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Title: Scientific Studies - or Practical, in Contrast with Chimerical Pursuits; etc, etc, etc
Author: Dircks, Henry
Language: English
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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.

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Transcriber's Notes

Changes to the text (corrections to typographical errors) are listed at
the end of the book.

On page 45, in the reference "Beccheri's Physica Subterranea, Lipsiæ,
1738 (with supplement), 8vo., 1681-80;", no satisfactory explanation of
"1681-80" has been found. Note that the publication date of Physica
Subterranea is 1669.

In Figure 2 on page 82, the following denote the conventional symbols
for planetary bodies: [Sun], [Moon], [Mercury], [Venus], [Mars],
[Jupiter], [Saturn], [Uranus].

On pages 83 & 84 in the explanation of Plate III, a single quote is used
to denote the decimal point: this convention has been retained.

In this Plain Text version of the e-book, the Latin-1 character set
only is used. Italic typeface is denoted by surrounding _underscores_;
small caps typeface is denoted by ALL CAPS; superscript symbols are
preceded by caret (^).

[Asterism] denotes three stars (asterisks).

[oe] represents the oe-ligature.

       *       *       *       *       *

[Illustration:

                            EDWARD SOMERSET,
                         SIXTH EARL AND SECOND
                         MARQUIS OF WORCESTER.

From a Bust by Mr. James Loft, Sculptor, exhibited at the Royal Academy,
1867; and now in the Sculpture Gallery of the Crystal Palace, Sydenham.

]



                         SCIENTIFIC STUDIES:


           PRACTICAL, IN CONTRAST WITH CHIMERICAL PURSUITS;

                            EXEMPLIFIED IN
                         TWO POPULAR LECTURES.


                                  I.

                     THE LIFE OF EDWARD SOMERSET,
                                SECOND
                         MARQUIS OF WORCESTER,
                    INVENTOR OF THE STEAM ENGINE.


                                 II.

                         CHIMERAS OF SCIENCE:
               ASTROLOGY, ALCHEMY, SQUARING THE CIRCLE,
                        PERPETUUM MOBILE, ETC.

                     With Illustrative Diagrams.

                                  BY

                     HENRY DIRCKS, C. E., LL.D.,
                 F.C.S., M.R.S.L., F.R.S.R., &c. &c.

          AUTHOR OF "THE LIFE OF THE MARQUIS OF WORCESTER;"
                         "WORCESTERIANA;" &c.


                                LONDON:
               E. & F. N. SPON, 48, CHARING CROSS, S.W.
                                 1879.



INTRODUCTION.


It forms a necessary part of popular lectures that they should possess
breadth with brevity, and interest without too great profundity. It is
possible to see a large extent of country from a lofty tower without
being cognizant of every blade of grass, the perfume of blossoms, or the
notes of the sweetest songsters of the groves. In like manner the
popular lecturer has to present only so much to the eye of the mind as
will give the prominent features of his theme, omitting those details
over which the scholar, or the true lover of his subject, dwells with
the affection of a fond parent over a darling child.

We must look with astonishment at a man of noble birth, who in a period
of civil commotion, with a monarch for his friend, and a court at his
command, secluded himself during his youth in a stately ancient tower,
engaged in abstruse studies and wonderful mechanical operations; and
who, late in life, amidst the terrors of civil war was found turning his
inventive faculties, like another Archimedes, to the construction of
means of defence, and terrible weapons of offence. But it is only those
who become immersed in studies, whether of theology, philosophy, or
kindred mental pursuits, who can appreciate the growing appetite for
what appears to unlettered men as the driest of all dry occupations. The
mere pleasure-seeker knows not how much is lost, and how little is
gained by sharing the most brilliant gaieties of fashionable life.

Look at the ancient astrologers, whose pursuits were once as pure and
noble as those of modern astronomers. Amidst wild theories,
superstitious beliefs, empirical systems, and pagan divination, a
rupture became inevitable: one side adopted stellary divination or
Astrology, the other Astronomy, or the simple and true study of the
stars.

Whatever a man's intellectual pursuits may be, he has the advantage over
the mere man of fashion of being engaged in employments which the
longest life cannot exhaust.

But intellectual pursuits partake either of the negative or the
positive; they are useful or useless, and when useless they fritter away
and render nugatory the talent that might have been better employed.

The Marquis of Worcester affords an eminent example of genius of a high
order, grandly and effectively directed towards the advancement of man's
political and social position. His contemporary, Dr. John Dee, the
Astrologer, together with his friend Kelly, the Alchemist, may be
appropriately distinguished as representing a class chimerically
inclined, and hurtful to the well-being of society; while a less eminent
and less blameable section of chimerical labourers are those of whom
the worst we can say is, that they waste much valuable time, energy, and
fortune, through attaching themselves to mathematics, mechanics, and
other learned pursuits, only in search of marvellous, instead of useful
applications.

All chimeras are built on assumptions, and so far are "castles in the
air;" in many forms they are simply ridiculous; but when they pretend to
the supernatural they are pernicious and often wicked.

In the two lectures now presented for his perusal, the reader will find
both these topics illustrated by suitable lives and authentic evidence.

                                                                   H. D.

_London, February, 1869._



                                  I.

                               Lecture
                                  ON
                     THE LIFE OF EDWARD SOMERSET,
                                SECOND
                         MARQUIS OF WORCESTER.

               "He was a man, take him for all in all,
               We shall not look upon his like again."

                             DELIVERED AT
                 THE LITERARY INSTITUTION, GREENWICH,
                         16TH FEBRUARY, 1864.



LECTURE I.


The Biographer of Edward, second MARQUIS OF WORCESTER, naturally finds
some difficulty in rendering prominent the political position that
nobleman enjoyed in the 17th century; or of impressing the minds of his
hearers or readers with a just sense of the wonderful genius of the
author of the "Century of Inventions," even although the fact be
established of that remarkable man being also the true and first
inventor of a veritable steam engine.

When we consider the eventful period in which he lived, (from 1601 to
1667,) and his personal character, together with the social, political,
and romantic incidents of his life, the career of the Marquis of
Worcester cannot fail to interest and instruct us. He was at once the
most fortunate and unfortunate of men, living in times of mingled
enlightenment, superstition, and civil discord, and finally finding
himself cast on the tender mercies of a corrupt Court; the possessor of
a high order of mechanical genius, yet proscribed politically and
theologically; most loyal, yet falling the victim of puritanism; and
closing his life neglected by a Sovereign whose father had been the
chief ruin of his patrimony.

Descended from the Plantagenets, Edward Somerset, second MARQUIS OF
WORCESTER, is supposed to have been born about, or soon after 1601, the
records to establish his natal year being wanting. His father, Henry
Somerset, created first Marquis of Worcester by Charles I., was married
on the 16th June, 1600, at Blackfriars; Queen Elizabeth, attending in
great state, graciously danced at the wedding ball; and the festivities
of the occasion were continued for three days.

We obtain little information respecting the Marquis of Worcester until
about the twenty-seventh year of his age, when he married Elizabeth,
daughter of Sir William Dormer, eldest son of Lord Dormer of Weng, and
sister of Robert, Earl of Carnarvon. It is not known where he was
educated, but it was certainly neither at Oxford nor Cambridge. Mention
is made of his preceptor, Mr. Adams, at Raglan Castle, the baronial seat
of the lords of Raglan, in Monmouthshire. There is every probability,
however, that he finished his education at some foreign university. His
son and heir, Henry, born in 1629, was created by Charles II. the first
Duke of Beaufort, and from him the present Duke of Beaufort is the
eighth of that rank in lineal descent.

It was during the first or second year of his married life that he
engaged the services of Caspar Kaltoff, whom he employed as a practical
assistant, to work out his numerous mechanical experiments, and whom he
extols as an "unparalleled workman, both for trust and skill."[1] There
are still to be seen on one side of the Keep--or citadel of Raglan
Castle, the remains of grooves in the wall, probably for the insertion
of large metal pipes, in some way or other connected with the waterworks
which are known to have been erected there, and which were most likely
carried out by Kaltoff, under his master's directions.

[1] Dedication to "The Century of Inventions."

Becoming a widower in 1635, his lordship married in 1639, his second
wife, Margaret, second daughter and co-heir of Henry O'Brien, Earl of
Thomond.

It must have been about this period of his life that the Marquis of
Worcester made one of his most singular and perplexing mechanical
experiments, which he exhibited at the Tower before Charles I., several
of his Court, some foreign ambassadors, and the lieutenant of that
fortress. As he names Sir William Balfour (who held the latter
appointment from 1630 to 1641) we can arrive at an approximate date. The
mechanical surprise which he states he thus presented to gratify his
royal master, was no other than a gigantic wheel, 14 feet in diameter,
weighted with 40 weights of 50 lbs. each, equal to 2000 lbs., by means
of which we are left to infer that the wheel maintained a rotatory
motion, without assistance from any external aid whatever; that it was
in fact, a realization of that long sought for curiosity--perpetual
motion. As he wrote deliberately a statement of this circumstance
fifteen years later, or more, which he afterwards printed, we are left
without any grounds to suppose otherwise than that he deceived himself,
or was deceived, from interested motives, by persons in his employment.
The circumstance is scarcely worth notice except as a singular proof
that such a hallucination could exist in the mind of the same genius
that perfected the first practical steam-engine. We can only say that if
the mystery could be cleared up, although it would be of little or no
value to mathematics or mechanics, it would go far to elevate the
scientific character of the Marquis, though he was not the only
celebrity of his time infatuated with a thorough belief in the
possibility of solving the paradox.

The Marquis of Worcester, born at the close of Queen Elizabeth's reign,
is not mentioned as appearing at the Court of James I; his courtier life
most likely commenced later, in the reign of Charles I, who was about
his own age, and with whose career, the fortunes of both the Marquis of
Worcester, and his father, family, and friends, were unhappily but too
intimately interwoven.

It requires a visit to Raglan Castle fully to realise the grandeur,
nobleness, and strength of that romantically situated, and almost regal
stronghold. It wears all the solemnity that antiquity can bestow, it is
so gothic, so solid, and embowered, as it were, in a constant dubious
shade. Then it is so extensive in its bounds, its apartments are so
capacious, and its massy walls so lofty and so finely chiseled and
proportioned, that when we consider there is no quarry within any
reasonable distance, nor any river or stream for conveyance, the whole
structure assumes the mystery of absolute romance. Its historic
associations also rivet the attention of every beholder who is
acquainted with the part it played in determining the fate of that great
struggle between the Crown and the Parliament, which commenced in 1640,
and ended with the establishment of a Commonwealth.

The county of Monmouth is eminently distinguished for its scenery, its
green hills and dales presenting a beautifully wooded and highly
picturesque landscape from every point of view. The village of Raglan is
a small unpretending hamlet, principally remarkable for its parish
church, which contains the chapel of the Beauforts, the resting place of
several members of the Somerset family. Peering above lofty neighbouring
trees, the Donjon, Keep, or Citadel of Raglan Castle is a conspicuous
object; itself very lofty and standing on a considerable eminence, it
commands a most delightful and extensive panoramic view of the
surrounding country in that fertile district.

The Castle may be described as consisting of two portions, distinguished
by two courts and two fortified arched entrances. The grand entrance,
between two hexagonal towers, leads to the paved court, with the closet
tower or library to the right, a withdrawing or ball-room overhead, and
a banqueting or stately hall to the left, which last apartment attracts
much notice from its great size and remarkable state of preservation.
Externally situated is the Citadel or Tower of Gwent, surrounded with a
broad moat over which there appears to have been a drawbridge on one
side, and on the other, adjoining the castle a permanent stone bridge.

During his youth, the Marquis of Worcester, as Lord Herbert, resided at
the Castle, and may have had his laboratory, workshop, and study
conveniently situated in the Citadel; at all events, in connection with
his early career, the ruined remains of the family mansion cannot be
visited without intense interest. His father was a noble minded, hearty,
generous man, living in princely state; an extensive and wealthy landed
proprietor, and in case of need capable of defending his Citadel against
any foe whatever. This last necessity made itself conspicuous between
the years 1640 and 1641, when the civil war broke out. After the fatal
battle of Naseby, 14th June, 1645, Charles I. three times rested at the
Castle, staying there in all twenty-seven days. The strength of that
fortress enabled it to resist the Parliamentary arms longer than any
other stronghold--its surrender following very shortly after that of
Pendennis Castle.

When civil war was raging in this country, when King and Parliament were
in opposition, when Puritan, Protestant, and Papist sought for mastery,
when cavaliers met roundheads in mortal conflict, and every man stood in
fear of his neighbour, the Marquis of Worcester could no longer remain a
mere student of mechanism and of mathematical problems: if like
Archimedes in one sense, he was now seen, unlike him, buckling on his
armour, raising troops, and doffing the student's gown to become the
soldier. Alas! his military career forms no brilliant page in the annals
of his country's history. He was essentially neither a statesman, nor a
military man. He was bold, courageous, and energetic, but he could
neither be fierce nor ferocious on occasion. He tampered with opponents,
lost means of surprise, and was ever being tricked by the cunning and
chicanery of adversaries not over-scrupulous in their promises or
proceedings. His very goodness of heart, urbanity and uprightness were
the sources of his utter ruin. Himself incapable of deceit, he was
perpetually being made the victim of it: those who appeared his assured
friends, and had every reason to be so, proving in any emergency
shallow, empty, and worthless. Flattered by Charles I. he became
instrumental in assisting that Prince from his parent's private
fortune; and when that was exhausted, the King sapped the property of
the son, repaying both with titles, promises, and valueless bonds. He
created the Marquis of Worcester Earl of Glamorgan, during his father's
life-time; and, inducing him to raise Irish troops to fight against
English subjects, he completed the Earl's ruin; for, that untoward
enterprise failing, and being followed by the fall of Raglan Castle, and
the victories of the Cromwellian army, the Marquis of Worcester had to
quit his native land to seek refuge, with many other political refugees,
at the Court of France. His wife, who had been residing at Raglan
Castle, obtained leave from the Parliament in 1646 to flee to Paris,
where the Marquis also arrived in 1648.

The Marquis was proscribed both as a Papist and a rebel. Throughout his
political career the religion of his father and himself had made many
weak-minded men their enemies; but that his loyalty should be considered
rebellion was nothing more than might be expected from the dominant
party of those troubled times: although undoubtedly the result of that
great moral earthquake benefited our nation.

His only son, Henry, sat in the Cromwellian Parliament, and this fact
may, in part, explain the circumstance that most probably induced the
Marquis of Worcester to visit London in 1652; for he must have been
well-advised before committing such an apparently rash act. He was
immediately incarcerated in the Tower, from which he was released in two
years and a quarter, no doubt on his parole, as in 1655 a warrant was
signed by Cromwell to pay the Marquis of Worcester the sum of _three
pounds per week_ for his maintenance.

He was utterly beggared; what was he to do? It seems to have occurred to
him to turn his mechanical ingenuity to account, the Pretender's
monetary consideration being insufficient for the purpose intended. This
high-minded nobleman in the same year wrote his remarkable "Century of
Inventions," although it was not printed until eight years afterwards.
The title-page declared its production to have been "at the instance of
a powerful friend," who was, as we have reason to think, no other than
Colonel Christopher Coppley, or Copley, who had served in the
Parliamentary army of the North, under the command of General Fairfax;
for agreements were drawn up between them to secure a participation in
any benefits arising from introducing the steam engine, or
water-commanding engine, as it was then called.

It is not to the historic page, but to the calm unobtrusive volumes of
scientific record, that we must turn to be enlightened with respect to
the mental and mechanical achievements of the Marquis of Worcester; and
we must at the same time not overlook the fact, that many branches of
science were, in his day, but just emerging from that thraldom of
empiricism, which had for centuries clouded every department of
philosophical research.

The Marquis of Worcester was so essentially a scientific, and not a
literary man, that Horace Walpole acted most inconsistently in classing
him among his _Royal and Noble Authors_. That brilliant cynic, however,
had a purpose to serve, and although he found in the Marquis a vein of
pursuit of which he was totally ignorant, he presumed to criticise the
"Century," and to question its author's veracity; a charge which, if
established, even in a minor degree, would serve a political purpose, by
proving the Marquis to be unreliable in other respects, and thus
weakening his authority in religion and politics. But the dilettante
Walpole, a connoisseur in paintings and works of _vertu_, was, in
matters of science, more ignorant of the Marquis of Worcester's worth,
than was the equally satirical Voltaire of Shakspeare's genius. Hume,
the historian, attracted by the sparkling wit of Walpole, adopted
without examination, his plausible criticism, unconscious of its
superficiality and absolute untruthfulness in every respect.

We would here notice the probable cause of the Marquis's indefatigable
study of, and attention to, practical mechanics. As in the time of
Charles II., so also during the reign of his father, there is reason to
believe that some distinguished public officer was appointed to
superintend Government works connected with the army and navy, and that
they were situated at Vauxhall. It was probably a department similar to
that held in 1661, by Sir Samuel Morland, designated Master of
Mechanics. Otherwise how are we to account for the Marquis of
Worcester's devoting his time, his energies, and his very fortune to
inventions affecting mechanical appliances generally, and particularly
to those connected with naval and military affairs, and hydraulic
engines?

One of his inventions (No. 56) he exhibited to Charles I. at the Tower,
and of another (No. 64) being an improvement in fire-arms, he observes
it was "tried and approved before the King (Charles I.), and an hundred
Lords and Commons." Then his great invention, the "Water-commanding
Engine," was set up at Vauxhall in 1663, where it was certainly at work
in 1667, or probably three years later. All these circumstances wear the
aspect of royal patronage, of public employment, and of the possession
of influence suitable to the holder of a dignified position.

This view of the high and honourable public official position held by
the Marquis is also borne out by the petition of William Lambert, about
1664, to be found in the State Paper Office. It was addressed to
Charles II. and sets forth:--"That your petitioner was founder to his
late Majesty of blessed memory, in Vauxhall, under the Marquis of
Worcester, for gun and water-work, or any other thing founded in brass."
Nothing surely can be more certain than that the Marquis's was a public
situation, and his "Century" affords ample evidence of his aptitude in
_that_ respect for the post which he filled; nor can we better account
for his numerous improvements in fire-arms, cannon, sailing vessels,
fortifications, and embankments.

His "Century of Inventions" is the mere syllabus or outline of a
proposed larger work, for he concludes with the statement of
his--"meaning to leave to posterity a book, wherein under each of these
heads the means to put in execution and visible trial all and every of
these inventions, with the shape and form of all things belonging to
them, shall be printed by brassplates,"--the usual substitute at that
time for copperplates. It is most unfortunate that he did not live to
complete his projected publication. But in common candour let it not be
forgotten that, the promise thus placed before us was published in 1663,
not long before the devastating plague, which almost depopulated the
metropolis in 1665, and the terrible conflagration of 1666, which laid
waste the city of London; and that it was in the midst of the
accumulated calamities thus inflicted on society, that his health
appears to have suddenly given way; aged, harassed, disappointed, and
dismayed, he was prematurely called to his long rest on the 3rd of
April, 1667; but whether he died at Vauxhall, at the family town
mansion, Worcester House, in the Strand, or at some other place is
unknown; so little was he understood or esteemed for his intellectual
capacity at the period of the Restoration. As though it were not a
sufficient infliction to be ruined, dishonoured, oppressed, and
neglected while living, it would almost appear that events conspired to
lessen, if possible, the lustre of his memory by the dark shades of
apocryphal history; which ascribed the invention of the steam-engine to
the pretended fact of the Marquis while in imprisonment, having seen a
pot lid blown off by the expanding steam; made out against him a false
case of political forgery; and, worse than all, scandalously forged a
letter in Paris to make it appear that in 1641 the Marquis borrowed his
idea of the steam engine from Salomon De Caus, during a visit to the
Bicêtre, at Paris. The fact that this same De Caus died at Paris, and
was buried in the Church of La Trinité, in February, 1626;[2] shows how
requisite it is for rogues to remember historical dates.

[2] See _Worcesteriana_, 8vo. 1866, page 257.

On the 3rd of June, in 1663, the Parliament passed an Act securing to
the Marquis of Worcester the full benefit and profit of his
"Water-commanding Engine," for the term of ninety-nine years. And in the
same year he printed his memorable "Century," in the Dedication of which
he alludes to the above Act, as one by which he feels "sufficiently
rewarded."

The "Century" is little more than a Catalogue Raisonné, although each
matter of invention is as fully and intelligibly stated as was required
in the Patent office specifications of the period. To give some idea of
its contents, we shall enumerate only the first twenty-five. 1. Seals
abundantly significant; 2. private and particular to each owner; 3. a
one line cipher; 4. reduced to a point; 5. varied significantly to all
the 24 letters; 6. a mute and perfect discourse by colours; 7. to hold
the same by night; 8. to level cannon by night; 9. a ship-destroying
engine; 10. how to be fastened from aloof and under water; 11. how to
prevent both; 12. an unsinkable ship; 13. false destroying decks; 14.
multiplied strength in little room; 15. a boat driving against wind and
tide; 16. a sea-sailing fort; 17. a pleasant floating garden; 18. an
hour-glass fountain; 19. a coach-saving engine; 20. a balance waterwork;
21. a bucket fountain; 22. an ebbing and flowing river; 23. an ebbing
and flowing castle clock; 24. a strength increasing spring; and 25. a
double drawing engine for weight.

We find in the "Century" that three of the articles refer to improved
seals and watches; two to games; two to arithmetic and perspective; six
to automata, or self-acting mechanical contrivances; no less than
twenty-three to ciphers, correspondence, and signals: in short, secret
writing and telegraphs; ten to useful appliances in domestic affairs;
nine are wholly mechanical; upwards of thirty-two were intended for use
in naval and military affairs; and thirteen, including his
Water-commanding Engine, were connected with hydraulics. It is singular
that he professes "to have _tried and perfected_ all these," words of
great import in all matters of novel invention.

That age was fond of patronizing what we should now-a-days be disposed
to call "nic-nacs." Ingenious automata, curious toys and works of art,
small fountains, singing birds, and similar curiosities attracted the
serious attention of the virtuosi of the 17th century; so that we need
not feel surprised that the Marquis set up a speaking Brazen Head; or
that it should be of gigantic proportions, for he was always regardless
of cost in such matters, and was never small where he could be great in
developing his resources of ingenious contrivance. Wherever it was
possible, he was magnificent--fortifications, embankments, ships rowing
against wind and tide, great floating baths, and gardens, large cannon,
in short, he was princely in his expenditure of his private fortune on
whatever he undertook to perform, whether in war or in peace. It was
thus he spent, lent, and lost for his King and country £918,000. He
particularly notices that he laid out on buildings and experiments at
Vauxhall, the sum of £59,000. But these items are far from representing
his actual expenditure, although they indicate the scale of his
operations; and taken at their value two centuries back such sums
manifest marvellous munificence.

We have no certain key to any of his inventions, if we except two
specimens of his cipher writing. One exists in the British Museum,[3]
and there is a deciphered letter in the Bodleian Library, Oxford.[4]

[3] See engraving and account of it in _The Life, Times, and Scientific
Labours of the Marquis of Worcester_, 8vo. p. 398. 1865.

[4] Ibid, page 180.

His noblest invention, that which must for ever embalm his memory in the
breasts not alone of Englishmen, but of all classes throughout the
civilized world, was in operation at Vauxhall from 1663 to 1667, during
his life time, and appears to have been working as late as 1670. It was
ordered by the Act granted him, "that a model thereof be delivered to
the Lord Treasurer or Commissioners for the Treasury for the time being,
at or before the 29th of September, 1663; and to be put into the
Exchequer, and kept there." And in the 98th article of the "Century,"
alluding to this same engine he says--"I call this a _semi_-omnipotent
engine, and do intend that a model thereof be buried with me." Yet,
strange to say, neither the one model nor the other, although zealously
searched for, has come to light: and so little attention did this
invention, notwithstanding its surprising utility, excite in the 17th
century, that all the account we have of it, besides that by the
inventor himself, is the briefest possible notice given by two foreign
travellers, Sorbière in 1663-4, and Cosmo the third, Grand Duke of
Tuscany, in 1669. It is satisfactorily ascertained, however, that
upwards of seventeen persons, all living in 1663, were more or less
acquainted with the Marquis's mechanical operations at Vauxhall, and
must have seen the great water-engine at work, if only as a novelty, and
a matter of curiosity.

Returning to the "Century of Inventions," we find it to be a journal of
the fruits of its noble author's study of mechanical philosophy for
nearly forty years, so that in it we may almost trace the youth and age
of his mental capacity. Viewed through a modern medium we might feel
disposed to discredit the genius of a man who could contrive so many
curious alphabets for secret writing as those he mentions, but such
systems were extensively practised in political and private
correspondence during the Civil war period to baffle the curiosity of
political opponents. What may be called mechanical tricks were also much
in vogue, such as singing and flying birds, artificial figures and
horses, and curiously contrived watches, cabinets, locks, and keys.
Unless we bear in mind the taste of the age, we shall read with surprise
such an announcement as the following, in the 88th article in the
"Century":--

"How to make a brazen or stone head, in the midst of a great field or
garden, so artificial and natural, that though a man speak never so
softly and even whispers into the ear thereof, it will presently open
its mouth, and resolve the question in French, Latin, Welsh, Irish, or
English, in good terms uttering it out of his mouth, and then shut it
until the next question be asked."

No doubt the Marquis had in mind the history of the renowned Brazen Head
attributed to Friar Bacon. The authors of the works on mechanical
subjects published down to the 17th century, did not disdain to describe
the way to manufacture automatic men, animals, and birds, with suitable
joints, springs, weights, and bellows; and therefore, the Marquis did
really no more than express the character of the times, without lowering
his own superior intelligence. He was seeking the patronage of royalty,
parliament, and the public, and if he offered occasionally such trifles
as commanded the attention of the multitude, he never in the whole
course of his chequered life lost sight of his more important
occupations, the conceptions of a mind far in advance of that dismal and
dark period. At the same time, that his age neglected to uphold applied
science, and pertinaciously opposed whatever appeared to savour of
innovation on time-honoured manufactures and trades, we cannot overlook
the anomalous fact that it gave birth to Shakspeare, Bacon, and Milton;
Sir Thomas Brown, Wallis, Hook, Newton, and Boyle, together with a
brilliant constellation of luminaries who adorned every department of
our general literature. Science alone stagnated, and the construction of
public works was chiefly conducted by foreign aid. The establishment of
the Royal Society in 1660, however, gave promise of that improvement
which has steadily gone on year by year to the present day.

We have thus before us a broad outline of the Marquis of Worcester's
birth, education, studies, and scientific pursuits. His tastes and
employments were not suited to a successful political or military
career, at a time when the rupture between the Crown and the Parliament
rendered it necessary for every man to take the side either of the
Cavaliers or the Roundheads. Both father and son displayed unbounded
loyalty, although professing the Roman Catholic faith. Had they, like
many other noble families, adopted the policy of taking opposite
courses, the family might eventually have retained estates which were
forfeited when the King was deposed, and were principally enjoyed by
Cromwell. Raglan Castle was demolished, all that could be carried away
was sold, the strong tower or citadel was partially blown up, its ditch
left dry, and all that could be most readily spoiled was mutilated, even
to the marble and alabaster monuments in Raglan Church, raised to the
memory of ancestors of the family. Such ruthless destruction and pillage
has failed, however, to obliterate the towers, walls, arches, chambers,
and numerous vaults of that once princely residence.

From the year 1601 to 1641, (forty years of his life) was a period to
which he refers as his "Golden Age" in the dedication of his "Century."
While that from 1641 to 1647-8, (when he fled from Ireland to France,)
was the most exciting, exhausting, and disastrous of his whole
existence, and closed with utter ruin to himself and his family. He had
then living his second wife, Henry, his son and heir, and two daughters.
The family town mansion, Worcester House in the Strand, partly used as a
State Paper Office, was eventually granted to the Marchioness of
Worcester for her residence. The wearisomeness and distress attendant
on his residence as a refugee in France during four years, was
embittered by above two years imprisonment in the Tower, the result of
his venturing to revisit London while proscribed by the Parliament as
"an enemy and traitor to the Commonwealth," all such being threatened
that they shall "die without mercy, whenever they shall be found within
the limits of this nation." Burton, in his interesting Diary of Oliver
Cromwell's Parliament, says in reference to the case of the Marquis on
this occasion:--"It was urged he was an old man, had lain long in
prison, and the small-pox then raging under the same roof where he lay;
and he had not, as was said, done any actions of hostility, but only as
a soldier; and in that capacity had always shown civilities to the
English prisoners and Protestants. It was therefore ordered that he
should be bailed out of prison." He was probably then about fifty-three
years of age, but so harassed and so worn down by fatigue that he might
well appear to be a prematurely "old man." He was not, however, too old
to write his "Century" in 1655, and to re-write and publish it in 1663;
to apply for and obtain an Act of Parliament for his great invention of
a steam water-raising engine; and to get a working engine set up at
Vauxhall, and project a public company for obtaining funds sufficient to
extend its utility to the supply of towns, and canals, and for draining
mines and marsh lands.

The Marquis of Worcester was sincerely impressed with the capabilities
and great value of his invention; and it affords a striking proof of his
high estimation and correct knowledge of the magnitude of his discovery,
that he should have bowed himself before his Maker in humble adoration,
acknowledging in a solemnly sublime strain his sense of obligation to
the Supreme Source of all intelligence, for permitting him to become
instrumental in the development of so great a mystery of nature. It is
so short and significant that no apology can be required for quoting it
entire:

     "_The Lord Marquis of Worcester's ejaculatory and extemporary
     thanksgiving prayer when first with his corporal eyes, he did see
     finished a perfect trial of his Water-commanding Engine, delightful
     and useful to whomsoever hath in recommendation either knowledge,
     profit, or pleasure._

     "Oh! infinitely omnipotent God whose mercies are fathomless, and
     whose knowledge is immense and inexhaustible, next to my creation
     and redemption I render Thee most humble thanks even from the very
     bottom of my heart and bowels, for thy vouchsafing me (the meanest
     in understanding), an insight in so great a secret of nature
     beneficial to all mankind, as this my Water-commanding Engine.
     Suffer me not to be puffed up, O Lord, by the knowing of it, and
     many more rare and unheard of, yea unparalleled inventions,
     trials, and experiments, but humble my haughty heart, by the true
     knowledge of my own ignorant, weak, and unworthy nature, prone to
     all evil. O most merciful Father, my Creator, most compassionating
     Son, my Redeemer, and Holiest of Spirits, the Sanctifier, three
     Divine persons and one God! grant me a further concurring grace
     with fortitude to take hold of thy goodness, to the end that
     whatever I do, unanimously and courageously to serve my king and
     country, to disabuse, rectify, and convert my undeserved, yet
     wilfully incredulous enemies, to reimburse thankfully my creditors,
     to remunerate my benefactors, to re-enhearten my distressed family,
     and with complacence to gratify my suffering and confiding friends
     may, void of vanity or self-ends, only be directed to thy honour
     and glory everlastingly. Amen."

Judging of the Marquis of Worcester's personal appearance from two
family portraits, one when he was probably about twenty-five years of
age, by Vandyck; the other when between forty and fifty years old, by
Hanneman; he must have been rather of a delicate frame, and in stature
somewhat under the average height; his face oval, with sharp bright
eyes, and wearing a cheerful benignant aspect. His dress was, of course,
the costume of the period of Charles the Second's reign, but its
character has not been observed in either of the portraits just named,
one of which represented him in armour, and the other, as was not then
unusual with artists, attired as a Roman general. We infer that he
laboured under a defect in his speech, from his remarking in a memorial
addressed to the King that he penned it--"To ease your Majesty of a
trouble incident to the prolixity of speech, and a _natural defect of
utterance_ which I accuse myself of." It might be interesting to
speculate how his sense of deficiency in physical strength, in eloquence
of speech, and volubility of language might have contributed to the
fostering of that disposition for intense application to scientific
studies which became to him like a second nature.

During the first two years of the Restoration, the Marquis was in pretty
regular attendance on his Parliamentary duties. In 1661, he was obliged
to seek protection so that proceedings might not be taken against him by
his creditors; and about the same time his forfeited estates were
restored to him, but so encumbered and impoverished as to yield him a
very insufficient income, if any. It was in the midst of such
distractions as these that this talented inventor and noble benefactor
to his species had to maintain his social position; and, at the same
time, endeavour to convince the bigoted age in which he may be said
rather to have existed than to have flourished, that he was master of a
power of such magnitude for the abridging of human labour, as the mind
of man had never before conceived.

It may be freely conceded that, _stupendous_ as he himself pronounced
the parent engine to be, it was but as the acorn compared to the
time-honoured monarch of the forest. Just as the existence of the plant
is dependent on that of the seed, so if the Water-commanding Engine, the
great Fire Water-work he constructed had never existed, we might have
been unacquainted, to this day, with the mechanical application of
steam, and should have been deprived in consequence of the manifold
blessings it bountifully bestows on mankind.


ADDENDUM.

Evidence of the Marquis of Worcester's claim to the Invention of the
Steam Engine.

1. His personal claim to have written a statement respecting it in 1655;
his MS. being afterwards lost.

2. The Act of Parliament[5] which was granted him for the term of
ninety-nine years, and which received the royal assent on the 3rd June,
1663.

[5] For lists of the names of members on the several Committees
appointed on the occasion of this Act being applied for, see--"The Life,
Times, &c.," 8vo. 1866, pages 254-5.

3. His "Century of Inventions," printed from a re-written copy of his
lost notes of 1655; and which names in the Dedication, the granting of
the above Act.

The following list[6] comprises upwards of seventeen persons all living
in 1663:--

[6] From "Worcesteriana," 8vo. 1866, page viii.

4. CASPAR KALTOFF, a confidential workman, engaged by the Marquis as his
engineer in 1628, who died about 1664, and is honourably mentioned in
the "Century."

5. MARTHA KALTOFF, wife of Caspar Kaltoff, who is named in letters
patent dated 1672, _as lately deceased_. Her family was--

  CATHARINE, married to Claude Denis.
  CASPAR KALTOFF, and his unmarried sister--
  ISABEL KALTOFF.

6. PETER JACOBSON, a sugar refiner, who married one of Kaltoff's
daughters, had a portion of the buildings at Vauxhall, where the
Water-commanding Engine was erected, and in operation from 1663, till at
least to the year 1669, if not some years later.

7. WILLIAM LAMBERT, another workman, a founder at Vauxhall, in the reign
of Charles I., "under the Marquis of Worcester, for gun and waterwork,
or any other thing founded in brass," in 1647, and who was living in
1664-5.

8. CHRISTOPHER COPLEY, who had been a Colonel in the Parliamentary
service, and was probably an iron master, having been the proprietor of
four Iron Works. He assisted the Marquis at an early period and held a
pecuniary interest in his invention of a Water-commanding Engine. Indeed
it is highly probable that he was the "powerful friend" at whose
instigation the "Century" was written in 1665.

9. The EARL OF LOTHERDALE, written to in January, 1660, had a copy of
the "Definition" of the Engine sent to him, and is promised an
ingeniously contrived box or cabinet. He was appointed as late as March,
1665, to be one of a Commission to report on the affairs of the Marquis,
and must, therefore, have been familiar with all matters relating to the
noble inventor.

10. DR. ROBERT HOOK, the eminent mathematician, was acquainted with
Caspar Kaltoff, and early in 1667, went purposely to see the engine
working at Vauxhall, having read the "Definition."

11. THE HONOURABLE ROBERT BOYLE received from Dr. Hook a copy of the
"Definition," sent to him with a letter on the subject.

12. LORD BRERETON is specially mentioned by Dr. Hook, as being so
confirmed in his doubts of the excellence of the Marquis's engine, that
he had laid a wager on the subject.

13. HENRY SOMERSET, Lord Herbert, afterwards created first Duke of
Beaufort, by Charles II., must have frequently seen the engine in
operation. He died in 1699.

14. JAMES ROLLOCK, who wrote a poetic eulogy on the Engine about 1663,
speaks of himself as "an ancient servant," having known his lordship
forty years, dating back to 1623.[7]

[7] He was the author of a pamphlet now very rare, and which is absurdly
enough attributed by Horace Walpole to the Marquis of Worcester. A
reprint will be found in "The Life, Times, and Scientific Labours of the
Marquis of Worcester," 8vo. 1866, page 559. It contains the following
intimation to the reader:--

"I think it not amiss to give further notice in his Lordship's behalf,
that he intends within a month or two, to erect an Office, and to
entrust some very responsible and honourable persons with power to treat
and conclude with such as desire at a reasonable rate, to reap the
benefit of the same Water-commanding Engine."

So that it is manifest a public company was intended to be established
in 1663-4, to extend operations with the engine then actually raising
water at Vauxhall.

15. SAMUEL SORBIÈRE visited the works at Vauxhall, and published
particulars of the engine he saw there in 1663.

16. LORD JOHN SOMERSET, the Marquis's eldest brother, appears latterly
to have lived at Vauxhall, according to a warrant dated September, 1664;
and would certainly be admitted into his brother's confidence.

17. COSMO THE THIRD, Grand Duke of Tuscany, in his Diary exactly
describes the engine he saw at Vauxhall in 1669, "considered to be of
_greater service to the public_ than the other machine near Somerset
House."

18. WALTER TRAVERS, a Roman Catholic priest, names the engine in a
letter which he wrote to the Dowager Marchioness of Worcester, in 1670.

19. DR. THOMAS SPRAT, F.R.S., published in 1665, a critical work on "M.
Sorbière's Voyage into England," and could not therefore be ignorant of
the Marquis's engine, as it was named by the French traveller, although
Sprat omitted to notice it specially in his own "Observations."

20. Among his other contemporaries were Sir Samuel Morland, Dr. Wallis,
Sir Christopher Wren, Sir Isaac Newton, and many more, who, however, (so
far as is at present known,) are silent in regard to all matters
relating to the Marquis.



                                  II.

                               LECTURE
                 DELIVERED ON THE 5TH NOVEMBER, 1868:
                 BEING THE FIRST OR INAUGURAL LECTURE
                                OF THE
                            FREE LECTURES,
                   AT THE CRYSTAL PALACE, SYDENHAM,
                                  ON
                         CHIMERAS OF SCIENCE:
                          ASTROLOGY, ALCHEMY,
                         SQUARING THE CIRCLE,
                          PERPETUUM MOBILE,
                                 ETC.

                     With Illustrative Diagrams.

                       AND RE-DELIVERED AT THE
            BIRKBECK LITERARY AND SCIENTIFIC INSTITUTION,
                         17TH FEBRUARY, 1869.

    "A little knowledge is a dangerous thing,
    Drink deep, or taste not the Pierian spring;
    There shallow draughts intoxicate the brain,
    But drinking largely sobers us again."--POPE.


PREFACE.

The present Lecture, embodying a variety of subjects, under the general
title of CHIMERAS OF SCIENCE, not only reviews them in succession, but
expresses sentiments with regard to each which result from a long
acquaintance with ancient and modern scientific authors; supported by an
experimental, and, not unfrequently, by a practical acquaintance with
several branches of natural philosophy. The consequence of this intimacy
with various scientific studies, has been a thorough conviction of the
necessity of possessing a knowledge of elementary principles, before
professing a belief in new doctrines, whose only recommendation is their
novelty, extravagance, and inutility. Without absolutely pretending to
any golden road, or short path to learning, superficial but ambitious
scholars are the first to seize on first impressions, build up some
grand theory, lay down certain postulates, seek proselytes, and display
a wonderful amount of enthusiasm in creating systems which, however
beautiful in appearance, can boast of no solid foundation. Imperfectly
educated, and shallow, but not unfrequently highly imaginative, men, if
not themselves absolute charlatans, are the easily led dupes, who become
the admirers and abettors of every "new wind of doctrine."

Every age has been sensational. Man delights in mystery, and mysticism
is a certain sign of imperfect knowledge. A classic age was not proof
against the tricks and deceitful practices of the oracles, soothsayers
and jugglers. The dark ages only served to keep alive the human desire
for sensation; and less than a century ago, poor, simple, half idiotic
women, were burnt at the stake as witches. The Mahometans had their
prophet, and so have the Mormons. Mesmer had his disciples, and so have
many modern Spiritualists. The Astrologer of the 17th century, is
presented to us in a modern dress by the seer Zadkiel. Jacob Behmen and
Emanuel Swedenborg, but represent a class that is continually dying out,
yet is as continually reproduced; the authors of pious romances,
theological enigmas, scientific spiritualisms, and spiritualized
transcendental philosophisms. Swedenborg introduces us to the
inhabitants of the moon; they are short, the size of a youth of seven
years of age; and they speak with a thunderous voice for want of an
atmosphere, and not from the mouth, but from the abdomen! But many
persons admire such wanderings of a pretended inward and prophetic
light.

There are still living a few faithful believers in _Alchemy_, who
earnestly look forward to the coming of the day when the grand, the
glorious secret, shall be fully revealed; not, however, to the vulgar
crowd, but to the noble, true, and virtuous adept,--to him, and him
only.

A class of _Mathematicians_ still continues to publish papers and
pamphlets on squaring, cubing, and trisecting. On this subject, the
reader might find some amusement in the critiques of Professor De
Morgan, who wrote several papers in the _Athenæum_, 1865, under the
title of _A Budget of Paradoxes_.

_Mechanics_ are still living who firmly believe in the possibility of
realizing a mechanical perpetual motion,--to spin, pump, or drive
carriages or machinery, by means of a constantly descending weight. And,
year by year, many such schemes, find their final resting place in the
archives of the Patent Office.

It is melancholy to reflect on the waste of mental energy, inflicted on
society by such vanities as Astrology, Alchemy, and their kindred
empirical employments. Look at the centuries wasted, and worse than
wasted, in studying such intellectual abortions, and in writing
thousands of volumes of inanity to uphold falsehood and delude the
unwary. What the sword has done physically, the pen and the wand of the
sorcerer have done mentally, in prostrating the intellectuality of
mankind.

It would tend to promote the progress of society at large, if education
were so far general that the acquirements of the middle and lower
classes should act on the upper classes as a stimulant to the pursuit of
those higher branches of study, which mostly fall to the lot of the
nobility and men of fortune: whose birth and ample means otherwise
relieve them from all incitements other than such as are fostered by the
necessities of public office. With title and fortune, and no ambition
to hold public employment, any education is thought to be sufficient
that serves to obtain the usual dignities, and to give that polish which
completes the accomplished gentleman. To the spread of education alone,
can we look with any reliance for the downfall, or at least the
diminishing of the hold on the human mind which Chimeras of every order
usurp in our own, in common with every other country.

Among other works that might be consulted by the curious in such
matters, in the Libraries of the British Museum, the Patent Office,
Chetham College Manchester, &c.; may be named, on ASTROLOGY,--B. Porta's
Works, folio, 1616;--The Compost of Ptolomeus, Prince of Astronomie,
1645;--W. Ramsey's Vox Stellarum, 8vo., 1652;--The Geomancie of Maister
Christopher Cattan, 4to., 1608;--Dr. John Dee's Work on Spirits, folio,
1659;--J. Goad's Astro-Meteorologica, folio, 1686;--Godfridus's Work on
the Effects of the Planets, &c., 1649;--M. Manilius's System of the
Ancient Astronomy and Astrology, &c., 8vo., 1697;--John Merrifield's
Catastasis Mundi, 4to., 1684;--Jo. Holwells's Catastrophe Mundi, 4to.,
1682;--with many others of modern date.

On ALCHEMY,--Ashmole's Theatrum Chemicum Britannicum, 4to., 1652;--Dr.
John French's Art of Distillation;--Four Books of J. S. Weidenfeld,
4to., 1685;--A Philosophicall Epitaph, in Hierogliphicall Figures,
1673;--George Ridley's Compound of Alchemy, 1591;--Roger Bacon's Art
and Nature, (in French,) 1557; his Mirror of Alchemy, 1597; his
Philosopher's Stone, or Grand Elixir, 8vo., 1739; Theatrum Chemicum, 6
vols., 8vo., 1659-61;--Sandivogius's New Light of Alchymie, 4to.,
1650;--Opuscula quædam Chemica, 8vo., 1514;--The Works of Geber,
1678;--Hermes Trismegistus's Works, collected in Theatrum Chemicum, 4
vols.;--Raimond Lully's De Secretis Naturæ, 1541;--Crollius's Philosophy
Reformed and Improved, in four profound Tractates, 1657;--Beguinus (J.)
Trocinium Chymicum, or Chymical Essays, 8vo., 1669;--Artis Auriferae,
Quam Chemiam Vocant (a collection of treatises), woodcuts, 2 vols. 8vo.
1593;--Balduinus's Aurum Superius et Inferius Hermeticum, plates, 1675;
Beccheri's Physica Subterranea, Lipsiæ, 1738 (with supplement), 8vo.,
1681-80; with many others, ancient and modern. Interesting compendious
treatises will be found in Dr. Thomas Thomson's History of Chemistry,
("The National Library,") 2 vols., 12mo., 1830; Justus von Liebig's
Familiar Letters on Chemistry, edited by Dr. Blyth, 8vo., 1859. And--

On MATHEMATICAL and MECHANICAL Chimeras, many popular notices may be
found in Encyclopædias; and particularly in Dr. Hutton's Mathematical
Dictionary, 2 vols., 4to.; and the Author's "Perpetuum Mobile; or,
History of the Search for Self-Motive Power; with an Introductory
Essay," post 8vo., 1861; to which work, a second series will shortly be
added.


CHIMERAS OF SCIENCE.


INTRODUCTION.

Although the present lecture seems to require some introductory remarks,
they must necessarily be brief--our time being limited and this
discourse rather discursive; yet it is sufficiently condensed to suit
the present occasion, and illustrates fully the truthfulness of the
axiom that--_A little learning is a dangerous thing_: from its tendency
to inspire its possessors with vanity rather than with the humility
which always accompanies profound knowledge.

You are no doubt all, or most of you, well acquainted with the use made
of Astrology and Alchemy in the dramas of Shakspeare--"The Antiquary" of
the "Wizard of the North"--the "Strange Story" of Lord Lytton--the
"Faust" of Goëthe; and are probably familiar with the more instructive
works of Scott on Demonology, and of Brewster on Natural Magic. Now we
always find that fiction is more suitable than truth for romantic
writings; truth is circumscribed, but the fictions whether of Astrology,
Alchemy, or any other pseudo-philosophy are erratic, the delight of
poets and romance writers, being the comets and _ignes fatui_ of many
popular compositions in our light literature.

There is no end of fabulous writings of the class we call novels and
romances, and no end of deceptions which we patronize as tricks of
legerdemain; the one gratifies our imagination and fancy, the other
takes our common sense by surprise; but all these are harmless because
only presented to us for our amusement.

Delusion, however, assumes a startling character when romance in the
form of mystic writings, and jugglery in the form of pretended
communication with the spirit-world demand our respect and serious
attention, by claiming to have a divine origin. But hallucination of the
human intellect, as we shall see, is not confined to such remote
visionary speculations, and it is not unimportant to remark that in
mathematics, as in physics, and in other branches of investigation,
there is a singular persistency in upholding errors.

A contemporary astrologer, assuming the pseudonym of Zadkiel, tauntingly
observes in his preface to a recent publication: "_This is the age of
inquiry_; and yet prejudice continues to press down her leaden foot upon
the neck of examination in this matter"--that is, Astrology. Now with
this reproof before us we hope to discuss the subject with becoming
propriety.


ASTROLOGY.

The splendour of the sun by day, the glories of the firmament by night,
together with the sublimity of all celestial phenomena, attract alike
the attention of the most simple and the most intellectual among
mankind. The distance, the magnitude, and the grandeur of the entire
planetary system while exciting emotions of awe, reverence, and devotion
among the mass of the human race, have at the same time been studied
from the earliest period of man's history to the present time
superstitiously by one class of observers, and scientifically by
another.

As the telescope was not invented before the 17th century, it is evident
that the study of Astronomy without that instrument must previously have
been pursued under amazing difficulties; and we might have expected that
when first used by Galileo at Venice in 1609, its introduction would
have been hailed without a dissentient voice. Such, however, was not the
fact, according to Sir David Brewster,[8] who says:--

"The principal Professor of Philosophy at Padua resisted Galileo's
repeated and urgent entreaties to look at the moon and planets through
his telescope; and he even laboured to convince Cosmo de Medici, the
Grand Duke of Tuscany, that the satellites of Jupiter could not possibly
exist. Sizzi, an astronomer of Florence, maintained that as there were
only _seven_ apertures in the head--_two_ eyes, _two_ ears, _two_
nostrils, and _one_ mouth--and as there were only _seven_ metals, and
_seven_ days in the week, so there could only be _seven_ planets. He
seems (eventually), however, to have admitted the visibility of the four
satellites through the telescope; but he argues, that as they are
invisible to the naked eye, they can exercise no influence on the earth;
and being useless they do not exist."

[8] See his "_Martyrs of Science_."

Such being the crude state of astronomical science in the 17th century,
it must have been comparatively imperfect throughout all preceding
centuries; and open to mystical appropriation and abuse by Egyptians,
Chaldeans, Hindus, Chinese, and European and other ancient astrologers.
Among that motley group the most learned were found strangely associated
with ignorant impostors, and their activity in writing and travelling
served to spread their different systems over the entire civilized
world. It was not until late in the 17th century that Astrology could be
absolutely declared to be in its decline. In England, William Lilly,
the Sidrophel of Hudibras, and the most famous astrologer of his time,
died in 1681, leaving behind him his _Introduction to Astrology_,
together with many other works of the same character.

Astrology is merely a philosophism, being empirical, wholly visionary, a
mere fanciful system compounded of incongruous mixtures of astronomical
with human events, of mythology with theology, and of facts with pure
fiction. It has been variously designated Judicial, Hororary,
Atmospherical, and Mundane, Astrology. It has also many off-shoots
subservient to Magic or the black art, Sorcery, Witchcraft, and other
pretended mysticisms ostentatiously styled occult philosophy.

We may first observe that Astrology lays no claim to inspiration, but
affects a very ancient unknown origin, tracing back to a dark,
heathenish, and superstitious age, in the very infancy of traditional
knowledge, when the boldest assertions of the seer were received as the
authority of an oracle, no one daring to question their validity.
Whatever is remotely possible the Astrologer accepts as a fact; while
ignorant of much around him, he assumes with the utmost complacency an
intimate acquaintance with the sun and planets thousands upon thousands
of miles off; yea with the sun 969,272 miles in diameter, while he
himself inhabits a globe only 7,916 miles in diameter; from which the
moon is 237,000 miles distant, and the sun 400 times that distance.[9]
And these immense bodies revolving millions on millions of miles away in
immeasurable space are described by him as fashioning an infant's nose,
directing the fortunes or misfortunes of lovers, ordering the property
of traders, meting out diseases, and improving or deranging man's mental
faculties. And as if such puerile influences were not sufficiently
preposterous we are informed by the modern seer, Zadkiel, that the 12
signs of the Zodiac not only rule the several parts of the human frame,
but also those of a ship, as _Aries_, the bows; _Taurus_, the cutwater;
_Gemini_, the rudder; _Cancer_, the bottom; _Leo_, the upper works;
_Virgo_, the hold; _Libra_, parts above the water's edge; _Scorpio_, the
seamen's berths; _Sagittarius_, the seamen; _Capricorn_, the ends of the
vessel; _Aquarius_, the Captain; _Pisces_, the oars in galleys, the
wheels in steam vessels, and the sails in others; but these latter being
above water, we are left in doubt about the ruler of the submerged screw
propeller.

[9] This portion of the subject was illustrated by means of a Diagram
exhibiting the Diameters and Magnitudes of Planets, thus:--

[Illustration:

        _Miles._
The Sun 882,000
Jupiter  91,522
Saturn   76,018
Uranus   35,100
Neptune  33,600
Earth     7,916
Venus     7,702
Mars      4,398
Mercury   3,123

The Moon's diameter is 2,160 miles; and its distance from the Earth is
237,000 miles.]

To show what a modicum of learning, and how trifling an acquaintance
with matters of natural philosophy will serve the Astrologer, we will
turn to a modern treatise published in the year 1801, by Francis
Barrett, (styling himself a student of Natural and Occult Philosophy) a
quarto volume of upwards of 370 pages, entitled, "The Magus, or
Celestial Intelligencer," which affords a pretty clear insight into the
nature of the superstitions which from an ancient period even to that
date obtained credence and were popular with the multitude.

Treating of the wonders of Natural Magic previous to entering on the
main topic of his treatise, he adduces a few of what he conceives to be
ordinary matters of fact, assuring us that:--

If any one shall, with an entire new knife, cut asunder a lemon, using
words expressive of hatred, contumely, or dislike, against any
individual, the absent party, though at an unlimited distance, feels a
certain inexpressible and cutting anguish of the heart, together with a
cold chilliness, and failure throughout the body;--likewise of living
animals, if a live pigeon be cut through the heart, it causes the heart
of the party intended, to be affected with a sudden failure;--likewise
fear is induced by suspending the magical image of a man by a single
thread;--also death and destruction by means similar to these; and all
these from a fatal and magical sympathy.

The loadstone, (he observes), possesses an eminent medical faculty
against many violent and implacable disorders;--the back of the
loadstone, as it repulses iron, so also it removes gout, swellings,
rheum, &c. that is of the nature or quality of iron. Likewise the
wearing the loadstone eases and prevents the cramp, and such like
disorders and pains.

The influences of the stars appear to be as intimately known to
Astrologers as though they had walked among, and carefully examined and
fully realized their occult properties, for example:--

In every work observe Mercury, for he is a messenger between the higher
gods and the infernal gods; when he goes to the good, he increases
their goodness--when to the bad, he hath influence on their wickedness.
It is an unfortunate sign or planet, when it is by the aspect of Saturn
or Mars especially, apposite or quadrant, for these are the aspects of
enmity; but a conjunction, a trine, and a sextile aspect, are of
friendship; but yet if you do already behold it through a trine, and the
planet be received, it is accounted as already conjoined. Now all
planets are afraid of the conjunction of the sun, rejoicing in the
trine, and sextile aspect thereof.

They say of the Sun and Moon:--

The Sun is the lord of all elementary virtues;--it disposes even the
very spirit and mind of men.

The Moon (says Barrett) measures the whole space of the Zodiac in the
time of 28 days, hence it is that the wise men of the Indians, and most
of the ancient astrologers have granted 28 mansions to the Moon, which,
being fixed in the eighth sphere, do enjoy divers names and properties,
from the various signs and stars which are contained in them; through
which, while the Moon wanders, it obtains many other powers and virtues;
but every one of these mansions, according to the opinion of Abraham,
contained twelve degrees, and fifty-one minutes, and almost twenty-six
seconds. In the first quarter of these mansions the 1st conduces to
discords and journies; the second to the finding of treasures, and to
the retaining of captives; the 3rd to benefit sailors, huntsmen, and
alchymists; the 4th the destruction and hindrances of buildings,
fountains, mills, gold mines, the flight of creeping things, and begets
discord; the 5th to help the return from a journey, the instruction of
scholars, and confirms edifices, gives good health and good will; the
6th to hunting and besieging towns, and revenge of princes, destroying
harvests and fruits, and hinders the operation of the physician; the 7th
to confirm gain and friendship; is profitable to lovers, and destroys
magistracies.

In a similar manner the remaining three quarters have the characters of
their several mansions allotted to them with equal exactness, and of
course indisputable veracity also.

We have here a fair example of the arrogant assumptions of ancient and
indeed of all astrologers, magicians, and sorcerers, men who are
incompetent to elucidate the ordinary phenomena of nature in the animal
or vegetable creation, and yet with unbounded effrontery affect to build
up an empirical system, delivered in a language of their own invention,
a pompous parade of jargon made up of the most incomprehensible
materials--which if wholly due to antiquity partakes of ancient
simplicity, credulity, deceit, and superstition; and if somewhat
polished and refined to suit the advances of literature and science, has
never been able to prove the correctness of its groundwork, or afford a
solitary instance of its possessing any meritorious quality beneficial
to mankind; while on the other hand its evil consequences have been
many, by destroying the peace and happiness of thousands, encouraging
deceit, and misapplying in its ignoble pursuit the time and labour and
property of its ardent but deluded admirers.

In Judicial Astrology it is not thought requisite to consider more than
a certain number of the planets, after a method simplified by antient
astrologers or astronomers, which is found to be so compact and so
complete in governing the destinies of the human race that modern
intelligence has failed to enlarge the field of heavenly influences.
Varley notes that:--the antients discovered that the circle of the
Zodiac, about 16 degrees in width, and through the middle of which runs
the Ecliptic, or sun's path through the 12 signs, contains the heavenly
bodies, named planets, and the principal fixed stars, and nearly the
whole of the materials or significators, from which predictions are
obtained.

He remarks that:--In forming a horoscope, this circle is divided into 12
equal parts, corresponding with the spaces containing the 12 hours.
These 12 divisions are called houses; and they always remain fixed,
while the Zodiac with the 12 signs, and all the heavenly bodies
belonging to it, are considered to be moving through them all, every 24
hours. The _lord_ of the ascendant is the planet which rules the signs
rising at birth. In drawing horoscopes it is usual to make the figure
square instead of round. (_See_ Plate 1, Fig. 1.)

The various significations arising from the aspects of the starry
heavens at the time of birth are so exceedingly numerous, that we must
refer the curious in such matters to the works themselves, in which all
these pretended revelations are minutely recorded.

Mankind rank astrologically as being of four temperaments.

1. One class is said to answer to the fiery trigon, also called diurnal,
masculine, and choleric, consisting of Aries, Leo, and Sagittarius,
which contains the spirited, generous, magnanimous, and princely
natures.

2. We have next the earthy trigon, being nocturnal, feminine, and
melancholic, consisting of Taurus, Virgo, and Capricorn, containing the
careful, sordid, and penurious qualities.

3. Thirdly, the aërial trigon, which is diurnal, masculine, and
sanguine, consisting of Gemini, Libra, and Aquarius, contains the humane
harmonies, and courteous principles. And--

4. Fourthly, the watery trigon, which is nocturnal, feminine, and
phlegmatic; namely, Cancer, Scorpio, and Pisces, including the cold,
prolific, cautious and severe qualities.

Take as a brief illustration of the manner in which Astrologers
presumptuously assign to the planets their several offices relating to
human nature the following:--

Those born when Aries ascends are born under the sign Aries and planet
Mars. This is the diurnal, fair, and masculine house of Mars, and
partakes also largely of the nature of the magnanimous Sun, and the
benevolent and moral Jupiter, who rule the fiery trigon, of which Aries
is the first sign.

As affecting physiognomy we are assured that:

The Scorpio noses are more aquiline than those of Aries, and are more
frequently conspicuous for a sort of bracket shape beneath, which
prevents the under part of the nose from forming a right angle with the
upper lip; while the under lip, both being usually small, recedes in a
greater degree, as if drawn tightly against the teeth; so that the
mouth appears in the act of pronouncing the word SEVERE.

When we meet in volume after volume with page after page of such
composition as this, when we reflect on the sublimity of the heavens and
the paltriness of such combinations as are here given of the planets
with mundane affairs, we ask the reasons for arriving at such judgments.
To be told that it is so because it is so; or because it was an ancient
belief, and is to be found in the writings of Ptolemy, Nostradamus, Dr.
John Dee, William Lilly, or Zadkiel; or because it has often proved as
true in its predictions as the telling fortunes by means of a pack of
cards, is no evidence whatever; yet the Astrologer boasts of his very
paralogisms.

Zadkiel, in prefacing a work by Lilly, says:--If a proposition of _any
nature_ be made to any individual, about the result of which he is
anxious, and, therefore, uncertain whether to accede to it or not, let
him but note the hour and minute when it was _first_ made, and erect a
figure of the heavens, (_See_ Plate 1, Fig. 1,)--and his doubts will be
instantly resolved. He may thus, in five minutes, learn infallibly
whether the affair will succeed or not; and, consequently, whether it is
prudent to adopt the offer made or not.

Such is the belief of this sound, intelligent man, as we fully believe
him to be in other respects. But we say it is not given to man to assign
special influences to the stars, to select one portion and discard all
the rest, or to be more intimately acquainted with the starry heavens
above him, than with the stony earth he inhabits, and with his fellow
creatures around him.

The works claiming to expound this pretended Occult Philosophy prescribe
such childish processes that one naturally wonders how in the midst of
so much impudent imposture Astrology and its kindred pursuits ever found
or retained any honest partizans.

Take, for example, the use of fumigations, such as of frankincense, &c.
to Saturn; of cloves, &c. to Jupiter; of odoriferous woods to Mars; of
all gums to the Sun; of roses, violets, &c. to Venus; of cinnamon, &c.
to Mercury; of the leaves of vegetables to the Moon; of all or any of
which there must be a good perfume, odoriferous, and precious, in good
matters; but in evil ones quite the contrary.

The Zodiac is also favourably affected by proper suffumigations.

Astrologers in their Demonology profess to be able to ascertain the
characters and seals of spirits,[10] and according to the Cabalists,
tables are given of many of these in their books, in the so-called
Theban Alphabet; in characters of Celestial Writing; in that called
Mallachim; or in the writing called Passing the River.

[10] See the Table, Plate I. Fig. 2, for distinguished names of their
angels, spirits, or demons.

They affect to have suitable bonds by which spirits can be bound,
invoked, or cast out.

Of Necromancy they pretend to two kinds, one of which is raising the
body of a deceased person, which it is said cannot be done without
blood;--the other sciomancy, which is the production of a mere shade or
shadow.

The exorcisms and conjurations of Magicians are so audaciously profane
and blasphemous as to be unworthy of even a passing notice.


ALCHEMY.

We shall now proceed to consider Alchemy, another but very different
chimerical pursuit, which was early cultivated in the East, and is
generally ascribed to Hermes Trismegistus, although its more
enthusiastic admirers pretend to trace a knowledge of it to Adam. From
the earliest periods of history man was acquainted with gold, silver,
and other metals, with bitumen, sulphur, sea salt, sal-ammoniac, gums,
and resins, together with other varieties of substances and liquids
common to modern chemistry. For the compounding and heating of certain
of these materials a multiplicity of means were adopted requiring
furnaces, crucibles, and distillatory apparatus. The first workers in
these experimental operations formed a body of investigators into the
nature and properties of all manner of substances, whether animal,
vegetable or mineral, the members of which were distinguished as adepts,
alchemists, and later in their career as common chemists. The most
esteemed branch of the art however was Alchemy, a pseudo-science which
ultimately took three forms. First, the Hermetic Art for the discovery
of the Philosopher's stone; and the Alkahest, or universal
solvent;--Second, a Medical Alchemy;--and Third, a Theological Alchemy
pretending to conceal divine mysteries under an allegorical form,
treating of the spiritual while apparently describing alchemical
discoveries.

Our principal business, however, is with the so-called Hermetic
Philosophy, treating of vaunted methods of transmuting the base metals
into gold. It is doubtful whether this particular delusion of the
adepts can be referred to a date earlier than the 8th century, but even
then we cannot refrain from surprise at the fallibility of the human
intellect, which could be swayed by a belief in the pretended _lapis
philosophorum_ for upwards of ten centuries. It was believed to be so
secret and rare that its possession was never ascribed at any time to
more than two or three favourite adepts, who transmitted it to some
single favoured individual after his taking the sacrament, and going
through certain prescribed religious ceremonies, preparatory to being
entrusted with a verbal recipe for the composition of a peculiar
smelling red powder, of which it was affirmed that when projected on
heated mercury or any solid metal, it would at once change it into pure
gold. Ashmole gravely assures us that Dr. John Dee and his associate
Kelly, having in some way procured this precious substance, Kelly--to
use Ashmole's own words--"made projection with one small grain thereof,
in proportion no bigger than the least grain of sand, upon one ounce and
a quarter of common mercury, and it produced almost an ounce of pure
gold." With equal simplicity and earnestness, Ashmole asserts that this
same Kelly was often seen to make these extraordinary transmutations,--
"and in particular (he adds) upon a piece of metal cut out of a
warming-pan, and without touching or handling it, or melting the metal,
only warming it in the fire, the elixir being put thereon, it was
transmuted into pure silver. The warming-pan and this piece of it, was
sent to Queen Elizabeth by her Ambassador who then lay at Prague, that
by fitting the piece into the place whence it was cut, it might exactly
appear to be once part of the warming-pan."

Among the adepts there were no doubt a select few who employed
themselves in their prolonged labours in all sincerity, and who were not
unfrequently repaid with remarkable, and unexpected results. Brass,
being the result of copper combined with zinc, would appear a singular
transformation. Many stones, or more properly, ores, would yield sulphur
and metals; sulphur would be found apparently to dissolve iron; and
certain salts, when distilled, would yield corrosive acids. Alchemy thus
presented to the ancient adepts many of the ordinary wonders of modern
chemistry; in short, the latest adept of the present century is no other
than an unlettered chemist. It was peculiar to the Alchemists to treat
all their operations as secrets; which, when recorded, were described
partly by symbols and partly in a novel nomenclature, invented to
conceal their mysteries from vulgar gaze or imitation. Thus, to prepare
the philosopher's stone, we have merely to--"Take of moisture, an ounce
and a half; of meridional redness, that is the soul of the sun, a fourth
part, that is, half an ounce; of yellow seyr, likewise half an ounce;
and of auripigmentum, a half ounce; making in all three ounces. Know
that the vine of wise men is extracted in threes, and its wine at last
is completed in thirty." To the incredulous in these matters, Ashmole
offers the admonition that, he knows "_Incredulity is given to the world
as a punishment!_" However, when the Alkahest, or pretended Universal
Solvent, was alluded to by the modern chemist Kunckel, he could not
refrain from incredulously enquiring--"If it dissolves all substances,
in what vessel can it be contained?"

Alchemical writings are very numerous, it might be impossible to procure
a complete bibliographical list of them, but they may be estimated at
from 3000 to 4000 works, and an astonishing number of manuscripts. Their
authors indulge in such terms as the Ph[oe]nix, to indicate the
quintessence of Fire; Realgar, for the fume of minerals; Guma, also Luna
Compacta, for quicksilver; Hadid, for iron; Aurum potabile, for liquor
of gold; Anathron, for saltpetre; Malek, for salt; Terra fidelis, for
silver; Tinkar, for borax; and in a similar strain for all matters and
operations; so that Dr. Johnson was justified in deriving the word
Gibberish from the mysterious jargon employed by Geber, a celebrated
Alchemist; who has, nevertheless, been appropriately styled the Pliny of
the 8th century.

Weidenfeld, in an Alchemical Treatise, published in 1685, addressing
students, says:--

"Under heaven is not such an art, more promoting the honour of God, more
conducing to mankind, and more narrowly searching into the most profound
secrets of nature, than is our true and more than laudable Chymy."

And at the conclusion of his address he observes:

"Nothing remains but upon our bended knees to return most humble thanks
to the Father of Lights, in vouchsafing us this art by the writings of
his servants, and the high priests of Nature; without which, it would be
beyond the power of man to arrive at so great a degree of knowledge."

Some notion of the extravagance of the language employed may be obtained
from his description of a Philosophical Wine, literally, rectified
spirits of wine, or alcohol. He assures us that, on opening a vessel of
it, "a wonderful scent" should arise: "so as that no fragrancy of the
world can be compared to it; inasmuch as putting the vessel to a corner
of the house, it can by an invisible miracle draw all that pass in to
it; or, the vessel being put upon a tower, draws all birds within the
reach of its scent, so as to cause them to stand about it. Then will you
have, my son, our quintessence, which is otherwise called Vegetable
Mercury, at your will, to apply in Magistery of the transmutation of
metals."

How ardent an adept this Alchemist was may be gathered from his
exclamation:--"May the God of Heaven put prudence in the heart of
evangelical men, for whom I compose this book, not to communicate this
venerable secret of God to the reprobates."

Among the remarkable discoveries made by Alchemists, due to the
carefully noted and carefully examined failures and accidents, as well
as successes, of their endless combinations of matter, under the
treatment of fire and water, the most distinguished is that of
gunpowder, noted in a recipe left on record by Roger Bacon, who died in
the year 1284. He clearly names the mixture of Saltpetre with Sulphur,
but the third ingredient, Carbon, is concealed in the form of an
anagram.

Lord Bacon, Luther, Spinoza, Leibnitz, and many eminent moderns, were
impressed with a belief in the possibility of transmuting lead, tin,
copper, or other metals, into gold; in short, as it was supposed there
were only four elements, fire, water, earth, and air, it was probably
assumed that a fifth might be found in the Philosopher's stone.

But if ever any pursuit was more open to fraudulent practices than
another, surely the pretended possession of a transmuting powder or
elixir afforded a grand arena for their exercise. In this enlightened
age, although we cannot fail to look with charity on the arduous labours
of those adepts who honestly mixed devotional exercises with laborious
experimental operations, selecting times and seasons for their
alchemical work, and noting with accuracy the hours and days of fusions,
sublimations, distillations, lixiviations, and so forth; still, it is
scarcely possible to refrain from smiling at the docile simplicity of
Ashmole in denouncing a certain class of Alchemists, as pretended
masters and adepts, seeing "they are mere practisers of legerdemain,"
while he himself gave credence to the story of the warming-pan, already
named as being shown to Queen Elizabeth, which was clearly a flagrant
piece of fraud practised by Kelly, a common adventurer, and from his
youth remarkable only for his indifferent character.

An easily performed trick was effected by means of nails, or other
light articles, made half of gold and half iron, but disguised, so as to
appear to be of one metal and colour. Sometimes these knaves employed
crucibles, having an interior false bottom, below which a small quantity
of gold was placed, which, being reproduced, as was pretended from base
materials, was offered as an example of success. Or, by having the gold
in a hollow rod, stopped at one end with wax, used to stir up the
materials, the gold would naturally enough appear in the crucible. Or,
their materials being conveyed into charcoal, a similar result would be
obtained on heating the crucible in a furnace. At other times, by the
employment of amalgams, or solutions in acids, they could perform a
species of electro-plating on common metals. The extent to which these
nefarious practices were carried might appear incredible, considering
the evident inconsistency of the owner of the pretended golden key to
countless wealth, being in such comparative poverty as to be indebted to
any one of moderate means for pecuniary assistance. But, it is some
apology for such credulity when we call to mind the state of public
morals, of education, of political institutions, and the prevalent
superstition, not only among common people, but also the higher classes
of all countries and creeds, down to the seventeenth century:
representing a phase of the human mind, liable to be overawed by
impostors, who boldly claimed supernatural aid in abetting their
impositions. And the trickery of the designing was further aided by the
close secrecy adopted by the adepts in their processes, their
conversations, and their writings. Ashmole freely admits that--"Their
chief study was to wrap up their secrets in fables, and spin out their
fancies in 'vailes' and shadows, whose radii seem to extend every way,
yet so that all meet in a common centre, and point only to one thing."
It was this very secrecy, this continual mystery from beginning to end,
that favoured deceptions of the grossest and most bungling character, as
viewed by the light of modern chemistry.

Alchemy no doubt tended to improve Medical science, by the introduction
of many new mineral and vegetable preparations, but the healing art
treated after the manner of the Hermetic Art, was laid open to every
description of quackery. It is not our intention, however, to enlarge on
this department, which has steadily advanced at every stage of
improvement in chemical science.


SQUARING THE CIRCLE.

Of Mathematical Problems, the most perplexing to ancient and modern
mathematicians, although of late years said to be satisfactorily
demonstrated, and no longer desiderata of Geometry, are--

1. The Quadrature or Squaring of the Circle;--2. The Duplication, or
doubling of the Cube;--and 3. The Trisection of the Angle.

In his "Popular Astronomy,"[11] Professor Arago, treating on the surface
of a circle, observes that,--

It is mathematically equal to the product of the length of the
circumference, multiplied by half the radius. To square a circle of a
given diameter in mètres, is the same as giving the number of squares,
of a mètre in each side, of which the surface is the equivalent. If, the
diameter being given, the exact circumference were known by a sort of
inspiration, the superficial extent of the circular space would be
deducible from the two numbers, by the mere multiplication of the
numerical length of the circumference by the fourth of the diameter, or
half the radius. But, the circumference being deducible from the
diameter only by approximation, the surface alluded to cannot be
computed with mathematical rigour; yet the result can be obtained with
all desirable precision by the aid of the ratios usually given for such
purpose; for instance, the area of the space included within a circle of
thirty-eight millions of leagues radius, may be determined within such a
degree of precision that the probable error shall not exceed the space
of a mite.

[11] See Translation, by Admiral W. H. Smith, and Robert Grant, M.A., in
2 vols. 8vo. 1855, Vol. I., page 10.

"The sect of squarers then," Arago adds,--"are searching after a
solution which is proved to be impossible, and which, moreover, would be
of no practical use, even if their foolish hopes were crowned with
success."

In the "Birds" of Aristophanes, the character is introduced of a
geometer, who is going to make a square circle, showing how early this
chimerical performance became an object of ridicule.

Thales, Anaxagoras, Pythagoras, Hippocrates, Plato, Apollonius, Ptolemy,
with other ancient mathematicians, have given methods for approximating
to the area of the circle; and many also among the moderns. In 1775, the
Paris Academy of Science determined to discourage papers devoted to this
subject, and their course in this respect was soon after adopted also
by The Royal Society, it being found that there was among certain
geometers a complete mania for settling this and similar problems, the
solution of which was either unattainable, or if attained of very
questionable value.


DUPLICATION OF THE CUBE.

The Duplication of the Cube it is asserted can readily be demonstrated.
It is usually called the Delian Problem, from its having been suggested
by the oracle of Apollo at Delphos, requiring that Apollo's cubical
altar should be doubled.

It is something in its favour to say that the enquiry has had the
attention of Newton and of Huygens.


TRISECTION OF AN ANGLE.

Lastly, we shall notice among problems of this class--the Trisection of
an Angle, which it is asserted can only be accomplished by means of the
conic sections and some other curves.

A rule for the cubic equation by which the problem of trisection is
solved has been given by Cardan.

The difficulty only arises when we attempt the trisection of any other
than a right angle, its trisection being easily effected with a pair of
compasses.

On this subject it has been observed that, "there is no more trouble in
trisecting an angle, not a right angle, than in finding a cube root."

       *       *       *       *       *

These three celebrated problems have received the attention of
mathematicians in every age and country, and led to many learned
discussions, and controversial writings. But in point of litigiousness
the Squarers of the Circle most decidedly carry off the palm, having
frequently laid and lost heavy wagers, and even appeared in a Court of
Justice to settle their monetary disputes. They are renowned for their
pamphlets, in which philosophers of every class are charged with
prejudice, conceit, and ignorance, and denounced for their want of
candour and consistency in not giving audience to the projector of the
last best demonstration.


PERPETUUM MOBILE.

To conclude this Lecture we shall offer a few remarks on Perpetuum
Mobile, or the search for a means of obtaining a mechanical perpetual
motion. As a mathematical problem it dates back some 2000 years or
more, but we know nothing of any actual attempt earlier than the 14th
century to construct a machine intended to be self motive, by containing
within itself the means of continually overbalancing. External motive
agency such as the tides, magnetism, and the like are not included; the
only admitted agent being gravity.

If we considered wear and tear the question would be settled at once,
but this is allowed as the single exception, and therefore any machine
constantly renewing the means that first moved it might be deservedly
called a perpetual motion.

Until a history of the schemes invented by numerous ingenious mechanics
was published in 1861, inventors of this class were continually though
unconsciously reproducing obsolete contrivances, from taking up the
ordinary idea that a wheel may be kept constantly over-weighted on one
side, so as to raise the next weight which is to perform the same
miracle of art. It is singular to observe this particular coincidence of
the inventive faculty of man, and it shows next to a demonstration, that
if all mechanical inventions were swept from the face of the earth they
would be reproduced in some remote age.

A common error with those who toil at perpetual motion machinery is
their aiming to produce a bottled-up power; or to apply the principles
of the ordinary scale or balance to a wheel, overlooking the simple
facts of friction on one side acting against their most ingenious
contrivances, and of non-production on the other. Sooner or later,
however, they discover the inertia of matter, that a pound will not
raise a pound, and that they cannot invent mechanism to move
independently of the laws of action and reaction.

A ball descending a semicircular path, as suggested by Dr. Henderson,
will only rise to the same height as that from which it fell; and will
afterwards gradually diminish in velocity until it rests at the centre.
If it would ascend to a height greater than that from which it
descended, then indeed an inclined path might return the ball to repeat
such evolutions until quite worn out.

And as regards the weighted wheels, it is always overlooked that they
come to rest from the same fact, that the vertical line of descent and
that of ascent are equal, however much the weights may on one side
recede from the centre, while on the other side the weights are
approaching the centre. (_See_ Plate 6, Fig. 1.)

The most famous perpetual motive schemes were those of the Marquis of
Worcester made 1630-41; (_See_ Plate 6, Fig. 2,) and of Bessler, better
known as Orfyreus, between 1712-19.

The Marquis gives a brief notice of his plan, in his "Century of
Inventions," a curious catalogue of his several ingenious schemes.

But of Orfyreus's wheel we know nothing more than was communicated by
the eminent mathematician, 'S Gravesande, to Sir Isaac Newton, after an
external view of it, while it was rotating in a chamber of the residence
of the Prince of Hesse Cassel.

The most singular part of this strange delusion is the fact of its
strong hold on the minds of its infatuated votaries. Once bewitched with
the idea of at last succeeding in the attainment of his grand design,
fortune, health, and reputation, are resolutely set at nought, in the
delirium of delight that follows; and more unreasonable creatures can
scarcely be found than such self-deluded individuals, for they cannot,
or will not, be convinced that their utmost efforts can at best but
produce an amazingly curious toy; and nothing can be more futile than to
expect any higher application, assuming such a discovery were possible.

The best proof of the sincerity and earnestness of those who seek the
attainment of a mechanical perpetual motion, is afforded by the variety
and number of their patented schemes; the patentees having among them
divines, doctors, lawyers, civil engineers, carpenters, draughtsmen,
jewellers, watchmakers, shoemakers, confectioners, and all classes of
professions and trades. It is not, as is generally supposed, only the
wholly ignorant and designing who can be cajoled by these chimeras;
there is in them a spice of mystery, of wonder, of singularity, and of
simplicity combined with much subtle difficulty, which, being once fully
imbibed, acts like an opiate draught.

We have thus reviewed summarily, chimeras which are mainly associated
with Astronomy, Chemistry, Mathematics, and Mechanics, and which have
swayed the human mind more or less from a period anterior to the
Christian era. The list of this species of deceitful systems of
pseudo-philosophy, and of profitless problems, might have been enlarged;
but what has been advanced may suffice as a warning to the uninitiated
to beware of blind guides and of visionary pursuits. Science has lost
nothing by its professors exercising that degree of caution, which all
classes of superficially learned men, affecting to possess original and
valuable views on certain matters, call _prejudice_: which, in such
cases, generally means no more than the natural aversion which the
learned have for all attempts to place specious dogmas on a level with
sound science. Such enthusiasts are generally men of no research or
depth of thought, who obtain an imperfect acquaintance with subjects
with which they are incompetent to grapple; and with whom it is,
therefore, hopeless to contend. Delusion will have its day, and will as
certainly decay, if not die out. Chimeras constantly spring up, and find
ardent professors and crowds of easily led proselytes, even up to this
very present time; so that although, undoubtedly with many--_Knowledge
is power_: yet it is to be feared that far too large a proportion of
mankind favour the delusion that--_Ignorance is bliss_.


EXPLANATIONS OF THE PLATES.


PLATE I.--FIGURE 1.

_Of the Twelve Houses._--The 1st, 4th, 7th, and 10th
houses--_angular_.--These are of more durable signification than the
others, denoting the wife or husband--a situation under Government, &c.
&c.

The twelve houses have signification of all the various concerns of
human life, and of nature at large.

_For Example._--When the cusp of the first house is well aspected by, or
has the presence of Jupiter or Venus, and these are not afflicted by the
aspects of evil planets, they preserve life in infancy, and give health,
and often an agreeable person.

But if their rays or presence (says Varley) should be thrown on the cusp
of the second house, then the native will have success in concerns of
property. The Sun in this house helps to disperse property; and if he be
peregrine, that is, in the sign of a contrary nature to his own, where
he has no dignities, and is without reception, then the native's
property is dispersed in vainglorious expenses; but if the Sun be in
Leo, his property in general will be ample enough to admit of instant
acts of bounty and benevolence.

In a similar strain, Astronomers particularize the remaining eleven
houses. It would be impossible, in any reasonable space, to describe
further the operations of the planets in the several houses thus
assigned to them.

_As to when the Planets are most powerful._--Barrett says:--The planets
are powerful when they are ruling in a house, or in exaltation, or
triplicity, or term, or face, without combustion of what is direct in
the figure of the heavens; but we must take care that they are not in
the bounds or under the dominion of Saturn or Mars. The angles of the
ascendant, and 10th and 7th are fortunate; as also the lord of the
ascendant, and place of the Sun and Moon.

The Moon is powerful if she be in her house, in exaltation, in
triplicity, in face, or in degree convenient for the desired work, &c.
&c.

FIGURE 2.

VARLEY'S TABLE OF SIGNS, HOUSES, EXALTATION, AND TRIPLICITY.

The falls of the Planets are opposite to their Exaltations, and their
Detriments opposite to their Houses.

  Aries and Scorpio are the house of Mars             [Mars]

  Taurus and Libra are the house of Venus             [Venus]

  Gemini and Virgo are under the dominion of Mercury  [Mercury]

  Cancer is the house of the Moon                     [Moon]

  Leo is the house of the Sun                         [Sun]

  Sagittarius and Pisces are the houses of Jupiter    [Jupiter]

  Capricorn is the house of Saturn                    [Saturn]

  And Aquarius is governed by the Herschel Planet     [Uranus]


PLATE II.

This table gives the usual symbols employed for indicating the several
planets, and which are still retained in Astronomy for simplicity of
expression, but which Astrologers venerate as possessing a cabalistic
character.

Associated with these symbols are the names of certain principal angels,
spirits, or demons, forming, however, but a small proportion of such
airy nothings.

The Astrological Symbols were also employed by the Alchemists to
indicate the seven metals then known.


PLATE III.--SQUARING THE CIRCLE.

Mr. James Smith, of Liverpool, the most laborious among recent workers
in this field of enquiry, claiming to have propounded several simple and
exact methods, offers the following as sufficiently demonstrative:--

I construct my diagrams in the following way:--I draw two straight lines
at right angles, making O the right angle. From the point O, in the
direction OA, I mark off four equal parts together equal to OA, and from
O, in the direction of OB, I mark off three of such equal parts
together, equal to OB, and join AB. It is obvious, or rather
self-evident, that AOB is a right-angled triangle, of which the sides
that contain the right angle are in the ratio of 4 to 3, by
construction. With A as centre and AB as interval, I describe the circle
X, produce AO and BO to meet and terminate in the circumference of the
circle at the points G and C, and join AC, CG, and BG, producing the
quadrilateral ACGB. I bisect AG at F, and with O as centre, and OF as
interval, describe the circle Z. The line OF is the line that joins the
middle points of the diagonals in the quadrilateral ACGB; and it follows
that, {AG^2 + CB^2 + 4(OF^2)} = {AC^2 + CG^2 + BG^2 + AB^2.}

When AO = 4, we get the following equation:--

{5^2 + 6^2 + (4 × 1'5^2)} = {5^2 + sqrt(10^2) + sqrt(10^2) + 5^2,} or,
{25 + 36 + 9} = {25 + 10 + 10 + 25} = 70. From the points B and C, I
draw straight lines at right angles to AB and AC, and therefore
tangential to the circle X, to meet AG produced at D, and join BD and
CD, producing the quadrilateral ACDB. I bisect AD at E, and with O as
centre, and EO as interval describe the circle XY, and with E as centre,
and EA or ED as interval describe the circle Y.

Now, to square the circle, or, in other words, to get exactly equal in
superficial area to the circle X, I will show how to find it. From the
point G draw a straight line--say G _m_--perpendicular to ED, making G
_m_ equal GD. Produce GA to a point _n_, making G _n_ equal to 2AG - GD,
and join _n m_. The square on _n m_ will be the required square. (I have
indicated this square by dotted lines.) For example:--If AO = 4, then AG
= 5, and GD = 1'25; therefore {2 AG - GD} = {10 - 1'25} = 8'75 = Gn: and
Gm = 1'25; therefore, Gn^2 + Gm^2 = 3-1/8 (AB^2); that is, {8'75^2 +
1'25^2} = 3-1/8 (5^2), or, {76'5625 + 1'5625} = {3'125 × 25}; and this
equation=Area of the Circle X; and area of the square on _n m_ :: and it
follows, that the area of every circle, is equal to the area of a square
on the hypotenuse of a right-angled triangle, of which the sides that
contain the right angle are in the ratio of 7 to 1, and the sum of these
two sides equal to the diameter of the circle. In many ways I have
proved this fact, by practical or constructive geometry.


PLATE IV.

_Duplication of the Cube._--In his "Young Geometrician; or, Practical
Geometry without Compasses," 1865, Mr. Oliver Byrne's 40th Problem is as
follows:--

Let AB be the side of a given cube BD. It is required to find AC, the
side of another cube CE, so that the solid contents of the cube CE are
double the solid contents of the cube BD.

Ancient and modern mathematicians (says Mr. Byrne) have in vain
attempted to solve this problem geometrically, that is, by the ruler and
compasses only.

Let AB = BG = GR = RQ = QP = QO = OR = VZ. The length of the shortest
side of the lesser set square; a line of any other given length may be
applied. Draw OP and VR parallel to it; then apply the set squares in
close contact, the edge OV of OVT passing through the point O, while the
points of V and Z of ZSV fall exactly on the lines RV, RZ. Then draw the
line ZBC, cutting FA produced in C; then the cube on AC is double the
cube on AB.


PLATE V.

_Trisection of an Angle._--In his work entitled _Young Geometrician_,
1865, Mr. Oliver Byrne gives as the 39th Problem: To divide a given
angle BAC into three equal angles:--

The line A _m_ is made = _p q_, the least side of the lesser triangular
ruler; by (II) _p m_ is drawn parallel, and _m n_ perpendicular to AB.
Then both rulers are kept in motion, and at the same time in close
contact, as represented in the figure, until _p_ falls on the line _p
m_, and _n_ on the line _m n_; _r n_A passing through the angular point
A.

Then the angle DAB is one-third of the angle CAB. Mr. Byrne asserts that
this problem is not capable of solution by the straight line and circle.
Mathematicians have in vain attempted to solve it geometrically, that
is, by the ruler and compasses only.


PLATE VI.--FIGURE 1.

_Perpetuum Mobile._ Desaguliers demonstrated the absurdity of attempting
to raise weights enclosed in a cellular wheel, simply by providing for
their approach in succession nearer to the centre on the ascending side,
while they should be projected further from the centre on the descending
side. He remarks:--

Those who think the velocity of the weight is the line it describes,
expect that that weight shall be overpoised, which describes the
shortest line, and therefore contrive machines to cause the ascending
weight to describe a shorter line than the descending weight.

For example, in the circle A B D _a_, the weights A and B being supposed
equal, it is imagined that, if by any contrivance whatever, whilst the
weight A describes the arc A _a_, the weight B is carried in any arc, as
B _b_, so as to come nearer the centre in its rising, than if it went up
the arc B D; the said weight shall be overpoised, and consequently, by a
number of such weights, a perpetual motion produced.

Now the velocity of any weight is _not_ the line which it describes in
general, but the height that it rises up to, or falls from, with respect
to its distance from the centre of the earth. So that when the weight
describes the arc A _a_, its velocity is the line A C, which shows the
perpendicular descent, and likewise the line B C denotes the velocity of
the weight B, or the height that it rises to, when it ascends in any of
the arcs B _b_, instead of the arc B D: so that, in this case, whether
the weight B, in its ascent be brought nearer the centre or not, it
loses no velocity, which it ought to do, in order to be raised up by the
weight A.

Indeed, if the weight at B, could by any means spring as it were, or be
lifted up to _x_, and move in the arc _x b_, the end would be answered,
because then the velocity would be diminished, and become _x_C.


FIGURE 2.

In "The Life, Times, and Scientific Labours of the Marquis of
Worcester," 1865, page 454, will be found a full account of the present
diagram, which is intended to illustrate as far as possible, an approach
to the probable construction of the wheel by the Marquis in the 56th
article of his memorable "Century of Inventions."

If any likely-looking method, could, more than another, render
hopelessness more hopeless, surely this mechanical demonstration must
prove most efficient for that purpose. For here, we actually produce a
wheel agreeing to the terms with which Desaguliers closes his
demonstration, when he suggests the only likely method to effect the end
proposed, namely, perpetual motion. We find the fallen weight is
absolutely "lifted up" as he desires, and "moves in the arc" he
describes, and yet although he declares that then "the end would be
answered"--it absolutely is _not_ answered in this instance.

It is not requisite to calculate throughout the effect of the Marquis's
entire number of 40 weights; four will suffice, taking the vertical and
horizontal spokes _a a a a_, showing two rings _a_ and _b_; one, _b_, 12
inches within the other, so that the wheel being, as the Marquis says,
14 feet diameter, the inner ring will be 12 feet diameter. Now let each
weight D be attached in the centre of a cord or chain _a_´, D, b´, 2
feet long, and then secure one end, as _a_´, so the extreme end of each
spoke _a_´, and the other end of the cord, as b´, to place on one lesser
ring, as at _b_, or 12 inches from each spoke.

We shall then find by admeasurement that the upper weight on the
vertical spoke is 7 feet from the centre, and the lower weight 6 feet;
while at the same time there appears to be a preponderance due to the
superior length of the horizontal arm A´; but against this latter we
have the rising weight _b_´D, 1 foot from the centre, which, added to
the 6 feet on the horizontal spoke, neutralizes the hoped-for effect,
and the wheel remains in _statu quo_.


THE END.

       *       *       *       *       *

[Illustration: Plate 1.

LONDON. E. & F. N. SPON. 48, CHARING CROSS.]

       *       *       *       *       *

[Illustration: Plate 2.

LONDON. E. & F. N. SPON. 48, CHARING CROSS.]

       *       *       *       *       *

[Illustration: Plate 3.

LONDON. E. & F. N. SPON. 48, CHARING CROSS.]

       *       *       *       *       *

[Illustration: Plate 4.

LONDON. E. & F. N. SPON. 48, CHARING CROSS.]

       *       *       *       *       *

[Illustration: Plate 5.

LONDON. E. & F. N. SPON. 48, CHARING CROSS.]

       *       *       *       *       *

[Illustration: Plate 6.

LONDON. E. & F. N. SPON. 48, CHARING CROSS.]

       *       *       *       *       *


OTHER WORKS BY THE SAME AUTHOR.

One Volume 8vo., of 650 pages, illustrated with Steel Engravings of two
    unpublished Portraits and 45 Wood Engravings, price 24_s_,

              THE LIFE, TIMES, AND SCIENTIFIC LABOURS OF
                           EDWARD SOMERSET,
                        SIXTH EARL AND SECOND
                        MARQUIS OF WORCESTER,

                          To which is added,

            A REPRINT OF HIS CENTURY OF INVENTIONS (1663),
                      WITH A COMMENTARY THEREON.

[Asterism] Thirty copies are printed on Large Paper, 1 vol. 4to. with
INDIA PROOFS before the Letters of the Portraits, price £3. 3_s_.

"A monument raised late, it is true, but not too late, to a great and
modest genius. A national biography which illustrates and elevates our
ideas of the past, and a contribution which the world will recognize to
the European history of Science."

                          _Dublin University Magazine_, September, 1865.

"A work which displays a high order of literary ability, careful
antiquarian research, much ingenuity, and withal thorough honesty of
purpose.

"[Lord Worcester], his life, told as Mr. Dircks has told it, is one of
much interest.

"Here we have an elaborate--although of course not a completely
exhaustive--account of his life; at any rate the most complete account
of him ever likely to be written--a work filled with abundant evidence
of the most painstaking research, a work written in a generous and
sympathising spirit, and with every attribute of conscientiousness."

                                       _Engineering_, 5th January, 1866.

"The production of this volume is no common achievement; Mr. Dircks has
undertaken to write the life of a man about whom the public know very
little.

"He has, we think, collected some curious information, and established
the claim of the Marquis to be the first constructor of a steam-engine.
The reprint of the celebrated _Century of Inventions_ adds greatly to
the interest of the volume."--_The Spectator_, 14th September, 1867.

       *       *       *       *       *

        One Volume, 8vo., price 21_s_, only 100 copies printed,

                             WORCESTERIANA;

                            A COLLECTION OF

        BIOGRAPHICAL AND OTHER NOTICES, ALPHABETICALLY ARRANGED,
                  RELATING TO EDWARD SOMERSET, SECOND

                         MARQUIS OF WORCESTER,

      AND HIS IMMEDIATE FAMILY CONNECTIONS; WITH OCCASIONAL NOTES.

"The present volume is, as it were, a supplement. [To. Mr. Dircks's
_Life of the Marquis of Worcester_.] It contains what the French call
'pièces justificatives,' on which that biography was founded; and such
other materials connected with the history of Lord Worcester's family
and his invention of the steam-engine as will prevent, as far as
possible, a repetition of the gross errors hitherto promulgated on these
subjects."

                                  _Notes and Queries_, February 3, 1866.

       *       *       *       *       *

   One Volume, post 8vo., with 130 wood engravings, price 10_s_ 6_d_,

                           PERPETUUM MOBILE;

                                  OR,

              HISTORY OF THE SEARCH FOR SELF-MOTIVE POWER
               DURING THE 17TH, 18TH, AND 19TH CENTURIES,

                      WITH AN INTRODUCTORY ESSAY.

"The literature of this subject [Perpetual Motion] is very extensive,
but scattered mainly through Patent Records and ephemeral pamphlets. We
would especially refer the curious reader to a recent work by Mr.
Dircks, entitled _Perpetuum Mobile_, to which we have been indebted for
historical notices. It is extremely complete and interesting as a
history."

                               _Chambers's Encyclopædia_, Part 15, 1865.

"A very useful collection on the history of the attempts at perpetual
motion, that is, of obtaining the consequences of power without any
power to produce them."--_Professor De Morgan's_ Budget of Paradoxes,
No. 28.--_Athenæum_, July 15, 1865.

       *       *       *       *       *

         One Volume, post 8vo., with portrait, price 3_s_ 6_d_,

                   CONTRIBUTION TOWARDS A HISTORY OF
                          ELECTRO-METALLURGY,
                  ESTABLISHING THE ORIGIN OF THE ART.

"In his Introduction, Mr. Dircks has clearly stated the claims of
invention, and fairly discussed the only just grounds that can give
claim to priority of invention."--_The Mining Journal_, February 7,
1863.

"In the collection of chronological and other data for the history of
various branches and application of science, Mr. Dircks appears to be
indefatigable."--_The Electrician_, February 27.

"It is a useful and clear digest of evidence, and apparently impartially
put together."--_The Practical Mechanics' Journal_ (_Glasgow_), July.

       *       *       *       *       *

         One Volume, post 8vo., with two portraits, price 4_s_,

                       INVENTORS AND INVENTIONS,

                            IN THREE PARTS.

  I. THE PHILOSOPHY OF INVENTION, considered strictly in relation to
    Ingenious Contrivances tending to facilitate Scientific Operations,
    to extend Manufacturing Skill, or to originate New Sources of
    Industry.--II. THE RIGHTS AND WRONGS OF INVENTORS, Legally and
    Politically Examined.--III. EARLY INVENTORS' INVENTORIES OF SECRET
    INVENTIONS, employed from the 13th to the 17th Century, in
    substitution of Letters Patent.

"The author enters fully and effectually into the claims and grievances
of the inventor. He discusses the arguments for and against the concession
of patent right, and examines very ably leaders in the _Times_ on patent
monopoly; very clearly dissipating the sophism of the opponents of patent
right; also Sir William Armstrong's evidence regarding 'patent monopoly,'
&c., affording an interesting and useful publication from its many
excellences."--_The Scientific Review_, September 2, 1867.

"The second part of the volume discusses the right of inventors to a
property in their inventions, and thus raises the question of the patent
laws, and the twofold issue, whether it will be better to retain them
and reform them, or to sweep them away altogether. We are bound to admit
that he treats this topic in a fair spirit, and without any taint of
bigotry. Mr. Dircks is a man whose opinions are entitled to a hearing."

                                       _The London Review_, September 21.

"Mr. Dircks treats the real problem and discusses the comparative merits
of the existing system, and the advantages which he, together with many
others, hopes would follow on the establishment of some judicial council
of inventions. The difficulties of the question are enormous, and no one
will think the less of them after having gone through this volume.

"The third part, or the lists of their inventions left by many great and
some ingenious persons, is interesting and curious."

                                      _The Westminster Review_, October.

       *       *       *       *       *

                One Volume, post 8vo., price 3_s_ 6_d_,

                        A BIOGRAPHICAL MEMOIR OF
                            SAMUEL HARTLIB,
                       MILTON'S FAMILIAR FRIEND,

 With Bibliographical Notices of Works published by him; and a reprint
                        of his Pamphlet entitled

                  "AN INVENTION OF ENGINES OF MOTION."

"Mr. Dircks's is the first careful attempt to make posterity his
(Hartlib's) friend."--_The Examiner_, 18th February, 1865.

"A scholar-like little monograph, giving all the information that can be
given about a man whose name occurs in the correspondence of almost
every eminent literary or scientific person of the time of the
Commonwealth."--_The Spectator_, 20th May.

       *       *       *       *       *

          One Volume, post 8vo., with engravings, price 2_s_,

                               THE GHOST!

                   AS PRODUCED IN THE SPECTRE DRAMA,

        POPULARLY ILLUSTRATING THE MARVELLOUS OPTICAL ILLUSIONS
             OBTAINED BY THE APPARATUS CALLED THE DIRCKSIAN
                            PHANTASMAGORIA.

"Mr. Dircks gives us the benefit of all his progressive discoveries in
the matter, from the paper first read at the British Association Meeting
at Leeds, in 1858, to the more recent improvements, with full
explanations of the machinery, apparatus, and processes adopted in these
ghost dramas, and further favours the public with a number of new
adaptations. As a curious description of these spectral illustrations,
the book is most interesting."--_The Technologist_, January, 1864.

"A volume explanatory of the uncommonly clever and scientific "spectral
illusion" which has of late fairly turned the public head."

                                        _The Dublin Builder_, January 1.

"A few months ago all London was rushing off to see Professor Pepper's
Ghost, as it was called, but which it now appears was the property of
Mr. Dircks, and from which his good name was filched in a very
unhandsome manner. Here then he tells us all about it, how the spectre
was raised, and how we may ourselves at pleasure call spirits from the
vasty deep."--_The Bookseller_, February 29.

       *       *       *       *       *


Transcriber's Notes

Page 36: changed "Sorbiere" to "Sorbière" (15. Samuel Sorbière visited
the works at Vauxhall)

Page 61: changed "Jupiper" to "Jupiter" (of cloves, &c. to Jupiter;)

Page 83: changed "BD^2" to "BG^2" ({AG^2 + CB^2 + 4(OF^2)} = {AC^2 +
CG^2 + BG^2 + AB^2.})

Page 83: changed "sqrt(10^2 5^2)" to "sqrt(10^2) + 5^2" ( ... = {5^2 +
sqrt(10^2) + sqrt(10^2) + 5^2,})

Page 84: changed closing parenthesis to closing braces ( ... 9} = {25 +
10 + 10 + 25} = 70)

Page 84: changed "tangental" to "tangential" (tangential to the circle
X)

Page 84: changed "Q" to "2" (making G _n_ equal to 2AG - GD)

Page 84: added missing opening parenthesis in "(I have indicated this
square by dotted lines.)"

Page 84: changed "+ 1'25}" to "× 25" ({76'5625 + 1'5625} = {3'125 × 25})

Page 84: changed "hypothenuse" to "hypotenuse" (the area of a square on
the hypotenuse)





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