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TO THE THIRD EDITION OF THE

ENCYCLOPÆDIA BRITANNICA,

OR, A

DICTIONARY

OF

ARTS, SCIENCES, U

AND

MISCELLANEOUS LITERATURE.

IN TWO VOLUMES.

Illustrated with Fifty Copperplates.

BY GEORGE GLEIG, LL. D. F. R. S. EDIN.

NON IGNORO, QUÆ BONA SINT, FIERI MELIORA POSSE DOCTRINA, ET QUÆ NON OPTIMA,
ALIQUO MODO ACUI TAMEN, ET CORRIGI POSSE. CICERO.

VOL. II.

Edinburgh:

PRINTED FOR THOMSON BONAR, PARLIAMENT-SQUARE;

BY JOHN BROWN, ANCHOR CLOSE, EDINBURGH.

1801.

[Entered in Stationers Hall.]

IT would ill become me to dismiss thefe Volumes from my hands without acknowledging that, from many of the most valuable difquifitions which they contain, I can claim no other merit than that of having ufhered them into the world.

THOSE who have read, and who understand, the articles in the Encyclopædia Britannica, which were furnished by Profeffor Robifon of Edinburgh, can hardly need to be informed, that to the fame eminent philofopher I am indebted for the valuable articles ARCH, ASTRONOMY, CARPENTRY, CENTRE, DYNAMICS, ELECTRICITY, IMPULSION, INVOLUTION and EVOLUTION of Curves, MACHINERY, MAGNETISM, MECHANICS, PERCUSSION, PIANO-Forte, Centre of POSITION, TEMPERAMENT in Mufic, THUNDER, Mufical TRUMPET, TSCHIRNHAUS, and WATCHWORK, in this Supplement. Of a friend and co-adjutor, whofe reputation is fo well established as Dr Robifon's, I am proud to say, that, while I looked up to him, during the progress of this Work, as to my master in mathematical and phyfical science, I found him ever ready to fupport,. with all his abilities, thofe great principles of religion, morality, and focial order, which. I felt it my own duty to maintain.

To Thomas Thomfon, M. D. of Edinburgh, a man of like principles, I am indebted for the beautiful articles CHEMISTRY, MINERALOGY, and Vegetable, Animal, and Dyeing SUBSTANCES; of which it is needlefs for me to fay any thing, fince the Public feems to be fully fatisfied that they prove their author eminently qualified to teach the science of chemistry.

THE account of the French REVOLUTION, and of the wars which it has occafioned,. has been continued in this Supplement by the fame Gentlemen by whom that account. was begun in the Encyclopædia; and, owing to the cause affigned in the article, probably with the fame merits and the fame defects..

My thanks are due to Dr William Wright for his continued kindness in communicating much curious botanical information and to Mr Profeffor Play fair of the uni-verfity of Edinburgh, for lending his affiftance, occafionally, in the mathematical department; and for writing one beautiful article in that fcience, which is noticed as his in the order of the alphabet.

IN compiling this Supplement, I have made very liberal ufe of the most refpectableliterary and scientific journals, both foreign and domeftic; of all the late accounts of travels and voyages of discovery, which have obtained, or feem indeed to deserve, the regard of the Public; of different and oppofite works on the French revolution, and what are emphatically called French principles; and even of the most approved Dictionaries, scientific and biographical. From no Dictionary, however, have I taken, without acknowledgment, any articles, except fuch as are floating everywhere on the furface of science, and are the property, therefore, of no living author.

AFTER all my labour and induftry, which, whatever be thought of my other merits, I am confcious have been great, no man can be more fenfible than myself, that the Encyclopædia Britannica, even with the addition of this Supplement, is ftill imperfect.. It would continue to be fo, were another Supplement added to this by the moft learned and laborious man on earth; for perfection feems to be incompatible with the nature. of works conftructed on fuch a plan, and embracing fuch a variety of fubjects.

No.

No candid reader will fuppofe that, by expreffing myself thus, I mean to cenfure the plan of the Encyclopædia Britannica in particular; for, to the general excellence of that plan I have elsewhere borne my teftimony, which I have yet feen no reason to retract. Experience has indeed led me to think, that it is fufceptible of fuch improvements as would enable the principal Editor to carry the work nearer to perfection, even with lefs trouble to himself; but the purchasers of the third edition and this Supplement need not regret the want of thofe improvements, for they are fuch as few would difcern, who have not paid the fame attention that I have done to dictionaries of arts, fciences, and literature.

BEFORE I take leave of the reader, I muft account for the omiffion of one or two articles (chiefly biographical) which I had given him reafon to expect in thefe volumes. It was my intention at firft to introduce into the Supplement articles on every fubject which had been admitted into the Encyclopædia itself; and hence in the firft fupplementary volume will be found biographical sketches of men whofe characters, though in fome refpects remarkable, have very little connection with science, arts, or literature. From this part of the original plan I was foon obliged to deviate. So many applications were made to me to infert accounts of perfons who, whatever may have been their private virtues, were never heard of in the republic of letters, that I was under the neceffity of excluding from the fecond volume the lives of all fuch as had not either been themfelves eminent in literature, or in fome liberal art or science, or been confpicuous as the patrons of science, arts, and literature, in others. Hence the omiflion of the life referred to from AUBIGNE in the first volume, and of one or two others to which references are made in the fame way. The life of Mr James Hay Beattie of Aberdeen, whofe originality of genius, ardent love of virtue, and early and extenfive attainments in fcience and literature, raise him almost to the eminence of BARRETIER, of whom we have fo pathetic an account from the pen of Johnfon, I omitted with regret; but I thought not myself authorized to publish what his father had then only diftributed among a few particular friends. For the omission of the life of Soame Jenyns I can make no apology: it was the confequence of forgetfulnefs.

For the errors of these two volumes, whether typographical or of a nature more important, I have perhaps no occafion to folicit greater indulgence than will be voluntarily extended to me by a generous public. The progrefs, however, of science, and of the revolutionary events in Europe, has been fuch, fince great part of them was printed, that I must request the reader, in justice to myself, to proceed directly from the article GALVANISM to TORPEDO, and from REVOLUTION to the life of Marshal SUWOROW.

UNDER the title TRANSLATION, both in the Encyclopædia and in the Supplement, expreffions are made ufe of, which may lead the reader to fuppofe that Mr Fraser Tytler was indebted for the general laws of the art, which he fo ably illuftrates, to Dr Campbell's Preliminary Differtations to his Tranflation of the Gofpels. It is but juftice to declare my perfect conviction, as it was that of Dr Campbell himself, that Mr Tytler and he were equally intitled to the merit of having difcovered those laws; and that however coincident in opinion, neither of them, when compofing their separate works, had the smallest fufpicion that the other had ever employed his thoughts on the fubject. The only difference feems to have been in the mode of their discovery: Mr Tytler having deduced the laws of the art by regular analytical inference from his own defcription of a perfect tranflation; whereas Dr Campbell appears to have fortunately discovered them without that procefs of deduction.

SUPPLE

TO THE

ENCYCLOPÆDIA BRITANNICA.

Increment, Indeterminate.

I

IND NCREMENT, is the fmall increase of a variable quantity. Newton, in his Treatife on Fluxions, calls thefe by the name Moments; and obferves, that they are proportional to the velocity or rate of increase of the flowing or variable quantities in an indefinitely fmall time. He denotes them by fubjoining a cypher o to the flowing quantity whofe moment or increment it is; thus, xo the moment of x. In the doctrine of Increments, by Dr Brooke Taylor and Mr Emerson, they are denoted by points below the variable quantities; as x. Some have alfo denoted them by accents underneath the letter, as x ; but it is now more ufual to express them by accents over the fame letter; as x. METHOD OF INCREMENTS, a branch of Analytics, in which a calculus is founded on the properties of the fucceffive values of variable quantities, and their differences or increments.

The inventor of the method of increments was the learned Dr Taylor, who, in the year 1715, publifhed a treatise upon it; and afterwards gave fome farther account and explication of it in the Philof. Tranf. as applied to the finding of the fums of feries. And another ingenious and eafy treatise on the fame, was published by Mr Emerfon, in the year 1763. The method is nearly allied to Newton's Doctrine of Fluxions, and arifes out of it. Allo the Differential method of Mr Stirling, which he applies to the fummation and interpolation of ferice, is of the fame nature as the method of increments, but not so general and extensive.

INDETERMINATE PROBLEM. See ALGEBRA, Part I Chap. VI. Encycl.

Diophantus was the first writer on indeterminate problems, which, after the publication of his work in 1621 by Bachet, employed much of the time of the most celebrated mathematicians in Europe. Af. terwards fuch problems were neglected as ufclefs, till the public attention was again drawn to them by Euler and la Grange. The example of fuch men was followed by Mr John Leflie, a very eminent and felf. taught mathematician; who, in the fecond vol. of the Tranfactions of the Royal Society of Edinburgh, has published an ingenious paper on indeterminate problems, refolving them by a new and general principle. "The doctrine of indeterminate equations (fays Mr Leflie) has been seldom treated in a form equally fyftematic SUPPL. VOL. II. Part I.

IND

Induction.

with the other parts of algebra. The folutions common- Indetermily given are devoid of uniformity, and often require a va- nate, riety of affumptions. The object of this paper is to refolve the complicated expreffions which we obtain in the folution of indeterminate problems, into fimple equations, and to do fo, without framing a number of affumptions, by help of a fingle principle, which, though extremely fimple, admits of a very extensive applica tion.

m

"Let A X B be any compound quantity equal to another, CX D, and let m be any rational number affumed at pleasure; it is manifeft that, taking equimultiples, Axm B=Cxm D. If, therefore, we fuppofe that AmD, it must follow that mBC, or C B= Thus two equations of a lower dimenfion are obtained. If these be capable of farther decompo fition, we may affume the multiples n and p, and form four equations ftill more fimple. By the repeated application of this principle, an higher equation, admitting of divifors, will be refolved into thofe of the first order, the number of which will be one greater than that of the multiples affumed."

viz. to find two rational numbers, the difference of the For example, refuming the problem at firft given, fquares of which fhall be a given number. Let the given number be the product of a and b; then by hypothefis, x-ab; but thefe compound quantities. admit of an ealy refolution, for x + y xx-y= axb. If, therefore, we fuppofe x + y = ma, we fhall obtain xy= ; where m is arbitrary, and if rational, x and y muft alfo be rational. Hence the refolution of these two equations gives the values of x and y, the numbers fought, in terms of m; viz. m2a + b

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b

-m

and y =

m2a b

-

2 m

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