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TO THE THIRD EDITION OF THE

ENCYCLOPÆDIA BRITANNICA,

OR, A

D I C T I 0 N A R Y

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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.]

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

Those who have read, and who understand, the articles in the Encyclopædia Britannica, which were furnished by Protessor Robison of Edinburgh, can hardly need to be informed, that to the same eminent philosopher 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, TEMPÉRAMENT in Music, Thunder, Musical TRUMPET, TscHIRNHAUS, and WATCHWORK, in this Supplement. Of a friend and co-adjutor, whose reputation is so 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 physical science, I found him ever ready to support, with all his abilities, those great principles of religion, morality, and social order, which. I felt it my own duty to maintain.

To Thomas Thomson, 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 needless for me to say any thing, since the Public seems to be fully satisfied 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 alligned 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 communi. cating much curious botanical information : and to Mr Professor Playfair of the uni. versity of Edinburgh, for lending his assistance, occasionally, in the mathematical department; and for writing one beautiful article in that science, which is noticed as his in the order of the alphabet.

'In compiling this Supplement, I have made very liberal use of the most respectable literary and scientific journals, both foreign and domestic ; of all the late accounts of travels and voyages of discovery, which have obtained, or seem indeed to deserve, the regard of the Public; of different and opposite works on the French revolution, and what are emphatically called French principles; and even of the most approved Dic. tionaries, scientific and biographical. From no Dictionary, however, have I taken, without acknowledgment, any articles, except such as are floating everywhere on the furface of science, and are the property, therefore, of no living author.

AFTER all my labour and industry, which, whatever be thought of my other merits, I am conscious have been great, no man can be more sensible than myself, that the Encyclopædia Britannica, even with the addition of this Supplement, is still imperfect.. It would continue to be fo, were another Supplement added to this by the most learned and laborious man on earth; for perfection leems to be incompatible with the naturo. of works constructed on such a plan,, and embracing such a variety of subjects.

No

No candid reader will suppose that, by expressing 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 testimony, which I have yet seen no reason to retract. Experience has indeed led me to think, that it is susceptible of such improvements as would enable the principal Editor to carry the work nearer to perfection, even with less trouble to himself; but the purchasers of the third edition and this Supplement need not regret the want of those improvements, for they are such as few would discern, who have not paid the same attention that I have done to dictionaries of arts, fciences, and literature.

BEFORE I take leave of the reader, I must account for the omission of one or two articles (chiefly biographical) which I had given him reason to expect in these velumes. It was my intention at first to introduce into the Supplement articles on every subject which had been admitted into the Encyclopædia itself; and hence in the first supplementary volume will be found biographical sketches of men whose characters, though in some respects remarkable, have very little connection with science, arts, or literature. From this part of the original plan I was soon obliged to deviate. So many applications were made to me to insert accounts of persons who, whatever may have been their private virtues, were never heard of in the republic of letters, that I was under the necessity of excluding from the second volume the lives of all such as had not either been themselves eminent in literature, or in some liberal art or science, or been conspicuous as the patrons of science, arts, and literature, in others. Hence the omission of the life referred to from AUBIGNE in the first volume, and of one or two others to which references are made in the same way. The life of Mr James Hay Beattie of Aberdeen, whose originality of genius, ardent love of virtue, and early and extensive attainments in science and literature, raise him almost to the eminence of BARRETIER, of whom we have so pathetic an account from the pen of Johnion, I omitted with regret; but I thought not myself authorized to publish what his father had then only distributed among a few particular friends. For the omislion of the life of Soame Jenyns I can make no apology: it was the consequence of forgetfulnefs.

For the errors of these two volumes, whether typographical or of a nature more important, I have perhaps no occasion to solicit greater indulgence than will be voluntarily extended to me by a generous public. The progress, however, of science, and of the revolutionary events in Europe, has been luch, 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, expressions are made use of, which may lead the reader to suppose that Mr Fraser Tytler was indebted for the general laws of the art, which he so ably illustrates, to Dr Campbell's Preliminary Differtations to his Translation of the Gospels. It is but justice 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 discovered those laws; and that however coincident in opinion, neither of them, when composing their separate works, had the smallest suspicion that the other had ever.employed his thoughts on the fubject. The only difference seems 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 description of a perfect translation; whereas Dr Campbell appears to have fortunately discovered them without that process of deduction.

SUPPLE

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m

I N D

I N D Increment, NCREMENT, is the small increase of a variable with the other parts of algebra. The solutions common- IndetermiIndetermin

quantity. Newton, in his Treatise on Fluxions, ly given are devoid of uniformity, and often require a vacalls these by the name Moments ; and observes, that riety of assumptions. The object of this paper is to

Induction. they are proportional to the velocity or rate of increase resolve the complicated expressions which we obtain in of the flowing or variable quantities in an indefinitely the solution of indeterminate problems, into furple small time. He denotes them by subjoining a cypher o equations, and to do so, without framing a number of to the Aowing quantity whose moment or increment it assumptions, by help of a single principle, which, though is ; thus, xo the moment of x. In the do&trine of In- extremely fimple, admits of a very extensive applicacrements, by Dr Brooke Taylor and Mr Emerson, tion. they are denoted by points below the variable quanti

“Let A x B be any compound quantity equal to ties; as r. Some have also denoted them by accents another, CX D, and let m be any rational number af underneath the letter, as x ; but it is now more usual sumed at pleasure ; it is manifeft that, taking equimul.

tiples, A X m B =C Xm D. If, therefore, we sup-
to express them by accents over the same letter ; as x.

METHOD OF INCREMENTS, a branch of Analy. pose that A = mD, it must follow that mB =c, or
tics, in which a calculus is founded on the properties of B= Thus two equations of a lower dimension
the successive values of variable quantities, and their

are obtained. If these be capable of farther decompo-
differences or increments.

The inventor of the method of increments was the fition, we may assume the multiples n and p, and form
learned Dr Taylor, who, in the year 1715, published four equations fill more fimple. By the repeated ap-
a treatise upon it; and afterwards gave some farther plication of this principle, an higher equation, admitting

of divisors, will be resolved into those of the firit order,
account and explication of it in the Philos. Trans. as
applied to the finding of the sums of series. And another the number of which will be one greater than that of
ingenious and easy treatise on the same was published the multiples affumed.”

For example, refuming the problem at first given,
by Mr Emerson, in the year 1763. The method is

viz. to find iwo rational numbers, the difference of the
nearly allied to Newton's Doctrine of Fluxions, and
arises out of it. Also the Differential method of Mr squares of which shall be a given number. Let the
Stirling, which he applies to the tummation and inter giver number be the product of a and b; then by hy.
polation of ferice, is of the fame nature as the method pothefis, *'—- 32 = ab; but these compound quantities
of increments, but not so general and extensive.

admit of an ealy resolution, for x + y x x -
INDETERMINATE PROBLEM. See Algebra, axb. If, therefore, we suppose x + y = ma, we
Part I Chap. VI. Encycl.

b

shall obtain a
Diophantus was the first writer on indeterminate

; where m is arbitrary, and if
problems, which, after the publication of his work in rational, x and y must also be rational. Hence the
1621 by Bachet, employed much of the time of resolution of these two equations gives the values of x
the most celebrated mathematicians in Europe. Af. and y, the numbers fought, in terms of m; viz.
terwards such problems were neglected as useless, m'a + 6
till the public attention was again drawn to them by
Euler and la Grange. The example of such men was INDUCTION, in logic, is that process of the une
followed by Mr John Leslie, a very eminent and self. derstanding by which from a number of particular truths
taught mathematician; who, in the fecond vol. of the perceived by simple apprehension, and diligently compa-
Transactions of the Royal Society of Edinburgh, has red together, we infer another truth which is always
published an ingenious paper on indeterminate problems, general and sometimes universal. It is perhaps needless
resolving them by, a new and general principle. “ The to observe, that in the process of induction the truths
doctrine of indeterminate equations (says Mr Leslie) to be compared must be of the same kind, or relate to
has been seldom treated in a form equally systematic objects having a fimilar nature ; for the merest tyro in
Suppl. Vol. II. Part I.

A

science

m

ma

b

and y =

2m

2m

.

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