (_Re Kemmler_, 1889;
136 U.S. 436), as providing "a cruel and unusual punishment" and
therefore being contrary to the Constitution; but it was sustained in
the state courts and finally in the Federal courts. By 1906 about one
hundred and fifteen murderers had been successfully executed by
electricity in New York state in Sing Sing, Auburn and Dannemora
prisons. The method has also been adopted by the states of Ohio (1896),
Massachusetts (1898), New Jersey (1906), Virginia (1908) and North
Carolina (1910).

The apparatus consists of a stationary engine, an alternating dynamo
capable of generating a current at a pressure of 2000 volts, a
"death-chair" with adjustable head-rest, binding straps and adjustable
electrodes devised by E.F. Davis, the state electrician of New York. The
voltmeter, ammeter and switch-board controlling the current are located
in the execution-room; the dynamo-room is communicated with by electric
signals. Before each execution the entire apparatus is thoroughly
tested. When everything is in readiness the criminal is brought in and
seats himself in the death-chair. His head, chest, arms and legs are
secured by broad straps; one electrode thoroughly moistened with
salt-solution is affixed to the head, and another to the calf of one
leg, both electrodes being moulded so as to secure good contact. The
application of the current is usually as follows: the contact is made
with a high voltage (1700-1800 volts) for 5 to 7 seconds, reduced to 200
volts until a half-minute has elapsed; raised to high voltage for 3 to 5
seconds, again reduced to low voltage for 3 to 5 seconds, again reduced
to a low voltage until one minute has elapsed, when it is again raised
to the high voltage for a few seconds and the contact broken. The
ammeter usually shows that from 7 to 10 amperes pass through the
criminal's body. A second or even a third brief contact is sometimes
made, partly as a precautionary measure, but rather the more completely
to abolish reflexes in the dead body. Calculations have shown that by
this method of execution from 7 to 10 h. p. of energy are liberated in
the criminal's body. The time consumed by the strapping-in process is
usually about 45 seconds, and the first contact is made about 70 seconds
after the criminal has entered the death-chamber.

When properly performed the effect is painless and instantaneous death.
The mechanism of life, circulation and respiration cease with the first
contact. Consciousness is blotted out instantly, and the prolonged
application of the current ensures permanent derangement of the vital
functions beyond recovery. Occasionally the drying of the sponges
through undue generation of heat causes desquamation or superficial
blistering of the skin at the site of the electrodes. Post-mortem
discoloration, or post-mortem lividity, often appears during the first
contact. The pupils of the eyes dilate instantly and remain dilated
after death.

The post-mortem examination of "electrocuted" criminals reveals a number
of interesting phenomena. The temperature of the body rises promptly
after death to a very high point. At the site of the leg electrode a
temperature of over 128° F. was registered within fifteen minutes in
many cases. After the removal of the brain the temperature recorded in
the spinal canal was often over 120° F. The development of this high
temperature is to be regarded as resulting from the active metabolism of
tissues not (somatically) dead within a body where all vital mechanisms
have been abolished, there being no circulation to carry off the
generated heat. The heart, at first flaccid when exposed soon after
death, gradually contracts and assumes a tetanized condition; it empties
itself of all blood and takes the form of a heart in systole. The lungs
are usually devoid of blood and weigh only 7 or 8 ounces (avoird.) each.
The blood is profoundly altered biochemically; it is of a very dark
colour and it rarely coagulates.     (E. A. S.*)



ELECTROKINETICS, that part of electrical science which is concerned with
the properties of electric currents.

_Classification of Electric Currents._--Electric currents are classified
into (a) conduction currents, (b) convection currents, (c) displacement
or dielectric currents. In the case of conduction currents electricity
flows or moves through a stationary material body called the conductor.
In convection currents electricity is carried from place to place with
and on moving material bodies or particles. In dielectric currents there
is no continued movement of electricity, but merely a limited
displacement through or in the mass of an insulator or dielectric. The
path in which an electric current exists is called an electric circuit,
and may consist wholly of a conducting body, or partly of a conductor
and insulator or dielectric, or wholly of a dielectric. In cases in
which the three classes of currents are present together the true
current is the sum of each separately. In the case of conduction
currents the circuit consists of a conductor immersed in a
non-conductor, and may take the form of a thin wire or cylinder, a
sheet, surface or solid. Electric conduction currents may take place in
space of one, two or three dimensions, but for the most part the
circuits we have to consider consist of thin cylindrical wires or tubes
of conducting material surrounded with an insulator; hence the case
which generally presents itself is that of electric flow in space of one
dimension. Self-closed electric currents taking place in a sheet of
conductor are called "eddy currents."

Although in ordinary language the current is said to flow in the
conductor, yet according to modern views the real pathway of the energy
transmitted is the surrounding dielectric, and the so-called conductor
or wire merely guides the transmission of energy in a certain direction.
The presence of an electric current is recognized by three qualities or
powers: (1) by the production of a magnetic field, (2) in the case of
conduction currents, by the production of heat in the conductor, and (3)
if the conductor is an electrolyte and the current unidirectional, by
the occurrence of chemical decomposition in it. An electric current may
also be regarded as the result of a movement of electricity across each
section of the circuit, and is then measured by the quantity conveyed
per unit of time. Hence if dq is the quantity of electricity which flows
across any section of the conductor in the element of time dt, the
current i = dq/dt.

[Illustration: FIG. 1.]

[Illustration: FIG. 2.]

Electric currents may be also classified as constant or variable and as
unidirectional or "direct," that is flowing always in the same
direction, or "alternating," that is reversing their direction at
regular intervals. In the last case the variation of current may follow
any particular law. It is called a "periodic current" if the cycle of
current values is repeated during a certain time called the periodic
time, during which the current reaches a certain maximum value, first in
one direction and then in the opposite, and in the intervals between has
a zero value at certain instants. The frequency of the periodic current
is the number of periods or cycles in one second, and alternating
currents are described as low frequency or high frequency, in the latter
case having some thousands of periods per second. A periodic current may
be represented either by a wave diagram, or by a polar diagram.[1] In
the first case we take a straight line to represent the uniform flow of
time, and at small equidistant intervals set up perpendiculars above or
below the time axis, representing to scale the current at that instant
in one direction or the other; the extremities of these ordinates then
define a wavy curve which is called the wave form of the current (fig.
1). It is obvious that this curve can only be a single valued curve. In
one particular and important case the form of the current curve is a
simple harmonic curve or simple sine curve. If T represents the periodic
time in which the cycle of current values takes place, whilst n is the
frequency or number of periods per second and p stands for 2[pi]n, and i
is the value of the current at any instant t, and I its maximum value,
then in this case we have i = I sin pt. Such a current is called a "sine
current" or simple periodic current.

In a polar diagram (fig. 2) a number of radial lines are drawn from a
point at small equiangular intervals, and on these lines are set off
lengths proportional to the current value of a periodic current at
corresponding intervals during one complete period represented by four
right angles. The extremities of these radii delineate a polar curve.
The polar form of a simple sine current is obviously a circle drawn
through the origin. As a consequence of Fourier's theorem it follows
that any periodic curve having any wave form can be imitated by the
superposition of simple sine currents differing in maximum value and in
phase.

_Definitions of Unit Electric Current._--In electrokinetic
investigations we are most commonly limited to the cases of
unidirectional continuous and constant currents (C.C. or D.C.), or of
simple periodic currents, or alternating currents of sine form (A.C.). A
continuous electric current is measured either by the magnetic effect it
produces at some point outside its circuit, or by the amount of
electrochemical decomposition it can perform in a given time on a
selected standard electrolyte. Limiting our consideration to the case of
linear currents or currents flowing in thin cylindrical wires, a
definition may be given in the first place of the unit electric current
in the centimetre, gramme, second (C.G.S.) of electromagnetic
measurement (see UNITS, PHYSICAL). H.C. Oersted discovered in 1820 that
a straight wire conveying an electric current is surrounded by a
magnetic field the lines of which are self-closed lines embracing the
electric circuit (see ELECTRICITY and ELECTROMAGNETISM). The unit
current in the electromagnetic system of measurement is defined as the
current which, flowing in a thin wire bent into the form of a circle of
one centimetre in radius, creates a magnetic field having a strength of
2[pi] units at the centre of the circle, and therefore would exert a
mechanical force of 2[pi] dynes on a unit magnetic pole placed at that
point (see MAGNETISM). Since the length of the circumference of the
circle of unit radius is 2[pi] units, this is equivalent to stating that
the unit current on the electromagnetic C.G.S. system is a current such
that unit length acts on unit magnetic pole with a unit force at a unit
of distance. Another definition, called the electrostatic unit of
current, is as follows: Let any conductor be charged with electricity
and discharged through a thin wire at such a rate that one electrostatic
unit of quantity (see ELECTROSTATICS) flows past any section of the wire
in one unit of time. The electromagnetic unit of current defined as
above is 3 × 10^10 times larger than the electrostatic unit.

In the selection of a practical unit of current it was considered that
the electromagnetic unit was too large for most purposes, whilst the
electrostatic unit was too small; hence a practical unit of current
called 1 ampere was selected, intended originally to be {1/10} of the
absolute electromagnetic C.G.S. unit of current as above defined. The
practical unit of current, called the international ampere, is, however,
legally defined at the present time as the continuous unidirectional
current which when flowing through a neutral solution of silver nitrate
deposits in one second on the cathode or negative pole 0.001118 of a
gramme of silver. There is reason to believe that the international unit
is smaller by about one part in a thousand, or perhaps by one part in
800, than the theoretical ampere defined as 1/10 part of the absolute
electromagnetic unit. A periodic or alternating current is said to have
a value of 1 ampere if when passed through a fine wire it produces in
the same time the same heat as a unidirectional continuous current of 1
ampere as above electrochemically defined. In the case of a simple
periodic alternating current having a simple sine wave form, the maximum
value is equal to that of the equiheating continuous current multiplied
by [root]2. This equiheating continuous current is called the effective
or root-mean-square (R.M.S.) value of the alternating one.

_Resistance._--A current flows in a circuit in virtue of an
electromotive force (E.M.F.), and the numerical relation between the
current and E.M.F. is determined by three qualities of the circuit
called respectively, its resistance (R), inductance (L), and capacity
(C). If we limit our consideration to the case of continuous
unidirectional conduction currents, then the relation between current
and E.M.F. is defined by Ohm's law, which states that the numerical
value of the current is obtained as the quotient of the electromotive
force by a certain constant of the circuit called its resistance, which
is a function of the geometrical form of the circuit, of its nature,
i.e. material, and of its temperature, but is independent of the
electromotive force or current. The resistance (R) is measured in units
called ohms and the electromotive force in volts (V); hence for a
continuous current the value of the current in amperes (A) is obtained
as the quotient of the electromotive force acting in the circuit
reckoned in volts by the resistance in ohms, or A = V/R. Ohm established
his law by a course of reasoning which was similar to that on which
J.B.J. Fourier based his investigations on the uniform motion of heat in
a conductor. As a matter of fact, however, Ohm's law merely states the
direct proportionality of steady current to steady electromotive force
in a circuit, and asserts that this ratio is governed by the numerical
value of a quality of the conductor, called its resistance, which is
independent of the current, provided that a correction is made for the
change of temperature produced by the current. Our belief, however, in
its universality and accuracy rests upon the close agreement between
deductions made from it and observational results, and although it is
not derivable from any more fundamental principle, it is yet one of the
most certainly ascertained laws of electrokinetics.

Ohm's law not only applies to the circuit as a whole but to any part of
it, and provided the part selected does not contain a source of
electromotive force it may be expressed as follows:--The difference of
potential (P.D.) between any two points of a circuit including a
resistance R, but not including any source of electromotive force, is
proportional to the product of the resistance and the current i in the
element, provided the conductor remains at the same temperature and the
current is constant and unidirectional. If the current is varying we
have, however, to take into account the electromotive force (E.M.F.)
produced by this variation, and the product Ri is then equal to the
difference between the observed P.D. and induced E.M.F.

We may otherwise define the resistance of a circuit by saying that it is
that physical quality of it in virtue of which energy is dissipated as
heat in the circuit when a current flows through it. The power
communicated to any electric circuit when a current i is created in it
by a continuous unidirectional electromotive force E is equal to Ei, and
the energy dissipated as heat in that circuit by the conductor in a
small interval of time dt is measured by Ei dt. Since by Ohm's law E =
Ri, where R is the resistance of the circuit, it follows that the energy
dissipated as heat per unit of time in any circuit is numerically
represented by Ri², and therefore the resistance is measured by the heat
produced per unit of current, provided the current is unvarying.

_Inductance._--As soon as we turn our attention, however, to alternating
or periodic currents we find ourselves compelled to take into account
another quality of the circuit, called its "inductance." This may be
defined as that quality in virtue of which energy is stored up in
connexion with the circuit in a magnetic form. It can be experimentally
shown that a current cannot be created instantaneously in a circuit by
any finite electromotive force, and that when once created it cannot be
annihilated instantaneously. The circuit possesses a quality analogous
to the inertia of matter. If a current i is flowing in a circuit at any
moment, the energy stored up in connexion with the circuit is measured
by ½Li², where L, the inductance of the circuit, is related to the
current in the same manner as the quantity called the mass of a body is
related to its velocity in the expression for the ordinary kinetic
energy, viz. ½Mv². The rate at which this conserved energy varies with
the current is called the "electrokinetic momentum" of this circuit (=
Li). Physically interpreted this quantity signifies the number of lines
of magnetic flux due to the current itself which are self-linked with
its own circuit.

_Magnetic Force and Electric Currents._--In the case of every circuit
conveying a current there is a certain magnetic force (see MAGNETISM) at
external points which can in some instances be calculated. Laplace
proved that the magnetic force due to an element of length dS of a
circuit conveying a current I at a point P at a distance r from the
element is expressed by IdS sin [theta]/r², where [theta] is the angle
between the direction of the current element and that drawn between the
element and the point. This force is in a direction perpendicular to the
radius vector and to the plane containing it and the element of current.
Hence the determination of the magnetic force due to any circuit is
reduced to a summation of the effects due to all the elements of length.
For instance, the magnetic force at the centre of a circular circuit of
radius r carrying a steady current I is 2[pi]I/r, since all elements
are at the same distance from the centre. In the same manner, if we take
a point in a line at right angles to the plane of the circle through its
centre and at a distance d, the magnetic force along this line is
expressed by 2[pi]r²I/(r² + d²)(3/2). Another important case is that of
an infinitely long straight current. By summing up the magnetic force
due to each element at any point P outside the continuous straight
current I, and at a distance d from it, we can show that it is equal to
2I/d or is inversely proportional to the distance of the point from the
wire. In the above formula the current I is measured in absolute
electromagnetic units. If we reckon the current in amperes A, then I =
A/10.

It is possible to make use of this last formula, coupled with an
experimental fact, to prove that the magnetic force due to an element of
current varies inversely as the square of the distance. If a flat
circular disk is suspended so as to be free to rotate round a straight
current which passes through its centre, and two bar magnets are placed
on it with their axes in line with the current, it is found that the
disk has no tendency to rotate round the current. This proves that the
force on each magnetic pole is inversely as its distance from the
current. But it can be shown that this law of action of the whole
infinitely long straight current is a mathematical consequence of the
fact that each element of the current exerts a magnetic force which
varies inversely as the square of the distance. If the current flows N
times round the circuit instead of once, we have to insert NA/10 in
place of I in all the above formulae. The quantity NA is called the
"ampere-turns" on the circuit, and it is seen that the magnetic field at
any point outside a circuit is proportional to the ampere-turns on it
and to a function of its geometrical form and the distance of the point.

[Illustration: FIG. 3.]

[Illustration: FIG. 4.]

There is therefore a distribution of magnetic force in the field of
every current-carrying conductor which can be delineated by lines of
magnetic force and rendered visible to the eye by iron filings (see
Magnetism). If a copper wire is passed vertically through a hole in a
card on which iron filings are sprinkled, and a strong electric current
is sent through the circuit, the filings arrange themselves in
concentric circular lines making visible the paths of the lines of
magnetic force (fig. 3). In the same manner, by passing a circular wire
through a card and sending a strong current through the wire we can
employ iron filings to delineate for us the form of the lines of
magnetic force (fig. 4). In all cases a magnetic pole of strength M,
placed in the field of an electric current, is urged along the lines of
force with a mechanical force equal to MH, where H is the magnetic
force. If then we carry a unit magnetic pole against the direction in
which it would naturally move we do _work_. The lines of magnetic force
embracing a current-carrying conductor are always loops or endless
lines.

  The work done in carrying a unit magnetic pole once round a circuit
  conveying a current is called the "line integral of magnetic force"
  along that path. If, for instance, we carry a unit pole in a circular
  path of radius r once round an infinitely long straight filamentary
  current I, the line integral is 4[pi]I. It is easy to prove that this
  is a general law, and that if we have any currents flowing in a
  conductor the line integral of magnetic force taken once round a path
  linked with the current circuit is 4[pi] times the total current
  flowing through the circuit. Let us apply this to the case of an
  endless solenoid. If a copper wire insulated or covered with cotton or
  silk is twisted round a thin rod so as to make a close spiral, this
  forms a "solenoid," and if the solenoid is bent round so that its two
  ends come together we have an endless solenoid. Consider such a
  solenoid of mean length l and N turns of wire. If it is made endless,
  the magnetic force H is the same everywhere along the central axis and
  the line integral along the axis is Hl. If the current is denoted by
  I, then NI is the total current, and accordingly 4[pi]NI = Hl, or H =
  4[pi]NI/l. For a thin endless solenoid the axial magnetic force is
  therefore 4[pi] times the current-turns per unit of length. This holds
  good also for a long straight solenoid provided its length is large
  compared with its diameter. It can be shown that if insulated wire is
  wound round a sphere, the turns being all parallel to lines of
  latitude, the magnetic force in the interior is constant and the lines
  of force therefore parallel. The magnetic force at a point outside a
  conductor conveying a current can by various means be measured or
  compared with some other standard magnetic forces, and it becomes then
  a means of measuring the current. Instruments called galvanometers and
  ammeters for the most part operate on this principle.

_Thermal Effects of Currents._--J.P. Joule proved that the heat produced
by a constant current in a given time in a wire having a constant
resistance is proportional to the square of the strength of the current.
This is known as Joule's law, and it follows, as already shown, as an
immediate consequence of Ohm's law and the fact that the power
dissipated electrically in a conductor, when an electromotive force E is
applied to its extremities, producing thereby a current I in it, is
equal to EI.

  If the current is alternating or periodic, the heat produced in any
  time T is obtained by taking the sum at equidistant intervals of time
  of all the values of the quantities Ri²dt, where dt represents a small
  interval of time and i is the current at that instant. The quantity
           _
          / T
   T^(-1) |    i²dt is called the mean-square-value of the variable
         _/ 0

  current, i being the instantaneous value of the current, that is, its
  value at a particular instant or during a very small interval of time
  dt. The square root of the above quantity, or
     _        _      _
    |        / T      | ½,
    | T^(-1) |  i²dt  |
    |_      _/ 0     _|

  is called the root-mean-square-value, or the effective value of the
  current, and is denoted by the letters R.M.S.

Currents have equal heat-producing power in conductors of identical
resistance when they have the same R.M.S. values. Hence periodic or
alternating currents can be measured as regards their R.M.S. value by
ascertaining the continuous current which produces in the same time the
same heat in the same conductor as the periodic current considered.
Current measuring instruments depending on this fact, called hot-wire
ammeters, are in common use, especially for measuring alternating
currents. The maximum value of the periodic current can only be
determined from the R.M.S. value when we know the wave form of the
current. The thermal effects of electric currents in conductors are
dependent upon the production of a state of equilibrium between the heat
produced electrically in the wire and the causes operative in removing
it. If an ordinary round wire is heated by a current it loses heat, (1)
by radiation, (2) by air convection or cooling, and (3) by conduction of
heat out of the ends of the wire. Generally speaking, the greater part
of the heat removal is effected by radiation and convection.

  If a round sectioned metallic wire of uniform diameter d and length l
  made of a material of resistivity [rho] has a current of A amperes
  passed through it, the heat in watts produced in any time t seconds is
  represented by the value of 4A²[rho]lt/10^9[pi]d², where d and l must
  be measured in centimetres and [rho] in absolute C.G.S.
  electromagnetic units. The factor 10^9 enters because one ohm is 10^9
  absolute electromagnetic C.G.S. units (see UNITS, PHYSICAL). If the
  wire has an emissivity e, by which is meant that e units of heat
  reckoned in joules or watt-seconds are radiated per second from unit
  of surface, then the power removed by radiation in the time t is
  expressed by [pi]dlet. Hence when thermal equilibrium is established
  we have 4A²[rho]lt/10^9[pi]d² = [pi]dlet, or A² = 10^9[pi]²ed³/4[rho].
  If the diameter of the wire is reckoned in mils (1 mil = .001 in.),
  and if we take e to have a value 0.1, an emissivity which will
  generally bring the wire to about 60° C., we can put the above formula
  in the following forms for circular sectioned copper, iron or
  platinoid wires, viz.

    A = [root](d³/500) for copper wires
    A = [root](d³/4000) for iron wires
    A = [root](d³/5000) for platinoid wires.

  These expressions give the ampere value of the current which will
  bring bare, straight or loosely coiled wires of d mils in diameter to
  about 60° C. when the steady state of temperature is reached. Thus,
  for instance, a bare straight copper wire 50 mils in diameter (=0.05
  in.) will be brought to a steady temperature of about 60° C. if a
  current of [root]50³/500 = [root]250 = 16 amperes (nearly) is passed
  through it, whilst a current of [root]25 = 5 amperes would bring a
  platinoid wire to about the same temperature.

A wire has therefore a certain safe current-carrying capacity which is
determined by its specific resistance and emissivity, the latter being
fixed by its form, surface and surroundings. The emissivity increases
with the temperature, else no state of thermal equilibrium could be
reached. It has been found experimentally that whilst for fairly thick
wires from 8 to 60 mils in diameter the safe current varies
approximately as the 1.5th power of the diameter, for fine wires of 1 to
3 mils it varies more nearly as the diameter.

_Action of one Current on Another._--The investigations of Ampère in
connexion with electric currents are of fundamental importance in
electrokinetics. Starting from the discovery of Oersted, Ampère made
known the correlative fact that not only is there a mechanical action
between a current and a magnet, but that two conductors conveying
electric currents exert mechanical forces on each other. Ampère devised
ingenious methods of making one portion of a circuit movable so that he
might observe effects of attraction or repulsion between this circuit
and some other fixed current. He employed for this purpose an astatic
circuit B, consisting of a wire bent into a double rectangle round which
a current flowed first in one and then in the opposite direction (fig.
5). In this way the circuit was removed from the action of the earth's
magnetic field, and yet one portion of it could be submitted to the
action of any other circuit C. The astatic circuit was pivoted by
suspending it in mercury cups q, p, one of which was in electrical
connexion with the tubular support A, and the other with a strong
insulated wire passing up it.

[Illustration: FIG. 5.]

Ampère devised certain crucial experiments, and the theory deduced from
them is based upon four facts and one assumption.[2] He showed (1) that
wire conveying a current bent back on itself produced no action upon a
proximate portion of a movable astatic circuit; (2) that if the return
wire was bent zig-zag but close to the outgoing straight wire the
circuit produced no action on the movable one, showing that the effect
of an element of the circuit was proportional to its projected length;
(3) that a closed circuit cannot cause motion in an element of another
circuit free to move in the direction of its length; and (4) that the
action of two circuits on one and the same movable circuit was null if
one of the two fixed circuits was n times greater than the other but n
times further removed from the movable circuit. From this last
experiment by an ingenious line of reasoning he proved that the action
of an element of current on another element of current varies inversely
as a square of their distance. These experiments enabled him to
construct a mathematical expression of the law of action between two
elements of conductors conveying currents. They also enabled him to
prove that an element of current may be resolved like a force into
components in different directions, also that the force produced by any
element of the circuit on an element of any other circuit was
perpendicular to the line joining the elements and inversely as the
square of their distance. Also he showed that this force was an
attraction if the currents in the elements were in the same direction,
but a repulsion if they were in opposite directions. From these
experiments and deductions from them he built up a complete formula for
the action of one element of a current of length dS of one conductor
conveying a current I upon another element dS' of another circuit
conveying another current I' the elements being at a distance apart
equal to r.

  If [theta] and [theta]' are the angles the elements make with the line
  joining them, and [phi] the angle they make with one another, then
  Ampère's expression for the mechanical force f the elements exert on
  one another is

    f = 2II'r^(-2) {cos [phi] - (3/2)cos [theta] cos [theta]'}dSdS'.

  This law, together with that of Laplace already mentioned, viz. that
  the magnetic force due to an element of length dS of a current I at a
  distance r, the element making an angle [theta] with the radius vector
  o is IdS sin [theta]/r², constitute the fundamental laws of
  electrokinetics.

Ampère applied these with great mathematical skill to elucidate the
mechanical actions of currents on each other, and experimentally
confirmed the following deductions: (1) Currents in parallel circuits
flowing in the same direction attract each other, but if in opposite
directions repel each other. (2) Currents in wires meeting at an angle
attract each other more into parallelism if both flow either to or from
the angle, but repel each other more widely apart if they are in
opposite directions. (3) A current in a small circular conductor exerts
a magnetic force in its centre perpendicular to its plane and is in all
respects equivalent to a magnetic shell or a thin circular disk of steel
so magnetized that one face is a north pole and the other a south pole,
the product of the area of the circuit and the current flowing in it
determining the magnetic moment of the element. (4) A closely wound
spiral current is equivalent as regards external magnetic force to a
polar magnet, such a circuit being called a finite solenoid. (5) Two
finite solenoid circuits act on each other like two polar magnets,
exhibiting actions of attraction or repulsion between their ends.

Ampère's theory was wholly built up on the assumption of action at a
distance between elements of conductors conveying the electric currents.
Faraday's researches and the discovery of the fact that the insulating
medium is the real seat of the operations necessitates a change in the
point of view from which we regard the facts discovered by Ampère.
Maxwell showed that in any field of magnetic force there is a tension
along the lines of force and a pressure at right angles to them; in
other words, lines of magnetic force are like stretched elastic threads
which tend to contract.[3] If, therefore, two conductors lie parallel
and have currents in them in the same direction they are impressed by a
certain number of lines of magnetic force which pass round the two
conductors, and it is the tendency of these to contract which draws the
circuits together. If, however, the currents are in opposite directions
then the lateral pressure of the similarly contracted lines of force
between them pushes the conductors apart. Practical application of
Ampère's discoveries was made by W.E. Weber in inventing the
electrodynamometer, and later Lord Kelvin devised ampere balances for
the measurement of electric currents based on the attraction between
coils conveying electric currents.

_Induction of Electric Currents._--Faraday[4] in 1831 made the important
discovery of the induction of electric currents (see ELECTRICITY). If
two conductors are placed parallel to each other, and a current in one
of them, called the primary, started or stopped or changed in strength,
every such alteration causes a transitory current to appear in the other
circuit, called the secondary. This is due to the fact that as the
primary current increases or decreases, its own embracing magnetic field
alters, and lines of magnetic force are added to or subtracted from its
fields. These lines do not appear instantly in their place at a
distance, but are propagated out from the wire with a velocity equal to
that of light; hence in their outward progress they cut through the
secondary circuit, just as ripples made on the surface of water in a
lake by throwing a stone on to it expand and cut through a stick held
vertically in the water at a distance from the place of origin of the
ripples. Faraday confirmed this view of the phenomena by proving that
the mere motion of a wire transversely to the lines of magnetic force of
a permanent magnet gave rise to an induced electromotive force in the
wire. He embraced all the facts in the single statement that if there
be any circuit which by movement in a magnetic field, or by the creation
or change in magnetic fields round it, experiences a change in the
number of lines of force linked with it, then an electromotive force is
set up in that circuit which is proportional at any instant to the rate
at which the total magnetic flux linked with it is changing. Hence if Z
represents the total number of lines of magnetic force linked with a
circuit of N turns, then -N(dZ/dt) represents the electromotive force
set up in that circuit. The operation of the induction coil (q.v.) and
the transformer (q.v.) are based on this discovery. Faraday also found
that if a copper disk A (fig. 6) is rotated between the poles of a
magnet NO so that the disk moves with its plane perpendicular to the
lines of magnetic force of the field, it has created in it an
electromotive force directed from the centre to the edge or vice versa.
The action of the dynamo (q.v.) depends on similar processes, viz. the
cutting of the lines of magnetic force of a constant field produced by
certain magnets by certain moving conductors called armature bars or
coils in which an electromotive force is thereby created.

[Illustration: FIG 6.]

  In 1834 H.F.E. Lenz enunciated a law which connects together the
  mechanical actions between electric circuits discovered by Ampère and
  the induction of electric currents discovered by Faraday. It is as
  follows: If a constant current flows in a primary circuit P, and if by
  motion of P a secondary current is created in a neighbouring circuit
  S, the direction of the secondary current will be such as to oppose
  the relative motion of the circuits. Starting from this, F.E. Neumann
  founded a mathematical theory of induced currents, discovering a
  quantity M, called the "potential of one circuit on another," or
  generally their "coefficient of mutual inductance." Mathematically M
  is obtained by taking the sum of all such quantities as ff dSdS' cos
  [phi]/r, where dS and dS' are the elements of length of the two
  circuits, r is their distance, and [phi] is the angle which they make
  with one another; the summation or integration must be extended over
  every possible pair of elements. If we take pairs of elements in the
  same circuit, then Neumann's formula gives us the coefficient of
  self-induction of the circuit or the potential of the circuit on
  itself. For the results of such calculations on various forms of
  circuit the reader must be referred to special treatises.

  H. von Helmholtz, and later on Lord Kelvin, showed that the facts of
  induction of electric currents discovered by Faraday could have been
  predicted from the electrodynamic actions discovered by Ampère
  assuming the principle of the conservation of energy. Helmholtz takes
  the case of a circuit of resistance R in which acts an electromotive
  force due to a battery or thermopile. Let a magnet be in the
  neighbourhood, and the potential of the magnet on the circuit be V, so
  that if a current I existed in the circuit the work done on the magnet
  in the time dt is I(dV/dt)dt. The source of electromotive force
  supplies in the time dt work equal to EIdt, and according to Joule's
  law energy is dissipated equal to RI²dt. Hence, by the conservation of
  energy,

    EIdt = RI²dt + I(dV/dt)dt.

  If then E = 0, we have I = -(dV/dt)/R, or there will be a current due
  to an induced electromotive force expressed by -dV/dt. Hence if the
  magnet moves, it will create a current in the wire provided that such
  motion changes the potential of the magnet with respect to the
  circuit. This is the effect discovered by Faraday.[5]

_Oscillatory Currents._--In considering the motion of electricity in
conductors we find interesting phenomena connected with the discharge of
a condenser or Leyden jar (q.v.). This problem was first mathematically
treated by Lord Kelvin in 1853 (_Phil. Mag._, 1853, 5, p. 292).

  If a conductor of capacity C has its terminals connected by a wire of
  resistance R and inductance L, it becomes important to consider the
  subsequent motion of electricity in the wire. If Q is the quantity of
  electricity in the condenser initially, and q that at any time t after
  completing the circuit, then the energy stored up in the condenser at
  that instant is ½q²/C, and the energy associated with the circuit is
  ½L(dq/dt)², and the rate of dissipation of energy by resistance is
  R(dq/dt)², since dq/dt = i is the discharge current. Hence we can
  construct an equation of energy which expresses the fact that at any
  instant the power given out by the condenser is partly stored in the
  circuit and partly dissipated as heat in it. Mathematically this is
  expressed as follows:--
          _    _        _         _
      d  |   q² |   d  |     /dq\² |      /dq\²
    - -- | ½ -- | = -- | ½L ( -- ) | + R ( -- )
      dt |_  C _|   dt |_    \dt/ _|      \dt/

  or

    d²q   R  dq   1
    --- + -- -- + -- q = 0.
    dt²   L  dt   LC

  The above equation has two solutions according as R²/4L² is greater or
  less than 1/LC. In the first case the current i in the circuit can be
  expressed by the equation

         [alpha]²+ß²
    i= Q ------------ e^(-[alpha]t) [e^(ßt) - e^(-ßt)],
             2ß
                               ________
                              /R²    1
  where [alpha] = R/2L, ß =  / --- - --, Q is the value of q when t = 0,
                           \/  4L²   LC

  and e is the base of Napierian logarithms; and in the second case
  by the equation

          [alpha]²+ß²
    i = Q ----------- e^(-[alpha]t) sin ßt
            ß
                                   ________
                                  /1    R²
  where [alpha] = R/2L, and ß =  / -- - ---.
                               \/  LC   4L²


  These expressions show that in the first case the discharge current of
  the jar is always in the same direction and is a transient
  unidirectional current. In the second case, however, the current is an
  oscillatory current gradually decreasing in amplitude, the frequency n
  of the oscillation being given by the expression
                  ________
          1      /1     R²
    n = -----   / -- - ---.
        2[pi] \/  LC   4L²

  In those cases in which the resistance of the discharge circuit is
  very small, the expression for the frequency n and for the time period
  of oscillation R take the simple forms n = 1, 2[pi][root]LC, or T =
  1/n = 2[pi][root]LC.

The above investigation shows that if we construct a circuit consisting
of a condenser and inductance placed in series with one another, such
circuit has a natural electrical time period of its own in which the
electrical charge in it oscillates if disturbed. It may therefore be
compared with a pendulum of any kind which when displaced oscillates
with a time period depending on its inertia and on its restoring force.

The study of these electrical oscillations received a great impetus
after H.R. Hertz showed that when taking place in electric circuits of a
certain kind they create electromagnetic waves (see ELECTRIC WAVES) in
the dielectric surrounding the oscillator, and an additional interest
was given to them by their application to telegraphy. If a Leyden jar
and a circuit of low resistance but some inductance in series with it
are connected across the secondary spark gap of an induction coil, then
when the coil is set in action we have a series of bright noisy sparks,
each of which consists of a train of oscillatory electric discharges
from the jar. The condenser becomes charged as the secondary
electromotive force of the coil is created at each break of the primary
current, and when the potential difference of the condenser coatings
reaches a certain value determined by the spark-ball distance a
discharge happens. This discharge, however, is not a single movement of
electricity in one direction but an oscillatory motion with gradually
decreasing amplitude. If the oscillatory spark is photographed on a
revolving plate or a rapidly moving film, we have evidence in the
photograph that such a spark consists of numerous intermittent sparks
gradually becoming feebler. As the coil continues to operate, these
trains of electric discharges take place at regular intervals. We can
cause a train of electric oscillations in one circuit to induce similar
oscillations in a neighbouring circuit, and thus construct an
oscillation transformer or high frequency induction coil.

_Alternating Currents._--The study of alternating currents of
electricity began to attract great attention towards the end of the 19th
century by reason of their application in electrotechnics and
especially to the transmission of power. A circuit in which a simple
periodic alternating current flows is called a single phase circuit. The
important difference between such a form of current flow and steady
current flow arises from the fact that if the circuit has inductance
then the periodic electric current in it is not in step with the
terminal potential difference or electromotive force acting in the
circuit, but the current lags behind the electromotive force by a
certain fraction of the periodic time called the "phase difference." If
two alternating currents having a fixed difference in phase flow in two
connected separate but related circuits, the two are called a two-phase
current. If three or more single-phase currents preserving a fixed
difference of phase flow in various parts of a connected circuit, the
whole taken together is called a polyphase current. Since an electric
current is a vector quantity, that is, has direction as well as
magnitude, it can most conveniently be represented by a line denoting
its maximum value, and if the alternating current is a simple periodic
current then the root-mean-square or effective value of the current is
obtained by dividing the maximum value by [root]2. Accordingly when we
have an electric circuit or circuits in which there are simple periodic
currents we can draw a vector diagram, the lines of which represent the
relative magnitudes and phase differences of these currents.

  A vector can most conveniently be represented by a symbol such as a +
  ib, where a stands for any length of a units measured horizontally and
  b for a length b units measured vertically, and the symbol i is a sign
  of perpendicularity, and equivalent analytically[6] to [root]-1.
  Accordingly if E represents the periodic electromotive force (maximum
  value) acting in a circuit of resistance R and inductance L and
  frequency n, and if the current considered as a vector is represented
  by I, it is easy to show that a vector equation exists between these
  quantities as follows:--

    E = RI + [iota]2[pi]nLI.

  Since the absolute magnitude of a vector a + [iota]b is [root](a² +
  b²), it follows that considering merely magnitudes of current and
  electromotive force and denoting them by symbols (E) (I), we have the
  following equation connecting (I) and (E):--

    (I) = (E)[root](R² + p²L²),

  where p stands for 2[pi]n. If the above equation is compared with the
  symbolic expression of Ohm's law, it will be seen that the quantity
  [root](R² + p²L²) takes the place of resistance R in the expression of
  Ohm. This quantity [root](R² + p²L²) is called the "impedance" of the
  alternating circuit. The quantity pL is called the "reactance" of the
  alternating circuit, and it is therefore obvious that the current in
  such a circuit lags behind the electromotive force by an angle, called
  the angle of lag, the tangent of which is pL/R.

  _Currents in Networks of Conductors._--In dealing with problems
  connected with electric currents we have to consider the laws which
  govern the flow of currents in linear conductors (wires), in plane
  conductors (sheets), and throughout the mass of a material
  conductor.[7] In the first case consider the collocation of a number
  of linear conductors, such as rods or wires of metal, joined at their
  ends to form a network of conductors. The network consists of a number
  of conductors joining certain points and forming meshes. In each
  conductor a current may exist, and along each conductor there is a
  fall of potential, or an active electromotive force may be acting in
  it. Each conductor has a certain resistance. To find the current in
  each conductor when the individual resistances and electromotive
  forces are given, proceed as follows:--Consider any one mesh. The sum
  of all the electromotive forces which exist in the branches bounding
  that mesh must be equal to the sum of all the products of the
  resistances into the currents flowing along them, or [Sigma](E) =
  [Sigma](C.R.). Hence if we consider each mesh as traversed by
  imaginary currents all circulating in the same direction, the real
  currents are the sums or differences of these imaginary cyclic
  currents in each branch. Hence we may assign to each mesh a cycle
  symbol x, y, z, &c., and form a cycle equation. Write down the cycle
  symbol for a mesh and prefix as coefficient the sum of all the
  resistances which bound that cycle, then subtract the cycle symbols of
  each adjacent cycle, each multiplied by the value of the bounding or
  common resistances, and equate this sum to the total electromotive
  force acting round the cycle. Thus if x y z are the cycle currents,
  and a b c the resistances bounding the mesh x, and b and c those
  separating it from the meshes y and z, and E an electromotive force in
  the branch a, then we have formed the cycle equation x(a + b + c) -
  by - cz = E. For each mesh a similar equation may be formed. Hence we
  have as many linear equations as there are meshes, and we can obtain
  the solution for each cycle symbol, and therefore for the current in
  each branch. The solution giving the current in such branch of the
  network is therefore always in the form of the quotient of two
  determinants. The solution of the well-known problem of finding the
  current in the galvanometer circuit of the arrangement of linear
  conductors called Wheatstone's Bridge is thus easily obtained. For if
  we call the cycles (see fig. 7) (x + y), y and z, and the resistances
  P, Q, R, S, G and B, and if E be the electromotive force in the
  battery circuit, we have the cycle equations

    (P + G + R)(x + y) - Gy - Rz = 0,
    (Q + G + S)y - G(x + y) - Sz = 0,
    (R + S + B)z - R(x + y) - Sy = E.

  [Illustration: FIG. 7.]

  From these we can easily obtain the solution for (x + y) - y = x,
  which is the current through the galvanometer circuit in the form

    x = E(PS - RQ)[Delta].

  where [Delta] is a certain function of P, Q, R, S, B and G.

  _Currents in Sheets._--In the case of current flow in plane sheets, we
  have to consider certain points called sources at which the current
  flows into the sheet, and certain points called sinks at which it
  leaves. We may investigate, first, the simple case of one source and
  one sink in an infinite plane sheet of thickness [delta] and
  conductivity k. Take any point P in the plane at distances R and r
  from the source and sink respectively. The potential V at P is
  obviously given by

              Q            r1
    V = -------------log_e --,
        2[pi]k[delta]      r2

  where Q is the quantity of electricity supplied by the source per
  second. Hence the equation to the equipotential curve is r1r2 = a
  constant.

  If we take a point half-way between the sink and the source as the
  origin of a system of rectangular co-ordinates, and if the distance
  between sink and source is equal to p, and the line joining them is
  taken as the axis of x, then the equation to the equipotential line is

    y² + (x + p)²
    ------------- = a constant.
    y² + (x - p)²

  This is the equation of a family of circles having the axis of y for a
  common radical axis, one set of circles surrounding the sink and
  another set of circles surrounding the source. In order to discover
  the form of the stream of current lines we have to determine the
  orthogonal trajectories to this family of coaxial circles. It is easy
  to show that the orthogonal trajectory of the system of circles is
  another system of circles all passing through the sink and the source,
  and as a corollary of this fact, that the electric resistance of a
  circular disk of uniform thickness is the same between any two points
  taken anywhere on its circumference as sink and source. These
  equipotential lines may be delineated experimentally by attaching the
  terminals of a battery or batteries to small wires which touch at
  various places a sheet of tinfoil. Two wires attached to a
  galvanometer may then be placed on the tinfoil, and one may be kept
  stationary and the other may be moved about, so that the galvanometer
  is not traversed by any current. The moving terminal then traces out
  an equipotential curve. If there are n sinks and sources in a plane
  conducting sheet, and if r, r', r" be the distances of any point from
  the sinks, and t, t', t" the distances of the sources, then

    r r' r" ...
    ----------- = a constant,
    t t' t" ...

  is the equation to the equipotential lines. The orthogonal
  trajectories or stream lines have the equation

    [Sigma]([theta] - [theta]') = a constant,

  where [theta] and [theta]' are the angles which the lines drawn from
  any point in the plane to the sink and corresponding source make with
  the line joining that sink and source. Generally it may be shown that
  if there are any number of sinks and sources in an infinite
  plane-conducting sheet, and if r, [theta] are the polar co-ordinates
  of any one, then the equation to the equipotential surfaces is given
  by the equation

    [Sigma](A log_er) = a constant,

  where A is a constant; and the equation to the stream of current lines
  is

    [Sigma]([theta]) = a constant.

  In the case of electric flow in three dimensions the electric
  potential must satisfy Laplace's equation, and a solution is therefore
  found in the form [Sigma](A/r) = a constant, as the equation to an
  equipotential surface, where r is the distance of any point on that
  surface from a source or sink.

_Convection Currents._--The subject of convection electric currents has
risen to great importance in connexion with modern electrical
investigations. The question whether a statically electrified body in
motion creates a magnetic field is of fundamental importance.
Experiments to settle it were first undertaken in the year 1876 by H.A.
Rowland, at a suggestion of H. von Helmholtz.[8] After preliminary
experiments, Rowland's first apparatus for testing this hypothesis was
constructed, as follows:--An ebonite disk was covered with radial strips
of gold-leaf and placed between two other metal plates which acted as
screens. The disk was then charged with electricity and set in rapid
rotation. It was found to affect a delicately suspended pair of astatic
magnetic needles hung in proximity to the disk just as would, by
Oersted's rule, a circular electric current coincident with the
periphery of the disk. Hence the statically-charged but rotating disk
becomes in effect a circular electric current.

The experiments were repeated and confirmed by W.C. Röntgen (_Wied.
Ann._, 1888, 35, p. 264; 1890, 40, p. 93) and by F. Himstedt (_Wied.
Ann._, 1889, 38, p. 560). Later V. Crémieu again repeated them and
obtained negative results (_Com. rend._, 1900, 130, p. 1544, and 131,
pp. 578 and 797; 1901, 132, pp. 327 and 1108). They were again very
carefully reconducted by H. Pender (_Phil. Mag._, 1901, 2, p. 179) and
by E.P. Adams (id. ib., 285). Pender's work showed beyond any doubt that
electric convection does produce a magnetic effect. Adams employed
charged copper spheres rotating at a high speed in place of a disk, and
was able to prove that the rotation of such spheres produced a magnetic
field similar to that due to a circular current and agreeing numerically
with the theoretical value. It has been shown by J.J. Thomson (_Phil.
Mag._, 1881, 2, p. 236) and O. Heaviside (_Electrical Papers_, vol. ii.
p. 205) that an electrified sphere, moving with a velocity v and
carrying a quantity of electricity q, should produce a magnetic force H,
at a point at a distance [rho] from the centre of the sphere, equal to
qv sin [theta]/[rho]², where [theta] is the angle between the direction
of [rho] and the motion of the sphere. Adams found the field produced by
a known electric charge rotating at a known speed had a strength not
very different from that predetermined by the above formula. An
observation recorded by R.W. Wood (_Phil. Mag._, 1902, 2, p. 659)
provides a confirmatory fact. He noticed that if carbon-dioxide strongly
compressed in a steel bottle is allowed to escape suddenly the cold
produced solidifies some part of the gas, and the issuing jet is full of
particles of carbon-dioxide snow. These by friction against the nozzle
are electrified positively. Wood caused the jet of gas to pass through a
glass tube 2.5 mm. in diameter, and found that these particles of
electrified snow were blown through it with a velocity of 2000 ft. a
second. Moreover, he found that a magnetic needle hung near the tube was
deflected as if held near an electric current. Hence the positively
electrified particles in motion in the tube create a magnetic field
round it.

_Nature of an Electric Current._--The question, What is an electric
current? is involved in the larger question of the nature of
electricity. Modern investigations have shown that negative electricity
is identical with the electrons or corpuscles which are components of
the chemical atom (see MATTER and ELECTRICITY). Certain lines of
argument lead to the conclusion that a solid conductor is not only
composed of chemical atoms, but that there is a certain proportion of
free electrons present in it, the electronic density or number per unit
of volume being determined by the material, its temperature and other
physical conditions. If any cause operates to add or remove electrons at
one point there is an immediate diffusion of electrons to re-establish
equilibrium, and this electronic movement constitutes an electric
current. This hypothesis explains the reason for the identity between
the laws of diffusion of matter, of heat and of electricity.
Electromotive force is then any cause making or tending to make an
inequality of electronic density in conductors, and may arise from
differences of temperature, i.e. thermoelectromotive force (see
THERMOELECTRICITY), or from chemical action when part of the circuit is
an electrolytic conductor, or from the movement of lines of magnetic
force across the conductor.

  BIBLIOGRAPHY.--For additional information the reader may be referred
  to the following books: M. Faraday, _Experimental Researches in
  Electricity_ (3 vols., London, 1839, 1844, 1855); J. Clerk Maxwell,
  _Electricity and Magnetism_ (2 vols., Oxford, 1892); W. Watson and
  S.H. Burbury, _Mathematical Theory of Electricity and Magnetism_, vol.
  ii. (Oxford, 1889); E. Mascart and J. Joubert, _A Treatise on
  Electricity and Magnetism_ (2 vols., London, 1883); A. Hay,
  _Alternating Currents_ (London, 1905); W.G. Rhodes, _An Elementary
  Treatise on Alternating Currents_ (London, 1902); D.C. Jackson and
  J.P. Jackson, _Alternating Currents and Alternating Current Machinery_
  (1896, new ed. 1903); S.P. Thompson, _Polyphase Electric Currents_
  (London, 1900); _Dynamo-Electric Machinery_, vol. ii., "Alternating
  Currents" (London, 1905); E.E. Fournier d'Albe, _The Electron Theory_
  (London, 1906).     (J. A. F.)


FOOTNOTES:

  [1] See J.A. Fleming, _The Alternate Current Transformer_, vol. i. p.
    519.

  [2] See Maxwell, _Electricity and Magnetism_, vol. ii. chap. ii.

  [3] See Maxwell, _Electricity and Magnetism_, vol. ii. 642.

  [4] _Experimental Researches_, vol. i. ser. 1.

  [5] See Maxwell, _Electricity and Magnetism_, vol. ii. § 542, p. 178.

  [6] See W.G. Rhodes, _An Elementary Treatise on Alternating Currents_
    (London, 1902), chap. vii.

  [7] See J.A. Fleming, "Problems on the Distribution of Electric
    Currents in Networks of Conductors," _Phil. Mag_. (1885), or Proc.
    Phys. Soc. Lond. (1885), 7; also Maxwell, _Electricity and Magnetism_
    (2nd ed.), vol. i. p. 374, § 280, 282b.

  [8] See _Berl. Acad. Ber._, 1876, p. 211; also H.A. Rowland and C.T.
    Hutchinson, "On the Electromagnetic Effect of Convection Currents,"
    _Phil. Mag._, 1889, 27, p. 445.



ELECTROLIER, a fixture, usually pendent from the ceiling, for holding
electric lamps. The word is analogous to chandelier, from which indeed
it was formed.



ELECTROLYSIS (formed from Gr. [Greek: lyein], to loosen). When the
passage of an electric current through a substance is accompanied by
definite chemical changes which are independent of the heating effects
of the current, the process is known as _electrolysis_, and the
substance is called an _electrolyte_. As an example we may take the case
of a solution of a salt such as copper sulphate in water, through which
an electric current is passed between copper plates. We shall then
observe the following phenomena. (1) The bulk of the solution is
unaltered, except that its temperature may be raised owing to the usual
heating effect which is proportional to the square of the strength of
the current. (2) The copper plate by which the current is said to enter
the solution, i.e. the plate attached to the so-called positive terminal
of the battery or other source of current, dissolves away, the copper
going into solution as copper sulphate. (3) Copper is deposited on the
surface of the other plate, being obtained from the solution. (4)
Changes in concentration are produced in the neighbourhood of the two
plates or electrodes. In the case we have chosen, the solution becomes
stronger near the anode, or electrode at which the current enters, and
weaker near the cathode, or electrode at which it leaves the solution.
If, instead of using copper electrodes, we take plates of platinum,
copper is still deposited on the cathode; but, instead of the anode
dissolving, free sulphuric acid appears in the neighbouring solution,
and oxygen gas is evolved at the surface of the platinum plate.

With other electrolytes similar phenomena appear, though the primary
chemical changes may be masked by secondary actions. Thus, with a dilute
solution of sulphuric acid and platinum electrodes, hydrogen gas is
evolved at the cathode, while, as the result of a secondary action on
the anode, sulphuric acid is there re-formed, and oxygen gas evolved.
Again, with the solution of a salt such as sodium chloride, the sodium,
which is primarily liberated at the cathode, decomposes the water and
evolves hydrogen, while the chlorine may be evolved as such, may
dissolve the anode, or may liberate oxygen from the water, according to
the nature of the plate and the concentration of the solution.

_Early History of Electrolysis._--Alessandro Volta of Pavia discovered
the electric battery in the year 1800, and thus placed the means of
maintaining a steady electric current in the hands of investigators,
who, before that date, had been restricted to the study of the isolated
electric charges given by frictional electric machines. Volta's cell
consists essentially of two plates of different metals, such as zinc and
copper, connected by an electrolyte such as a solution of salt or acid.
Immediately on its discovery intense interest was aroused in the new
invention, and the chemical effects of electric currents were speedily
detected. W. Nicholson and Sir A. Carlisle found that hydrogen and
oxygen were evolved at the surfaces of gold and platinum wires connected
with the terminals of a battery and dipped in water. The volume of the
hydrogen was about double that of the oxygen, and, since this is the
ratio in which these elements are combined in water, it was concluded
that the process consisted essentially in the decomposition of water.
They also noticed that a similar kind of chemical action went on in the
battery itself. Soon afterwards, William Cruickshank decomposed the
magnesium, sodium and ammonium chlorides, and precipitated silver and
copper from their solutions--an observation which led to the process of
electroplating. He also found that the liquid round the anode became
acid, and that round the cathode alkaline. In 1804 W. Hisinger and J.J.
Berzelius stated that neutral salt solutions could be decomposed by
electricity, the acid appearing at one pole and the metal at the other.
This observation showed that nascent hydrogen was not, as had been
supposed, the primary cause of the separation of metals from their
solutions, but that the action consisted in a direct decomposition into
metal and acid. During the earliest investigation of the subject it was
thought that, since hydrogen and oxygen were usually evolved, the
electrolysis of solutions of acids and alkalis was to be regarded as a
direct decomposition of water. In 1806 Sir Humphry Davy proved that the
formation of acid and alkali when water was electrolysed was due to
saline impurities in the water. He had shown previously that
decomposition of water could be effected although the two poles were
placed in separate vessels connected by moistened threads. In 1807 he
decomposed potash and soda, previously considered to be elements, by
passing the current from a powerful battery through the moistened
solids, and thus isolated the metals potassium and sodium.

The electromotive force of Volta's simple cell falls off rapidly when
the cell is used, and this phenomenon was shown to be due to the
accumulation at the metal plates of the products of chemical changes in
the cell itself. This reverse electromotive force of polarization is
produced in all electrolytes when the passage of the current changes the
nature of the electrodes. In batteries which use acids as the
electrolyte, a film of hydrogen tends to be deposited on the copper or
platinum electrode; but, to obtain a constant electromotive force,
several means were soon devised of preventing the formation of the film.
Constant cells may be divided into two groups, according as their action
is chemical (as in the bichromate cell, where the hydrogen is converted
into water by an oxidizing agent placed in a porous pot round the carbon
plate) or electrochemical (as in Daniell's cell, where a copper plate is
surrounded by a solution of copper sulphate, and the hydrogen, instead
of being liberated, replaces copper, which is deposited on the plate
from the solution).

[Illustration: FIG. 1.]

_Faraday's Laws._--The first exact quantitative study of electrolytic
phenomena was made about 1830 by Michael Faraday (_Experimental
Researches_, 1833). When an electric current flows round a circuit,
there is no accumulation of electricity anywhere in the circuit, hence
the current strength is everywhere the same, and we may picture the
current as analogous to the flow of an incompressible fluid. Acting on
this view, Faraday set himself to examine the relation between the flow
of electricity round the circuit and the amount of chemical
decomposition. He passed the current driven by a voltaic battery ZnPt
(fig. 1) through two branches containing the two electrolytic cells A
and B. The reunited current was then led through another cell C, in
which the strength of the current must be the sum of those in the arms A
and B. Faraday found that the mass of substance liberated at the
electrodes in the cell C was equal to the sum of the masses liberated in
the cells A and B. He also found that, for the same current, the amount
of chemical action was independent of the size of the electrodes and
proportional to the time that the current flowed. Regarding the current
as the passage of a certain amount of electricity per second, it will be
seen that the results of all these experiments may be summed up in the
statement that the amount of chemical action is proportional to the
quantity of electricity which passes through the cell.

Faraday's next step was to pass the same current through different
electrolytes in series. He found that the amounts of the substances
liberated in each cell were proportional to the chemical equivalent
weights of those substances. Thus, if the current be passed through
dilute sulphuric acid between hydrogen electrodes, and through a
solution of copper sulphate, it will be found that the mass of hydrogen
evolved in the first cell is to the mass of copper deposited in the
second as 1 is to 31.8. Now this ratio is the same as that which gives
the relative chemical equivalents of hydrogen and copper, for 1 gramme
of hydrogen and 31.8 grammes of copper unite chemically with the same
weight of any acid radicle such as chlorine or the sulphuric group, SO4.
Faraday examined also the electrolysis of certain fused salts such as
lead chloride and silver chloride. Similar relations were found to hold
and the amounts of chemical change to be the same for the same electric
transfer as in the case of solutions.

We may sum up the chief results of Faraday's work in the statements
known as Faraday's laws: The mass of substance liberated from an
electrolyte by the passage of a current is proportional (1) to the total
quantity of electricity which passes through the electrolyte, and (2) to
the chemical equivalent weight of the substance liberated.

Since Faraday's time his laws have been confirmed by modern research,
and in favourable cases have been shown to hold good with an accuracy of
at least one part in a thousand. The principal object of this more
recent research has been the determination of the quantitative amount of
chemical change associated with the passage for a given time of a
current of strength known in electromagnetic units. It is found that the
most accurate and convenient apparatus to use is a platinum bowl filled
with a solution of silver nitrate containing about fifteen parts of the
salt to one hundred of water. Into the solution dips a silver plate
wrapped in filter paper, and the current is passed from the silver plate
as anode to the bowl as cathode. The bowl is weighed before and after
the passage of the current, and the increase gives the mass of silver
deposited. The mean result of the best determinations shows that when a
current of one ampere is passed for one second, a mass of silver is
deposited equal to 0.001118 gramme. So accurate and convenient is this
determination that it is now used conversely as a practical definition
of the ampere, which (defined theoretically in terms of magnetic force)
is defined practically as the current which in one second deposits 1.118
milligramme of silver.

Taking the chemical equivalent weight of silver, as determined by
chemical experiments, to be 107.92, the result described gives as the
electrochemical equivalent of an ion of unit chemical equivalent the
value 1.036 × 10^(-5). If, as is now usual, we take the equivalent
weight of oxygen as our standard and call it 16, the equivalent weight
of hydrogen is 1.008, and its electrochemical equivalent is 1.044 ×
10^(-5). The electrochemical equivalent of any other substance, whether
element or compound, may be found by multiplying its chemical equivalent
by 1.036 × 10^(-5). If, instead of the ampere, we take the C.G.S.
electromagnetic unit of current, this number becomes 1.036 × 10^(-4).

_Chemical Nature of the Ions._--A study of the products of decomposition
does not necessarily lead directly to a knowledge of the ions actually
employed in carrying the current through the electrolyte. Since the
electric forces are active throughout the whole solution, all the ions
must come under its influence and therefore move, but their separation
from the electrodes is determined by the electromotive force needed to
liberate them. Thus, as long as every ion of the solution is present in
the layer of liquid next the electrode, the one which responds to the
least electromotive force will alone be set free. When the amount of
this ion in the surface layer becomes too small to carry all the current
across the junction, other ions must also be used, and either they or
their secondary products will appear also at the electrode. In aqueous
solutions, for instance, a few hydrogen (H) and hydroxyl (OH) ions
derived from the water are always present, and will be liberated if the
other ions require a higher decomposition voltage and the current be
kept so small that hydrogen and hydroxyl ions can be formed fast enough
to carry all the current across the junction between solution and
electrode.

The issue is also obscured in another way. When the ions are set free at
the electrodes, they may unite with the substance of the electrode or
with some constituent of the solution to form secondary products. Thus
the hydroxyl mentioned above decomposes into water and oxygen, and the
chlorine produced by the electrolysis of a chloride may attack the metal
of the anode. This leads us to examine more closely the part played by
water in the electrolysis of aqueous solutions. Distilled water is a
very bad conductor, though, even when great care is taken to remove all
dissolved bodies, there is evidence to show that some part of the trace
of conductivity remaining is due to the water itself. By careful
redistillation F. Kohlrausch has prepared water of which the
conductivity compared with that of mercury was only 0.40 × 10^(-11) at
18° C. Even here some little impurity was present, and the conductivity
of chemically pure water was estimated by thermodynamic reasoning as
0.36 × 10^(-11) at 18° C. As we shall see later, the conductivity of
very dilute salt solutions is proportional to the concentration, so that
it is probable that, in most cases, practically all the current is
carried by the salt. At the electrodes, however, the small quantity of
hydrogen and hydroxyl ions from the water are liberated first in cases
where the ions of the salt have a higher decomposition voltage. The
water being present in excess, the hydrogen and hydroxyl are re-formed
at once and therefore are set free continuously. If the current be so
strong that new hydrogen and hydroxyl ions cannot be formed in time,
other substances are liberated; in a solution of sulphuric acid a strong
current will evolve sulphur dioxide, the more readily as the
concentration of the solution is increased. Similar phenomena are seen
in the case of a solution of hydrochloric acid. When the solution is
weak, hydrogen and oxygen are evolved; but, as the concentration is
increased, and the current raised, more and more chlorine is liberated.

  An interesting example of secondary action is shown by the common
  technical process of electroplating with silver from a bath of
  potassium silver cyanide. Here the ions are potassium and the group
  Ag(CN)2.[1] Each potassium ion as it reaches the cathode precipitates
  silver by reacting with the solution in accordance with the chemical
  equation

    K + KAg(CN)2 = 2KCN + Ag,

  while the anion Ag(CN)2 dissolves an atom of silver from the anode,
  and re-forms the complex cyanide KAg(CN)2 by combining with the 2KCN
  produced in the reaction described in the equation. If the anode
  consist of platinum, cyanogen gas is evolved thereat from the anion
  Ag(CN)2, and the platinum becomes covered with the insoluble silver
  cyanide, AgCN, which soon stops the current. The coating of silver
  obtained by this process is coherent and homogeneous, while that
  deposited from a solution of silver nitrate, as the result of the
  primary action of the current, is crystalline and easily detached.

  In the electrolysis of a concentrated solution of sodium acetate,
  hydrogen is evolved at the cathode and a mixture of ethane and carbon
  dioxide at the anode. According to H. Jahn,[2] the processes at the
  anode can be represented by the equations

    2CH3·COO + H2O = 2CH3·COOH + O

    2CH3·COOH + O = C2H6 + 2CO2 + H2O.

  The hydrogen at the cathode is developed by the secondary action

    2Na + 2H2O = 2NaOH + H2.

  Many organic compounds can be prepared by taking advantage of
  secondary actions at the electrodes, such as reduction by the cathodic
  hydrogen, or oxidation at the anode (see ELECTROCHEMISTRY).

  It is possible to distinguish between double salts and salts of
  compound acids. Thus J.W. Hittorf showed that when a current was
  passed through a solution of sodium platino-chloride, the platinum
  appeared at the anode. The salt must therefore be derived from an
  acid, chloroplatinic acid, H2PtCl6, and have the formula Na2PtCl6, the
  ions being Na and PtCl6", for if it were a double salt it would
  decompose as a mixture of sodium chloride and platinum chloride and
  both metals would go to the cathode.

_Early Theories of Electrolysis._--The obvious phenomena to be explained
by any theory of electrolysis are the liberation of the products of
chemical decomposition at the two electrodes while the intervening
liquid is unaltered. To explain these facts, Theodor Grotthus
(1785-1822) in 1806 put forward an hypothesis which supposed that the
opposite chemical constituents of an electrolyte interchanged partners
all along the line between the electrodes when a current passed. Thus,
if the molecule of a substance in solution is represented by AB,
Grotthus considered a chain of AB molecules to exist from one electrode
to the other. Under the influence of an applied electric force, he
imagined that the B part of the first molecule was liberated at the
anode, and that the A part thus isolated united with the B part of the
second molecule, which, in its turn, passed on its A to the B of the
third molecule. In this manner, the B part of the last molecule of the
chain was seized by the A of the last molecule but one, and the A part
of the last molecule liberated at the surface of the cathode.

Chemical phenomena throw further light on this question. If two
solutions containing the salts AB and CD be mixed, double decomposition
is found to occur, the salts AD and CB being formed till a certain part
of the first pair of substances is transformed into an equivalent amount
of the second pair. The proportions between the four salts AB, CD, AD
and CB, which exist finally in solution, are found to be the same
whether we begin with the pair AB and CD or with the pair AD and CB. To
explain this result, chemists suppose that both changes can occur
simultaneously, and that equilibrium results when the rate at which AB
and CD are transformed into AD and CB is the same as the rate at which
the reverse change goes on. A freedom of interchange is thus indicated
between the opposite parts of the molecules of salts in solution, and it
follows reasonably that with the solution of a single salt, say sodium
chloride, continual interchanges go on between the sodium and chlorine
parts of the different molecules.

These views were applied to the theory of electrolysis by R.J.E.
Clausius. He pointed out that it followed that the electric forces did
not cause the interchanges between the opposite parts of the dissolved
molecules but only controlled their direction. Interchanges must be
supposed to go on whether a current passes or not, the function of the
electric forces in electrolysis being merely to determine in what
direction the parts of the molecules shall work their way through the
liquid and to effect actual separation of these parts (or their
secondary products) at the electrodes. This conclusion is supported also
by the evidence supplied by the phenomena of electrolytic conduction
(see CONDUCTION, ELECTRIC, § II.). If we eliminate the reverse
electromotive forces of polarization at the two electrodes, the
conduction of electricity through electrolytes is found to conform to
Ohm's law; that is, once the polarization is overcome, the current is
proportional to the electromotive force applied to the bulk of the
liquid. Hence there can be no reverse forces of polarization inside the
liquid itself, such forces being confined to the surface of the
electrodes. No work is done in separating the parts of the molecules
from each other. This result again indicates that the parts of the
molecules are effectively separate from each other, the function of the
electric forces being merely directive.

_Migration of the Ions._--The opposite parts of an electrolyte, which
work their way through the liquid under the action of the electric
forces, were named by Faraday the ions--the travellers. The changes of
concentration which occur in the solution near the two electrodes were
referred by W. Hittorf (1853) to the unequal speeds with which he
supposed the two opposite ions to travel. It is clear that, when two
opposite streams of ions move past each other, equivalent quantities are
liberated at the two ends of the system. If the ions move at equal
rates, the salt which is decomposed to supply the ions liberated must be
taken equally from the neighbourhood of the two electrodes. But if one
ion, say the anion, travels faster through the liquid than the other,
the end of the solution from which it comes will be more exhausted of
salt than the end towards which it goes. If we assume that no other
cause is at work, it is easy to prove that, with non-dissolvable
electrodes, the ratio of salt lost at the anode to the salt lost at the
cathode must be equal to the ratio of the velocity of the cation to the
velocity of the anion. This result may be illustrated by fig. 2. The
black circles represent one ion and the white circles the other. If the
black ions move twice as fast as the white ones, the state of things
after the passage of a current will be represented by the lower part of
the figure. Here the middle part of the solution is unaltered and the
number of ions liberated is the same at either end, but the amount of
salt left at one end is less than that at the other. On the right,
towards which the faster ion travels, five molecules of salt are left,
being a loss of two from the original seven. On the left, towards which
the slower ion moves, only three molecules remain--a loss of four. Thus,
the ratio of the losses at the two ends is two to one--the same as the
ratio of the assumed ionic velocities. It should be noted, however, that
another cause would be competent to explain the unequal dilution of the
two solutions. If either ion carried with it some of the unaltered salt
or some of the solvent, concentration or dilution of the liquid would be
produced where the ion was liberated. There is reason to believe that in
certain cases such complex ions do exist, and interfere with the results
of the differing ionic velocities.

[Illustration: FIG. 2.]

Hittorf and many other observers have made experiments to determine the
unequal dilution of a solution round the two electrodes when a current
passes. Various forms of apparatus have been used, the principle of them
all being to secure efficient separation of the two volumes of solution
in which the changes occur. In some cases porous diaphragms have been
employed; but such diaphragms introduce a new complication, for the
liquid as a whole is pushed through them by the action of the current,
the phenomenon being known as electric endosmose. Hence experiments
without separating diaphragms are to be preferred, and the apparatus may
be considered effective when a considerable bulk of intervening solution
is left unaltered in composition. It is usual to express the results in
terms of what is called the migration constant of the anion, that is,
the ratio of the amount of salt lost by the anode vessel to the whole
amount lost by both vessels. Thus the statement that the migration
constant or transport number for a decinormal solution of copper
sulphate is 0.632 implies that of every gramme of copper sulphate lost
by a solution containing originally one-tenth of a gramme equivalent per
litre when a current is passed through it between platinum electrodes,
0.632 gramme is taken from the cathode vessel and 0.368 gramme from the
anode vessel. For certain concentrated solutions the transport number is
found to be greater than unity; thus for a normal solution of cadmium
iodide its value is 1.12. On the theory that the phenomena are wholly
due to unequal ionic velocities this result would mean that the cation
like the anion moved against the conventional direction of the current.
That a body carrying a positive electric charge should move against the
direction of the electric intensity is contrary to all our notions of
electric forces, and we are compelled to seek some other explanation. An
alternative hypothesis is given by the idea of complex ions. If some of
the anions, instead of being simple iodine ions represented chemically
by the symbol I, are complex structures formed by the union of iodine
with unaltered cadmium iodide--structures represented by some such
chemical formula as I(CdI2), the concentration of the solution round the
anode would be increased by the passage of an electric current, and the
phenomena observed would be explained. It is found that, in such cases
as this, where it seems necessary to imagine the existence of complex
ions, the transport number changes rapidly as the concentration of the
original solution is changed. Thus, diminishing the concentration of the
cadmium iodine solution from normal to one-twentieth normal changes the
transport number from 1.12 to 0.64. Hence it is probable that in cases
where the transport number keeps constant with changing concentration
the hypothesis of complex ions is unnecessary, and we may suppose that
the transport number is a true migration constant from which the
relative velocities of the two ions may be calculated in the matter
suggested by Hittorf and illustrated in fig. 2. This conclusion is
confirmed by the results of the direct visual determination of ionic
velocities (see CONDUCTION, ELECTRIC, § II.), which, in cases where the
transport number remains constant, agree with the values calculated from
those numbers. Many solutions in which the transport numbers vary at
high concentration often become simple at greater dilution. For
instance, to take the two solutions to which we have already referred,
we have--

  +----------------------------------+------+------+------+------+------+------+------+-----+-----------+
  |Concentration                     | 2.0  | 1.5  | 1.0  | 0.5  | 0.2  | 0.1  | 0.05 | 0.02|0.01 normal|
  |Copper sulphate transport numbers | 0.72 | 0.714| 0.696| 0.668| 0.643| 0.632| 0.626| 0.62|     ..    |
  |Cadmium iodide     "         "    | 1.22 | 1.18 | 1.12 | 1.00 | 0.83 | 0.71 | 0.64 | 0.59|0.56       |
  +----------------------------------+------+------+------+------+------+------+------+-----+-----------+

It is probable that in both these solutions complex ions exist at fairly
high concentrations, but gradually gets less in number and finally
disappear as the dilution is increased. In such salts as potassium
chloride the ions seem to be simple throughout a wide range of
concentration since the transport numbers for the same series of
concentrations as those used above run--

  Potassium chloride--
  0.515, 0.515, 0.514, 0.513, 0.509, 0.508, 0.507, 0.507, 0.506.

The next important step in the theory of the subject was made by F.
Kohlrausch in 1879. Kohlrausch formulated a theory of electrolytic
conduction based on the idea that, under the action of the electric
forces, the oppositely charged ions moved in opposite directions through
the liquid, carrying their charges with them. If we eliminate the
polarization at the electrodes, it can be shown that an electrolyte
possesses a definite electric resistance and therefore a definite
conductivity. The conductivity gives us the amount of electricity
conveyed per second under a definite electromotive force. On the view of
the process of conduction described above, the amount of electricity
conveyed per second is measured by the product of the number of ions,
known from the concentration of the solution, the charge carried by each
of them, and the velocity with which, on the average, they move through
the liquid. The concentration is known, and the conductivity can be
measured experimentally; thus the average velocity with which the ions
move past each other under the existent electromotive force can be
estimated. The velocity with which the ions move past each other is
equal to the sum of their individual velocities, which can therefore be
calculated. Now Hittorf's transport number, in the case of simple salts
in moderately dilute solution, gives us the ratio between the two ionic
velocities. Hence the absolute velocities of the two ions can be
determined, and we can calculate the actual speed with which a certain
ion moves through a given liquid under the action of a given potential
gradient or electromotive force. The details of the calculation are
given in the article CONDUCTION, ELECTRIC, § II., where also will be
found an account of the methods which have been used to measure the
velocities of many ions by direct visual observation. The results go to
show that, where the existence of complex ions is not indicated by
varying transport numbers, the observed velocities agree with those
calculated on Kohlrausch's theory.

_Dissociation Theory._--The verification of Kohlrausch's theory of ionic
velocity verifies also the view of electrolysis which regards the
electric current as due to streams of ions moving in opposite directions
through the liquid and carrying their opposite electric charges with
them. There remains the question how the necessary migratory freedom of
the ions is secured. As we have seen, Grotthus imagined that it was the
electric forces which sheared the ions past each other and loosened the
chemical bonds holding the opposite parts of each dissolved molecule
together. Clausius extended to electrolysis the chemical ideas which
looked on the opposite parts of the molecule as always changing partners
independently of any electric force, and regarded the function of the
current as merely directive. Still, the necessary freedom was supposed
to be secured by interchanges of ions between molecules at the instants
of molecular collision only; during the rest of the life of the ions
they were regarded as linked to each other to form electrically neutral
molecules.

In 1887 Svante Arrhenius, professor of physics at Stockholm, put forward
a new theory which supposed that the freedom of the opposite ions from
each other was not a mere momentary freedom at the instants of molecular
collision, but a more or less permanent freedom, the ions moving
independently of each other through the liquid. The evidence which led
Arrhenius to this conclusion was based on van 't Hoff's work on the
osmotic pressure of solutions (see SOLUTION). If a solution, let us say
of sugar, be confined in a closed vessel through the walls of which the
solvent can pass but the solution cannot, the solvent will enter till a
certain equilibrium pressure is reached. This equilibrium pressure is
called the osmotic pressure of the solution, and thermodynamic theory
shows that, in an ideal case of perfect separation between solvent and
solute, it should have the same value as the pressure which a number of
molecules equal to the number of solute molecules in the solution would
exert if they could exist as a gas in a space equal to the volume of the
solution, provided that the space was large enough (i.e. the solution
dilute enough) for the intermolecular forces between the dissolved
particles to be inappreciable. Van 't Hoff pointed out that measurements
of osmotic pressure confirmed this value in the case of dilute solutions
of cane sugar.

Thermodynamic theory also indicates a connexion between the osmotic
pressure of a solution and the depression of its freezing point and its
vapour pressure compared with those of the pure solvent. The freezing
points and vapour pressures of solutions of sugar are also in conformity
with the theoretical numbers. But when we pass to solutions of mineral
salts and acids--to solutions of electrolytes in fact--we find that the
observed values of the osmotic pressures and of the allied phenomena are
greater than the normal values. Arrhenius pointed out that these
exceptions would be brought into line if the ions of electrolytes were
imagined to be separate entities each capable of producing its own
pressure effects just as would an ordinary dissolved molecule.

Two relations are suggested by Arrhenius' theory. (1) In very dilute
solutions of simple substances, where only one kind of dissociation is
possible and the dissociation of the ions is complete, the number of
pressure-producing particles necessary to produce the observed osmotic
effects should be equal to the number of ions given by a molecule of the
salt as shown by its electrical properties. Thus the osmotic pressure,
or the depression of the freezing point of a solution of potassium
chloride should, at extreme dilution, be twice the normal value, but of
a solution of sulphuric acid three times that value, since the potassium
salt contains two ions and the acid three. (2) As the concentration of
the solutions increases, the ionization as measured electrically and the
dissociation as measured osmotically might decrease more or less
together, though, since the thermodynamic theory only holds when the
solution is so dilute that the dissolved particles are beyond each
other's sphere of action, there is much doubt whether this second
relation is valid through any appreciable range of concentration.

At present, measurements of freezing point are more convenient and
accurate than those of osmotic pressure, and we may test the validity of
Arrhenius' relations by their means. The theoretical value for the
depression of the freezing point of a dilute solution per
gramme-equivalent of solute per litre is 1.857° C. Completely ionized
solutions of salts with two ions should give double this number or
3.714°, while electrolytes with three ions should have a value of 5.57°.

The following results are given by H.B. Loomis for the concentration of
0.01 gramme-molecule of salt to one thousand grammes of water. The salts
tabulated are those of which the equivalent conductivity reaches a
limiting value indicating that complete ionization is reached as
dilution is increased. With such salts alone is a valid comparison
possible.

  _Molecular Depressions of the Freezing Point._

  _Electrolytes with two Ions._

  Potassium chloride  3.60
  Sodium chloride     3.67
  Potassium hydrate   3.71
  Hydrochloric acid   3.61
  Nitric acid         3.73
  Potassium nitrate   3.46
  Sodium nitrate      3.55
  Ammonium nitrate    3.58

  _Electrolytes with three Ions._

  Sulphuric acid      4.49
  Sodium sulphate     5.09
  Calcium chloride    5.04
  Magnesium chloride  5.08

At the concentration used by Loomis the electrical conductivity
indicates that the ionization is not complete, particularly in the case
of the salts with divalent ions in the second list. Allowing for
incomplete ionization the general concordance of these numbers with the
theoretical ones is very striking.

The measurements of freezing points of solutions at the extreme dilution
necessary to secure complete ionization is a matter of great difficulty,
and has been overcome only in a research initiated by E.H. Griffiths.[3]
Results have been obtained for solutions of sugar, where the
experimental number is 1.858, and for potassium chloride, which gives a
depression of 3.720. These numbers agree with those indicated by theory,
viz. 1.857 and 3.714, with astonishing exactitude. We may take
Arrhenius' first relation as established for the case of potassium
chloride.

The second relation, as we have seen, is not a strict consequence of
theory, and experiments to examine it must be treated as an
investigation of the limits within which solutions are dilute within the
thermodynamic sense of the word, rather than as a test of the soundness
of the theory. It is found that divergence has begun before the
concentration has become great enough to enable freezing points to be
measured with any ordinary apparatus. The freezing point curve usually
lies below the electrical one, but approaches it as dilution is
increased.[4]

Returning once more to the consideration of the first relation, which
deals with the comparison between the number of ions and the number of
pressure-producing particles in dilute solution, one caution is
necessary. In simple substances like potassium chloride it seems evident
that one kind of dissociation only is possible. The electrical phenomena
show that there are two ions to the molecule, and that these ions are
electrically charged. Corresponding with this result we find that the
freezing point of dilute solutions indicates that two pressure-producing
particles per molecule are present. But the converse relation does not
necessarily follow. It would be possible for a body in solution to be
dissociated into non-electrical parts, which would give osmotic pressure
effects twice or three times the normal value, but, being uncharged,
would not act as ions and impart electrical conductivity to the
solution. L. Kahlenberg (_Jour. Phys. Chem._, 1901, v. 344, 1902, vi.
43) has found that solutions of diphenylamine in methyl cyanide possess
an excess of pressure-producing particles and yet are non-conductors of
electricity. It is possible that in complicated organic substances we
might have two kinds of dissociation, electrical and non-electrical,
occurring simultaneously, while the possibility of the association of
molecules accompanied by the electrical dissociation of some of them
into new parts should not be overlooked. It should be pointed out that
no measurements on osmotic pressures or freezing points can do more than
tell us that an excess of particles is present; such experiments can
throw no light on the question whether or not those particles are
electrically charged. That question can only be answered by examining
whether or not the particles move in an electric field.

The dissociation theory was originally suggested by the osmotic pressure
relations. But not only has it explained satisfactorily the electrical
properties of solutions, but it seems to be the only known hypothesis
which is consistent with the experimental relation between the
concentration of a solution and its electrical conductivity (see
CONDUCTION, ELECTRIC, § II., "Nature of Electrolytes"). It is probable
that the electrical effects constitute the strongest arguments in favour
of the theory. It is necessary to point out that the dissociated ions of
such a body as potassium chloride are not in the same condition as
potassium and chlorine in the free state. The ions are associated with
very large electric charges, and, whatever their exact relations with
those charges may be, it is certain that the energy of a system in such
a state must be different from its energy when unelectrified. It is not
unlikely, therefore, that even a compound as stable in the solid form as
potassium chloride should be thus dissociated when dissolved. Again,
water, the best electrolytic solvent known, is also the body of the
highest specific inductive capacity (dielectric constant), and this
property, to whatever cause it may be due, will reduce the forces
between electric charges in the neighbourhood, and may therefore enable
two ions to separate.

This view of the nature of electrolytic solutions at once explains many
well-known phenomena. Other physical properties of these solutions, such
as density, colour, optical rotatory power, &c., like the
conductivities, are _additive_, i.e. can be calculated by adding
together the corresponding properties of the parts. This again suggests
that these parts are independent of each other. For instance, the colour
of a salt solution is the colour obtained by the superposition of the
colours of the ions and the colour of any undissociated salt that may be
present. All copper salts in dilute solution are blue, which is
therefore the colour of the copper ion. Solid copper chloride is brown
or yellow, so that its concentrated solution, which contains both ions
and undissociated molecules, is green, but changes to blue as water is
added and the ionization becomes complete. A series of equivalent
solutions all containing the same coloured ion have absorption spectra
which, when photographed, show identical absorption bands of equal
intensity.[5] The colour changes shown by many substances which are used
as indicators (q.v.) of acids or alkalis can be explained in a similar
way. Thus para-nitrophenol has colourless molecules, but an intensely
yellow negative ion. In neutral, and still more in acid solutions, the
dissociation of the indicator is practically nothing, and the liquid is
colourless. If an alkali is added, however, a highly dissociated salt of
para-nitrophenol is formed, and the yellow colour is at once evident. In
other cases, such as that of litmus, both the ion and the undissociated
molecule are coloured, but in different ways.

Electrolytes possess the power of coagulating solutions of colloids such
as albumen and arsenious sulphide. The mean values of the relative
coagulative powers of sulphates of mono-, di-, and tri-valent metals
have been shown experimentally to be approximately in the ratios
1:35:1023. The dissociation theory refers this to the action of electric
charges carried by the free ions. If a certain minimum charge must be
collected in order to start coagulation, it will need the conjunction of
6n monovalent, or 3n divalent, to equal the effect of 2n tri-valent
ions. The ratios of the coagulative powers can thus be calculated to be
1:x:x², and putting x = 32 we get 1:32:1024, a satisfactory agreement
with the numbers observed.[6]

The question of the application of the dissociation theory to the case
of fused salts remains. While it seems clear that the conduction in this
case is carried on by ions similar to those of solutions, since
Faraday's laws apply equally to both, it does not follow necessarily
that semi-permanent dissociation is the only way to explain the
phenomena. The evidence in favour of dissociation in the case of
solutions does not apply to fused salts, and it is possible that, in
their case, a series of molecular interchanges, somewhat like Grotthus's
chain, may represent the mechanism of conduction.

An interesting relation appears when the electrolytic conductivity of
solutions is compared with their chemical activity. The readiness and
speed with which electrolytes react are in sharp contrast with the
difficulty experienced in the case of non-electrolytes. Moreover, a
study of the chemical relations of electrolytes indicates that it is
always the electrolytic ions that are concerned in their reactions. The
tests for a salt, potassium nitrate, for example, are the tests not for
KNO3, but for its ions K and NO3, and in cases of double decomposition
it is always these ions that are exchanged for those of other
substances. If an element be present in a compound otherwise than as an
ion, it is not interchangeable, and cannot be recognized by the usual
tests. Thus neither a chlorate, which contains the ion ClO3, nor
monochloracetic acid, shows the reactions of chlorine, though it is, of
course, present in both substances; again, the sulphates do not answer
to the usual tests which indicate the presence of sulphur as sulphide.
The chemical activity of a substance is a quantity which may be measured
by different methods. For some substances it has been shown to be
independent of the particular reaction used. It is then possible to
assign to each body a specific coefficient of affinity. Arrhenius has
pointed out that the coefficient of affinity of an acid is proportional
to its electrolytic ionization.

  The affinities of acids have been compared in several ways. W. Ostwald
  (_Lehrbuch der allg. Chemie_, vol. ii., Leipzig, 1893) investigated
  the relative affinities of acids for potash, soda and ammonia, and
  proved them to be independent of the base used. The method employed
  was to measure the changes in volume caused by the action. His results
  are given in column I. of the following table, the affinity of
  hydrochloric acid being taken as one hundred. Another method is to
  allow an acid to act on an insoluble salt, and to measure the quantity
  which goes into solution. Determinations have been made with calcium
  oxalate, CaC2O4+H2O, which is easily decomposed by acids, oxalic acid
  and a soluble calcium salt being formed. The affinities of acids
  relative to that of oxalic acid are thus found, so that the acids can
  be compared among themselves (column II.). If an aqueous solution of
  methyl acetate be allowed to stand, a slow decomposition goes on. This
  is much quickened by the presence of a little dilute acid, though the
  acid itself remains unchanged. It is found that the influence of
  different acids on this action is proportional to their specific
  coefficients of affinity. The results of this method are given in
  column III. Finally, in column IV. the electrical conductivities of
  normal solutions of the acids have been tabulated. A better basis of
  comparison would be the ratio of the actual to the limiting
  conductivity, but since the conductivity of acids is chiefly due to
  the mobility of the hydrogen ions, its limiting value is nearly the
  same for all, and the general result of the comparison would be
  unchanged.

    +-----------------+---------+---------+---------+---------+
    |      Acid.      |    I.   |   II.   |   III.  |   IV.   |
    +-----------------+---------+---------+---------+---------+
    | Hydrochloric    |  100    |  100    |  100    |  100    |
    | Nitric          |  102    |  110    |   92    |   99.6  |
    | Sulphuric       |   68    |   67    |   74    |   65.1  |
    | Formic          |    4.0  |    2.5  |    1.3  |    1.7  |
    | Acetic          |    1.2  |    1.0  |    0.3  |    0.4  |
    | Propionic       |    1.1  |     ..  |    0.3  |    0.3  |
    | Monochloracetic |    7.2  |    5.1  |    4.3  |    4.9  |
    | Dichloracetic   |   34    |   18    |   23.0  |   25.3  |
    | Trichloracetic  |   82    |   63    |   68.2  |   62.3  |
    | Malic           |   3.0   |    5.0  |    1.2  |    1.3  |
    | Tartaric        |   5.3   |    6.3  |    2.3  |    2.3  |
    | Succinic        |   0.1   |    0.2  |    0.5  |    0.6  |
    +-----------------+---------+---------+---------+---------+

  It must be remembered that, the solutions not being of quite the same
  strength, these numbers are not strictly comparable, and that the
  experimental difficulties involved in the chemical measurements are
  considerable. Nevertheless, the remarkable general agreement of the
  numbers in the four columns is quite enough to show the intimate
  connexion between chemical activity and electrical conductivity. We
  may take it, then, that only that portion of these bodies is
  chemically active which is electrolytically active--that ionization is
  necessary for such chemical activity as we are dealing with here, just
  as it is necessary for electrolytic conductivity.

  The ordinary laws of chemical equilibrium have been applied to the
  case of the dissociation of a substance into its ions. Let x be the
  number of molecules which dissociate per second when the number of
  undissociated molecules in unit volume is unity, then in a dilute
  solution where the molecules do not interfere with each other, xp is
  the number when the concentration is p. Recombination can only occur
  when two ions meet, and since the frequency with which this will
  happen is, in dilute solution, proportional to the square of the ionic
  concentration, we shall get for the number of molecules re-formed in
  one second yq² where q is the number of dissociated molecules in one
  cubic centimetre. When there is equilibrium, xp = yq². If µ be the
  molecular conductivity, and µ_([oo]) its value at infinite dilution,
  the fractional number of molecules dissociated is µ/µ_([oo]), which
  we may write as [alpha]. The number of undissociated molecules is then
  1 - [alpha], so that if V be the volume of the solution containing 1
  gramme-molecule of the dissolved substance, we get

    q = [alpha]/V and p = (1 - [alpha])/V,

  hence   x(1 - [alpha])V = ya²/V²,

           [alpha]²      x
  and   -------------- = -- = constant = k.
        V(1 - [alpha])   y

  This constant k gives a numerical value for the chemical affinity, and
  the equation should represent the effect of dilution on the molecular
  conductivity of binary electrolytes.

  In the case of substances like ammonia and acetic acid, where the
  dissociation is very small, 1 - [alpha] is nearly equal to unity, and
  only varies slowly with dilution. The equation then becomes [alpha]²/V
  = k, or [alpha] = [root](Vk), so that the molecular conductivity is
  proportional to the square root of the dilution. Ostwald has confirmed
  the equation by observation on an enormous number of weak acids
  (_Zeits. physikal. Chemie_, 1888, ii. p. 278; 1889, iii. pp. 170, 241,
  369). Thus in the case of cyanacetic acid, while the volume V changed
  by doubling from 16 to 1024 litres, the values of k were 0.00 (376,
  373, 374, 361, 362, 361, 368). The mean values of k for other common
  acids were--formic, 0.0000214; acetic, 0.0000180; monochloracetic,
  0.00155; dichloracetic, 0.051; trichloracetic, 1.21; propionic,
  0.0000134. From these numbers we can, by help of the equation,
  calculate the conductivity of the acids for any dilution. The value of
  k, however, does not keep constant so satisfactorily in the case of
  highly dissociated substances, and empirical formulae have been
  constructed to represent the effect of dilution on them. Thus the
  values of the expressions [alpha]²/(1 - [alpha][root]V) (Rudolphi,
  _Zeits. physikal. Chemie_, 1895, vol. xvii. p. 385) and [alpha]³/(1 -
  [alpha])²V (van 't Hoff, ibid., 1895, vol. xviii. p. 300) are found to
  keep constant as V changes. Van 't Hoff's formula is equivalent to
  taking the frequency of dissociation as proportional to the square of
  the concentration of the molecules, and the frequency of recombination
  as proportional to the cube of the concentration of the ions. An
  explanation of the failure of the usual dilution law in these cases
  may be given if we remember that, while the electric forces between
  bodies like undissociated molecules, each associated with equal and
  opposite charges, will vary inversely as the fourth power of the
  distance, the forces between dissociated ions, each carrying one
  charge only, will be inversely proportional to the square of the
  distance. The forces between the ions of a strongly dissociated
  solution will thus be considerable at a dilution which makes forces
  between undissociated molecules quite insensible, and at the
  concentrations necessary to test Ostwald's formula an electrolyte will
  be far from dilute in the thermodynamic sense of the term, which
  implies no appreciable intermolecular or interionic forces.

  When the solutions of two substances are mixed, similar considerations
  to those given above enable us to calculate the resultant changes in
  dissociation. (See Arrhenius, loc. cit.) The simplest and most
  important case is that of two electrolytes having one ion in common,
  such as two acids. It is evident that the undissociated part of each
  acid must eventually be in equilibrium with the free hydrogen ions,
  and, if the concentrations are not such as to secure this condition,
  readjustment must occur. In order that there should be no change in
  the states of dissociation on mixing, it is necessary, therefore, that
  the concentration of the hydrogen ions should be the same in each
  separate solution. Such solutions were called by Arrhenius
  "isohydric." The two solutions, then, will so act on each other when
  mixed that they become isohydric. Let us suppose that we have one very
  active acid like hydrochloric, in which dissociation is nearly
  complete, another like acetic, in which it is very small. In order
  that the solutions of these should be isohydric and the concentrations
  of the hydrogen ions the same, we must have a very large quantity of
  the feebly dissociated acetic acid, and a very small quantity of the
  strongly dissociated hydrochloric, and in such proportions alone will
  equilibrium be possible. This explains the action of a strong acid on
  the salt of a weak acid. Let us allow dilute sodium acetate to react
  with dilute hydrochloric acid. Some acetic acid is formed, and this
  process will go on till the solutions of the two acids are isohydric:
  that is, till the dissociated hydrogen ions are in equilibrium with
  both. In order that this should hold, we have seen that a considerable
  quantity of acetic acid must be present, so that a corresponding
  amount of the salt will be decomposed, the quantity being greater the
  less the acid is dissociated. This "replacement" of a "weak" acid by a
  "strong" one is a matter of common observation in the chemical
  laboratory. Similar investigations applied to the general case of
  chemical equilibrium lead to an expression of exactly the same form as
  that given by C.M. Guldberg and P. Waage, which is universally
  accepted as an accurate representation of the facts.

The temperature coefficient of conductivity has approximately the same
value for most aqueous salt solutions. It decreases both as the
temperature is raised and as the concentration is increased, ranging
from about 3.5% per degree for extremely dilute solutions (i.e.
practically pure water) at 0° to about 1.5 for concentrated solutions
at 18°. For acids its value is usually rather less than for salts at
equivalent concentrations. The influence of temperature on the
conductivity of solutions depends on (1) the ionization, and (2) the
frictional resistance of the liquid to the passage of the ions, the
reciprocal of which is called the ionic fluidity. At extreme dilution,
when the ionization is complete, a variation in temperature cannot
change its amount. The rise of conductivity with temperature, therefore,
shows that the fluidity becomes greater when the solution is heated. As
the concentration is increased and un-ionized molecules are formed, a
change in temperature begins to affect the ionization as well as the
fluidity. But the temperature coefficient of conductivity is now
generally less than before; thus the effect of temperature on ionization
must be of opposite sign to its effect on fluidity. The ionization of a
solution, then, is usually diminished by raising the temperature, the
rise in conductivity being due to the greater increase in fluidity.
Nevertheless, in certain cases, the temperature coefficient of
conductivity becomes negative at high temperatures, a solution of
phosphoric acid, for example, reaching a maximum conductivity at 75° C.

The dissociation theory gives an immediate explanation of the fact that,
in general, no heat-change occurs when two neutral salt solutions are
mixed. Since the salts, both before and after mixture, exist mainly as
dissociated ions, it is obvious that large thermal effects can only
appear when the state of dissociation of the products is very different
from that of the reagents. Let us consider the case of the
neutralization of a base by an acid in the light of the dissociation
theory. In dilute solution such substances as hydrochloric acid and
potash are almost completely dissociated, so that, instead of
representing the reaction as

  HCl + KOH = KCl + H2O,

we must write

  +   -    +   -    +   -
  H + Cl + K + OH = K + Cl + H2O.

The ions K and Cl suffer no change, but the hydrogen of the acid and the
hydroxyl (OH) of the potash unite to form water, which is only very
slightly dissociated. The heat liberated, then, is almost exclusively
that produced by the formation of water from its ions. An exactly
similar process occurs when any strongly dissociated acid acts on any
strongly dissociated base, so that in all such cases the heat evolution
should be approximately the same. This is fully borne out by the
experiments of Julius Thomsen, who found that the heat of neutralization
of one gramme-molecule of a strong base by an equivalent quantity of a
strong acid was nearly constant, and equal to 13,700 or 13,800 calories.
In the case of weaker acids, the dissociation of which is less complete,
divergences from this constant value will occur, for some of the
molecules have to be separated into their ions. For instance, sulphuric
acid, which in the fairly strong solutions used by Thomsen is only about
half dissociated, gives a higher value for the heat of neutralization,
so that heat must be evolved when it is ionized. The heat of formation
of a substance from its ions is, of course, very different from that
evolved when it is formed from its elements in the usual way, since the
energy associated with an ion is different from that possessed by the
atoms of the element in their normal state. We can calculate the heat of
formation from its ions for any substance dissolved in a given liquid,
from a knowledge of the temperature coefficient of ionization, by means
of an application of the well-known thermodynamical process, which also
gives the latent heat of evaporation of a liquid when the temperature
coefficient of its vapour pressure is known. The heats of formation thus
obtained may be either positive or negative, and by using them to
supplement the heat of formation of water, Arrhenius calculated the
total heats of neutralization of soda by different acids, some of them
only slightly dissociated, and found values agreeing well with
observation (_Zeits. physikal. Chemie_, 1889, 4, p. 96; and 1892, 9, p.
339).

_Voltaic Cells._--When two metallic conductors are placed in an
electrolyte, a current will flow through a wire connecting them provided
that a difference of any kind exists between the two conductors in the
nature either of the metals or of the portions of the electrolyte which
surround them. A current can be obtained by the combination of two
metals in the same electrolyte, of two metals in different electrolytes,
of the same metal in different electrolytes, or of the same metal in
solutions of the same electrolyte at different concentrations. In
accordance with the principles of energetics (q.v.), any change which
involves a decrease in the total available energy of the system will
tend to occur, and thus the necessary and sufficient condition for the
production of electromotive force is that the available energy of the
system should decrease when the current flows.

In order that the current should be maintained, and the electromotive
force of the cell remain constant during action, it is necessary to
ensure that the changes in the cell, chemical or other, which produce
the current, should neither destroy the difference between the
electrodes, nor coat either electrode with a non-conducting layer
through which the current cannot pass. As an example of a fairly
constant cell we may take that of Daniell, which consists of the
electrical arrangement--zinc | zinc sulphate solution | copper sulphate
solution | copper,--the two solutions being usually separated by a pot
of porous earthenware. When the zinc and copper plates are connected
through a wire, a current flows, the conventionally positive electricity
passing from copper to zinc in the wire and from zinc to copper in the
cell. Zinc dissolves at the anode, an equal amount of zinc replaces an
equivalent amount of copper on the other side of the porous partition,
and the same amount of copper is deposited on the cathode. This process
involves a decrease in the available energy of the system, for the
dissolution of zinc gives out more energy than the separation of copper
absorbs. But the internal rearrangements which accompany the production
of a current do not cause any change in the original nature of the
electrodes, fresh zinc being exposed at the anode, and copper being
deposited on copper at the cathode. Thus as long as a moderate current
flows, the only variation in the cell is the appearance of zinc sulphate
in the liquid on the copper side of the porous wall. In spite of this
appearance, however, while the supply of copper is maintained, copper,
being more easily separated from the solution than zinc, is deposited
alone at the cathode, and the cell remains constant.

It is necessary to observe that the condition for change in a system is
that the total available energy of the whole system should be decreased
by the change. We must consider what change is allowed by the mechanism
of the system, and deal with the sum of all the alterations in energy.
Thus in the Daniell cell the dissolution of copper as well as of zinc
would increase the loss in available energy. But when zinc dissolves,
the zinc ions carry their electric charges with them, and the liquid
tends to become positively electrified. The electric forces then soon
stop further action unless an equivalent quantity of positive ions are
removed from the solution. Hence zinc can only dissolve when some more
easily separable substance is present in solution to be removed pari
passu with the dissolution of zinc. The mechanism of such systems is
well illustrated by an experiment devised by W. Ostwald. Plates of
platinum and pure or amalgamated zinc are separated by a porous pot, and
each surrounded by some of the same solution of a salt of a metal more
oxidizable than zinc, such as potassium. When the plates are connected
together by means of a wire, no current flows, and no appreciable amount
of zinc dissolves, for the dissolution of zinc would involve the
separation of potassium and a gain in available energy. If sulphuric
acid be added to the vessel containing the zinc, these conditions are
unaltered and still no zinc is dissolved. But, on the other hand, if a
few drops of acid be placed in the vessel with the platinum, bubbles of
hydrogen appear, and a current flows, zinc dissolving at the anode, and
hydrogen being liberated at the cathode. In order that positively
electrified ions may enter a solution, an equivalent amount of other
positive ions must be removed or negative ions be added, and, for the
process to occur spontaneously, the possible action at the two
electrodes must involve a decrease in the total available energy of the
system.

Considered thermodynamically, voltaic cells must be divided into
reversible and non-reversible systems. If the slow processes of
diffusion be ignored, the Daniell cell already described may be taken as
a type of a reversible cell. Let an electromotive force exactly equal to
that of the cell be applied to it in the reverse direction. When the
applied electromotive force is diminished by an infinitesimal amount,
the cell produces a current in the usual direction, and the ordinary
chemical changes occur. If the external electromotive force exceed that
of the cell by ever so little, a current flows in the opposite
direction, and all the former chemical changes are reversed, copper
dissolving from the copper plate, while zinc is deposited on the zinc
plate. The cell, together with this balancing electromotive force, is
thus a reversible system in true equilibrium, and the thermodynamical
reasoning applicable to such systems can be used to examine its
properties.

Now a well-known relation connects the available energy of a reversible
system with the corresponding change in its total internal energy.

  The available energy A is the amount of external work obtainable by an
  infinitesimal, reversible change in the system which occurs at a
  constant temperature T. If I be the change in the internal energy, the
  relation referred to gives us the equation

    A = I + T(dA/dT),

  where dA/dT denotes the rate of change of the available energy of the
  system per degree change in temperature. During a small electric
  transfer through the cell, the external work done is Ee, where E is
  the electromotive force. If the chemical changes which occur in the
  cell were allowed to take place in a closed vessel without the
  performance of electrical or other work, the change in energy would be
  measured by the heat evolved. Since the final state of the system
  would be the same as in the actual processes of the cell, the same
  amount of heat must give a measure of the change in internal energy
  when the cell is in action. Thus, if L denote the heat corresponding
  with the chemical changes associated with unit electric transfer, Le
  will be the heat corresponding with an electric transfer e, and will
  also be equal to the change in internal energy of the cell. Hence we
  get the equation

    Ee = Le + Te(dE/dT) or E = L + T(dE/dT),

  as a particular case of the general thermodynamic equation of
  available energy. This equation was obtained in different ways by J.
  Willard Gibbs and H. von Helmholtz.

  It will be noticed that when dE/dT is zero, that is, when the
  electromotive force of the cell does not change with temperature, the
  electromotive force is measured by the heat of reaction per unit of
  electrochemical change. The earliest formulation of the subject, due
  to Lord Kelvin, assumed that this relation was true in all cases, and,
  calculated in this way, the electromotive force of Daniell's cell,
  which happens to possess a very small temperature coefficient, was
  found to agree with observation.

  When one gramme of zinc is dissolved in dilute sulphuric acid, 1670
  thermal units or calories are evolved. Hence for the electrochemical
  unit of zinc or 0.003388 gramme, the thermal evolution is 5.66
  calories. Similarly, the heat which accompanies the dissolution of one
  electrochemical unit of copper is 3.00 calories. Thus, the thermal
  equivalent of the unit of resultant electrochemical change in
  Daniell's cell is 5.66 - 3.00 = 2.66 calories. The dynamical
  equivalent of the calorie is 4.18 × 10^7 ergs or C.G.S. units of work,
  and therefore the electromotive force of the cell should be 1.112 ×
  10^8 C.G.S. units or 1.112 volts--a close agreement with the
  experimental result of about 1.08 volts. For cells in which the
  electromotive force varies with temperature, the full equation given
  by Gibbs and Helmholtz has also been confirmed experimentally.

As stated above, an electromotive force is set up whenever there is a
difference of any kind at two electrodes immersed in electrolytes. In
ordinary cells the difference is secured by using two dissimilar metals,
but an electromotive force exists if two plates of the same metal are
placed in solutions of different substances, or of the same substance at
different concentrations. In the latter case, the tendency of the metal
to dissolve in the more dilute solution is greater than its tendency to
dissolve in the more concentrated solution, and thus there is a decrease
in available energy when metal dissolves in the dilute solution and
separates in equivalent quantity from the concentrated solution. An
electromotive force is therefore set up in this direction, and, if we
can calculate the change in available energy due to the processes of the
cell, we can foretell the value of the electromotive force. Now the
effective change produced by the action of the current is the
concentration of the more dilute solution by the dissolution of metal in
it, and the dilution of the originally stronger solution by the
separation of metal from it. We may imagine these changes reversed in
two ways. We may evaporate some of the solvent from the solution which
has become weaker and thus reconcentrate it, condensing the vapour on
the solution which had become stronger. By this reasoning Helmholtz
showed how to obtain an expression for the work done. On the other hand,
we may imagine the processes due to the electrical transfer to be
reversed by an osmotic operation. Solvent may be supposed to be squeezed
out from the solution which has become more dilute through a
semi-permeable wall, and through another such wall allowed to mix with
the solution which in the electrical operation had become more
concentrated. Again, we may calculate the osmotic work done, and, if the
whole cycle of operations be supposed to occur at the same temperature,
the osmotic work must be equal and opposite to the electrical work of
the first operation.

  The result of the investigation shows that the electrical work Ee is
  given by the equation
          _
         / p2
    Ee = |   vdp,
        _/ p1

  where v is the volume of the solution used and p its osmotic pressure.
  When the solutions may be taken as effectively dilute, so that the gas
  laws apply to the osmotic pressure, this relation reduces to

        nrRT               c1
    E = ---- log_[epsilon] --
         ey                c2

  where n is the number of ions given by one molecule of the salt, r the
  transport ratio of the anion, R the gas constant, T the absolute
  temperature, y the total valency of the anions obtained from one
  molecule, and c1 and c2 the concentrations of the two solutions.

  If we take as an example a concentration cell in which silver plates
  are placed in solutions of silver nitrate, one of which is ten times
  as strong as the other, this equation gives

    E = 0.060 × 10^8 C.G.S. units
      = 0.060 volts.

W. Nernst, to whom this theory is due, determined the electromotive
force of this cell experimentally, and found the value 0.055 volt.

The logarithmic formulae for these concentration cells indicate that
theoretically their electromotive force can be increased to any extent
by diminishing without limit the concentration of the more dilute
solution, log c1/c2 then becoming very great. This condition may be
realized to some extent in a manner that throws light on the general
theory of the voltaic cell. Let us consider the arrangement--silver |
silver chloride with potassium chloride solution | potassium nitrate
solution | silver nitrate solution | silver. Silver chloride is a very
insoluble substance, and here the amount in solution is still further
reduced by the presence of excess of chlorine ions of the potassium
salt. Thus silver, at one end of the cell in contact with many silver
ions of the silver nitrate solution, at the other end is in contact with
a liquid in which the concentration of those ions is very small indeed.
The result is that a high electromotive force is set up, which has been
calculated as 0.52 volt, and observed as 0.51 volt. Again, Hittorf has
shown that the effect of a cyanide round a copper electrode is to
combine with the copper ions. The concentration of the simple copper
ions is then so much diminished that the copper plate becomes an anode
with regard to zinc. Thus the cell--copper | potassium cyanide solution
| potassium sulphate solution--zinc sulphate solution | zinc--gives a
current which carries copper into solution and deposits zinc. In a
similar way silver could be made to act as anode with respect to
cadmium.

It is now evident that the electromotive force of an ordinary chemical
cell such as that of Daniell depends on the concentration of the
solutions as well as on the nature of the metals. In ordinary cases
possible changes in the concentrations only affect the electromotive
force by a few parts in a hundred, but, by means such as those indicated
above, it is possible to produce such immense differences in the
concentrations that the electromotive force of the cell is not only
changed appreciably but even reversed in direction. Once more we see
that it is the total impending change in the available energy of the
system which controls the electromotive force.

Any reversible cell can theoretically be employed as an accumulator,
though, in practice, conditions of general convenience are more sought
after than thermodynamic efficiency. The effective electromotive force
of the common lead accumulator (q.v.) is less than that required to
charge it. This drop in the electromotive force has led to the belief
that the cell is not reversible. F. Dolezalek, however, has attributed
the difference to mechanical hindrances, which prevent the equalization
of acid concentration in the neighbourhood of the electrodes, rather
than to any essentially irreversible chemical action. The fact that the
Gibbs-Helmholtz equation is found to apply also indicates that the lead
accumulator is approximately reversible in the thermodynamic sense of
the term.

_Polarization and Contact Difference of Potential._--If we connect
together in series a single Daniell's cell, a galvanometer, and two
platinum electrodes dipping into acidulated water, no visible chemical
decomposition ensues. At first a considerable current is indicated by
the galvanometer; the deflexion soon diminishes, however, and finally
becomes very small. If, instead of using a single Daniell's cell, we
employ some source of electromotive force which can be varied as we
please, and gradually raise its intensity, we shall find that, when it
exceeds a certain value, about 1.7 volt, a permanent current of
considerable strength flows through the solution, and, after the initial
period, shows no signs of decrease. This current is accompanied by
chemical decomposition. Now let us disconnect the platinum plates from
the battery and join them directly with the galvanometer. A current will
flow for a while in the reverse direction; the system of plates and
acidulated water through which a current has been passed, acts as an
accumulator, and will itself yield a current in return. These phenomena
are explained by the existence of a reverse electromotive force at the
surface of the platinum plates. Only when the applied electromotive
force exceeds this reverse force of polarization, will a permanent
steady current pass through the liquid, and visible chemical
decomposition proceed. It seems that this reverse electromotive force of
polarization is due to the deposit on the electrodes of minute
quantities of the products of chemical decomposition. Differences
between the two electrodes are thus set up, and, as we have seen above,
an electromotive force will therefore exist between them. To pass a
steady current in the direction opposite to this electromotive force of
polarization, the applied electromotive force E must exceed that of
polarization E', and the excess E - E' is the effective electromotive
force of the circuit, the current being, in accordance with Ohm's law,
proportional to the applied electromotive force and represented by (E -
E')/R, where R is a constant called the resistance of the circuit.

When we use platinum electrodes in acidulated water, hydrogen and oxygen
are evolved. The opposing force of polarization is about 1.7 volt, but,
when the plates are disconnected and used as a source of current, the
electromotive force they give is only about 1.07 volt. This
irreversibility is due to the work required to evolve bubbles of gas at
the surface of bright platinum plates. If the plates be covered with a
deposit of platinum black, in which the gases are absorbed as fast as
they are produced, the minimum decomposition point is 1.07 volt, and the
process is reversible. If secondary effects are eliminated, the
deposition of metals also is a reversible process; the decomposition
voltage is equal to the electromotive force which the metal itself gives
when going into solution. The phenomena of polarization are thus seen to
be due to the changes of surface produced, and are correlated with the
differences of potential which exist at any surface of separation
between a metal and an electrolyte.

Many experiments have been made with a view of separating the two
potential-differences which must exist in any cell made of two metals
and a liquid, and of determining each one individually. If we regard the
thermal effect at each junction as a measure of the potential-difference
there, as the total thermal effect in the cell undoubtedly is of the sum
of its potential-differences, in cases where the temperature coefficient
is negligible, the heat evolved on solution of a metal should give the
electrical potential-difference at its surface. Hence, if we assume
that, in the Daniell's cell, the temperature coefficients are negligible
at the individual contacts as well as in the cell as a whole, the sign
of the potential-difference ought to be the same at the surface of the
zinc as it is at the surface of the copper. Since zinc goes into
solution and copper comes out, the electromotive force of the cell will
be the difference between the two effects. On the other hand, it is
commonly thought that the single potential-differences at the surface of
metals and electrolytes have been determined by methods based on the use
of the capillary electrometer and on others depending on what is called
a dropping electrode, that is, mercury dropping rapidly into an
electrolyte and forming a cell with the mercury at rest in the bottom of
the vessel. By both these methods the single potential-differences found
at the surfaces of the zinc and copper have opposite signs, and the
effective electromotive force of a Daniell's cell is the sum of the two
effects. Which of these conflicting views represents the truth still
remains uncertain.

_Diffusion of Electrolytes and Contact Difference of Potential between
Liquids._--An application of the theory of ionic velocity due to W.
Nernst[7] and M. Planck[8] enables us to calculate the diffusion
constant of dissolved electrolytes. According to the molecular theory,
diffusion is due to the motion of the molecules of the dissolved
substance through the liquid. When the dissolved molecules are uniformly
distributed, the osmotic pressure will be the same everywhere throughout
the solution, but, if the concentration vary from point to point, the
pressure will vary also. There must, then, be a relation between the
rate of change of the concentration and the osmotic pressure gradient,
and thus we may consider the osmotic pressure gradient as a force
driving the solute through a viscous medium. In the case of
non-electrolytes and of all non-ionized molecules this analogy
completely represents the facts, and the phenomena of diffusion can be
deduced from it alone. But the ions of an electrolytic solution can move
independently through the liquid, even when no current flows, as the
consequences of Ohm's law indicate. The ions will therefore diffuse
independently, and the faster ion will travel quicker into pure water in
contact with a solution. The ions carry their charges with them, and, as
a matter of fact, it is found that water in contact with a solution
takes with respect to it a positive or negative potential, according as
the positive or negative ion travels the faster. This process will go on
until the simultaneous separation of electric charges produces an
electrostatic force strong enough to prevent further separation of ions.
We can therefore calculate the rate at which the salt as a whole will
diffuse by examining the conditions for a steady transfer, in which the
ions diffuse at an equal rate, the faster one being restrained and the
slower one urged forward by the electric forces. In this manner the
diffusion constant can be calculated in absolute units (HCl = 2.49, HNO3
= 2.27, NaCl = 1.12), the unit of time being the day. By experiments on
diffusion this constant has been found by Scheffer, and the numbers
observed agree with those calculated (HCl = 2.30, HNO3 = 2.22, NaCl =
1.11).

As we have seen above, when a solution is placed in contact with water
the water will take a positive or negative potential with regard to the
solution, according as the cation or anion has the greater specific
velocity, and therefore the greater initial rate of diffusion. The
difference of potential between two solutions of a substance at
different concentrations can be calculated from the equations used to
give the diffusion constants. The results give equations of the same
logarithmic form as those obtained in a somewhat different manner in the
theory of concentration cells described above, and have been verified by
experiment.

The contact differences of potential at the interfaces of metals and
electrolytes have been co-ordinated by Nernst with those at the surfaces
of separation between different liquids. In contact with a solvent a
metal is supposed to possess a definite solution pressure, analogous to
the vapour pressure of a liquid. Metal goes into solution in the form of
electrified ions. The liquid thus acquires a positive charge, and the
metal a negative charge. The electric forces set up tend to prevent
further separation, and finally a state of equilibrium is reached, when
no more ions can go into solution unless an equivalent number are
removed by voltaic action. On the analogy between this case and that of
the interface between two solutions, Nernst has arrived at similar
logarithmic expressions for the difference of potential, which becomes
proportional to log (P1/P2) where P2 is taken to mean the osmotic
pressure of the cations in the solution, and P1 the osmotic pressure of
the cations in the substance of the metal itself. On these lines the
equations of concentration cells, deduced above on less hypothetical
grounds, may be regained.

_Theory of Electrons._--Our views of the nature of the ions of
electrolytes have been extended by the application of the ideas of the
relations between matter and electricity obtained by the study of
electric conduction through gases. The interpretation of the phenomena
of gaseous conduction was rendered possible by the knowledge previously
acquired of conduction through liquids; the newer subject is now
reaching a position whence it can repay its debt to the older.

Sir J.J. Thomson has shown (see CONDUCTION, ELECTRIC, § III.) that the
negative ions in certain cases of gaseous conduction are much more
mobile than the corresponding positive ions, and possess a mass of about
the one-thousandth part of that of a hydrogen atom. These negative
particles or corpuscles seem to be the ultimate units of negative
electricity, and may be identified with the electrons required by the
theories of H.A. Lorentz and Sir J. Larmor. A body containing an excess
of these particles is negatively electrified, and is positively
electrified if it has parted with some of its normal number. An electric
current consists of a moving stream of electrons. In gases the electrons
sometimes travel alone, but in liquids they are always attached to
matter, and their motion involves the movement of chemical atoms or
groups of atoms. An atom with an extra corpuscle is a univalent negative
ion, an atom with one corpuscle detached is a univalent positive ion. In
metals the electrons can slip from one atom to the next, since a current
can pass without chemical action. When a current passes from an
electrolyte to a metal, the electron must be detached from the atom it
was accompanying and chemical action be manifested at the electrode.

  BIBLIOGRAPHY.--Michael Faraday, _Experimental Researches in
  Electricity_ (London, 1844 and 1855); W. Ostwald, _Lehrbuch der
  allgemeinen Chemie_, 2te Aufl. (Leipzig, 1891); _Elektrochemie_
  (Leipzig, 1896); W Nernst, _Theoretische Chemie_, 3te Aufl.
  (Stuttgart, 1900; English translation, London, 1904); F. Kohlrausch
  and L. Holborn, _Das Leitvermögen der Elektrolyte_ (Leipzig, 1898);
  W.C.D. Whetham, _The Theory of Solution and Electrolysis_ (Cambridge,
  1902); M. Le Blanc, _Elements of Electrochemistry_ (Eng. trans.,
  London, 1896); S. Arrhenius, _Text-Book of Electrochemistry_ (Eng.
  trans., London, 1902); H.C. Jones, _The Theory of Electrolytic
  Dissociation_ (New York, 1900); N. Munroe Hopkins, _Experimental
  Electrochemistry_ (London, 1905); Lüphe, _Grundzüge der Elektrochemie_
  (Berlin, 1896).

  Some of the more important papers on the subject have been reprinted
  for Harper's _Series of Scientific Memoirs in Electrolytic Conduction_
  (1899) and the _Modern Theory of Solution_ (1899). Several journals
  are published specially to deal with physical chemistry, of which
  electrochemistry forms an important part. Among them may be mentioned
  the _Zeitschrift für physikalische Chemie_ (Leipzig); and the _Journal
  of Physical Chemistry_ (Cornell University). In these periodicals will
  be found new work on the subject and abstracts of papers which appear
  in other physical and chemical publications.     (W. C. D. W.)


FOOTNOTES:

  [1] See Hittorf, _Pogg. Ann._ cvi. 517 (1859).

  [2] _Grundriss der Elektrochemie_ (1895), p. 292; see also F. Kaufler
    and C. Herzog, _Ber._, 1909, 42, p. 3858.

  [3] _Brit. Ass. Rep._, 1906, Section A, Presidential Address.

  [4] See _Theory of Solution_, by W.C.D. Whetham (1902), p. 328.

  [5] W. Ostwald, _Zeits. physikal. Chemie_, 1892, vol. IX. p. 579; T.
    Ewan, _Phil. Mag._ (5), 1892, vol. xxxiii. p. 317; G.D. Liveing,
    _Cambridge Phil. Trans._, 1900, vol. xviii. p. 298.

  [6] See W.B. Hardy, _Journal of Physiology_, 1899, vol. xxiv. p. 288;
    and W.C.D. Whetham, _Phil. Mag._, November 1899.

  [7] _Zeits. physikal. Chem._ 2, p. 613.

  [8] _Wied. Ann._, 1890, 40, p. 561.



ELECTROMAGNETISM, that branch of physical science which is concerned
with the interconnexion of electricity and magnetism, and with the
production of magnetism by means of electric currents by devices called
electromagnets.

_History._--The foundation was laid by the observation first made by
Hans Christian Oersted (1777-1851), professor of natural philosophy in
Copenhagen, who discovered in 1820 that a wire uniting the poles or
terminal plates of a voltaic pile has the property of affecting a
magnetic needle[1] (see ELECTRICITY). Oersted carefully ascertained
that the nature of the wire itself did not influence the result but saw
that it was due to the electric conflict, as he called it, round the
wire; or in modern language, to the magnetic force or magnetic flux
round the conductor. If a straight wire through which an electric
current is flowing is placed above and parallel to a magnetic compass
needle, it is found that if the current is flowing in the conductor in a
direction from south to north, the north pole of the needle under the
conductor deviates to the left hand, whereas if the conductor is placed
under the needle, the north pole deviates to the right hand; if the
conductor is doubled back over the needle, the effects of the two sides
of the loop are added together and the deflection is increased. These
results are summed up in the mnemonic rule: _Imagine yourself swimming
in the conductor with the current, that is, moving in the direction of
the positive electricity, with your face towards the magnetic needle;
the north pole will then deviate to your left hand._ The deflection of
the magnetic needle can therefore reveal the existence of an electric
current in a neighbouring circuit, and this fact was soon utilized in
the construction of instruments called galvanometers (q.v.).

Immediately after Oersted's discovery was announced, D.F.J. Arago and
A.M. Ampère began investigations on the subject of electromagnetism. On
the 18th of September 1820, Ampère read a paper before the Academy of
Sciences in Paris, in which he announced that the voltaic pile itself
affected a magnetic needle as did the uniting wire, and he showed that
the effects in both cases were consistent with the theory that electric
current was a circulation round a circuit, and equivalent in magnetic
effect to a very short magnet with axis placed at right angles to the
plane of the circuit. He then propounded his brilliant hypothesis that
the magnetization of iron was due to molecular electric currents. This
suggested to Arago that wire wound into a helix carrying electric
current should magnetize a steel needle placed in the interior. In the
_Ann. Chim._ (1820, 15, p. 94), Arago published a paper entitled
"Expériences relatives à l'aimantation du fer et de l'acier par l'action
du courant voltaïque," announcing that the wire conveying the current,
even though of copper, could magnetize steel needles placed across it,
and if plunged into iron filings it attracted them. About the same time
Sir Humphry Davy sent a communication to Dr W.H. Wollaston, read at the
Royal Society on the 16th of November 1820 (reproduced in the _Annals of
Philosophy_ for August 1821, p. 81), "On the Magnetic Phenomena produced
by Electricity," in which he announced his independent discovery of the
same fact. With a large battery of 100 pairs of plates at the Royal
Institution, he found in October 1820 that the uniting wire became
strongly magnetic and that iron filings clung to it; also that steel
needles placed across the wire were permanently magnetized. He placed a
sheet of glass over the wire and sprinkling iron filings on it saw that
they arranged themselves in straight lines at right angles to the wire.
He then proved that Leyden jar discharges could produce the same
effects. Ampère and Arago then seem to have experimented together and
magnetized a steel needle wrapped in paper which was enclosed in a
helical wire conveying a current. All these facts were rendered
intelligible when it was seen that a wire when conveying an electric
current becomes surrounded by a magnetic field. If the wire is a long
straight one, the lines of magnetic force are circular and concentric
with centres on the wire axis, and if the wire is bent into a circle the
lines of magnetic force are endless loops surrounding and linked with
the electric circuit. Since a magnetic pole tends to move along a line
of magnetic force it was obvious that it should revolve round a wire
conveying a current. To exhibit this fact involved, however, much
ingenuity. It was first accomplished by Faraday in October 1821 (_Exper.
Res._ ii. p. 127). Since the action is reciprocal a current free to move
tends to revolve round a magnetic pole. The fact is most easily shown by
a small piece of apparatus made as follows: In a glass cylinder (see
fig. 1) like a lamp chimney are fitted two corks. Through the bottom one
is passed the north end of a bar magnet which projects up above a little
mercury lying in the cork. Through the top cork is passed one end of a
wire from a battery, and a piece of wire in the cylinder is flexibly
connected to it, the lower end of this last piece just touching the
mercury. When a current is passed in at the top wire and out at the
lower end of the bar magnet, the loose wire revolves round the magnet
pole. All text-books on physics contain in their chapters on
electromagnetism full accounts of various forms of this experiment.

[Illustration: FIG. 1.]

In 1825 another important step forward was taken when William Sturgeon
(1783-1850) of London produced the electromagnet. It consisted of a
horseshoe-shaped bar of soft iron, coated with varnish, on which was
wrapped a spiral coil of bare copper wire, the turns not touching each
other. When a voltaic current was passed through the wire the iron
became a powerful magnet, but on severing the connexion with the
battery, the soft iron lost immediately nearly all its magnetism.[2]

At that date Ohm had not announced his law of the electric circuit, and
it was a matter of some surprise to investigators to find that
Sturgeon's electromagnet could not be operated at a distance through a
long circuit of wire with such good results as when close to the
battery. Peter Barlow, in January 1825, published in the _Edinburgh
Philosophical Journal_, a description of such an experiment made with a
view of applying Sturgeon's electromagnet to telegraphy, with results
which were unfavourable. Sturgeon's experiments, however, stimulated
Joseph Henry (q.v.) in the United States, and in 1831 he gave a
description of a method of winding electromagnets which at once put a
new face upon matters (_Silliman's Journal_, 1831, 19, p. 400). Instead
of insulating the iron core, he wrapped the copper wire round with silk
and wound in numerous turns and many layers upon the iron horseshoe in
such fashion that the current went round the iron always in the same
direction. He then found that such an electromagnet wound with a long
fine wire, if worked with a battery consisting of a large number of
cells in series, could be operated at a considerable distance, and he
thus produced what were called at that time _intensity electromagnets_,
and which subsequently rendered the electric telegraph a possibility. In
fact, Henry established in 1831, in Albany, U.S.A., an electromagnetic
telegraph, and in 1835 at Princeton even used an earth return, thereby
anticipating the discovery (1838) of C.A. Steinheil (1801-1870) of
Munich.

[Illustration: FIG. 2.]

Inventors were then incited to construct powerful electromagnets as
tested by the weight they could carry from their armatures. Joseph Henry
made a magnet for Yale College, U.S.A., which lifted 3000 lb.
(_Silliman's Journal_, 1831, 20, p. 201), and one for Princeton which
lifted 3000 with a very small battery. Amongst others J.P. Joule, ever
memorable for his investigations on the mechanical equivalent of heat,
gave much attention about 1838-1840 to the construction of
electromagnets and succeeded in devising some forms remarkable for their
lifting power. One form was constructed by cutting a thick soft iron
tube longitudinally into two equal parts. Insulated copper wire was then
wound longitudinally over one of both parts (see fig. 2) and a current
sent through the wire. In another form two iron disks with teeth at
right angles to the disk had insulated wire wound zigzag between the
teeth; when a current was sent through the wire, the teeth were so
magnetized that they were alternately N. and S. poles. If two such
similar disks were placed with teeth of opposite polarity in contact, a
very large force was required to detach them, and with a magnet and
armature weighing in all 11.575 lb. Joule found that a weight of 2718
was supported. Joule's papers on this subject will be found in his
_Collected Papers_ published by the Physical Society of London, and in
_Sturgeon's Annals of Electricity_, 1838-1841, vols. 2-6.

  _The Magnetic Circuit._--The phenomena presented by the electromagnet
  are interpreted by the aid of the notion of the magnetic circuit. Let
  us consider a thin circular sectioned ring of iron wire wound over
  with a solenoid or spiral of insulated copper wire through which a
  current of electricity can be passed. If the solenoid or wire windings
  existed alone, a current having a strength A amperes passed through it
  would create in the interior of the solenoid a magnetic force H,
  numerically equal to 4[pi]/10 multiplied by the number of windings N
  on the solenoid, and by the current in amperes A, and divided by the
  mean length of the solenoid l, or H = 4[pi]AN/10l. The product AN is
  called the "ampere-turns" on the solenoid. The product Hl of the
  magnetic force H and the length l of the magnetic circuit is called
  the "magnetomotive force" in the magnetic circuit, and from the above
  formula it is seen that the magnetomotive force denoted by (M.M.F.) is
  equal to 4[pi]/10 (= 1.25 nearly) times the ampere-turns (A.N.) on the
  exciting coil or solenoid. Otherwise (A.N.) = 0.8(M.M.F.). The
  magnetomotive force is regarded as creating an effect called magnetic
  flux (Z) in the magnetic circuit, just as electromotive force E.M.F.
  produces electric current (A) in the electric circuit, and as by Ohm's
  law (see ELECTROKINETICS) the current varies as the E.M.F. and
  inversely as a quality of the electric circuit called its
  "resistance," so in the magnetic circuit the magnetic flux varies as
  the magnetomotive force and inversely as a quality of the magnetic
  circuit called its "reluctance." The great difference between the
  electric circuit and the magnetic circuit lies in the fact that
  whereas the electric resistance of a solid or liquid conductor is
  independent of the current and affected only by the temperature, the
  magnetic reluctance varies with the magnetic flux and cannot be
  defined except by means of a curve which shows its value for different
  flux densities. The quotient of the total magnetic flux, Z, in a
  circuit by the cross section, S, of the circuit is called the mean
  "flux density," and the reluctance of a magnetic circuit one
  centimetre long and one square centimetre in cross section is called
  the "reluctivity" of the material. The relation between reluctivity
  [rho] = 1/µ magnetic force H, and flux density B, is defined by the
  equation H = [rho]B, from which we have Hl = Z([rho]l/S) = M.M.F.
  acting on the circuit. Again, since the ampere-turns (AN) on the
  circuit are equal to 0.8 times the M.M.F., we have finally AN/l =
  0.8(Z/µS). This equation tells us the exciting force reckoned in
  ampere-turns, AN, which must be put on the ring core to create a total
  magnetic flux Z in it, the ring core having a mean perimeter l and
  cross section S and reluctivity [rho] = 1/µ corresponding to a flux
  density Z/S. Hence before we can make use of the equation for
  practical purposes we need to possess a curve for the particular
  material showing us the value of the reluctivity corresponding to
  various values of the possible flux density. The reciprocal of [rho]
  is usually called the "permeability" of the material and denoted by µ.
  Curves showing the relation of 1/[rho] and ZS or µ and B, are called
  "permeability curves." For air and all other non-magnetic matter the
  permeability has the same value, taken arbitrarily as unity. On the
  other hand, for iron, nickel and cobalt the permeability may in some
  cases reach a value of 2000 or 2500 for a value of B = 5000 in C.G.S.
  measure (see UNITS, PHYSICAL). The process of taking these curves
  consists in sending a current of known strength through a solenoid of
  known number of turns wound on a circular iron ring of known
  dimensions, and observing the time-integral of the secondary current
  produced in a secondary circuit of known turns and resistance R wound
  over the iron core N times. The secondary electromotive force is by
  Faraday's law (see ELECTROKINETICS) equal to the time rate of change
  of the total flux, or E = NdZ/dt. But by Ohm's law E = Rdq/dt, where q
  is the quantity of electricity set flowing in the secondary circuit by
  a change dZ in the co-linked total flux. Hence if 2Q represents this
  total quantity of electricity set flowing in the secondary circuit by
  suddenly reversing the direction of the magnetic flux Z in the iron
  core we must have

    RQ = NZ or Z = RQ/N.

  The measurement of the total quantity of electricity Q can be made by
  means of a ballistic galvanometer (q.v.), and the resistance R of the
  secondary circuit includes that of the coil wound on the iron core and
  the galvanometer as well. In this manner the value of the total flux Z
  and therefore of Z/S = B or the flux density, can be found for a given
  magnetizing force H, and this last quantity is determined when we know
  the magnetizing current in the solenoid and its turns and dimensions.
  The curve which delineates the relation of H and B is called the
  magnetization curve for the material in question. For examples of
  these curves see MAGNETISM.

  The fundamental law of the non-homogeneous magnetic circuit traversed
  by one and the same total magnetic flux Z is that the sum of all the
  magnetomotive forces acting in the circuit is numerically equal to the
  product of the factor 0.8, the total flux in the circuit, and the sum
  of all the reluctances of the various parts of the circuit. If then
  the circuit consists of materials of different permeability and it is
  desired to know the ampere-turns required to produce a given total of
  flux round the circuit, we have to calculate from the magnetization
  curves of the material of each part the necessary magnetomotive forces
  and add these forces together. The practical application of this
  principle to the predetermination of the field windings of dynamo
  magnets was first made by Drs J. and E. Hopkinson (_Phil. Trans._,
  1886, 177, p. 331).

  We may illustrate the principles of this predetermination by a simple
  example. Suppose a ring of iron has a mean diameter of 10 cms. and a
  cross section of 2 sq. cms., and a transverse cut on air gap made in
  it 1 mm. wide. Let us inquire the ampere-turns to be put upon the ring
  to create in it a total flux of 24,000 C.G.S. units. The total length
  of the iron part of the circuit is (10[pi] - 0.1) cms., and its
  section is 2 sq. cms., and the flux density in it is to be 12,000.
  From Table II. below we see that the permeability of pure iron
  corresponding to a flux density of 12,000 is 2760. Hence the
  reluctance of the iron circuits is equal to

    10[pi] - 0.1    220
    ------------ = ----- C.G.S. units.
      2760 × 2     38640

  The length of the air gap is 0.1 cm., its section 2 sq. cms., and its
  permeability is unity. Hence the reluctance of the air gap is

     0.1     1
    ----- = -- C.G.S. unit.
    1 × 2   20

  Accordingly the magnetomotive force in ampere-turns required to
  produce the required flux is equal to

                 / 1    220 \
    0.8(24,000) ( -- + ----- ) = 1070 nearly.
                 \20   38640/

  It follows that the part of the magnetomotive force required to
  overcome the reluctance of the narrow air gap is about nine times that
  required for the iron alone.

  In the above example we have for simplicity assumed that the flux in
  passing across the air gap does not spread out at all. In dealing with
  electromagnet design in dynamo construction we have, however, to take
  into consideration the spreading as well as the leakage of flux across
  the circuit (see DYNAMO). It will be seen, therefore, that in order
  that we may predict the effect of a certain kind of iron or steel when
  used as the core of an electromagnet, we must be provided with tables
  or curves showing the reluctivity or permeability corresponding to
  various flux densities or--which comes to the same thing--with (B, H)
  curves for the sample.

_Iron and Steel for Electromagnetic Machinery._--In connexion with the
technical application of electromagnets such as those used in the field
magnets of dynamos (q.v.), the testing of different kinds of iron and
steel for magnetic permeability has therefore become very important.
Various instruments called permeameters and hysteresis meters have been
designed for this purpose, but much of the work has been done by means
of a ballistic galvanometer and test ring as above described. The
"hysteresis" of an iron or steel is that quality of it in virtue of
which energy is dissipated as heat when the magnetization is reversed or
carried through a cycle (see MAGNETISM), and it is generally measured
either in ergs per cubic centimetre of metal per cycle of magnetization,
or in watts per lb. per 50 or 100 cycles per second at or corresponding
to a certain maximum flux density, say 2500 or 600 C.G.S. units. For the
details of various forms of permeameter and hysteresis meter technical
books must be consulted.[3]

An immense number of observations have been carried out on the magnetic
permeability of different kinds of iron and steel, and in the following
tables are given some typical results, mostly from experiments made by
J.A. Ewing (see _Proc. Inst. C.E._, 1896, 126, p. 185) in which the
ballistic method was employed to determine the flux density
corresponding to various magnetizing forces acting upon samples of iron
and steel in the form of rings.

  The figures under heading I. are values given in a paper by A.W.S.
  Pocklington and F. Lydall (_Proc. Roy. Soc_., 1892-1893, 52, pp. 164
  and 228) as the results of a magnetic test of an exceptionally pure
  iron supplied for the purpose of experiment by Colonel Dyer, of the
  Elswick Works. The substances other than iron in this sample were
  stated to be: carbon, _trace_; silicon, _trace_; phosphorus, _none_;
  sulphur, 0.013%; manganese, 0.1%. The other five specimens, II. to
  VI., are samples of commercial iron or steel. No. II. is a sample of
  Low Moor bar iron forged into a ring, annealed and turned. No. III. is
  a steel forging furnished by Mr R. Jenkins as a sample of forged
  ingot-metal for dynamo magnets. No. IV. is a steel casting for dynamo
  magnets, unforged, made by Messrs Edgar Allen & Company by a special
  pneumatic process under the patents of Mr A. Tropenas. No. V. is also
  an unforged steel casting for dynamo magnets, made by Messrs Samuel
  Osborne & Company by the Siemens process. No. VI. is also an unforged
  steel casting for dynamo magnets, made by Messrs Fried. Krupp, of
  Essen.

    TABLE I.--_Magnetic Flux Density corresponding to various Magnetizing
    Forces in the case of certain Samples of Iron and Steel_ (_Ewing_).

    +------------+-----------------------------------------------------+
    |Magnetizing |                                                     |
    |   Force    |                                                     |
    |  H (C.G.S. |       Magnetic Flux Density B (C.G.S. Units).       |
    |   Units).  |                                                     |
    +------------+--------+--------+--------+--------+--------+--------+
    |            |   I.   |   II.  |  III.  |   IV.  |   V.   |   VI.  |
    +------------+--------+--------+--------+--------+--------+--------+
    |      5     | 12,700 | 10,900 | 12,300 |  4,700 |  9,600 | 10,900 |
    |     10     | 14,980 | 13,120 | 14,920 | 12,250 | 13,050 | 13,320 |
    |     15     | 15,800 | 14,010 | 15,800 | 14,000 | 14,600 | 14,350 |
    |     20     | 16,300 | 14,580 | 16,280 | 15,050 | 15,310 | 14,950 |
    |     30     | 16,950 | 15,280 | 16,810 | 16,200 | 16,000 | 15,660 |
    |     40     | 17,350 | 15,760 | 17,190 | 16,800 | 16,510 | 16,150 |
    |     50     |   ..   | 16,060 | 17,500 | 17,140 | 16,900 | 16,480 |
    |     60     |   ..   | 16,340 | 17,750 | 17,450 | 17,180 | 16,780 |
    |     70     |   ..   | 16,580 | 17,970 | 17,750 | 17,400 | 17,000 |
    |     80     |   ..   | 16,800 | 18,180 | 18,040 | 17,620 | 17,200 |
    |     90     |   ..   | 17,000 | 18,390 | 18,230 | 17,830 | 17,400 |
    |    100     |   ..   | 17,200 | 18,600 | 18,420 | 18,030 | 17,600 |
    +------------+--------+--------+--------+--------+--------+--------+

  It will be seen from the figures and the description of the materials
  that the steel forgings and castings have a remarkably high
  permeability under small magnetizing force.

Table II. shows the magnetic qualities of some of these materials as
found by Ewing when tested with small magnetizing forces.

  TABLE II.--_Magnetic Permeability of Samples of Iron and Steel under
  Weak Magnetizing Forces._

  +-----------------+-------------+----------------+---------------+
  |  Magnetic Flux  |      I.     |      III.      |       VI.     |
  |    Density B    |  Pure Iron. | Steel Forging. | Steel Casting.|
  | (C.G.S. Units). |             |                |               |
  +-----------------+-------------+----------------+---------------+
  |                 |  H      µ   |   H       µ    |  H       µ    |
  |      2,000      | 0.90   2220 |  1.38    1450  | 1.18    1690  |
  |      4,000      | 1.40   2850 |  1.91    2090  | 1.66    2410  |
  |      6,000      | 1.85   3240 |  2.38    2520  | 2.15    2790  |
  |      8,000      | 2.30   3480 |  2.92    2740  | 2.83    2830  |
  |     10,000      | 3.10   3220 |  3.62    2760  | 4.05    2470  |
  |     12,000      | 4.40   2760 |  4.80    2500  | 6.65    1810  |
  +-----------------+-------------+----------------+---------------+

The numbers I., III. and VI. in the above table refer to the samples
mentioned in connexion with Table I.

It is a remarkable fact that certain varieties of low carbon steel
(commonly called mild steel) have a higher permeability than even
annealed Swedish wrought iron under large magnetizing forces. The term
_steel_, however, here used has reference rather to the mode of
production than the final chemical nature of the material. In some of
the mild-steel castings used for dynamo electromagnets it appears that
the total foreign matter, including carbon, manganese and silicon, is
not more than 0.3% of the whole, the material being 99.7% pure iron.
This valuable magnetic property of steel capable of being cast is,
however, of great utility in modern dynamo building, as it enables field
magnets of very high permeability to be constructed, which can be
fashioned into shape by casting instead of being built up as formerly
out of masses of forged wrought iron. The curves in fig. 3 illustrate
the manner in which the flux density or, as it is usually called, the
magnetization curve of this mild cast steel crosses that of Swedish
wrought iron, and enables us to obtain a higher flux density
corresponding to a given magnetizing force with the steel than with the
iron.

From the same paper by Ewing we extract a number of results relating to
permeability tests of thin sheet iron and sheet steel, such as is used
in the construction of dynamo armatures and transformer cores.

  No. VII. is a specimen of good transformer-plate, 0.301 millimetre
  thick, rolled from Swedish iron by Messrs Sankey of Bilston. No. VIII.
  is a specimen of specially thin transformer-plate rolled from scrap
  iron. No. IX. is a specimen of transformer-plate rolled from
  ingot-steel. No. X. is a specimen of the wire which was used by J.
  Swinburne to form the core of his "hedgehog" transformers. Its
  diameter was 0.602 millimetre. All these samples were tested in the
  form of rings by the ballistic method, the rings of sheet-metal being
  stamped or turned in the flat. The wire ring No. X. was coiled and
  annealed after coiling.

  [Illustration: FIG. 3.]

    TABLE III.--_Permeability Tests of Transformer Plate and Wire_.

    +---------+--------------+--------------+--------------+--------------+
    |Magnetic |     VII.     |     VIII.    |      IX.     |      X.      |
    |  Flux   | Transformer- | Transformer- | Transformer- | Transformer- |
    |Density B|   plate of   |   plate of   |   plate of   |     wire.    |
    | (C.G.S. | Swedish Iron.|  Scrap Iron. |   of Steel.  |              |
    | Units). |              |              |              |              |
    +---------+--------------+--------------+--------------+--------------+
    |         |   H      µ   |   H      µ   |   H      µ   |   H      µ   |
    |  1,000  |  0.81   1230 |  1.08    920 |  0.60   1470 |  1.71    590 |
    |  2,000  |  1.05   1900 |  1.46   1370 |  0.90   2230 |  2.10    950 |
    |  3,000  |  1.26   2320 |  1.77   1690 |  1.04   2880 |  2.30   1300 |
    |  4,000  |  1.54   2600 |  2.10   1900 |  1.19   3360 |  2.50   1600 |
    |  5,000  |  1.82   2750 |  2.53   1980 |  1.38   3620 |  2.70   1850 |
    |  6,000  |  2.14   2800 |  3.04   1970 |  1.59   3770 |  2.92   2070 |
    |  7,000  |  2.54   2760 |  3.62   1930 |  1.89   3700 |  3.16   2210 |
    |  8,000  |  3.09   2590 |  4.37   1830 |  2.25   3600 |  3.43   2330 |
    |  9,000  |  3.77   2390 |  5.3    1700 |  2.72   3310 |  3.77   2390 |
    | 10,000  |  4.6    2170 |  6.5    1540 |  3.33   3000 |  4.17   2400 |
    | 11,000  |  5.7    1930 |  7.9    1390 |  4.15   2650 |  4.70   2340 |
    | 12,000  |  7.0    1710 |  9.8    1220 |  5.40   2220 |  5.45   2200 |
    | 13,000  |  8.5    1530 | 11.9    1190 |  7.1    1830 |  6.5    2000 |
    | 14,000  | 11.0    1270 | 15.0     930 | 10.0    1400 |  8.4    1670 |
    | 15,000  | 15.1     990 | 19.5     770 |   ..     ..  | 11.9    1260 |
    | 16,000  | 21.4     750 | 27.5     580 |   ..     ..  | 21.0     760 |
    +---------+--------------+--------------+--------------+--------------+

Some typical flux-density curves of iron and steel as used in dynamo and
transformer building are given in fig. 4.

[Illustration: FIG. 4.]

The numbers in Table III. well illustrate the fact that the
permeability, µ = B/H has a maximum value corresponding to a certain
flux density. The tables are also explanatory of the fact that mild
steel has gradually replaced iron in the manufacture of dynamo
electromagnets and transformer-cores.

Broadly speaking, the materials which are now employed in the
manufacture of the cores of electromagnets for technical purposes of
various kinds may be said to fall into three classes, namely, forgings,
castings and stampings. In some cases the iron or steel core which is to
be magnetized is simply a mass of iron hammered or pressed into shape by
hydraulic pressure; in other cases it has to be fused and cast; and for
certain other purposes it must be rolled first into thin sheets, which
are subsequently stamped out into the required forms.

[Illustration: FIG. 5.]

For particular purposes it is necessary to obtain the highest possible
magnetic permeability corresponding to a high, or the highest attainable
flux density. This is generally the case in the electromagnets which are
employed as the field magnets in dynamo machines. It may generally be
said that whilst the best wrought iron, such as annealed Low Moor or
Swedish iron, is more permeable for low flux densities than steel
castings, the cast steel may surpass the wrought metal for high flux
density. For most electro-technical purposes the best magnetic results
are given by the employment of forged ingot-iron. This material is
probably the most permeable throughout the whole scale of attainable
flux densities. It is slightly superior to wrought iron, and it only
becomes inferior to the highest class of cast steel when the flux
density is pressed above 18,000 C.G.S. units (see fig. 5). For flux
densities above 13,000 the forged ingot-iron has now practically
replaced for electric engineering purposes the Low Moor or Swedish iron.
Owing to the method of its production, it might in truth be called a
soft steel with a very small percentage of combined carbon. The best
description of this material is conveyed by the German term
"Flusseisen," but its nearest British equivalent is "ingot-iron."
Chemically speaking, the material is for all practical purposes very
nearly pure iron. The same may be said of the cast steels now much
employed for the production of dynamo magnet cores. The cast steel which
is in demand for this purpose has a slightly lower permeability than the
ingot-iron for low flux densities, but for flux densities above 16,000
the required result may be more cheaply obtained with a steel casting
than with a forging. When high tensile strength is required in addition
to considerable magnetic permeability, it has been found advantageous to
employ a steel containing 5% of nickel. The rolled sheet iron and sheet
steel which is in request for the construction of magnet cores,
especially those in which the exciting current is an alternating
current, are, generally speaking, produced from Swedish iron. Owing to
the mechanical treatment necessary to reduce the material to a thin
sheet, the permeability at low flux densities is rather higher than,
although at high flux densities it is inferior to, the same iron and
steel when tested in bulk. For most purposes, however, where a laminated
iron magnet core is required, the flux density is not pressed up above
6000 units, and it is then more important to secure small hysteresis
loss than high permeability. The magnetic permeability of cast iron is
much inferior to that of wrought or ingot-iron, or the mild steels taken
at the same flux densities.

The following Table IV. gives the flux density and permeability of a
typical cast iron taken by J.A. Fleming by the ballistic method:--

  TABLE IV.--_Magnetic Permeability and Magnetization Curve of Cast
  Iron._

  +------+------+-----++-------+------+-----++--------+--------+-----+
  |  H   |  B   |  µ  ||   H   |  B   |  µ  ||    H   |   B    |  µ  |
  |  .19 |  27  | 139 ||  8.84 | 4030 | 456 ||  44.65 |  8,071 | 181 |
  |  .41 |   62 | 150 || 10.60 | 4491 | 424 ||  56.57 |  8,548 | 151 |
  | 1.11 |  206 | 176 || 12.33 | 4884 | 396 ||  71.98 |  9,097 | 126 |
  | 2.53 |  768 | 303 || 13.95 | 5276 | 378 ||  88.99 |  9,600 | 108 |
  | 3.41 | 1251 | 367 || 15.61 | 5504 | 353 || 106.35 | 10,066 |  95 |
  | 4.45 | 1898 | 427 || 18.21 | 5829 | 320 || 120.60 | 10,375 |  86 |
  | 5.67 | 2589 | 456 || 26.37 | 6814 | 258 || 140.37 | 10,725 |  76 |
  | 7.16 | 3350 | 468 || 36.54 | 7580 | 207 || 152.73 | 10,985 |  72 |
  +------+------+-----++-------+------+-----++--------+--------+-----+

The metal of which the tests are given in Table IV. contained 2% of
silicon, 2.85% of total carbon, and 0.5% of manganese. It will be seen
that a magnetizing force of about 5 C.G.S. units is sufficient to impart
to a wrought-iron ring a flux density of 18,000 C.G.S. units, but the
same force hardly produces more than one-tenth of this flux density in
cast iron.

The testing of sheet iron and steel for magnetic hysteresis loss has
developed into an important factory process, giving as it does a means
of ascertaining the suitability of the metal for use in the manufacture
of transformers and cores of alternating-current electromagnets.

In Table V. are given the results of hysteresis tests by Ewing on
samples of commercial sheet iron and steel. The numbers VII., VIII., IX.
and X. refer to the same samples as those for which permeability results
are given in Table III.

  TABLE V.--_Hysteresis Loss in Transformer-iron._

  +-------+------------------------------+-------------------------------+
  |       |  Ergs per Cubic Centimetre   | Watts per lb. at a Frequency  |
  |       |          per Cycle.          |            of 100.            |
  |Maximum+-------+-------+-------+------+-------+-------+-------+-------+
  | Flux  |  VII. | VIII. |  IX.  |  X.  |       |       |       |       |
  |Density|Swedish| Forged| Ingot-| Soft |       |       |       |       |
  |   B.  | Iron. |Scrap- | steel.| Iron |  VII. | VIII. |  IX.  |   X.  |
  |       |       | iron. |       | Wire.|       |       |       |       |
  +-------+-------+-------+-------+------+-------+-------+-------+-------+
  | 2000  |  240  |  400  |  215  |  600 | 0.141 | 0.236 | 0.127 | 0.356 |
  | 3000  |  520  |  790  |  430  | 1150 | 0.306 | 0.465 | 0.253 | 0.630 |
  | 4000  |  830  | 1220  |  700  | 1780 | 0.490 | 0.720 | 0.410 | 1.050 |
  | 5000  | 1190  | 1710  | 1000  | 2640 | 0.700 | 1.010 | 0.590 | 1.550 |
  | 6000  | 1600  | 2260  | 1350  | 3360 | 0.940 | 1.330 | 0.790 | 1.980 |
  | 7000  | 2020  | 2940  | 1730  | 4300 | 1.200 | 1.730 | 1.020 | 2.530 |
  | 8000  | 2510  | 3710  | 2150  | 5300 | 1.480 | 2.180 | 1.270 | 3.120 |
  | 9000  | 3050  | 4560  | 2620  | 6380 | 1.800 | 2.680 | 1.540 | 3.750 |
  +-------+-------+-------+-------+------+-------+-------+-------+-------+

In Table VI. are given the results of a magnetic test of some
exceedingly good transformer-sheet rolled from Swedish iron.

  TABLE VI.--_Hysteresis Loss in Strip of Transformer-plate rolled
  Swedish Iron._

  +------------+---------------------------+--------------------+
  |Maximum Flux| Ergs per Cubic Centimetre | Watts per lb. at a |
  |Density B.  |         per Cycle.        |  Frequency of 100. |
  +------------+---------------------------+--------------------+
  |    2000    |            220            |       0.129        |
  |    3000    |            410            |       0.242        |
  |    4000    |            640            |       0.376        |
  |    5000    |            910            |       0.535        |
  |    6000    |           1200            |       0.710        |
  |    7000    |           1520            |       0.890        |
  |    8000    |           1900            |       1.120        |
  |    9000    |           2310            |       1.360        |
  +------------+---------------------------+--------------------+

In Table VII. are given some values obtained by Fleming for the
hysteresis loss in the sample of cast iron, the permeability test of
which is recorded in Table IV.

  TABLE VII.--_Observations on the Magnetic Hysteresis of Cast Iron._

  +------+---------+-----------------------------------+
  |      |         |         Hysteresis Loss.          |
  |      |         +-------------+---------------------+
  | Loop.| B (max.)| Ergs per cc.|  Watts per lb. per. |
  |      |         |  per Cycle. | 100 Cycles per sec. |
  +------+---------+-------------+---------------------+
  |   I. |  1475   |      466    |         .300        |
  |  II. |  2545   |    1,288    |         .829        |
  | III. |  3865   |    2,997    |        1.934        |
  |  IV. |  5972   |    7,397    |        4.765        |
  |   V. |  8930   |   13,423    |        8.658        |
  +------+---------+-------------+---------------------+

For most practical purposes the constructor of electromagnetic machinery
requires his iron or steel to have some one of the following
characteristics. If for dynamo or magnet making, it should have the
highest possible permeability at a flux density corresponding to
practically maximum magnetization. If for transformer or
alternating-current magnet building, it should have the smallest
possible hysteresis loss at a maximum flux density of 2500 C.G.S. units
during the cycle. If required for permanent magnet making, it should
have the highest possible coercivity combined with a high retentivity.
Manufacturers of iron and steel are now able to meet these demands in a
very remarkable manner by the commercial production of material of a
quality which at one time would have been considered a scientific
curiosity.

It is usual to specify iron and steel for the first purpose by naming
the minimum permeability it should possess corresponding to a flux
density of 18,000 C.G.S. units; for the second, by stating the
hysteresis loss in watts per lb. per 100 cycles per second,
corresponding to a maximum flux density of 2500 C.G.S. units during the
cycle; and for the third, by mentioning the coercive force required to
reduce to zero magnetization a sample of the metal in the form of a long
bar magnetized to a stated magnetization. In the cyclical reversal of
magnetization of iron we have two modes to consider. In the first case,
which is that of the core of the alternating transformer, the magnetic
force passes through a cycle of values, the iron remaining stationary,
and the direction of the magnetic force being always the same. In the
other case, that of the dynamo armature core, the direction of the
magnetic force in the iron is constantly changing, and at the same time
undergoing a change in magnitude.

It has been shown by F.G. Baily (_Proc. Roy. Soc._, 1896) that if a mass
of laminated iron is rotating in a magnetic field which remains constant
in direction and magnitude in any one experiment, the hysteresis loss
rises to a maximum as the magnitude of the flux density in the iron is
increased and then falls away again to nearly zero value. These
observations have been confirmed by other observers. The question has
been much debated whether the values of the hysteresis loss obtained by
these two different methods are identical for magnetic cycles in which
the flux density reaches the same maximum value. This question is also
connected with another one, namely, whether the hysteresis loss per
cycle is or is not a function of the speed with which the cycle is
traversed. Early experiments by C.P. Steinmetz and others seemed to show
that there was a difference between slow-speed and high-speed hysteresis
cycles, but later experiments by J. Hopkinson and by A. Tanakadaté,
though not absolutely exhaustive, tend to prove that up to 400 cycles
per second the hysteresis loss per cycle is practically unchanged.

Experiments made in 1896 by R. Beattie and R.C. Clinker on magnetic
hysteresis in rotating fields were partly directed to determine whether
the hysteresis loss at moderate flux densities, such as are employed in
transformer work, was the same as that found by measurements made with
alternating-current fields on the same iron and steel specimens (see
_The Electrician_, 1896, 37, p. 723). These experiments showed that
over moderate ranges of induction, such as may be expected in
electro-technical work, the hysteresis loss per cycle per cubic
centimetre was practically the same when the iron was tested in an
alternating field with a periodicity of 100, the field remaining
constant in direction, and when the iron was tested in a rotating field
giving the same maximum flux density.

With respect to the variation of hysteresis loss in magnetic cycles
having different maximum values for the flux density, Steinmetz found
that the hysteresis loss (W), as measured by the area of the complete
(B, H) cycle and expressed in ergs per centimetre-cube per cycle, varies
proportionately to a constant called the _hysteretic constant_, and to
the 1.6th power of the maximum flux density (B), or W = [eta]B^(1.6).

The hysteretic constants ([eta]) for various kinds of iron and steel are
given in the table below:--

    Metal.                                  Hysteretic Constant.

  Swedish wrought iron, well annealed         .0010 to .0017
  Annealed cast steel of good quality; small
    percentage of carbon                      .0017 to .0029
  Cast Siemens-Martin steel                   .0019 to .0028
  Cast ingot-iron                             .0021 to .0026
  Cast steel, with higher percentages of
    carbon, or inferior qualities of wrought
    iron                                      .0031 to .0054

Steinmetz's law, though not strictly true for very low or very high
maximum flux densities, is yet a convenient empirical rule for obtaining
approximately the hysteresis loss at any one maximum flux density and
knowing it at another, provided these values fall within a range varying
say from 1 to 9000 C.G.S. units. (See MAGNETISM.)

The standard maximum flux density which is adopted in electro-technical
work is 2500, hence in the construction of the cores of
alternating-current electromagnets and transformers iron has to be
employed having a known hysteretic constant at the standard flux
density. It is generally expressed by stating the number of watts per
lb. of metal which would be dissipated for a frequency of 100 cycles,
and a maximum flux density (B max.) during the cycle of 2500. In the
case of good iron or steel for transformer-core making, it should not
exceed 1.25 watt per lb. per 100 cycles per 2500 B (maximum value).

It has been found that if the sheet iron employed for cores of
alternating electromagnets or transformers is heated to a temperature
somewhere in the neighbourhood of 200° C. the hysteresis loss is very
greatly increased. It was noticed in 1894 by G.W. Partridge that
alternating-current transformers which had been in use some time had a
very considerably augmented core loss when compared with their initial
condition. O.T. Bláthy and W.M. Mordey in 1895 showed that this
augmentation in hysteresis loss in iron was due to heating. H.F.
Parshall investigated the effect up to moderate temperatures, such as
140° C., and an extensive series of experiments was made in 1898 by S.R.
Roget (_Proc. Roy. Soc._, 1898, 63, p. 258, and 64, p. 150). Roget found
that below 40° C. a rise in temperature did not produce any augmentation
in the hysteresis loss in iron, but if it is heated to between 40° C.
and 135° C. the hysteresis loss increases continuously with time, and
this increase is now called "ageing" of the iron. It proceeds more
slowly as the temperature is higher. If heated to above 135° C., the
hysteresis loss soon attains a maximum, but then begins to decrease.
Certain specimens heated to 160° C. were found to have their hysteresis
loss doubled in a few days. The effect seems to come to a maximum at
about 180° C. or 200° C. Mere lapse of time does not remove the
increase, but if the iron is reannealed the augmentation in hysteresis
disappears. If the iron is heated to a higher temperature, say between
300° C. and 700° C., Roget found the initial rise of hysteresis happens
more quickly, but that the metal soon settles down into a state in which
the hysteresis loss has a small but still augmented constant value. The
augmentation in value, however, becomes more nearly zero as the
temperature approaches 700° C. Brands of steel are now obtainable which
do not age in this manner, but these _non-ageing_ varieties of steel
have not generally such low initial hysteresis values as the "Swedish
Iron," commonly considered best for the cores of transformers and
alternating-current magnets.

The following conclusions have been reached in the matter:--(1) Iron and
mild steel in the annealed state are more liable to change their
hysteresis value by heating than when in the harder condition; (2) all
changes are removed by re-annealing; (3) the changes thus produced by
heating affect not only the amount of the hysteresis loss, but also the
form of the lower part of the (B, H) curve.

_Forms of Electromagnet._--The form which an electromagnet must take
will greatly depend upon the purposes for which it is to be used. A
design or form of electromagnet which will be very suitable for some
purposes will be useless for others. Supposing it is desired to make an
electromagnet which shall be capable of undergoing very rapid changes of
strength, it must have such a form that the coercivity of the material
is overcome by a self-demagnetizing force. This can be achieved by
making the magnet in the form of a short and stout bar rather than a
long thin one. It has already been explained that the ends or poles of a
polar magnet exert a demagnetizing power upon the mass of the metal in
the interior of the bar. If then the electromagnet has the form of a
long thin bar, the length of which is several hundred times its
diameter, the poles are very far removed from the centre of the bar, and
the demagnetizing action will be very feeble; such a long thin
electromagnet, although made of very soft iron, retains a considerable
amount of magnetism after the magnetizing force is withdrawn. On the
other hand, a very thick bar very quickly demagnetizes itself, because
no part of the metal is far removed from the action of the free poles.
Hence when, as in many telegraphic instruments, a piece of soft iron,
called an armature, has to be attracted to the poles of a
horseshoe-shaped electromagnet, this armature should be prevented from
quite touching the polar surfaces of the magnet. If a soft iron mass
does quite touch the poles, then it completes the magnetic circuit and
abolishes the free poles, and the magnet is to a very large extent
deprived of its self-demagnetizing power. This is the explanation of the
well-known fact that after exciting the electromagnet and then stopping
the current, it still requires a good pull to detach the "keeper"; but
when once the keeper has been detached, the magnetism is found to have
nearly disappeared. An excellent form of electromagnet for the
production of very powerful fields has been designed by H. du Bois (fig.
6).

[Illustration: FIG. 6.--Du Bois's Electromagnet.]

Various forms of electromagnets used in connexion with dynamo machines
are considered in the article DYNAMO, and there is, therefore, no
necessity to refer particularly to the numerous different shapes and
types employed in electrotechnics.

  BIBLIOGRAPHY.--For additional information on the above subject the
  reader may be referred to the following works and original papers:--

  H. du Bois, _The Magnetic Circuit in Theory and Practice_; S.P.
  Thompson, _The Electromagnet_; J.A. Fleming, _Magnets and Electric
  Currents_; J.A. Ewing, _Magnetic Induction in Iron and other Metals_;
  J.A. Fleming, "The Ferromagnetic Properties of Iron and Steel,"
  _Proceedings of Sheffield Society of Engineers and Metallurgists_
  (Oct. 1897); J.A. Ewing, "The Magnetic Testing of Iron and Steel,"
  _Proc. Inst. Civ. Eng._, 1896, 126, p. 185; H.F. Parshall, "The
  Magnetic Data of Iron and Steel," _Proc. Inst. Civ. Eng._, 1896, 126,
  p. 220; J.A. Ewing, "The Molecular Theory of Induced Magnetism,"
  _Phil. Mag._, Sept. 1890; W.M. Mordey, "Slow Changes in the
  Permeability of Iron," _Proc. Roy. Soc._ 57, p. 224; J.A. Ewing,
  "Magnetism," James Forrest Lecture, _Proc. Inst. Civ. Eng._ 138; S.P.
  Thompson, "Electromagnetic Mechanism," _Electrician_, 26, pp. 238,
  269, 293; J.A. Ewing, "Experimental Researches in Magnetism," _Phil.
  Trans._, 1885, part ii.; Ewing and Klassen, "Magnetic Qualities of
  Iron," _Proc. Roy. Soc._, 1893.     (J. A. F.)


FOOTNOTES:

  [1] In the _Annals of Philosophy_ for November 1821 is a long article
    entitled "Electromagnetism" by Oersted, in which he gives a detailed
    account of his discovery. He had his thoughts turned to it as far
    back as 1813, but not until the 20th of July 1820 had he actually
    made his discovery. He seems to have been arranging a compass needle
    to observe any deflections during a storm, and placed near it a
    platinum wire through which a galvanic current was passed.

  [2] See _Trans. Soc. Arts_, 1825, 43, p. 38, in which a figure of
    Sturgeon's electromagnet is given as well as of other pieces of
    apparatus for which the Society granted him a premium and a silver
    medal.

  [3] See S.P. Thompson, _The Electromagnet_ (London, 1891); J.A.
    Fleming, _A Handbook for the Electrical Laboratory and Testing Room_,
    vol. 2 (London, 1903); J.A. Ewing, _Magnetic Induction in Iron and
    other Metals_ (London, 1903, 3rd ed.).



ELECTROMETALLURGY. The present article, as explained under
ELECTROCHEMISTRY, treats only of those processes in which electricity is
applied to the production of chemical reactions or molecular changes at
furnace temperatures. In many of these the application of heat is
necessary to bring the substances used into the liquid state for the
purpose of electrolysis, aqueous solutions being unsuitable. Among the
earliest experiments in this branch of the subject were those of Sir H.
Davy, who in 1807 (_Phil. Trans._, 1808, p. 1), produced the alkali
metals by passing an intense current of electricity from a platinum wire
to a platinum dish, through a mass of fused caustic alkali. The action
was started in the cold, the alkali being slightly moistened to render
it a conductor; then, as the current passed, heat was produced and the
alkali fused, the metal being deposited in the liquid condition. Later,
A. Matthiessen (_Quarterly Journ. Chem. Soc._ viii. 30) obtained
potassium by the electrolysis of a mixture of potassium and calcium
chlorides fused over a lamp. There are here foreshadowed two types of
electrolytic furnace-operations: (a) those in which external heating
maintains the electrolyte in the fused condition, and (b) those in which
a current-density is applied sufficiently high to develop the heat
necessary to effect this object unaided. Much of the earlier
electro-metallurgical work was done with furnaces of the (a) type, while
nearly all the later developments have been with those of class (b).
There is a third class of operations, exemplified by the manufacture of
calcium carbide, in which electricity is employed solely as a heating
agent; these are termed _electrothermal_, as distinguished from
_electrolytic_. In certain electrothermal processes (e.g. calcium
carbide production) the heat from the current is employed in raising
mixtures of substances to the temperature at which a desired chemical
reaction will take place between them, while in others (e.g. the
production of graphite from coke or gas-carbon) the heat is applied
solely to the production of molecular or physical changes. In ordinary
electrolytic work only the continuous current may of course be used, but
in electrothermal work an alternating current is equally available.

_Electric Furnaces._--Independently of the question of the application
of external heating, the furnaces used in electrometallurgy may be
broadly classified into (i.) arc furnaces, in which the intense heat of
the electric arc is utilized, and (ii.) resistance and incandescence
furnaces, in which the heat is generated by an electric current
overcoming the resistance of an inferior conductor.


  Arc furnaces.

Excepting such experimental arrangements as that of C.M. Despretz
(_C.R._, 1849, 29) for use on a small scale in the laboratory, Pichou in
France and J.H. Johnson in England appear, in 1853, to have introduced
the earliest practical form of furnace. In these arrangements, which
were similar if not identical, the furnace charge was crushed to a fine
powder and passed through two or more electric arcs in succession. When
used for ore smelting, the reduced metal and the accompanying slag were
to be caught, after leaving the arc and while still liquid, in a hearth
fired with ordinary fuel. Although this primitive furnace could be made
to act, its efficiency was low, and the use of a separate fire was
disadvantageous. In 1878 Sir William Siemens patented a form of
furnace[1] which is the type of a very large number of those designed by
later inventors.

  In the best-known form a plumbago crucible was used with a hole cut in
  the bottom to receive a carbon rod, which was ground in so as to make
  a tight joint. This rod was connected with the positive pole of the
  dynamo or electric generator. The crucible was fitted with a cover in
  which were two holes; one at the side to serve at once as sight-hole
  and charging door, the other in the centre to allow a second carbon
  rod to pass freely (without touching) into the interior. This rod was
  connected with the negative pole of the generator, and was suspended
  from one arm of a balance-beam, while from the other end of the beam
  was suspended a vertical hollow iron cylinder, which could be moved
  into or out of a wire coil or solenoid joined as a shunt across the
  two carbon rods of the furnace. The solenoid was above the iron
  cylinder, the supporting rod of which passed through it as a core.
  When the furnace with this well-known regulating device was to be
  used, say, for the melting of metals or other conductors of
  electricity, the fragments of metal were placed in the crucible and
  the positive electrode was brought near them. Immediately the current
  passed through the solenoid it caused the iron cylinder to rise, and,
  by means of its supporting rod, forced the end of the balance beam
  upwards, so depressing the other end that the negative carbon rod was
  forced downwards into contact with the metal in the crucible. This
  action completed the furnace-circuit, and current passed freely from
  the positive carbon through the fragments of metal to the negative
  carbon, thereby reducing the current through the shunt. At once the
  attractive force of the solenoid on the iron cylinder was
  automatically reduced, and the falling of the latter caused the
  negative carbon to rise, starting an arc between it and the metal in
  the crucible. A counterpoise was placed on the solenoid end of the
  balance beam to act against the attraction of the solenoid, the
  position of the counterpoise determining the length of the arc in the
  crucible. Any change in the resistance of the arc, either by
  lengthening, due to the sinking of the charge in the crucible, or by
  the burning of the carbon, affected the proportion of current flowing
  in the two shunt circuits, and so altered the position of the iron
  cylinder in the solenoid that the length of arc was, within limits,
  automatically regulated. Were it not for the use of some such device
  the arc would be liable to constant fluctuation and to frequent
  extinction. The crucible was surrounded with a bad conductor of heat
  to minimize loss by radiation. The positive carbon was in some cases
  replaced by a water-cooled metal tube, or ferrule, closed, of course,
  at the end inserted in the crucible. Several modifications were
  proposed, in one of which, intended for the heating of non-conducting
  substances, the electrodes were passed horizontally through
  perforations in the upper part of the crucible walls, and the charge
  in the lower part of the crucible was heated by radiation.

The furnace used by Henri Moissan in his experiments on reactions at
high temperatures, on the fusion and volatilization of refractory
materials, and on the formation of carbides, silicides and borides of
various metals, consisted, in its simplest form, of two superposed
blocks of lime or of limestone with a central cavity cut in the lower
block, and with a corresponding but much shallower inverted cavity in
the upper block, which thus formed the lid of the furnace. Horizontal
channels were cut on opposite walls, through which the carbon poles or
electrodes were passed into the upper part of the cavity. Such a
furnace, to take a current of 4 H.P. (say, of 60 amperes and 50 volts),
measured externally about 6 by 6 by 7 in., and the electrodes were about
0.4 in. in diameter, while for a current of 100 H.P. (say, of 746
amperes and 100 volts) it measured about 14 by 12 by 14 in., and the
electrodes were about 1.5 in. in diameter. In the latter case the
crucible, which was placed in the cavity immediately beneath the arc,
was about 3 in. in diameter (internally), and about 3½ in. in height.
The fact that energy is being used at so high a rate as 100 H.P. on so
small a charge of material sufficiently indicates that the furnace is
only used for experimental work, or for the fusion of metals which, like
tungsten or chromium, can only be melted at temperatures attainable by
electrical means. Moissan succeeded in fusing about ¾ lb. of either of
these metals in 5 or 6 minutes in a furnace similar to that last
described. He also arranged an experimental tube-furnace by passing a
carbon tube horizontally beneath the arc in the cavity of the lime
blocks. When prolonged heating is required at very high temperatures it
is found necessary to line the furnace-cavity with alternate layers of
magnesia and carbon, taking care that the lamina next to the lime is of
magnesia; if this were not done the lime in contact with the carbon
crucible would form calcium carbide and would slag down, but magnesia
does not yield a carbide in this way. Chaplet has patented a muffle or
tube furnace, similar in principle, for use on a larger scale, with a
number of electrodes placed above and below the muffle-tube. The arc
furnaces now widely used in the manufacture of calcium carbide on a
large scale are chiefly developments of the Siemens furnace. But
whereas, from its construction, the Siemens furnace was intermittent in
operation, necessitating stoppage of the current while the contents of
the crucible were poured out, many of the newer forms are specially
designed either to minimize the time required in effecting the
withdrawal of one charge and the introduction of the next, or to ensure
absolute continuity of action, raw material being constantly charged in
at the top and the finished substance and by-products (slag, &c.)
withdrawn either continuously or at intervals, as sufficient quantity
shall have accumulated. In the King furnace, for example, the crucible,
or lowest part of the furnace, is made detachable, so that when full it
may be removed and an empty crucible substituted. In the United States a
revolving furnace is used which is quite continuous in action.


  Incandescence furnaces.

The class of furnaces heated by electrically incandescent materials has
been divided by Borchers into two groups: (1) those in which the
substance is heated by contact with a substance offering a high
resistance to the current passing through it, and (2) those in which the
substance to be heated itself affords the resistance to the passage of
the current whereby electric energy is converted into heat. Practically
the first of these furnaces was that of Despretz, in which the mixture
to be heated was placed in a carbon tube rendered incandescent by the
passage of a current through its substance from end to end. In 1880 W.
Borchers introduced his resistance-furnace, which, in one sense, is the
converse of the Despretz apparatus. A thin carbon pencil, forming a
bridge between two stout carbon rods, is set in the midst of the mixture
to be heated. On passing a current through the carbon the small rod is
heated to incandescence, and imparts heat to the surrounding mass. On a
larger scale several pencils are used to make the connexions between
carbon blocks which form the end walls of the furnace, while the side
walls are of fire-brick laid upon one another without mortar. Many of
the furnaces now in constant use depend mainly on this principle, a core
of granular carbon fragments stamped together in the direct line between
the electrodes, as in Acheson's carborundum furnace, being substituted
for the carbon pencils. In other cases carbon fragments are mixed
throughout the charge, as in E.H. and A.H. Cowles's zinc-smelting
retort. In practice, in these furnaces, it is possible for small local
arcs to be temporarily set up by the shifting of the charge, and these
would contribute to the heating of the mass. In the remaining class of
furnace, in which the electrical resistance of the charge itself is
utilized, are the continuous-current furnaces, such as are used for the
smelting of aluminium, and those alternating-current furnaces, (e.g. for
the production of calcium carbide) in which a portion of the charge is
first actually fused, and then maintained in the molten condition by the
current passing through it, while the reaction between further portions
of the charge is proceeding.


  Uses and advantages.

For ordinary metallurgical work the electric furnace, requiring as it
does (excepting where waterfalls or other cheap sources of power are
available) the intervention of the boiler and steam-engine, or of the
gas or oil engine, with a consequent loss of energy, has not usually
proved so economical as an ordinary direct fired furnace. But in some
cases in which the current is used for electrolysis and for the
production of extremely high temperatures, for which the calorific
intensity of ordinary fuel is insufficient, the electric furnace is
employed with advantage. The temperature of the electric furnace,
whether of the arc or incandescence type, is practically limited to
that at which the least easily vaporized material available for
electrodes is converted into vapour. This material is carbon, and as its
vaporizing point is (estimated at) over 3500° C., and less than 4000°
C., the temperature of the electric furnace cannot rise much above 3500°
C. (6330° F.); but H. Moissan showed that at this temperature the most
stable of mineral combinations are dissociated, and the most refractory
elements are converted into vapour, only certain borides, silicides and
metallic carbides having been found to resist the action of the heat. It
is not necessary that all electric furnaces shall be run at these high
temperatures; obviously, those of the incandescence or resistance type
may be worked at any convenient temperature below the maximum. The
electric furnace has several advantages as compared with some of the
ordinary types of furnace, arising from the fact that the heat is
generated from within the mass of material operated upon, and (unlike
the blast-furnace, which presents the same advantage) without a large
volume of gaseous products of combustion and atmospheric nitrogen being
passed through it. In ordinary reverberatory and other heating furnaces
the burning fuel is without the mass, so that the vessel containing the
charge, and other parts of the plant, are raised to a higher temperature
than would otherwise be necessary, in order to compensate for losses by
radiation, convection and conduction. This advantage is especially
observed in some cases in which the charge of the furnace is liable to
attack the containing vessel at high temperatures, as it is often
possible to maintain the outer walls of the electric furnace relatively
cool, and even to keep them lined with a protecting crust of unfused
charge. Again, the construction of electric furnaces may often be
exceedingly crude and simple; in the carborundum furnace, for example,
the outer walls are of loosely piled bricks, and in one type of furnace
the charge is simply heaped on the ground around the carbon resistance
used for heating, without containing-walls of any kind. There is,
however, one (not insuperable) drawback in the use of the electric
furnace for the smelting of pure metals. Ordinarily carbon is used as
the electrode material, but when carbon comes in contact at high
temperatures with any metal that is capable of forming a carbide a
certain amount of combination between them is inevitable, and the carbon
thus introduced impairs the mechanical properties of the ultimate
metallic product. Aluminium, iron, platinum and many other metals may
thus take up so much carbon as to become brittle and unforgeable. It is
for this reason that Siemens, Borchers and others substituted a hollow
water-cooled metal block for the carbon cathode upon which the melted
metal rests while in the furnace. Liquid metal coming in contact with
such a surface forms a crust of solidified metal over it, and this crust
thickens up to a certain point, namely, until the heat from within the
furnace just overbalances that lost by conduction through the solidified
crust and the cathode material to the flowing water. In such an
arrangement, after the first instant, the melted metal in the furnace
does not come in contact with the cathode material.


  Aluminium alloys.

_Electrothermal Processes._--In these processes the electric current is
used solely to generate heat, either to induce chemical reactions
between admixed substances, or to produce a physical (allotropic)
modification of a given substance. Borchers predicted that, at the high
temperatures available with the electric furnace, every oxide would
prove to be reducible by the action of carbon, and this prediction has
in most instances been justified. Alumina and lime, for example, which
cannot be reduced at ordinary furnace temperatures, readily give up
their oxygen to carbon in the electric furnace, and then combine with an
excess of carbon to form metallic carbides. In 1885 the brothers Cowles
patented a process for the electrothermal reduction of oxidized ores by
exposure to an intense current of electricity when admixed with carbon
in a retort. Later in that year they patented a process for the
reduction of aluminium by carbon, and in 1886 an electric furnace with
sliding carbon rods passed through the end walls to the centre of a
rectangular furnace. The impossibility of working with just sufficient
carbon to reduce the alumina, without using any excess which would be
free to form at least so much carbide as would suffice, when diffused
through the metal, to render it brittle, practically restricts the use
of such processes to the production of aluminium alloys. Aluminium
bronze (aluminium and copper) and ferro-aluminium (aluminium and iron)
have been made in this way; the latter is the more satisfactory product,
because a certain proportion of carbon is expected in an alloy of this
character, as in ferromanganese and cast iron, and its presence is not
objectionable. The furnace is built of fire-brick, and may measure
(internally) 5 ft. in length by 1 ft. 8 in. in width, and 3 ft. in
height. Into each end wall is built a short iron tube sloping downwards
towards the centre, and through this is passed a bundle of five 3-in.
carbon rods, bound together at the outer end by being cast into a head
of cast iron for use with iron alloys, or of cast copper for aluminium
bronze. This head slides freely in the cast iron tubes, and is connected
by a copper rod with one of the terminals of the dynamo supplying the
current. The carbons can thus, by the application of suitable mechanism,
be withdrawn from or plunged into the furnace at will. In starting the
furnace, the bottom is prepared by ramming it with charcoal-powder that
has been soaked in milk of lime and dried, so that each particle is
coated with a film of lime, which serves to reduce the loss of current
by conduction through the lining when the furnace becomes hot. A sheet
iron case is then placed within the furnace, and the space between it
and the walls rammed with limed charcoal; the interior is filled with
fragments of the iron or copper to be alloyed, mixed with alumina and
coarse charcoal, broken pieces of carbon being placed in position to
connect the electrodes. The iron case is then removed, the whole is
covered with charcoal, and a cast iron cover with a central flue is
placed above all. The current, either continuous or alternating, is then
started, and continued for about 1 to 1½ hours, until the operation is
complete, the carbon rods being gradually withdrawn as the action
proceeds. In such a furnace a continuous current, for example, of 3000
amperes, at 50 to 60 volts, may be used at first, increasing to 5000
amperes in about half an hour. The reduction is not due to electrolysis,
but to the action of carbon on alumina, a part of the carbon in the
charge being consumed and evolved as carbon monoxide gas, which burns at
the orifice in the cover so long as reduction is taking place. The
reduced aluminium alloys itself immediately with the fused globules of
metal in its midst, and as the charge becomes reduced the globules of
alloy unite until, in the end, they are run out of the tap-hole after
the current has been diverted to another furnace. It was found in
practice (in 1889) that the expenditure of energy per pound of reduced
aluminium was about 23 H.P.-hours, a number considerably in excess of
that required at the present time for the production of pure aluminium
by the electrolytic process described in the article ALUMINIUM. Calcium
carbide, graphite (q.v.), phosphorus (q.v.) and carborundum (q.v.) are
now extensively manufactured by the operations outlined above.

_Electrolytic Processes._--The isolation of the metals sodium and
potassium by Sir Humphry Davy in 1807 by the electrolysis of the fused
hydroxides was one of the earliest applications of the electric current
to the extraction of metals. This pioneering work showed little
development until about the middle of the 19th century. In 1852
magnesium was isolated electrolytically by R. Bunsen, and this process
subsequently received much attention at the hands of Moissan and
Borchers. Two years later Bunsen and H.E. Sainte Claire Deville working
independently obtained aluminium (q.v.) by the electrolysis of the fused
double sodium aluminium chloride. Since that date other processes have
been devised and the electrolytic processes have entirely replaced the
older methods of reduction with sodium. Methods have also been
discovered for the electrolytic manufacture of calcium (q.v.), which
have had the effect of converting a laboratory curiosity into a product
of commercial importance. Barium and strontium have also been produced
by electro-metallurgical methods, but the processes have only a
laboratory interest at present. Lead, zinc and other metals have also
been reduced in this manner.

  For further information the following books, in addition to those
  mentioned at the end of the article ELECTROCHEMISTRY, may be
  consulted: Borchers, _Handbuch der Elektrochemie_; _Electric Furnaces_
  (Eng. trans. by H.G. Solomon, 1908); Moissan, _The Electric Furnace_
  (1904); J. Escard, _Fours électriques_ (1905); _Les Industries
  électrochimiques_ (1907).     (W. G. M.)


FOOTNOTE:

  [1] Cf. Siemens's account of the use of this furnace for experimental
    purposes in _British Association Report_ for 1882.



ELECTROMETER, an instrument for measuring difference of potential, which
operates by means of electrostatic force and gives the measurement
either in arbitrary or in absolute units (see UNITS, PHYSICAL). In the
last case the instrument is called an absolute electrometer. Lord Kelvin
has classified electrometers into (1) Repulsion, (2) Attracted disk, and
(3) Symmetrical electrometers (see W. Thomson, _Brit. Assoc. Report_,
1867, or _Reprinted Papers on Electrostatics and Magnetization_, p.
261).

_Repulsion Electrometers._--The simplest form of repulsion electrometer
is W. Henley's pith ball electrometer (_Phil. Trans._, 1772, 63, p. 359)
in which the repulsion of a straw ending in a pith ball from a fixed
stem is indicated on a graduated arc (see ELECTROSCOPE). A double pith
ball repulsion electrometer was employed by T. Cavallo in 1777.

  It may be pointed out that such an arrangement is not merely an
  arbitrary electrometer, but may become an absolute electrometer within
  certain rough limits. Let two spherical pith balls of radius r and
  weight W, covered with gold-leaf so as to be conducting, be suspended
  by parallel silk threads of length l so as just to touch each other.
  If then the balls are both charged to a potential V they will repel
  each other, and the threads will stand out at an angle 2[theta], which
  can be observed on a protractor. Since the electrical repulsion of the
  balls is equal to C²V²4l² sin²[theta] dynes, where C = r is the
  capacity of either ball, and this force is balanced by the restoring
  force due to their weight, Wg dynes, where g is the acceleration of
  gravity, it is easy to show that we have

        2l sin [theta] [root](Wg tan [theta])
    V = -------------------------------------
                         r

  as an expression for their common potential V, provided that the balls
  are small and their distance sufficiently great not sensibly to
  disturb the uniformity of electric charge upon them. Observation of
  [theta] with measurement of the value of l and r reckoned in
  centimetres and W in grammes gives us the potential difference of the
  balls in absolute C.G.S. or electrostatic units. The gold-leaf
  electroscope invented by Abraham Bennet (see ELECTROSCOPE) can in like
  manner, by the addition of a scale to observe the divergence of the
  gold-leaves, be made a repulsion electrometer.

[Illustration: FIG. 1.--Snow-Harris's Disk Electrometer.]

_Attracted Disk Electrometers._--A form of attracted disk absolute
electrometer was devised by A. Volta. It consisted of a plane conducting
plate forming one pan of a balance which was suspended over another
insulated plate which could be electrified. The attraction between the
two plates was balanced by a weight put in the opposite pan. A similar
electric balance was subsequently devised by Sir W. Snow-Harris,[1] one
of whose instruments is shown in fig. 1. C is an insulated disk over
which is suspended another disk attached to the arm of a balance. A
weight is put in the opposite scale pan and a measured charge of
electricity is given to the disk C just sufficient to tip over the
balance. Snow-Harris found that this charge varied as the square root of
the weight in the opposite pan, thus showing that the attraction
between the disks at given distance apart varies as the square of their
difference of potential.

The most important improvements in connexion with electrometers are due,
however, to Lord Kelvin, who introduced the guard plate and used gravity
or the torsion of a wire as a means for evaluating the electrical
forces.

[Illustration: FIG. 2.--Kelvin's Portable Electrometer.]

[Illustration: FIG. 3.]

  His portable electrometer is shown in fig. 2. H H (see fig. 3) is a
  plane disk of metal called the guard plate, fixed to the inner coating
  of a small Leyden jar (see fig. 2). At F a square hole is cut out of H
  H, and into this fits loosely without touching, like a trap door, a
  square piece of aluminium foil having a projecting tail, which carries
  at its end a stirrup L, crossed by a fine hair (see fig. 3). The
  square piece of aluminium is pivoted round a horizontal stretched
  wire. If then another horizontal disk G is placed over the disk H H
  and a difference of potential made between G and H H, the movable
  aluminium trap door F will be attracted by the fixed plate G. Matters
  are so arranged by giving a torsion to the wire carrying the aluminium
  disk F that for a certain potential difference between the plates H
  and G, the movable part F comes into a definite sighted position,
  which is observed by means of a small lens. The plate G (see fig. 2)
  is moved up and down, parallel to itself, by means of a screw. In
  using the instrument the conductor, whose potential is to be tested,
  is connected to the plate G. Let this potential be denoted by V, and
  let v be the potential of the guard plate and the aluminium flap. This
  last potential is maintained constant by guard plate and flap being
  part of the interior coating of a charged Leyden jar. Since the
  distribution of electricity may be considered to be constant over the
  surface S of the attracted disk, the mechanical force f on it is given
  by the expression,[2]

        S(V - v)²
    f = ---------,
         8[pi]d²

  where d is the distance between the two plates. If this distance is
  varied until the attracted disk comes into a definite sighted position
  as seen by observing the end of the index through the lens, then since
  the force f is constant, being due to the torque applied by the wire
  for a definite angle of twist, it follows that the difference of
  potential of the two plates varies as their distance. If then two
  experiments are made, first with the upper plate connected to earth,
  and secondly, connected to the object being tested, we get an
  expression for the potential V of this conductor in the form

    V = A(d' - d),

  where d and d' are the distances of the fixed and movable plates from
  one another in the two cases, and A is some constant. We thus find V
  in terms of the constant and the difference of the two screw readings.

  [Illustration: FIG. 4.--Kelvin's Absolute Electrometer.]

  Lord Kelvin's absolute electrometer (fig. 4) involves the same
  principle. There is a certain fixed guard disk B having a hole in it
  which is loosely occupied by an aluminium trap door plate, shielded by
  D and suspended on springs, so that its surface is parallel with that
  of the guard plate. Parallel to this is a second movable plate A, the
  distances between the two being measurable by means of a screw. The
  movable plate can be drawn down into a definite sighted position when
  a difference of potential is made between the two plates. This
  sighted position is such that the surface of the trap door plate is
  level with that of the guard plate, and is determined by observations
  made with the lenses H and L. The movable plate can be thus depressed
  by placing on it a certain standard weight W grammes.

  Suppose it is required to measure the difference of potentials V and
  V' of two conductors. First one and then the other conductor is
  connected with the electrode of the lower or movable plate, which is
  moved by the screw until the index attached to the attracted disk
  shows it to be in the sighted position. Let the screw readings in the
  two cases be d and d'. If W is the weight required to depress the
  attracted disk into the same sighted position when the plates are
  unelectrified and g is the acceleration of gravity, then the
  difference of potentials of the conductors tested is expressed by the
  formula
                         _______
                        /8[pi]gW
    V - V' = (d - d')  / -------,
                     \/     S

  where S denotes the area of the attracted disk.

  The difference of potentials is thus determined in terms of a weight,
  an area and a distance, in absolute C.G.S. measure or electrostatic
  units.

[Illustration: FIG. 5.]

_Symmetrical Electrometers_ include the dry pile electrometer and
Kelvin's quadrant electrometer. The principle underlying these
instruments is that we can measure differences of potential by means of
the motion of an electrified body in a symmetrical field of electric
force. In the dry pile electrometer a single gold-leaf is hung up
between two plates which are connected to the opposite terminals of a
dry pile so that a certain constant difference of potential exists
between these plates. The original inventor of this instrument was
T.G.B. Behrens (_Gilb. Ann._, 1806, 23), but it generally bears the name
of J.G.F. von Bohnenberger, who slightly modified its form. G.T. Fechner
introduced the important improvement of using only one pile, which he
removed from the immediate neighbourhood of the suspended leaf. W.G.
Hankel still further improved the dry pile electrometer by giving a slow
motion movement to the two plates, and substituted a galvanic battery
with a large number of cells for the dry pile, and also employed a
divided scale to measure the movements of the gold-leaf (_Pogg. Ann._,
1858, 103). If the gold-leaf is unelectrified, it is not acted upon by
the two plates placed at equal distances on either side of it, but if
its potential is raised or lowered it is attracted by one disk and
repelled by the other, and the displacement becomes a measure of its
potential.

[Illustration: FIG. 6.--Kelvin's Quadrant Electrometer.]

A vast improvement in this instrument was made by the invention of the
quadrant electrometer by Lord Kelvin, which is the most sensitive form
of electrometer yet devised. In this instrument (see fig. 5) a flat
paddle-shaped needle of aluminium foil U is supported by a bifilar
suspension consisting of two cocoon fibres. This needle is suspended in
the interior of a glass vessel partly coated with tin-foil on the
outside and inside, forming therefore a Leyden jar (see fig. 6). In the
bottom of the vessel is placed some sulphuric acid, and a platinum wire
attached to the suspended needle dips into this acid. By giving a charge
to this Leyden jar the needle can thus be maintained at a certain
constant high potential. The needle is enclosed by a sort of flat box
divided into four insulated quadrants A, B, C, D (fig. 5), whence the
name. The opposite quadrants are connected together by thin platinum
wires. These quadrants are insulated from the needle and from the case,
and the two pairs are connected to two electrodes. When the instrument
is to be used to determine the potential difference between two
conductors, they are connected to the two opposite pairs of quadrants.
The needle in its normal position is symmetrically placed with regard to
the quadrants, and carries a mirror by means of which its displacement
can be observed in the usual manner by reflecting the ray of light from
it. If the two quadrants are at different potentials, the needle moves
from one quadrant towards the other, and the image of a spot of light on
the scale is therefore displaced. Lord Kelvin provided the instrument
with two necessary adjuncts, viz. a replenisher or rotating
electrophorus (q.v.), by means of which the charge of the Leyden jar
which forms the enclosing vessel can be increased or diminished, and
also a small aluminium balance plate or gauge, which is in principle the
same as the attracted disk portable electrometer by means of which the
potential of the inner coating of the Leyden jar is preserved at a known
value.

  According to the mathematical theory of the instrument,[3] if V and V'
  are the potentials of the quadrants and v is the potential of the
  needle, then the torque acting upon the needle to cause rotation is
  given by the expression,

    C(V - V') {v - ½(V + V')},

  where C is some constant. If v is very large compared with the mean
  value of the potentials of the two quadrants, as it usually is, then
  the above expression indicates that the couple varies as the
  difference of the potentials between the quadrants.

  Dr J. Hopkinson found, however, before 1885, that the above formula
  does not agree with observed facts (_Proc. Phys. Soc. Lond._, 1885, 7,
  p. 7). The formula indicates that the sensibility of the instrument
  should increase with the charge of the Leyden jar or needle, whereas
  Hopkinson found that as the potential of the needle was increased by
  working the replenisher of the jar, the deflection due to three volts
  difference between the quadrants first increased and then diminished.
  He found that when the potential of the needle exceeded a certain
  value, of about 200 volts, for the particular instrument he was using
  (made by White of Glasgow), the above formula did not hold good. W.E.
  Ayrton, J. Perry and W.E. Sumpner, who in 1886 had noticed the same
  fact as Hopkinson, investigated the matter in 1891 (_Proc. Roy. Soc._,
  1891, 50, p. 52; _Phil. Trans._, 1891, 182, p. 519). Hopkinson had
  been inclined to attribute the anomaly to an increase in the tension
  of the bifilar threads, owing to a downward pull on the needle, but
  they showed that this theory would not account for the discrepancy.
  They found from observations that the particular quadrant electrometer
  they used might be made to follow one or other of three distinct laws.
  If the quadrants were near together there were certain limits between
  which the potential of the needle might vary without producing more
  than a small change in the deflection corresponding with the fixed
  potential difference of the quadrants. For example, when the quadrants
  were about 2.5 mm. apart and the suspended fibres near together at the
  top, the deflection produced by a P.D. of 1.45 volts between the
  quadrants only varied about 11% when the potential of the needle
  varied from 896 to 3586 volts. When the fibres were far apart at the
  top a similar flatness was obtained in the curve with the quadrants
  about 1 mm. apart. In this case the deflection of the needle was
  practically quite constant when its potential varied from 2152 to 3227
  volts. When the quadrants were about 3.9 mm. apart, the deflection for
  a given P.D. between the quadrants was almost directly proportional to
  the potential of the needle. In other words, the electrometer nearly
  obeyed the theoretical law. Lastly, when the quadrants were 4 mm. or
  more apart, the deflection increased much more rapidly than the
  potential, so that a maximum sensibility bordering on instability was
  obtained. Finally, these observers traced the variation to the fact
  that the wire supporting the aluminium needle as well as the wire
  which connects the needle with the sulphuric acid in the Leyden jar in
  the White pattern of Leyden jar is enclosed in a metallic guard tube
  to screen the wire from external action. In order that the needle may
  project outside the guard tube, openings are made in its two sides;
  hence the moment the needle is deflected each half of it becomes
  unsymmetrically placed relatively to the two metallic pieces which
  join the upper and lower half of the guard tube. Guided by these
  experiments, Ayrton, Perry and Sumpner constructed an improved
  unifilar quadrant electrometer which was not only more sensitive than
  the White pattern, but fulfilled the theoretical law of working. The
  bifilar suspension was abandoned, and instead a new form of adjustable
  magnetic control was adopted. All the working parts of the instrument
  were supported on the base, so that on removing a glass shade which
  serves as a Leyden jar they can be got at and adjusted in position.
  The conclusion to which the above observers came was that any quadrant
  electrometer made in any manner does not necessarily obey a law of
  deflection making the deflections proportional to the potential
  difference of the quadrants, but that an electrometer can be
  constructed which does fulfil the above law.

  The importance of this investigation resides in the fact that an
  electrometer of the above pattern can be used as a wattmeter (q.v.),
  provided that the deflection of the needle is proportional to the
  potential difference of the quadrants. This use of the instrument was
  proposed simultaneously in 1881 by Professors Ayrton and G.F.
  Fitzgerald and M.A. Potier. Suppose we have an inductive and a
  non-inductive circuit in series, which is traversed by a periodic
  current, and that we desire to know the power being absorbed to the
  inductive circuit. Let v1, v2, v3 be the instantaneous potentials of
  the two ends and middle of the circuit; let a quadrant electrometer be
  connected first with the quadrants to the two ends of the inductive
  circuit and the needle to the far end of the non-inductive circuit,
  and then secondly with the needle connected to one of the quadrants
  (see fig. 5). Assuming the electrometer to obey the above-mentioned
  theoretical law, the first reading is proportional to

             /     v1 + v2\
    v1 - v2 ( v3 - ------- )
             \        2   /

  and the second to

             /     v1 + v2\
    v1 - v2 ( v2 - ------- ).
             \        2   /

  The difference of the readings is then proportional to

    (v1 - v2)(v2 - v3).

  But this last expression is proportional to the instantaneous power
  taken up in the inductive circuit, and hence the difference of the two
  readings of the electrometer is proportional to the mean power taken
  up in the circuit (_Phil. Mag._, 1891, 32, p. 206). Ayrton and Perry
  and also P.R. Blondlot and P. Curie afterwards suggested that a single
  electrometer could be constructed with two pairs of quadrants and a
  duplicate needle on one stem, so as to make two readings
  simultaneously and produce a deflection proportional at once to the
  power being taken up in the inductive circuit.

[Illustration: FIG. 7.--Quadrant Electrometer. Dolezalek Pattern.]

Quadrant electrometers have also been designed especially for measuring
extremely small potential differences. An instrument of this kind has
been constructed by Dr. F. Dolezalek (fig. 7). The needle and quadrants
are of small size, and the electrostatic capacity is correspondingly
small. The quadrants are mounted on pillars of amber which afford a very
high insulation. The needle, a piece of paddle-shaped paper thinly
coated with silver foil, is suspended by a quartz fibre, its extreme
lightness making it possible to use a very feeble controlling force
without rendering the period of oscillation unduly great. The resistance
offered by the air to a needle of such light construction suffices to
render the motion nearly dead-beat. Throughout a wide range the
deflections are proportional to the potential difference producing them.
The needle is charged to a potential of 50 to 200 volts by means of a
dry pile or voltaic battery, or from a lighting circuit. To facilitate
the communication of the charge to the needle, the quartz fibre and its
attachments are rendered conductive by a thin film of solution of
hygroscopic salt such as calcium chloride. The lightness of the needle
enables the instrument to be moved without fear of damaging the
suspension. The upper end of the quartz fibre is rotated by a torsion
head, and a metal cover serves to screen the instrument from stray
electrostatic fields. With a quartz fibre 0.009 mm. thick and 60 mm.
long, the needle being charged to 110 volts, the period and swing of the
needle was 18 seconds. With the scale at a distance of two metres, a
deflection of 130 mm. was produced by an electromotive force of 0.1
volt. By using a quartz fibre of about half the above diameter the
sensitiveness was much increased. An instrument of this form is valuable
in measuring small alternating currents by the fall of potential
produced down a known resistance. In the same way it may be employed to
measure high potentials by measuring the fall of potential down a
fraction of a known non-inductive resistance. In this last case,
however, the capacity of the electrometer used must be small, otherwise
an error is introduced.[4]

  See, in addition to references already given, A. Gray, _Absolute
  Measurements in Electricity and Magnetism_ (London, 1888), vol. i. p.
  254; A. Winkelmann, _Handbuch der Physik_ (Breslau, 1905), pp. 58-70,
  which contains a large number of references to original papers on
  electrometers.     (J. A. F.)


FOOTNOTES:

  [1] It is probable that an experiment of this kind had been made as
    far back as 1746 by Daniel Gralath, of Danzig, who has some claims to
    have suggested the word "electrometer" in connexion with it. See Park
    Benjamin, _The Intellectual Rise in Electricity_ (London, 1895), p.
    542.

  [2] See Maxwell, _Treatise on Electricity and Magnetism_ (2nd ed.),
    i. 308.

  [3] See Maxwell, _Electricity and Magnetism_ (2nd ed., Oxford, 1881),
    vol. i. p. 311.

  [4] See J.A. Fleming, _Handbook for the Electrical Laboratory and
    Testing Room_, vol. i. p. 448 (London, 1901).



ELECTRON, the name suggested by Dr G. Johnstone Stoney in 1891 for the
natural unit of electricity to which he had drawn attention in 1874, and
subsequently applied to the ultra-atomic particles carrying negative
charges of electricity, of which Professor Sir J.J. Thomson proved in
1897 that the cathode rays consisted. The electrons, which Thomson at
first called corpuscles, are point charges of negative electricity,
their inertia showing them to have a mass equal to about {1/2000} that
of the hydrogen atom. They are apparently derivable from all kinds of
matter, and are believed to be components at any rate of the chemical
atom. The electronic theory of the chemical atom supposes, in fact, that
atoms are congeries of electrons in rapid orbital motion. The size of
the electron is to that of an atom roughly in the ratio of a pin's head
to the dome of St Paul's cathedral. The electron is always associated
with the unit charge of negative electricity, and it has been suggested
that its inertia is wholly electrical. For further details see the
articles on ELECTRICITY; MAGNETISM; MATTER; RADIOACTIVITY; CONDUCTION,
ELECTRIC; _The Electron Theory_, E. Fournier d'Albe (London, 1907); and
the original papers of Dr G. Johnstone Stoney, _Proc. Brit. Ass._
(Belfast, August 1874), "On the Physical Units of Nature," and _Trans.
Royal Dublin Society_ (1891), 4, p. 583.



ELECTROPHORUS, an instrument invented by Alessandro Volta in 1775, by
which mechanical work is transformed into electrostatic charge by the
aid of a small initial charge of electricity. The operation depends on
the facts of electrostatic induction discovered by John Canton in 1753,
and, independently, by J.K. Wilcke in 1762 (see ELECTRICITY). Volta, in
a letter to J. Priestley on the 10th of June 1775 (see _Collezione dell'
opere_, ed. 1816, vol. i. p. 118), described the invention of a device
he called an _elettroforo perpetuo_, based on the fact that a conductor
held near an electrified body and touched by the finger was found, when
withdrawn, to possess an electric charge of opposite sign to that of the
electrified body. His electrophorus in one form consisted of a disk of
non-conducting material, such as pitch or resin, placed between two
metal sheets, one being provided with an insulating handle. For the
pitch or resin may be substituted a sheet of glass, ebonite,
india-rubber or any other good dielectric placed upon a metallic sheet,
called the sole-plate. To use the apparatus the surface of the
dielectric is rubbed with a piece of warm flannel, silk or catskin, so
as to electrify it, and the upper metal plate is then placed upon it.
Owing to the irregularities in the surfaces of the dielectric and upper
plate the two are only in contact at a few points, and owing to the
insulating quality of the dielectric its surface electrical charge
cannot move over it. It therefore acts inductively upon the upper plate
and induces on the adjacent surface an electric charge of opposite sign.
Suppose, for instance, that the dielectric is a plate of resin rubbed
with catskin, it will then be negatively electrified and will act by
induction on the upper plate across the film of air separating the upper
resin surface and lower surface of the upper metal plate. If the upper
plate is touched with the finger or connected to earth for a moment, a
negative charge will escape from the metal plate to earth at that
moment. The arrangement thus constitutes a condenser; the upper plate on
its under surface carries a charge of positive electricity and the resin
plate a charge of negative electricity on its upper surface, the air
film between them being the dielectric of the condenser. If, therefore,
the upper plate is elevated, mechanical work has to be done to separate
the two electric charges. Accordingly on raising the upper plate, the
charge on it, in old-fashioned nomenclature, becomes _free_ and can be
communicated to any other insulated conductor at a lower potential, the
upper plate thereby becoming more or less discharged. On placing the
upper plate again on the resin and touching it for a moment, the process
can be repeated, and so at the expense of mechanical work done in
lifting the upper plate against the mutual attraction of two electric
charges of opposite sign, an indefinitely large electric charge can be
accumulated and given to any other suitable conductor. In course of
time, however, the surface charge of the resin becomes dissipated and it
then has to be again excited. To avoid the necessity for touching the
upper plate every time it is put down on the resin, a metal pin may be
brought through the insulator from the sole-plate so that each time that
the upper plate is put down on the resin it is automatically connected
to earth. We are thus able by a process of merely lifting the upper
plate repeatedly to convey a large electrical charge to some conductor
starting from the small charge produced by friction on the resin. The
above explanation does not take into account the function of the
sole-plate, which is important. The sole-plate serves to increase the
electrical capacity of the upper plate when placed down upon the resin
or excited insulator. Hence when so placed it takes a larger charge.
When touched by the finger the upper plate is brought to zero potential.
If then the upper plate is lifted by its insulating handle its capacity
becomes diminished. Since, however, it carries with it the charge it had
when resting on the resin, its potential becomes increased as its
capacity becomes less, and it therefore rises to a high potential, and
will give a spark if the knuckle is approached to it when it is lifted
after having been touched and raised.

The study of Volta's electrophorus at once suggested the performance of
these cyclical operations by some form of rotation instead of elevation,
and led to the invention of various forms of doubler or multiplier. The
instrument was thus the first of a long series of machines for
converting mechanical work into electrostatic energy, and the
predecessor of the modern type of influence machine (see ELECTRICAL
MACHINE). Volta himself devised a double and reciprocal electrophorus
and also made mention of the subject of multiplying condensers in a
paper published in the _Phil. Trans._ for 1782 (p. 237, and appendix, p.
vii.). He states, however, that the use of a condenser in connexion with
an electrophorus to make evident and multiply weak charges was due to T.
Cavallo (_Phil. Trans._, 1788).

  For further information see S.P. Thompson, "The Influence Machine from
  1788 to 1888," _Journ. Inst. Tel. Eng._, 1888, 17, p. 569. Many
  references to original papers connected with the electrophorus will be
  found in A. Winkelmann's _Handbuch der Physik_ (Breslau, 1905), vol.
  iv. p. 48.     (J. A. F.)



ELECTROPLATING, the art of depositing metals by the electric current. In
the article ELECTROLYSIS it is shown how the passage of an electric
current through a solution containing metallic ions involves the
deposition of the metal on the cathode. Sometimes the metal is deposited
in a pulverulent form, at others as a firm tenacious film, the nature of
the deposit being dependent upon the particular metal, the concentration
of the solution, the difference of potential between the electrodes, and
other experimental conditions. As the durability of the
electro-deposited coat on plated wares of all kinds is of the utmost
importance, the greatest care must be taken to ensure its complete
adhesion. This can only be effected if the surface of the metal on which
the deposit is to be made is chemically clean. Grease must be removed by
potash, whiting or other means, and tarnish by an acid or potassium
cyanide, washing in plenty of water being resorted to after each
operation. The vats for depositing may be of enamelled iron, slate,
glazed earthenware, glass, lead-lined wood, &c. The current densities
and potential differences frequently used for some of the commoner
metals are given in the following table, taken from M'Millan's _Treatise
on Electrometallurgy_. It must be remembered, however, that variations
in conditions modify the electromotive force required for any given
process. For example, a rise in temperature of the bath causes an
increase in its conductivity, so that a lower E.M.F. will suffice to
give the required current density; on the other hand, an abnormally
great distance between the electrodes, or a diminution in acidity of an
acid bath, or in the strength of the solution used, will increase the
resistance, and so require the application of a higher E.M.F.

  +----------------------+------------------------------------+---------------+
  |                      |               Amperes.             |               |
  |                      +-------------------+----------------+ Volts between |
  |        Metal.        | Per sq. decimetre | Per sq. in. of |   Anode and   |
  |                      |    of Cathode     |    Cathode     |    Cathode.   |
  |                      |      Surface.     |    Surface.    |               |
  +----------------------+-------------------+----------------+---------------+
  | Antimony             |      0.4-0.5      |    0.02-0.03   |    1.0-1.2    |
  | Brass                |      0.5-0.8      |    0.03-0.05   |    3.0-4.0    |
  | Copper, acid bath    |      1.0-1.5      |   0.065-0.10   |    0.5-1.5    |
  |   "     alkaline bath|      0.3-0.5      |    0.02-0.03   |    3.0-5.0    |
  | Gold                 |        0.1        |     0.006      |    0.5-4.0    |
  | Iron                 |        0.5        |      0.03      |      1.0      |
  | Nickel, at first     |      1.4-1.5      |    0.09-0.10   |      5.0      |
  |   "     after        |      0.2-0.3      |   0.015-0.02   |    1.5-2.0    |
  |   "     on zinc      |        0.4        |     0.025      |    4.0-5.0    |
  | Silver               |      0.2-0.5      |   0.015-0.03   |   0.75-1.0    |
  | Zinc                 |      0.3-0.6      |    0.02-0.04   |    2.5-3.0    |
  +----------------------+-------------------+----------------+---------------+

Large objects are suspended in the tanks by hooks or wires, care being
taken to shift their position and so avoid wire-marks. Small objects are
often heaped together in perforated trays or ladles, the cathode
connecting-rod being buried in the midst of them. These require constant
shifting because the objects are in contact at many points, and because
the top ones shield those below from the depositing action of the
current. Hence processes have been patented in which the objects to be
plated are suspended in revolving drums between the anodes, the rotation
of the drum causing the constant renewal of surfaces and affording a
burnishing action at the same time. Care must be taken not to expose
goods in the plating-bath to too high a current density, else they may
be "burnt"; they must never be exposed one at a time to the full anode
surface, with the current flowing in an empty bath, but either one piece
at a time should be replaced, or some of the anodes should be
transferred temporarily to the place of the cathodes, in order to
distribute the current over a sufficient cathode-area. Burnt deposits
are dark-coloured, or even pulverulent and useless. The strength of the
current may also be regulated by introducing lengths of German silver or
iron wire, carbon rod, or other inferior conductors in the path of the
current, and a series of such resistances should always be provided
close to the tanks. Ammeters to measure the volume, and voltmeters to
determine the pressure of current supplied to the baths, should also be
provided. Very irregular surfaces may require the use of specially
shaped anodes in order that the distance between the electrodes may be
fairly uniform, otherwise the portion of the cathode lying nearest to
the anode may receive an undue share of the current, and therefore a
greater thickness of coat. Supplementary anodes are sometimes used in
difficult cases of this kind. Large metallic surfaces (especially
external surfaces) are sometimes plated by means of a "doctor," which,
in its simplest form, is a brush constantly wetted with the electrolyte,
with a wire anode buried amid the hairs or bristles; this brush is
painted slowly over the surface of the metal to be coated, which must be
connected to the negative terminal of the electrical generator. Under
these conditions electrolysis of the solution in the brush takes place.
Iron ships' plates have recently been coated with copper in sections (to
prevent the adhesion of barnacles), by building up a temporary trough
against the side of the ship, making the thoroughly cleansed plate act
both as cathode and as one side of the trough. Decorative plating-work
in several colours (e.g. "parcel-gilding") is effected by painting a
portion of an object with a stopping-out (i.e. a non-conducting)
varnish, such as copal varnish, so that this portion is not coated. The
varnish is then removed, a different design stopped out, and another
metal deposited. By varying this process, designs in metals of different
colours may readily be obtained.

Reference must be made to the textbooks (see ELECTROCHEMISTRY) for a
fuller account of the very varied solutions and methods employed for
electroplating with silver, gold, copper, iron and nickel. It should be
mentioned here, however, that solutions which would deposit their metal
on any object by simple immersion should not be generally used for
electroplating that object, as the resulting deposit is usually
non-adhesive. For this reason the acid copper-bath is not used for iron
or zinc objects, a bath containing copper cyanide or oxide dissolved in
potassium cyanide being substituted. This solution, being an inferior
conductor of electricity, requires a much higher electromotive force to
drive the current through it, and is therefore more costly in use. It
is, however, commonly employed hot, whereby its resistance is reduced.
_Zinc_ is commonly deposited by electrolysis on iron or steel goods
which would ordinarily be "galvanized," but which for any reason may not
conveniently be treated by the method of immersion in fused zinc. The
zinc cyanide bath may be used for small objects, but for heavy goods the
sulphate bath is employed. Sherard Cowper-Coles patented a process in
which, working with a high current density, a lead anode is used, and
powdered zinc is kept suspended in the solution to maintain the
proportion of zinc in the electrolyte, and so to guard against the
gradual acidification of the bath. _Cobalt_ is deposited by a method
analogous to that used for its sister-metal nickel. _Platinum_,
_palladium_ and _tin_ are occasionally deposited for special purposes.
In the deposition of _gold_ the colour of the deposit is influenced by
the presence of impurities in the solution; when copper is present, some
is deposited with the gold, imparting to it a reddish colour, whilst a
little silver gives it a greenish shade. Thus so-called coloured-gold
deposits may be produced by the judicious introduction of suitable
impurities. Even pure gold, it may be noted, is darker or lighter in
colour according as a stronger or a weaker current is used. The
electro-deposition of _brass_--mainly on iron ware, such as bedstead
tubes--is now very widely practised, the bath employed being a mixture
of copper, zinc and potassium cyanides, the proportions of which vary
according to the character of the brass required, and to the mode of
treatment. The colour depends in part upon the proportion of copper and
zinc, and in part upon the current density, weaker currents tending to
produce a redder or yellower metal. Other alloys may be produced, such
as bronze, or German silver, by selecting solutions (usually cyanides)
from which the current is able to deposit the constituent metals
simultaneously.

Electrolysis has in a few instances been applied to processes of
manufacture. For example, Wilde produced copper printing surfaces for
calico printing-rollers and the like by immersing rotating iron
cylinders as cathodes in a copper bath. Elmore, Dumoulin, Cowper-Coles
and others have prepared copper cylinders and plates by depositing
copper on rotating mandrels with special arrangements. Others have
arranged a means of obtaining high conductivity wire from cathode-copper
without fusion, by depositing the metal in the form of a spiral strip on
a cylinder, the strip being subsequently drawn down in the usual way; at
present, however, the ordinary methods of wire production are found to
be cheaper. J.W. Swan (_Journ. Inst. Elec. Eng._, 1898, vol. xxvii. p.
16) also worked out, but did not proceed with, a process in which a
copper wire whilst receiving a deposit of copper was continuously passed
through the draw-plate, and thus indefinitely extended in length.
Cowper-Coles (_Journ. Inst. Elec. Eng._, 1898, 27, p. 99) very
successfully produced true parabolic reflectors for projectors, by
depositing copper upon carefully ground and polished glass surfaces
rendered conductive by a film of deposited silver.



ELECTROSCOPE, an instrument for detecting differences of electric
potential and hence electrification. The earliest form of scientific
electroscope was the _versorium_ or electrical needle of William Gilbert
(1544-1603), the celebrated author of the treatise _De magnete_ (see
ELECTRICITY). It consisted simply of a light metallic needle balanced on
a pivot like a compass needle. Gilbert employed it to prove that
numerous other bodies besides amber are susceptible of being electrified
by friction.[1] In this case the visible indication consisted in the
attraction exerted between the electrified body and the light pivoted
needle which was acted upon and electrified by induction. The next
improvement was the invention of simple forms of repulsion electroscope.
Two similarly electrified bodies repel each other. Benjamin Franklin
employed the repulsion of two linen threads, C.F. de C. du Fay, J.
Canton, W. Henley and others devised the pith ball, or double straw
electroscope (fig. 1). T. Cavallo about 1770 employed two fine silver
wires terminating in pith balls suspended in a glass vessel having
strips of tin-foil pasted down the sides (fig. 2). The object of the
thimble-shaped dome was to keep moisture from the stem from which the
pith balls were supported, so that the apparatus could be used in the
open air even in the rainy weather. Abraham Bennet (_Phil. Trans._,
1787, 77, p. 26) invented the modern form of gold-leaf electroscope.
Inside a glass shade he fixed to an insulated wire a pair of strips of
gold-leaf (fig. 3). The wire terminated in a plate or knob outside the
vessel. When an electrified body was held near or in contact with the
knob, repulsion of the gold leaves ensued. Volta added the condenser
(_Phil. Trans._, 1782), which greatly increased the power of the
instrument. M. Faraday, however, showed long subsequently that to bestow
upon the indications of such an electroscope definite meaning it was
necessary to place a cylinder of metallic gauze connected to the earth
inside the vessel, or better still, to line the glass shade with
tin-foil connected to the earth and observe through a hole the
indications of the gold leaves (fig. 4). Leaves of aluminium foil may
with advantage be substituted for gold-leaf, and a scale is sometimes
added to indicate the angular divergence of the leaves.

[Illustration: FIG. 1.--Henley's Electroscope.]

[Illustration: FIG. 2.--Cavallo's Electroscope.]

[Illustration: FIG. 3.--Bennet's Electroscope.]

The uses of an electroscope are, first, to ascertain if any body is in a
state of electrification, and secondly, to indicate the sign of that
charge. In connexion with the modern study of radioactivity, the
electroscope has become an instrument of great usefulness, far
outrivalling the spectroscope in sensibility. Radio-active bodies are
chiefly recognized by the power they possess of rendering the air in
their neighbourhood conductive; hence the electroscope detects the
presence of a radioactive body by losing an electric charge given to it
more quickly than it would otherwise do. A third great use of the
electroscope is therefore to detect electric conductivity either in the
air or in any other body.

[Illustration: FIG. 4.--Gold-Leaf Electroscope.]

To detect electrification it is best to charge the electroscope by
induction. If an electrified body is held near the gold-leaf
electroscope the leaves diverge with electricity of the same sign as
that of the body being tested. If, without removing the electrified
body, the plate or knob of the electroscope is touched, the leaves
collapse. If the electroscope is insulated once more and the electrified
body removed, the leaves again diverge with electricity of the opposite
sign to that of the body being tested. The sign of charge is then
determined by holding near the electroscope a glass rod rubbed with silk
or a sealing-wax rod rubbed with flannel. If the approach of the glass
rod causes the leaves in their final state to collapse, then the charge
in the rod was positive, but if it causes them to expand still more the
charge was negative, and vice versa for the sealing-wax rod. When
employing a Volta condensing electroscope, the following is the method
of procedure:--The top of the electroscope consists of a flat, smooth
plate of lacquered brass on which another plate of brass rests,
separated from it by three minute fragments of glass or shellac, or a
film of shellac varnish. If the electrified body is touched against the
upper plate whilst at the same time the lower plate is put to earth, the
condenser formed of the two plates and the film of air or varnish
becomes charged with positive electricity on the one plate and negative
on the other. On insulating the lower plate and raising the upper plate
by the glass handle, the capacity of the condenser formed by the plates
is vastly decreased, but since the charge on the lower plate including
the gold leaves attached to it remains the same, as the capacity of the
system is reduced the potential is raised and therefore the gold leaves
diverge widely. Volta made use of such an electroscope in his celebrated
experiments (1790-1800) to prove that metals placed in contact with one
another are brought to different potentials, in other words to prove the
existence of so-called contact electricity. He was assisted to detect
the small potential differences then in question by the use of a
multiplying condenser or revolving doubler (see ELECTRICAL MACHINE). To
employ the electroscope as a means of detecting radioactivity, we have
first to test the leakage quality of the electroscope itself. Formerly
it was usual to insulate the rod of the electroscope by passing it
through a hole in a cork or mass of sulphur fixed in the top of the
glass vessel within which the gold leaves were suspended. A further
improvement consisted in passing the metal wire to which the gold leaves
were attached through a glass tube much wider than the rod, the latter
being fixed concentrically in the glass tube by means of solid shellac
melted and run in. This insulation, however, is not sufficiently good
for an electroscope intended for the detection of radioactivity; for
this purpose it must be such that the leaves will remain for hours or
days in a state of steady divergence when an electrical charge has been
given to them.

In their researches on radioactivity M. and Mme P. Curie employed an
electroscope made as follows:--A metal case (fig. 5), having two holes
in its sides, has a vertical brass strip B attached to the inside of the
lid by a block of sulphur SS or any other good insulator. Joined to the
strip is a transverse wire terminating at one end in a knob C, and at
the other end in a condenser plate P'. The strip B carries also a strip
of gold-leaf L, and the metal case is connected to earth. If a charge is
given to the electroscope, and if any radioactive material is placed on
a condenser plate P attached to the outer case, then this substance
bestows conductivity on the air between the plates P and P', and the
charge of the electroscope begins to leak away. The collapse of the
gold-leaf is observed through an aperture in the case by a microscope,
and the time taken by the gold-leaf to fall over a certain distance is
proportional to the ionizing current, that is, to the intensity of the
radioactivity of the substance.

[Illustration: FIG. 5.--Curie's Electroscope.]

A very similar form of electroscope was employed by J.P.L.J. Elster and
H.F.K. Geitel (fig. 6), and also by C.T.R. Wilson (see _Proc. Roy.
Soc._, 1901, 68, p. 152). A metal box has a metal strip B suspended from
a block or insulator by means of a bit of sulphur or amber S, and to it
is fastened a strip of gold-leaf L. The electroscope is provided with a
charging rod C. In a dry atmosphere sulphur or amber is an early perfect
insulator, and hence if the air in the interior of the box is kept dry
by calcium chloride, the electroscope will hold its charge for a long
time. Any divergence or collapse of the gold-leaf can be viewed by a
microscope through an aperture in the side of the case.

[Illustration: FIG. 6.--Elster and Geitel Electroscope.]

[Illustration: FIG. 7.--Wilson's Electroscope.]

Another type of sensitive electroscope is one devised by C.T.R. Wilson
(_Proc. Cam. Phil. Soc._, 1903, 12, part 2). It consists of a metal box
placed on a tilting stand (fig. 7). At one end is an insulated plate P
kept at a potential of 200 volts or so above the earth by a battery. At
the other end is an insulated metal wire having attached to it a thin
strip of gold-leaf L. If the plate P is electrified it attracts the
strip which stretches out towards it. Before use the strip is for one
moment connected to the case, and the arrangement is then tilted until
the strip extends at a certain angle. If then the strip of gold-leaf is
raised or lowered in potential it moves to or from the plate P, and its
movement can be observed by a microscope through a hole in the side of
the box. There is a particular angle of tilt of the case which gives a
maximum sensitiveness. Wilson found that with the plate electrified to
207 volts and with a tilt of the case of 30°, if the gold-leaf was
raised one volt in potential above the case, it moved over 200 divisions
of the micrometer scale in the eye-piece of the microscope, 54 divisions
being equal to one millimetre. In using the instrument the insulated rod
to which the gold-leaf is attached is connected to the conductor, the
potential of which is being examined. In the use of all these
electroscopic instruments it is essential to bear in mind (as first
pointed out by Lord Kelvin) that what a gold-leaf electroscope really
indicates is the difference of potential between the gold-leaf and the
solid walls enclosing the air space in which they move.[2] If these
enclosing walls are made of anything else than perfectly conducting
material, then the indications of the instrument may be uncertain and
meaningless. As already mentioned, Faraday remedied this defect by
coating the inside of the glass vessel in which the gold-leaves were
suspended to form an electroscope with tinfoil (see fig. 4). In spite of
these admonitions all but a few instrument makers have continued to make
the vicious type of instrument consisting of a pair of gold-leaves
suspended within a glass shade or bottle, no means being provided for
keeping the walls of the vessel continually at zero potential.

  See J. Clerk Maxwell, _Treatise on Electricity and Magnetism_, vol. i.
  p. 300 (2nd ed., Oxford, 1881); H.M. Noad, _A Manual of Electricity_,
  vol. i. p. 25 (London, 1855); E. Rutherford, _Radioactivity_.
       (J. A. F.)


FOOTNOTES:

  [1] See the English translation by the Gilbert Club of Gilbert's _De
    magnete_, p. 49 (London, 1900).

  [2] See Lord Kelvin, "Report on Electrometers and Electrostatic
    Measurements," _Brit. Assoc. Report_ for 1867, or Lord Kelvin's
    _Reprint of Papers on Electrostatics and Magnetism_, p. 260.





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