Encyclopaedia Britannica [S1, 3 ed.]

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S U P P h E M .E N T TO THE THIRD EDITION OF THE

OR, A

DICTIONARY O F

AKTS, SCIENCES, AND

MISCELLANEOUS LITERATURE. IN TWO VOLUMES.

Illustrated with Fifty Copperplates.

BY

GEORGE GLEIG, LL. O. F.R.S.

EDIN!

NON IGNORO, QUjE BONA SINT, FIERI MELIORA POSSE DOCTRINA, ET QU^: NON OPTIMA) ALIQUO MODO ACUI TAMEN, ET CORRIGI POSSE.

ClCERO.

VOL. I.

OBDinlmrgft: PRINTED FOR THOMSON BONAR, PARLIAMENT-SQUARE} BY JOHN BROIVNy ANCHOR CLOSE, EDINBURGH.

ib'oi.

f «EntPir«i in Stationer* fi)aii,j

TO THE KIJVG. SIR, IT proceeds from no vain confidence in my own abilities, that I presume to solicit for this WORK the Protection of a MONARCH, who is not more exalted in station, than he is distinguished, among the Potentates of the Earth, by his 'Taste in Literature, and his: Patronage of Science and the Arts, «

IN

conducting to its conclusion the

BRITANNIC A,

ENCYCLOPAEDIA

I am conscious only of having been uni-

formly influenced by a sincere desire to do Justice to those Principles of Religion, Morality, and Social Order, of which the Maintenance constitutes the Glory of Tour MAJESTY’S

Reign, and will, I trust, record Tour Name

to the latest Posterity, as the Guardian of the Laws and Liberties of Europe.

iv

DEDICATION.

‘THE

French Encyclopedie has been accused, and

justly accused, of having disseminated, jar and wide, the seeds of Anarchy and Atheism. If the ENCYCLOPJEDIA BRITANNLC A shall, in any degree, counteract the tendency of that pestiferous TFork, even these two Volumes will not be wholly unworthy of Your MAJESTY’S Patronage; and the Approbation of my SOVEREIGN, t

added to the consciousness of my own upright intentions, will, to me, be an ample reward for the many years of labour which I have employed on them, and on the Volumes to which they are Supplementary.

I am,

SIR, YOUR MAJESTY’S

Most faithful Subject, And most devoted Servant, STIRLING,

Dec.

~l

io. 1800.3

GEORGE GLEIG.

ADVERTISEMENT would ill become me to difmifs tbefe Volumes from my hands without acknowledging that, from many of the mofl: valuable difquifitions which they contain, I cart claim no other merit than that of having ulhered them into the world. IT

THOSE who have read, and who underftand, the articles in the Encyclopaedia Britannica, which were furnilhed by ProfefTor Robifon of Edinburgh, can liardly need to be informed, that to the fame eminent pbilofbpher I am indebted for the valuable articles ARCH, ASTRONOMY, CARPENTRY, CENTRE, DYNAMICS, ELECTRICITY, IMPUL-

SION, INVOLUTION and EVOLUTION of Curves, MACHINERY, MAGNETISM, MECHANICS, PERCUSSION, PI A NO--Forte, Centre of POSITION, TEMPERAMENT in Mufc, THUNDER, TRUMPET, TSCHIRNHAUS, and WATCHWORK, in this Supplement, Of a friend and co-adjutor, whofe reputation is fo well eftablifhed as Dr Robifon’s, I am proud to fay, that, while 1 looked up to him, during the progrefs of this Work, as to my mafter in mathematical and phylical fcience, 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 needlels for me to fay any thing, lince the Public feems to be fully fatisfied that they prove their author eminently qualified to teach the fcience of chemiftry.

THE account of the French REVOLUTION, and of the wTars which it has occafioned,, has been continued in this Supplement by the fame Gentlemen by whom that account was begun in the Encyclopaedia ; and, owing to the caufe affigned in the article, probably with the fame merits and the fame defects* MY thanks are due to Dr William Wright for his continued kindnefs in communicating much curious botanical information : and to Mr Profeffor Playfair of the univerfity of Edinburgh, for lending his affiftance, occafionally, in the mathematical de-partment; and for writing one beautiful article in that faience, which is noticed as his in the order of the alphabet.

IN compiling this Supplement, I have made very liberal ufe of the mofl refpedtable literary and fcientific journals, both foreign and domeftic ; of all the late accounts of travels and voyages of difcovery, which have obtained, or feem indeed to deferve, 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 mofl approved Dictionaries, fcientific and biographical. From no Dictionary, however, have I taken, without acknowledgment, any articles, except fuch as are floating everywhere on the furface of fcience, and are the property, therefore, of no living author.

AFTER all my labour and induflry, wdiich, whatever be thought of my other merits,. I am confcious have been great, no man can be more fepfible than my fell, that the Encyclopaedia Britannica, even with the addition of this Supplement, is hill i in per fe Chit would continue to be fo, were another Supplement added to this by the mofl learned and laborious man on earth; for perfection eems to be incompatible with the nature: of works conftruCted on fuch a plan, and embracing fuch a variety of fubjeCls.

ADVERTISEMENT. VI

No candid reader will fuppofe .that, by exprcffing myfelf thus I mean to ^nftre the plan of the Encyclopedia Bn.anuca^ no realon to of that plan I have elfewhere home in. . 'V' . j fuiceptiole of fuch iniproveretraa. Experience has indeed “^trry JheVoik Llcr to perfedion, even whriear: rr:ul1ef tr^mfel^t^ve purcha^^^

sz&ss&s t£SSSSr& 'J.» «—» i'ciences, and literature. Hi FORE I take leave of the reader, I muft account for the

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fi7ft Cp^mentaryVlfm^wilfb^f^nd’^ (kvrchesof men whole characters Zugh in fome refpeas remarkable, have very little connedion w.tti fcence, 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 accountsot perfons who whatever may have been their private virtues, were never heard of in the republic of letteis, that I was under the neceffity of excluding from the fecond volume the lives of n// Inch as had not either been themfelves eminent m literature, or in lome liberal ait 01 fcience, or been confpicuous as the patrons of fcience, arts, and literature, in others. Hence the omiffion of the life referred to from AUBIGNE in the firft volume, and of one or two others to which references are made in the iame way. I he lite ot Mr Tames Hay Beattie of Aberdeen, whofe originality of genius, ardent love or virtue, and early and extenfive attainments in fcience and literature, raiie him aim oil to the eminence of BARRET IER, of whom we have fo pathetic an account from the pen of Jobnibn I omitted with regret •, but 1 thought not myfelf authorized to publifli what his^ father had then only diftributed among a few particular friends. For the omiflion of the life of Soame Jenyns 1 can make no apology : it was the confequence of toigetiulnefs. FOR the errors of thefe 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 progreis* however, of fcience, and of the revolutionary events in Europe, has been fuch, lince great part of them was printed, that I muft requeft the reader, in juftice to myfelf, to proceed diretfly from the article GALVANISM to TORPEDO, and from REVOLUTION to the life of Marfhal SUWOROW. UNDER the title TRANSLATION, both in the Encyclopaedia and in the Supplement, expreffions are made ufe of, which may lead the reader to fuppofe that Mr Frafer Tytler was indebted for the general laws of the art, which he fo ably illuftrates, to Dr CampbelPs Preliminary DifTertations to his Tranflation of the Gofpels. It is but juftice to declare my perfect convi&ion, as it was that of Dr Campbell himfelf, that Mr Fytler and he were equally infilled to the merit of having difcovered thofe laws; and that however coincident in opinion, neither of them, when compofing their feparate works, had the fmaileft fufpicion that the other had ever employed his thoughts on the fubject. The only difference feems to have been in the mode of their difcovery : Mr Tytier having deduced the laws of the art by regular analytical inference from his own defcription of a perfed tranflation ; whereas D Campbell appears to have fortunately difcovered them without that proceis of dedudion.

SUPPLE-

SUPPLEMENT TO THE

ENCYCLOPAEDIA BRITANNICA.

ABE IlcUS

I . 1

1.

A BACISCUS, in architefture, the fame with AJ~\ BACUS ; for which, fee Encyclopedia. ABATIS, or ABATTIS, is, in military language, the name of a kind of retrenchment made of felled trees. When the emergency is fudden, the trees are merely laid lengthwife befide each other, with their branches pointed towards the enemy, to prevent his approach, vvhilft the trunks ferve as a breaftwork before thofe by whom the abatis is raifed. When the abatis is meant for the defence of a oafs or entiance, the boughs of the trees are generally flripped of their leaves and pointed ; the trunks are planted In the ground; and the boughs are interwoven with each other. It is needlefs to add, that the clofer the trees are laid or planted together, the more tecure is the defence which they afford ; and if, when they are planted, a fmall ditch be dug towards the enemy, and the earth thrown up properly againft the lower part of the abatis, it will be very difficult to pafs it if well defended.—Simes's Military Guide. ABBREVIATION OK FRACTIONS, in arithmetic and algebra, is the reducing of them to lower terms; which is done by dividing the numerator and denominator by fome number or quantity which will divide both without leaving a remainder of either. ABERRATION, in optics (in Encycl.), refers the reader to the article OPTICS, ng 17, 136, 173. It fhould have referred hira to OPTICS, R° 17, and 251 — 256. ABERRATION of the Vifual Ray, is a phenomenon, of which, though fome account of it has been given in the Encyclopedia (fee ABERRATION, in allronomy; and the aiticle ASTRONOMY, ^337.,), one of the moft candid of our correfpondents requires a fuller explanation. If fuch an explanation be requifite to him, it muff be much morefo to many others; and we know not where to find, or how to devife, one which would be more fatisfaclory, or more familiar, than the following by Dr Hutton.' “ This effeft (fays he) may be explained and familiarized by the motion of a line parallel to itfelf, much after the manner that the compofition and refolution of Jorces are explained. If light have a progreffive motion, let the proportion .of its velocity to that of the earth in her orbit be as the line BC to the line AC ; then, by the compofition of thefe two motions, the particle of light will feem to deferibe the line BA or DC, SyppL. VOL. I. Part I.

A B S inftead of its real courfe BC ; and will appear in the di-Aberration reftion AB or CD, inftead of its true dire&ion CB. II So that if AB reprefent a tube, carried with a parallel Abfcif~5, , motion by an obferver along the line AC, in the time that a particle of light would move over the fpace BC, the different places of the tube being AB, ab, cd, CD; and when the eye, or end of the tube, is at A, let a particle of light enter the other end at B ; then when the tube is at ab, the particle of light will be at e, exaftly in the axis of the tube; and when the tube is at cd, the particle of light will arrive at/, Hill in the axis of the tube; and, laftly, when the tube arrives at CD, the particle of light will arrive at the eye or point C, and confequently will appear to come in the diredlion DC of the tube, inftead of the true dire&ion BC': and fo on, one particle fuccceding another, and forming a continued ftream or ray of light in the apparent dire&ion DC. So that the apparent angle made by the ray of light with the line AE is the angle DCE, inftead of the true angle BCE; and the difference BCD, or ABC, is the quantity of the aberration.” ABERRATION of the Planets, is equal to their geocentric motion, or, in other words, to the fpace which each appears to move as feen from the earth, during the time that light employs in paffing from the planet to the eye of the obferver. Thus the fun’s aberration in longitude is conftantly 20", that being the fpace a&uallv moved by the earth; but apparently by the fun in 8 minutes and 7 feconds, the time in which light pafles from the fun to the earth. If then the diftance of any planet from the earth be known, the time which light empl@ys in paffing from the planet to the earth muft likewife be known ; for as the diftanee of the fun is to the diftance of the planet, fb is 8 minutes and 7 feconda to that time; and the planet’s geocentric motion in that time is its aberratiow, whether it be in longitude, latitude, right afcenlion, or declination. See ASTRONOMY in this Supplement. ABO/lB, cefles levied, in India, under different denominations, beyond the ftandard rent. ABSCISS, A BSCISSE, or Abfctjfa, i? a part cut off from a ftraight line, and terminated at fome certain point by an ordinate to a curve ; as AP (fig. 2.), or Plate 1' BP (fig. 3.) The abfeifs may commence either at the vertex of the curve, or at any other fixed point; and it may be taken either upon the axis or upon the diaA meter

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he knows well that the diagonal of a fquarc is not cor*. Accelerated menfurate with its fide; but the tyro m geometry ^ would have been no wifer than before. He knew from the beginning, that the propofition and its contrary cannot both be true ; but which of them is true, and which falfe, fuch a demonilration could not have taught him becaufe he is ignorant of the incommenfuraDility of the diagonal and fide of a fquare. No man, however, is ignorant, that two ftraight lines cannot indofe a fpace; and fince Euclid (hows that the contrary of his propofition implies this abfurdity, no man of common feme can entertain a doubt but that the propoiition ilfelf muft Ult be UC true. IHM-. _ 1 v „ ACCELERATED MOTION.? bee (Encycl.) AcACCELERATING FORCE, y CELEIATION; anu the Encyclopaedia; but there is another abfoibing power poffeffed by different fubftances, which ,s worthy of at- MICHAS.CS, Seft-VI—and (this Supplement)^tention, becaufe it is only by our knowledge of it that we can adapt our clothing to the various chmates of the ACTION is a term which has been fufficiently exearth. The power to which we allude is that o. diffe- plained in the Encyclopaedia; but fince that article was - rent fubftances ; fuch as wool, cotton, filk, and linen, written, queftions have been agitated refpeAing agents, to abforb or attraft moifture from the atmofphere. On agency, and affion, which, as they have employed fome this lubieft the reader will find feme very inftruftive ex- of the moft eminent philofophers of the age, and are periments detailed (inEncycL), where perhaps he may conneAed with the deareft interefts of man, are certainnot have looked for them, under the title r LANEL. > 4’ entitled to notice in this place. ABSURDUM, a term made ute of by mathemati It is the opinion of Dr Reid, and we have' adopted clans when they demonftrate any truth, by Ihowmg it (fee METAPHYSICS, na 109, See.. Encycl.), that no that its contrary is impoffible, or ^volves an abfurdity. being can be an agent, or perform an adkn, in the proThus Euclid demonftrates the truth of the fourth pro- per fenfe of the word, which does not poffefs, in fome pofition of the firft book of his Elements, by fhowing degree, the powers of will and underftanding. If this that its contrary implies this obvious abfurdity— that opinion be juft, it is obvious, that what are called the two ftraight lines may mclofe a ipace. powers of nature, inch as impufe, attraction, repufon, This mode of demonftration is called rcJufro ad ab- elaftcity, Sec. are net, ftriAly fpeaking,/>*W«v or caufes, furdum, and is every whit asconclufive as the ^ircct m^ but the effeAs of the agency of fome aAive and intellithod ; becaufe the contrary of every falfehoo^ muf. be gent being ; and that phyfical caufes, to make ufe cf truth.’ and of every truth, falfehood. common language, are notlring more than laws or rmec, The vouncr creometrician, however, docs not, we be- according to which the agent produces the cffeA. _ lieve, feel himfelf fo perfcAly fatisfied with a demonThis doctrine has been controverted by a writer firatien of this kind, as with thofe which, ptoceeing whofe acutenefs is equalled only by his virtues; and we from a few fdf-evident truths, conduAs him direAly, fhall confider fome of his objeAions to it in another by neceffary confequences, to the truth of the propoii- place (fee CAUSE): but a queftion of a different kind tion to be proved. The reafon is, that he has not yet falls under our prefent confidcration ; and perhaps the learned to diftinguifh accurately between the words anfwer which we muft give to it, may go tar to remove falfe and impojjible, different and contrary. Many diffe- the objeAions to which we allude. _ rent affertions may be made relating to the fame thing, Can an agent operate where, either by itfelf or by and vet be all true or all falle; but it is impoffible to an inftrument, it is not prefent? Wc think not ; beot make two affertions direAly contrary to each caufe agency, or the exertion of power, muft be the which the one (hall not be true and the other falfe agency of fomething. The conftitution of the human Thus “ fnow is white,” « fnow is cold,” are different mind compels us to attribute every aAion to fome beaffertions relating to the fame thing, and both true; as, ing; but if a being could aA in one place from which it « fnow is black,” “ fnow is red, are both falle . but is abfent, it might do the fame in a fecond, in a third, let it be remembered* that of the firft and fecond, and and in all places ; and thus we fhould have aAion withof the third and fourth of thefe affertions, neither is di- out an agent: for to be abfent from all places is a phrafe reAly contrary to the other ; nor is any one ot them, of the fame import as not to exift. But if a living and abftraAly confidered, mpoffble, or fuch as a blind man, intelligent being cannot aA but where it is either im•who had never felt nor heard of fnow, might not believe mediately or inftrumentally prefent, much lefs furely can upon ordinary teftimony. But were all the men in we attribute events of any kind to. the agency of an abEurope to tell a native of the interior parts of Africa fent and inanimated body. Yet it has been faid, that that fnow is a thing at once white and not white, cold and « we have every reafon, which the nature of the fubjeA not cold, the woolly-headed lavage would know as well as and of our own faculties can admit of, to believe, that the moft fagacious philofopher, that of thefe are among things inanimate fuch relations, that affertions the one mujl be true and the other muft be falfe. they may be mutually caufes or principles of change ta fuft fo it is with rel'peA to Euclid’s fourth propoiition. one another, without any exertion oi power, or any Had he proved its truth by fhowing that its contrary operation of an agent, ftriAly fo called. Such relations, involves this propofition, that “ the diagonal of a fquare for aught that we know, may take place among bodies is commenfurate with its fide,” the fkihul geometrician at great diftances from one another, well as among would indeed have admitted the demonftration, because

AbforpMon, meter of the curve, or upon any other line V? * Abfurdum. g;ven pofition. Hence there are on t e arn 2 g or diameter an Infinite number ot variable atfaffes, teiminated all at one end by the fame fi«d pmnt. In the common parabola (fig-4-)V^h ordmate PQJias but one abfclfs AP. In the ehpfe or circle (fig. 2.), the ordinate has two abfcifTes lying on the op no file t of it. In general, to each ordinate a line of the feco kind, or a curve of the firft kind, may have two abfcifles; a line of the third order, three; a line of the fourth order, four ; and fo on. ABSORPTION, in ANATOMY and PHYSIOLOGY, has been fufficiently explained under thefe articies in

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bodies really or feemingly in aftual contafl; and they which take place among bodies at great diftancei from Afiion may vary both in degree and in kind, according to the each other, vary both in degree and in kind according I! diftances between the bodies.” to the diftances; for this variation, which we acknow- Aer°‘*T'f That any thing fhould be a caufe or principle of ledge to be a fad, appears to us wholly unaccountable change to another, without the exertion of power or the upon any other hypothefis than that which attributes operation of an agent, appears to us a palpable contra- the different changes to agents diftind from the bodies di&ion ; and we could as eafily conceive any two fides themfelves. Did we perceive all the particles of r.atof a triangle to be not greater than the third fide, as re- ter, at all diftances, tending towards each other by a cencile fuch a propofition to that faculty of our minds fixed law', we might be led to confidei mutual attracby which we diltinguilh truth from falfehood. When tion as an effential property of that fubftance, and think we fee one body the apparent caufe of change in ano- no more of inquiring into its caufe, than we think of ther body, we cannot poffbly entertain a doubt of the inquiring into the caufe of extenfion. But when we exertion of power; but whether that power be in the find that the fame particles, which at one diftance feem body apparently producing the change, or in a diftind to attrad each other, are at a different diftance kept agent, is a queftion to which an anfwer will not fo readi- aiunder by a pow'er of repulfion, which no force, with ly be found. That it is in a diftinCt agent, we are ftrong- which we are acquainted, is able to overcome, we canly inclined to believe, not only by the received dodrine not attribute the principle or caufe of thefe changes to concerning the inertia of matter, which, though it has brute matter, but muft refer it to fome other agent exbeen frequently controverted, we have never feen dif- erting power according to a fixed law. pvoved, but much more by cor.iidering the import of It is the faftiioa at prefent to defpife all meUDhvfian obfervation frequently introduced to prove the dired cal enquiries as abftrufe and ufelefs: and on this account contrary of our belief. “ We cannot be charged (fays we doubt not but fome of our readers will turn away the writer whom we have juft quoted) with maintain- from this difquifition with affeded difguft, whilft the ing the abfurdity, that there may be an effed without petulant and unthinking chemift, proud of poffeffin^ the G caufe, when we refer the fall of a ftone to the ground, fecrets of his fcience, will deem it fuperfluous to inquire and the ebbing and flowing of the fea, to the infuence after any other natural agents than thofe of which he f o the earth on the ftone, and of the fun and moon on has been accuftomed to talk. But with the utmoft rethe ocean, according to the principle of general gravita- iped for the difeoveries made by modern chemift;, tion.” wdiich we acknowledge to be both numerous and imWe admit the truth of this obfervation, provided the portant, we beg leave to obferve, that though thefe influence of the fun and moon on the ocean be poflible; gentlemen have brought to light many events and opebut, to us at leaft, it appears impoflible, and is certain- rations of nature formerly unknown/ and have ffiown ly inconceiveable. The influence of the fun and moon that thofe operations are carried on by eftabliftied laws, can here mean nothing but the action or operation of the none of them can fay with certainty that he has difeolun and moon; but if thefe two bodies be inanimate, yered a fingle agent. The moft enlightened of them they cannot act at all, in the proper fenfe of the word ; indeed pretend not to have difeovered in one departand whatever they be, it is obvious that they cannot ment of fcience more than Newton difeovered in anoad immediately on an objed at fuch a diftance from them ther ; for they well know that agents and agency canas the earth and the ocean. If they be the agents, they not be fubjeded to any kind of phyfical experiments. muft operate by an inftrument, as vve do when moving Onr very notions of thefe things are derived wholly objeds to which our hands cannot reach ; but as it has from our own conicioufaefs and refledion ; and when been fhown elfewhere (fee METAPHYSICS, n° 199. and it is confidered what dreadful confequences have in anOPTICS, n 63- Encycl.), that neither air, nor asther, other country refulted from that pretended philofophy nor any other material inllrument which has yet been which excludes the agency pf mind from the univeiffe, thought o>, is fufiicient to account for the phenomena it is furely time to inquire whether our confeioufnefs of attradion and repulfion, it is furely much more ra- and refledion do not lead us to refer real agency to tional to conclude, that the ebbing and flowing of the mmd alone. Let this be our apology both to the real fea are produced, not by the influence of the fun and and to the affeded enemies of metaphyfics for endeamoon, but by the power of feme diftind agent or vouring to draw' their attention to the prefent queftion. agents. It is a queftion of the utmoft importance, as well to What thofe agents are, we pretend not to fay. If fcience as to religion : and if the law's of human thought the Supreme Being himfelf be the immediate author of decide it, as we have endeavoured to fhow that they' do, every change which takes place in the corporeal world, we may without hefitation affirm, that the impious phiit is obvious that he ads by fixed rules, of which many lofophy of France can never gain ground but among are apparent to the moft heedlefs obferver, whilft the men incapable of pacient thinking. difeovery of others is referved for the reward of the juADAMAS, a name given, in aftrology, to the dicious application of the faculties which he has given moon. us. If he employs inferior agents to carry on the great b, in mechanics, a fmall machine invented operations of nature, it is furely not difficult to con- by Mr Tidd for refreftiing or changing the air in rooms ceive that the powers of thofe agents which were de- when it becomes too hot or otherwife unfit for refpirarived from him, may by him be reftrained within cer- tion. The aeolus is fo contrived as to fupply the place tain limits, and their exercife regulated by determined of a fquare of glafs in the window, where it works, laws, in fuch a manner as to make them produce the with very little noife, like the fails of a wind-mill or a greateft benefit to the whole creation. Nor let it be fmoke-jack. thought an objedion to this theory, that the changes AEROLOGY is a branch of fcience which was deA 2 tailed

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merly called Roh; and hence is derived the name of the Afghan,. Afcten.. taM In the Encyclop^.u at fufficient length, and ac. Rohillas. The city which was eftablifhed in it by the ' r—^ conMne to the principles which were then geneially adAfghans was called by them Paifh-wer or Paijher, and mitted by chemifts. Subfequent experiments, however, lo . is IIUVV now the name of the whole diftridt. I he .fedls of the have fhown, that fomeof thofe principles are erroneous, Afghans are very numerous ; or winch the principal are, and of courfe that feme of the opinions advanced in the Lodi, Lohovni, Sur, Serwani, Tufufzibi, BangUh, Di/aarticle AEROLOGY are inconfiftent with fa&s. ihefe %aui, Khetti, Tafin, Khail, and Beloje. They are Muopinions muft be correded; but inftead of fwellmg this fulmans, partly of the Sunni, and partly of the Shiek volume with a new article AEROLOGY, vve apprehen perfuafion. that it will be more acceptable to our fcientihc readers Though they are great boafters, as we have teen, of to refer them for thole corrections to the article CHE- the antiquity oi their origin, and the reputation oi their MISTRY in this Supplement. race, other Mifulmans rejett their claim, and confider AFGHANS, are a people in India who inhabit a them as ot modern, and even of bale, extraction. province of CABUL or CABULISTAN (fee EncycL), and This is probably a calumny; for it feeir.s inconfiftent have always been conneaed with the kingdoms of l er- with their attention to the purity of their defeent—an fia and Hindoftan. They boall of being defeended of attention which would hardly be paid by a people not Saul the firft king of Ifrael ; of whofc advancement to convinced of their own antiquity. They are divided tire royal dignity they give an account which deviates into four clafles. The firft is the pure clafs, confifting not very widely from the truth. 1 hey fay indeed, that of thofe whole fathers and mothers were Afghans. The their great anceltor was raifed from the rank of a Shep- fecond clafs confifts of thofe whole fathers were Afghans herd, not for any princely qualities which he pofTefTed, and mothers of another nation. The third clals conbut becaufe his itature was exadly equal to the length tains thole whofe mothers were Afghans and fathers of of a rod which the angel Gabriel had given to the pro-k phet Samuel as the meaiure of the Itature of him whom another nation. The fourth clais is compofed of the children of women whofe mothers were Afghans and faGod had deftined to fill the throne of Ifiael. thers and hulbands of a different nation. Perfons who do SAUL, whofe defeent, according to fomeof them, not belong to one of thefe claffes are not called Afghans. was of Judah, and according to others of Benjamin, This people have at all times diftinguilhed themfelves had, they fay, two fons, BERKIA and IRMIA, who fer- by their courage, both fingly and unitedly, as piincived David, and was beloved by him. I he fons ot Ber- pals and auxiliaries. They have conquered for their kia and Irmia were AFGHAN and USBEC, who, during own princes and lor foreigners, and have always been the reigns of David and Solomon, dittmguifhed them- confidered as the main ftrength of the army in whiclx felves, the one for bis corporeal iDength, and the other they ferved. As they have been applauded for virtues, for his learning. So great indeed was the flrength of Afghan, that we are told it {truck terror even into de- they have alfo been reproached for vices, having fometimes been guilty of treachery, and oi a&ing the bafe mons and genii. This hero ufed frequently to make excurfions to the part even of affaffins. Such is the account of the Afghans puhlilhed in the • mountains, where his progeny, after his death, eftabliftrfecond volume of the A.fiatic Refearches. It vvas tranfed themfelves, lived in a ftate of independence, built forts, and exterminated infidels. When the feledt of lated from a Perfian abridgment of a book written in creatures (the appellation which this people give to the Pufhto language, and called The Secrets of the AfMahomet) appeared upon earth, his fame reached the ghans, and communicated by Henry Vanfittart, Efq;to Afghans, who fought him in multitudes under their Sir William Jones, then prelident of the Afiatic Soleaders Khalid and Abdul Refpid, fons of IVahd; and ciety. Their claim to a defeent from Saul king of Ifthe prophet honouring them with tins reception — rael, whom they call ME Lie TALUT, is probably of not “ Come, O Muluc, or Kings1.” they affumed the title a very ancient date ; for the introduHion of the angel Gabriel with his rod, gives to the whole ftory the air of Mtlic, which they retain to this day. of one of thofe many fiftions which Mahomet borrowed The hiftory, from which this abftradh is taken, gives a long and uninterefting detail of the exploits of the from the later rabbins. Sir William Jones, however, Afghans, and of their zeal in overthrowing the temples though he furely gave no credit to this fable, feems to of idols. It boafts of the following monarchs of their have had no doubt but the Afghans are defeendants of race who have fat upon the throne of Debit: Sultan Ifrael. “ We learn (fays he) from ESDRAS, that the BEHLOLE, Afghan LODI, Sultan SECANDER, Sultan ton tribes, after a wandering journey, came to a counIBRAHIM, SHIR SHAH, ISLAM SHAH, ADIL SHAH try called Arfareth, where we may fuppofe they letSUR. It alfo numbers the following kings of Gaur tied : now the Afghans are find by the heft P erf an hifdefeended of the Afghan chiefs: SOLAIMAN Shah Gur- torians to be delceoded from the ffe'tvs. ihey have scant, BEYAZID Shah, and KUTB Shah ; befides whom, traditions among themfelves of fuch a defeent ; and it / their nation, we are told, has produced many conquerors is even afferted, that their families are diftinguilhed by of provinces. The Afghans are fometimes called Solai- the names of 'Jenvf: tribes, although, ftnee their conmani, either becaufe they were formerly the fubjefis of verfion to If am, they ftudioufly conceal their origin SOLOMON king of Ifrael, or becaufe they inhabit the from all whom they admit not to their fecrets. The mountains of Solomon. They are likevvife called PA- Pufoto language, of which I have feen a dictionary, has TANS, a name derived from the Hindi verb Paitna “to a manifeft refemblance to the Chahlaick; and a confiruffi,” which was given to them by one of the Sultans derable diftriCt under their dominion is called Hazareh whom they ferved, in confequence of the alacrity with or Hazaret, which might eafiiy have been changed into which they had attacked and conquered his enemies. the word uled by ESDRAS. I ftrongly recommend an The province which they occupy at prefent was for- Inquiry into the literature andhiftoryot the AfghansP

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It is to co-operate with this accomplilhed fcholar who, in the beginning of the 9th century, afeended the Almamon* Alniamon. t}iat we have Jnferted into our Work this fhort account throne of the caliphs of Bagdat. He was the fon of Aloe* y " ^ of thxt fmgular people; and it is with pleafure that, Harun Al-Ralhid, and grandfon of Almanfor. His' * upon the authority of Mr Vanfittart, we can add, that name is otherwife written Mamon, Almaon, Almamun,, a very particular account of the slfghans has been writ- Alamoun, or ALMaimon. Having been educated with ten by the late HAFI.Z RAHMAT Khan, a chief of the great care, and with a love for the liberal fciences, he Rohillahs, from which luch of our readers as are orien- applied himfelf to cultivate and encourage them in his tal fcholars may derive much curious information. own country, h or this purpofe he requefted the Greek A L BAT EON 1, an Arabic prince of Batan in Me- emperors to fupply him with fuch books on philofophyfopotamia, was a celebrated aftronomer, about the year as they had among them; and he collected fkilful interof Chrift 880, as appears by his obfervations. lie is preters to tranflate them into the Arabic language. alio called Muhammcd ben Geler Albatam, Mahomet the He alfo encouraged his fubje&s to ftudy them ; frefon of Gcber, and Muhamedes AraEtenfs. He made af- quenting the meetings of the learned, and a (Tilting at tronomical obfervations at Antioch, and at Racah or their exercifes and deliberations. He caufed Ptolemy’s Aradta, a town of Chaldea, which fome authors call a Almageft to fee tranftated in 827, by Ifaac Ben-honain, town of Syria or of Mefopotamia. He is highly fpo- and I habet Ben-korah, according to Herbelot, but, acken of by Dr Halley, as vir adrmrandi acuminis, ac in cording to others, by Sergius, and Alhazen the (on of adminijirandis obfervationibus exercitatiffimus. Jofeph. In his reign, and doubtlefs by his encourageFinding that the tables ©f Ptolemy were imperfeft, ment, an aftronomer of Bagdat, named Habafh, comlie computed new ones, which were long ufed as the pofed three fets of aftronomical tables. bell among the Arabs : thefe were adapted to the meAlmamon himfelf made many aftronomical obfervaridian of Aradla or Racah. Albategni cotnpofed in tions, and determined the obliquity of the ecliptic to in fome manuferipts), but Arabic a work under the title of The Science of the be then 23°35' (or Stars, com priding all parts of allronomy, according to Voffius fays 23° 51' or 23“ 34'. He alio cauied (kilful his own obfervations and thofe of Ptolemy. This work, obfervers to procure proper inftruments to be made* tranflated into Latin by Plato of Tibur, was publilhcd and to exercife themfelves in aftronomical obfervations;. at Nuremberg in 1537, with fome additions and demon- which they did accordingly at Shemafi in the province ilrations of Regiomontanus; and the fame was reprint- of Bagdat, and upon Mount Cafrus near Damns. ed at Bologna in 1645, author’s notes. Dr Under the aufpices of Almamon alfo a degree of the Halley detected many faults in thefe editions.—Phil. meridian was meafured on the plains of Sinjar or SindTranf. for 1693. N° 204. giar (or, according, to fome, Frngar), upon'the borders In this work Albatcgni gives the motion of the fun’s of the Red Sea ; by which the degree was found to apogee iince Ptolemy’s time, as well as the motion of contain miles, of 4000 coudees each, the coudee the liars, which he makes one degree in 70 years. He being a foot and a half: but it is not known what foot made the longitude of the firll ftar of Aries to be 189 24 is here meant, whether the Roman, the Alexandrian, or • and the obliquity of the ecliptic 230 35'. And upon fome other. Riccioli makes this meafure of the degree Albategni’s obfervations wrere founded the Aiphonline amount to 81 ancient Reman miles, which value antables of the moon’s motions; as is obferved by Nic. (wers to 62,046 French toifes; a quantity more than Muler, in the Tab. Frificee, p. 2484 the true value of the degree by almoft one-third. FiALDER A1MIN, a liar of the third magnitude, in nally, Almamon revived the fciences in the Fall to fuch ’the tight (boulder of the conflellation Cepheus. a degree, that many learned men were found, not enly ALFRAGAN, AMFERGANI, or Fargani, a cele- in his own time, but after him, in a country where the brated Arabic aftronomer, who flourifhed about the year (Indy of the Iciences had been long forgotten. This 800. He was fo called from the place of his nativity, learned king died near Tarfus in Cilicia, by having Fergan, in Spgdiana, now called Maracanda, or Samar- eaten too freely of fome dates, on his return from a micand, anciently a part of Badtria. He is alfo called litary expedition, in the year 833. Ahmed (or Muhammed) ben- Cot hair, or Katir. He ALOE mcHOTOMA, in botany, called by the Dutch wrote the Elements of Aftronomy in 30 chapters or Kooker-boom or Quiver-tree, is a native of the fouthern fedlions. In this work the author chiefly follows Pto- parts of Africa, and feems to be a fpecies of the AGAlemy, ufing the fame hypothefis, and the lame terms, VE or American aloe (fee AGAVE, Encycl.) It is thus and frequently citing him. Of Alfragan’s work there deferibed by LE VAILLANT in his Neva Travels into are three Latin tranflations, of the arch are given, we have j = y' C X L ( ±d-Jl±^2 a.}.J-..A2 ), and confe\ a ' quentiy \/C-

h

2a h

/j2\

Therefore

+ V^2 x -j- x2 > L ('rt the general value of j — s X— a -X. h 2 a h b2\y L (^ a’\-X-\-Ay2ax-irx'1 h *y 2 ah hz a T a JLj ' a" ' r . As an example of the ufe of this formula, we fubjoin a table calculated by Dr Hutton of Woolwich for an arch, the fpan of which is 100 feet and the height 40, which are nearly the dimenfions of the middle arch of Blackfriars Bridge in London.

26 Befedts of The figure for this propofition is exaftly drawn acthe Catiiiama curve. cording to thefe dimenfions, that the reader may judge of it as an object of fight. It is by no means deficient in gracefulnefs, and is abundantly roomy for the pafiage of craft; fo that no objection can be offered again(t its being adapted on account of its mechanical excellency. The reader will perhaps be furprifed that we have made no mention of the celebrated Catenarean curve, which is commonly faid to be the beft form for an arch ; but a little refleftion will convince him, that although it is the only form for an arch connfling of {tones of equal weight, and touching each other only in fingle points, it cannot fuit an arch which mufl be filled up in the haunches, in order to form a road-way. He will be more furprifed to hear, after this, that there is a certain thicknefs at the crown, which will put the Catenarea in equihbrio, even with a horizontal road-way

I ARC but this thieknefs is fo great as to make it unfit for a Arch, bridge, being fuch that the prefftire at the vertex is equal to the horizontal thruft. This would have been about 37 feet in the middle arch of Blackfriars Bridge. The only fituation therefore in which the Catenarean form would be proper, is an arcade carrying a height of dead wall; but in this fituxtion it would be very ungraceful. Without troubling the reader with the invelligation, it is fufficient to inform him that in a Catenarean arch of equilibration the abfeiffa VH is to the * abfeififa v h in the conftant ratio of the horizontal thruft to its excefs above the preffure on the vertex. This much will ferve, we hope, to give the reader a Inutility of clear notion of this celebrated theory of the equilibriumd16 com* of arches, one of the mo ft delicate and important applications of mathematical fcience. Volumes have beenbrat;on;>" written on the fubjedt, and it flill occupies the attention of mechanicians. But we beg leave to fay, with great deference to the eminent perfons who have profecuted this theory, that their fpeculations have been of little fervfce, and are little attended to by the prasflitiener. Nay, we may add, that Sir Chriftopher Wren, perhaps the moft accomplifhed architeQ: that Europe has feen, feems to have thought it of little value: for, among the fragments which have been preferved of his fludies, there are to be feen fome imperfedl differtations on this very fubjedt, in which he takes no notice of this theory, and confiders the balance of arches in quite another way. Thefe are collefted by the author of the account of Sir Chriftopher Wren’s family. This man’s great fagacity, and his great experience in building, and, ft ill more his experience in the repairs of old and crazy fabrics, had fhown him many things very inconfiftent with this theory, which appears fo fpecious and fafe. The general fa£ts which occur in the failure of old arches are highly inflruftive, and deferve the moft careful attention of the engineer; for it is In this ftate that their defeats, and the procefs of nature in their deftruction, are moft diftinftly feen. We venture to affirm, that a very great majority of thefe fafts are irreconcileable to the theory. The way in which circular arches commonly fail, is by the finking of the crown and the rifing of the flanks. It will be found by calculation, that in moft of the cafes it ought to have been juft the contrary. But the cleareft proof is, that arches very rarely fail where their load differs moft remarkably *rom that which this theory allows. Semicircular arches have flood the power of ages, as may be feen i:* the bridges of ancient Rome, and in the numerous arcades which the ancient inhabitants have eredled. Now all arches which fpring perpendicularly from the horizontal line, require, by this theory, a load of infinite height; and, even to a confiderable diftance from the fpringing of the arch, the load neceflary for the theoretical equilibrium is many times greater than what is ever laid on thofe parts ; yet a failure in the immediate neighbourhood of the fpring of an arch is a moft rare phenomenon, it it ever was obferved. Here is a moft remarkable deviation from the theory ; for, as is already obferved, the load is frequently not the fourth part of what the theory requires. Many other fads might be adduced which fhow great deviations from the legitimate refults from the theory. We hope to be excuied, therefore, by the rnathernnticiacs for doubting of the juftnefs of this theory, We do

ARC r 2 not think it erroneous, but defective, leaving out t ” circumftances which we apprehend to be of great imIts dcfcdb. portance; and we imagine that the defefts of the theoryhave arifen from the very anxiety of the mechanicians to make it perfect. The arch ilones are fuppofed to be perfeftly fmooth or polifhed, and not to be connected by any cement, and therefore to fuftain each other merely by the equilibrium of their vertical preffure. The theory enfures this equilibrium, and this only, leaving unnoticed any other caufes of mutual adtion. The authors who have written on the fubjeCt fay exptefsly, that an arch which thus luftains itfelf mud be llronger than another which would not; becaufc when, in imagination, we fuppofe both to acquire connection by cement, the firft preferves the influence or this connection unimpaired ; whereas in the other, part of the cohefion is wafted in counteracting the tendency of feme parts to break off from the reft by their want of equilibrium. This, is a very fpecious argument, and would be juft, if .the forces which are mutually exerted between the parts of the arch in its fettled Hate were merely vertical preffures, or, where different, were inconfiderable in comparifon with thofe which are really attended to in the conftruCfion. But this is by no means the cafe. The forms which the ufes for which arches are ereCled oblige us to adopt, and the loads laid on the different points of the arch, frequently deviate confiderably from what are neceffary for the equilibrium of vertical preffures. The varying load on a bridge, when a great waggon paffes along it, fometimes bears a very fenlible proportion to the weight of that point of the arch on which it refts. It is even very doubtful whether the preffures which are occafioned by the weight of the fluff employed for tilling up the flanks really aCt in a vertical direftion, and in the proportion which is fuppofed We are pretty certain that this is not the cafe with fand, gravel, fat mould, and many fubftances in very general ufe for this purpofe. When this is the cafe, the preffures fuftained by the different parts of the arch are often very inconfiftent with the theory—a part of the arch is overloaded, and tends to fall in, but is prevented by the cement. This part of the arch therefore aCta on the remoter parts by the intervention of the parts between, employing thofe intermediate parts as a kind of levers to break the arch in a remote part, juft as a lintel would be broken. We apprehend that a mathematician would be puzzled how to explain the ftability of an arch cut out of a folid and uniform mafs of rock. His theory confiders the mutual thrufts of the arch ftones as in the dbe&ion of the tangents to the arch. Why fo ? hecaufe he fnppofes that all his polifhed joints are perpendicular to thofe tangents- But in the prefent cafe he has no exifting joints ; and there feems to be nothing to diredt his imagination in the affumption of joints, which, however, are abfolutely neceffary for employing his theory, becaufe, without a fuppofttion of this kind, there feems no conceiving any mutual abutment of the arch ftones. Afk a common, but intelligent, mafon what notion he forms of ftlch an arch ? We apprehend that he will confider it as no arch, but as a lintel, which may be broken like a wooden lintel, and which refifts entirely by its cohelion. He will not readily conceive that, by cutting ihe under fide of a ftone lintel into an arched form, and thus taking away more than half of Arch.

j

] ARC its fubftance, he has changed its nature of a lintel, op Arch, given it any additional ftrength. Nor would there be "■'v*""* any change made in the way in which fuch a mafs of ftone would refill being broken down, if nothing were done but forming the under fide into an arch. If the lintel be fo laid or. the piers that it can be broken without its parts pufhing the piers afide (which will be the cafe if it lies on the piers with horizontal joints), it will break like any other lintel; but if the joints are directed downwards, and converging to a point within the arch, the broken ftone (iuppofe it broken at the crown by an overload in that part) cannot be prefled down without forcing the piers outwards. Now, in this mode of afting, the mind cannot trace any thing of the ftatical equilibrium that we have proceeded on in the foregoing theory. The two parts of the broken lintel feem to puflr the piers afide in the fame manner that two rafters pufh outwards the walls of a houfe, when their feet are not held together by a tye-beam. If the piers cannot be pufhed afide (as when the arch abuts on two folia rocks), nothing can prefs down the crewn which does not crufh the ftone. This concluflon will be ftriftly true if the arch is of fuch a form that a ftraight line drawn from the crown to the pier lies wholly within the folid mafonry. Thus if the vault confift of two ftraight ftones, as in fig. r. or if it confift of feveral ftones, as in fig. 14. difpofed in two ftraight lines, no weight laid on the crown can deftroy it in any other w'ay but by crufhing it to powder. _ _ 29 But when ftraight lines cannot be drawn from the Whet: it is overloaded part to the firm abutments through the fo. to be called lid mafonry, and when the cohefion of the parts is not u:to, t^.e au* able to withftand the tranfverfe ftrains, we muft call the ‘e U1 * principles of equilibrium to our aid ; and, in order to employ them with fafety, we muft confider how they are modified by the excitement of the cohering forces. The cohefion of the ftones with each other by cement orotherwife, has, in almoft every fituation, a bad effedt. It enables an overload at the crown to break the arch near the haunches, caufing thofe parts to rife, and then to fpread outwards, juft as a Manfarde or Kirb roof would do if the trufs-beam which connedls the heads of the lower rafters were fawn through. This can be prevented only by loading that part move than is requiiite for equilib) ium. It would be prudent to do this to a certain degree, becaufe it is by this coheiion that the crown always becomes the weakeft part of the arch, and fuffers more by any occafional load. We expedl that it will be faid in anfwer to all this, that the cohefion given by the ftrongeft cement that we can employ, nay the cohefion of the ftone itfelf, is a mere nothing in comparifon with the enormous thrufts that are in a ftate of continual exeition in the different parts of an arch. This is very true ; but there is another force which produces the fame effedl, and which increafes nearly in the proportion that thofe thrufts increafe, becaufe it arifes from them. This is the fri&ton of the ftones on each other. In dry freeftone this friction confiderably exceeds one half of the mutual preffure. The refledling reader will fee that this produces the fame effedt, in the cafe under confideration, that cohefion would do ; for while the arch is in the adl of failing, the mutual preffure of the arch ftones is adling with full force, and thus produces a fridlion more than adequate

ARC L 23 1 ARC adequate to all the effects v/e have been fpeaking till the whole took a firmer bed. The fnbfequent phe- Arch, nomena are evident confequences of this diilribution and Prortf f When thefe circumftances are confldered, we imagine modification ot preffure, and can hardly be explained iu the break.- that it will appear that an arch, when expofed to a any other way; at leaft not on the theoretical principles ing of an great overload on the crown (or indeed on any part), already fet forth : tor in this bridge the loads at B and arch. divides, of itfelf, into a number of parts, each of which D were very confiderably greater than what the equilicontains as many arch ftones as can be pierced (fo to brium required ; and we think that the firft obterved (peak) by one ftraight line, and that it may then be fplintering at H, F, and G, was moft in'ltrudlivc, thowconsidered as nearly in the fame fituation with a poly- ing that there was an extraordinary prefiureat the inner gonal arch of long ftones buiting on each other like fo joints in thofe places, which cannot be explained by the many beams in a Norman roof (lee Roof, n° 49.), but ufual theory. Not latisfied with this fingle ob'ervation, after this without their braces and ties. It tends to break at all thofe angles ; and it is not fufficiently refilled there, way of explaining it oecurre-d to us, and not being able becaufe the materials with which the flanks are filled to find any fimilar fadt on record, the writer of this arup have fo little cohefion, that the angle feels no load ticle got fome fmall models of arches executed in chalk, except what is immediately above it; whereas it fhould and fubjedted them to many trials, in hopes of collectbe immediately loaded with all the weight which is dif- ing fomc general laws of the internal workings of archfufed over the adjoining fide of the polygon. This will es which finally produce their dovvnfal. He had the be the cafe, even though the curvelineal arch be per- pleafure of obferving the above mentioned eifeumftanfe&ly equilibrated. We recolleft fome circumftances in ces take place very regularly and uniformly, when he the failure of a confiderable arch, which may be worth overloaded the models at A. The arch always broke mentioning. It had been built of an exceedingly foft at fome place B confiderably beyond another point F, and friable ftone, and the arch ftones were too fhort. where the fiift chipping had been obferved. This is a About a fortnight before it fell, chips were obferved method of trial that deferves the attention both of the to be dropping off from the joints of the archltones fpeculatiil and the pra&itioner. If thefe refleClions are any thing like a juft account about ten feet on each fide of the middle, and alio from another place on one fide of the arch, about twenty of the procedure of nature in the failure of an arch, it feet from its middle. The mafons in the neighbourhood is evident that the ingenious mathematical theory of prognofticated its fpeedy downfal, and laid that it equilibrated arches is of little value to the engineer. would feparate in thofe places where the chips were We ventured to fay as much already, and we refted a breaking off. At length it fell; but it firft fplit in good deal on the authority of Sir Chriftopher Wren. the middle, and about 15 or 16 feet on each fide, and He was a good mathematician, and delighted in the apalfo at the very fpringing of the arch. Immediately plication of this fcience to the arts. He was a celebrabefore the fall a fhivering or crackling noife was heard, ted architeCl; and his reports on the various works comand a great many chips dropped down from the middle mitted to his charge, fhow that he was in the continual between the two places from whence they had dropped habit of making this application. Several fpecimens a fortnight before. The joints opened above at thofe remain of his own methods of applying them. The roof new places above two inches, and in the middle of the of the theatre of Oxford, the roof of the cupola of arch the joints opened below, and in about five minutes St Paul’s, and in particular the mould on which he after this the whole came down. Even this movement turned the inner dome of that cathedral, are proofs of was plainly diftinguifhable into two parts. The crown his having ftudied this theory moft attentively. He funk a little, and the haunches rofe very fenfibly, and flourifhed at the very time that it occupied the attention in this ftate it hung for about half a minute. The of the greateft mechanicians of Europe; but there 13 arch ftones of the crown were hanging by their up- nothing to be found among his papers which fhows per corners. When thefe fplintered off, the whole fell that he had paid much regard to it. On the contrary, down. when he has occafion to deliver his opinion for the inWe apprehend that the procedure of nature was fome- ftruCtion of others, and to explain to the Dean and what in this manner. Straight lines can be drawn Chapter of Weftminfter his operations in repairing that within the archftones from A (fig. if.) to B and D, collegiate church, this great archited confiders an arch and from thofe points to C and E. Each of the por- juft as a fenfible and fagacious tnafon would do, and tions ED, DA, AB, BC, refill as if they were of one very much in the way that we have juft now been treatftone, compofing a polygonal vault ED ABC. When ing it: (See Account of the Family, of Wren, p. 356, this is overloaded at A, A can defeend in no other way &e.) Supported therefore by fpeh authority, we would than by pufhing the angles B and D outwards, caufing recommend this way of confidering an arch to the ftudy the portions BC, DE, to turn round C and E. This of the mathematician ; and vve would defire the expemotion mull raife the points B and D, and caufe the rienced mafon to think of the moft efficacious methods arch ftones to prefs on each other at their inner joints for refiftirig this tendency of arches to rife in the flanks. b and d. This produced the copious fplintering at thofe Unfortunately there feems to be no precife principle to joints immediately preceding the total downfal. The point out the place where this tendency is moft remarkfplintering which happened a fortnight before arofe from able. this circumftance, that the lines AB and AD, along We are therefore highly pleafed with the ingenioui which the pieffure of the overload was propagated, were contrivance of Mr Mylne, the architect of Blackfriars tangents to the foffit of the arch in the points F, H, Bridge in London, by which he determines this point and G. and therefore the ftrain lay all on thofe comers with precifion, by making it impeflible for the overof the arch ftones, and fplintered a little from off them loaded arch to Ipring in any other place. Having thus confined' Arch,

A it c ARC l M 1 confined the failure to a particular fpot, he with equal built up to their intended height, the thruft of the Arch. art oppofes a reliftance which he believes to be fuffi- arches fqueezes the rubble-work horizontally, after the cient; and the prefent condition of that noble bridge, mortar has fet, but before it has dried and acquired its which does not in any place {how the fmalleft change utmoft hardnefs. Its bond is broken by this motion, of (hape, proves that he was not miftaken. Looking and it is fqueezed up, and never acquires its former firmon this work as the fir ft, or at leaft the fecond, Speci- nefs. This is effeftually prevented by the prefiure exmen of mafonic ingenuity that is to be feen in tbe erted by the back or the inverted arch. Above this counter arch is another mafs of courfed world, we imagine that our readers will be pleafed with a particular account of its moft remarkable circum- rubble, and all is covered by a horizontal courfe of large blocks of Portland ftone, butting againft the back of ftances. the arch ttone ZI and its correfponding one in the adConftrueThe fpan la (fig. 16 ) of the an middle arch is ico joining arch. This courfe connects the feet ef the two tion of feet, and its height OV is d the thicknefs Kv Blackfriars 0f the cr0wn is lix feet feven inches. Its form is nearly arches, preserves the rubble-work from too great comelliptical; the part AVZ being an arch of a circle preftion, and protefts it fromfoaking water. This lait whofe centre is C, and radius 56 feet, and the two la- circumftance is important^ for if the water which falls teral portions A i B and Z ^ E being arches defcribed on the road-way is not carried off in pipes, it foaka , wfth a radius of 35 feet nearly. The thicknefs of the through the gravel or other rubbifti, reftson the moitar, pier at «£ is 19 feet. The thicknefs of the arch in- and keeps it continually wer and foft. It cannot efcape creafes from the crown V to Y, where it is eight or through the joints of good mafonry, and therefore fills nine feet. All the arch (tones have their joints dire&ed up this part like a funnel. Suppofing the adjoining arch fallen, and all tumbled to the centres of their curvature. The joints are all joggled, having a cubic foot of hard (tone let half way off that is not withheld by its fituation, there will ftili into each. By this contrivance the joints cannot Hide, remain in the pier a mafs of about 3500 tons. The nor can any weight laid on the crown ever break the weight of the portion VY is about 2oco tons. The arch in that part, if the piers do not yield ; for a direftions of the thrufts RY and YF are fuch, that it ftraight line from the middle of KV to the middle of would require a load of 4500 tons on VY to overturn tbe joint YI is contained within the folid mafonry, and the pier round F. This exceeds VY by 2500 tons; a does not even come near the inner joints of the arch weight incomparably greater than any that can ever be ftones. Therefore the whole refifts like one (lone, and laid on it. Such is the ingenious conftruftion of Mr Mylne. It can be broken only by cruftiing it. 'I he joint at Z is . very nearly perpendicular to a line Yb drawn to the evidently proceeds on the principles recommended above; outer edge of the foundation of the pier. By this it principles which have occurred to his experience and was intended to take off all tendency of the preffure on fagacious mind during the courfe of bis extenfive practhe joint dZ to overfet the pier; for if we fuppofe, ac- tice. We have feen attempts by ether engineers to cording to the theory of equilibration, that this preffure withftand the horizontal thrufts of the arch by means is neceffarily exerted perpendicularly to the joint, its of counter arches inferted in the fame manner as here, dire&ion paffes through the fulcrum at F, round which but extending much farther over the main arch ; but it is thought that the pier muft turn in the aft of over- they did not appear to be well calculated for producing fetting. This precaution was adopted, in order to make this effeft. A counter arch fpringing from any point the arch quite independent of the adjoining arches ; fo between Y and V has no tendency to hinder that point that although any of them ftiould fall, this arch (hould from riling by the finking of the crown ; and fuch a counter arch will not refill the precifely horizontal thruft run no rifle. fo well as the ftraight courfe of Mr Mylne. Still farther to fecure the independence of the arch, the following conftruftion was praftifed to unite it into 3* The great incorporation of architefts who built the Oriirin of one mafs, which {hould rife all together. All below the t e h Gothic line a b h built of large blocks of Portland ftone, dove- cathedrals of Europe departed entirely from the ftyles arcll£S * tailed with found oak. Four places in each courfe are ©f ancient Greece and Rome, and introduced another, interrupted by equal blocks of a hard ftone sailed Ken- in which arcades made the principal part Not finding iiJJj rag, funk half way in each courfe. i’hefe aft as in every place quarries from which blocks could be joggles, breaking the courfes, and preventing them from raifed in abundance of fufficient fixe for forming the farprojecting corniches of the Greek orders, they idinAiding laterally. The portion a Y of the arch is joggled like the up- quiihed thole proportions, and adopted a ftyle ol ornaper part. The interior part is filled up with large blocks ment which required no fuch projeftions : and having Kentiih rag, forming a kind of courfed rubble-work, fubftituted arches for the horizontal architrave or lintel, the courfes tending to the centres of the arch. ' The they were now able to ereft buildings of vail extent -tinder corner of each arch ftone projefts over the one with fpacious openings, and all this with very finall below it. By this form it takes (aft hold of the rubble- pieces of ftone. The form which had been adopted for work behind it. Above this nibble there is conftruft- a Chtiftian temple occafioned many interfeftions of ed the inverted arch I e G of Portland ftone. This arch vaultings, and multiplied the arches exceedingly. Con{hares the preffure of the two adjoining arches, along ftant praftice gave opportunities of giving every pofiible with the arch (tones in Y a and in G b. Thus all tend variety of theie interfeftions, and taught the art of batogether to comprefs and keep down the rubble-work lancing arch againft arch in every variety of fituation. in the heart of this part of the pier. This is a very An art fo multifarious, and fo r> rich out of the road uitful precaution ; for it often happens, that when the of ordinary thought, could not but become an object centres of the arches are (truck, before the piers.arc of fond ftudy to the architefts molt eminent for ingenuity Arch,

ARC r 25 ] ARC Arch, nuity and invention Becoming thus the dupes of their clofely we examine the ornaments of this architecture, Arch, r*-*''——i own ingenuity, they were fond of difplaying it even the more ftiall we perceive that they are eflential parts, *—>r~mm when not necefiary. At laft arches became their princi- or derived from them by imitation : and the more we pal ornament, and a wall or ceiling wa$> not thought dref- confider the whole ftyle of it, the more clearly do we fed out as it Ihould be till filled full of mock arches, fee that it is all deduced from the relifh for arcades, incroffing and butting on each other in every dire&ion. dulged in the extreme, and pufhed to the limit of pofIn this procefs in their ceilings they found that the pro- fibility of execution. jecting mouldings, which we now call the Gothic tracery, formed the chief fupports of the roofs. The plane There is another fpecies of arch which muft not be Dome or fuifaces included between thofe ribs were commonly overlooked, namely, the Dome or Cupola, with all it3cuPola vaulted with very fmall ftones, feldom exceeding fix or varieties, which include even the pyramidal fteeple or eight inches in thickneis. This tracery therefore was fpire. not a random ornament. Every rib had a pofition and It is evident that the ere&ion of a dome is alfo a direction that was not only proper, but even neceflary. fcientific art, proceeding on the principles of equilibraHabituated to this fcientific arrangement of the mould- tion, and that thefe principles admit and require the ings, they did not deviate from it when they ornament- fame or fimilar modifications, in confequence of the coed a fmooth furface with mock arches ; and in none of hefion and fruftion of the materials. At firlt fight, too, the highly ornamented ancient buildings will we find a dome appears a more difficult piece of work than a 33 Degrnera- any pofitions. This is by no means the cafe in plain arch ; but when we obferve potters kilns and cy of that many of the modern imitations of Gothic architefture, glaishoufe domes and cones, of vaft extent, ere&ed by %le. Ignorant of the dire&ing ordinary bricklayers, and with materials vaftly inferior even ^ our beft archittfts. principle, or not attending to it, in their ftucco work, in lize to what can be employed in common arches of they pleafe the nnlldlled eye with pretty radiated fi- equal extent, we muft conclude that the circumftance of gures ; hut in thefe we frequently fee fuch abutments curvature in the horizontal direction, or the abutment of mouldings as would infallibly break the arches, if of a circular bafe, gives fome afiiftance to the artift. Of thefe mouldings were really performing their ancient this we have complete demonftration in the cafe of the office, and iupporting a vaulting of confiderable extent. cone. We know that a vaulting in the form of a pent Nay, this began even before the Gothic ftyle was finally roof could not be executed to any confiderable extent, abandoned. Several inftances are to be found in the and would be extremely hazardous, even in the fmalleft highly enriched vaultings of New College, and Chrifl dimenfions; while a cone of the greateft magnitude can Church in Oxford, in St George’s Chaoel at Windfor, be raifed with very fmall ftones, provided only that we and Henry Vll.’s Chapel in Weftminfter. prevent the bottom from flying out, by a hoop, or any -5 We call the middle ages rude and barbarous; but fimilar contrivance. And when we think a little of the Of eafier c mllruc there was furely much knowledge in thofe who could matter, we fee plainly, that if the horizontal iedfion be ! execute fuch magnificent and difficult works. The perfe&ly round, and the joints be all dire&ed to the *10"atjIiaa working drafts which were neceffary *or fuch varieties axis, they all equally endeavour to Hide inwards, while arch.' of oblique interfe&ions muft have required confiderable no reafon can be offered why any individual ftone fhould fkill, and would at prefent occupy many very expenfive prevail. They are all wedges, and operate only as volumes of mafons jewels, and carpenters manuals, and wedges. When we confider any fingle courfe, therethe like. All this knowledge was kept a profound fe- fore, we fee that it cannot fall in, even though it may cret by the corporation, and on its breaking up we had be part of a curve which could not ftand as a common all to learn again. arch ; nay, we fee that a dome may be conftru&ed, haThere is no appearance, however, that thofe archi- ving the convexity of the curve, by the revolution of tects had ftudied the theory of equilibrated arches. which it is formed, turned towards the axis, fo that the J hey had adopted an arch which was very ftrong, and outline is concave. We fhall afterwards find that this permitted confiderable irregularities of preffure—we is a ftronger dome by far than if the convexity were mean the pointed arch. The very deep mouldings with outwards, as in a common arch. We fee alfo that a which it was ornamented, made the arch ftones very cone may be loaded on the top with the greateft weight, Great fkill in proportion to the fpan of the arch. But they without the fmalleft danger of forcing it down, lo of the a- . had ftudied the mutual thruft of arches on each other long as the bottom courfe is firmly kept from burfting care an( archited! ^ vention 8reat ^ theybecome contrived to make every in- outwards. The ftone lanthern on the top of St Paul's for this ’purpofe an ornament, fo that cathedral in London weighs ieveral hundred tons, and the eye required it as a nectflary part of the building. is carried by a brick cone or eighteen inches thick, with Thus we frequently fee fmall buildings having buttreffies perfect fafety, as long as the bottom courfe is preventat the fides. Thefe are necefiary in a large vaulted ed from burfting outwards. The reafon is evident: building, for withftanding the outward thruft of the The preffure on the top is propagated along the cone vaulting; but they are uielefs when we have a flat ceil- in the direction of the flant fide ; and, fo far from haing within. Pinnacles on the heads of the buttrefies ving any tendency to break it in any part, it tends raare now confidered as ornaments ; but originally they ther to prevent its being broken by any irregular prefwere put there to increafe the weight of the burtrefs: fure from foreign caufes. even the great tower, in the centre of a cathedral, For the fame reafons the octagonal pyramids, whichpro ^conwhich now conftitutes its great ornament, is a load al- form the fpires of Gothic architedture, are abundantly ruction of nioft indifpenfably necefiary, for enabling the four prin- firm, although very thin. The lides of the fpire ofo&agonal cipal columns to withftand the combined thruft of the Salifbury cathedral are not eight inches thick after thePyramuk‘ aifles, of the nave, and tranieptg. In fhort, the more o&agon is fully formed. It is proper, however, to diSup?l. Vot. I. Part I. D reft

ARC ARC [ 26 3 change, becaufe the weight of each courfe is fuperadded Arch. re£i the joint? to the axis of the pyramid, and to make to that of the portion above it, to complete the preffure the courting joints perpendicular to the flant tide, becaufe the projefting mouldings which run along the on the courfe* below. Through B draw the vertical anglei are the abutments on which the whole pannel line BCG, meeing /3 produced in C. We may take depends. A confiderable art is necefleuyfor fupporting b c to prefs the preffure of all that is above it, propathofe pannels or tides of the oftagon which fpring from gated in this direftion to the joint KL. We may alfo the angles of the fquare tower. This is done by be- fuppofe the weight c*f the courfe HL united in £, and ginning a very narrow pointed arch on the fquare tower adiing on the vertical. Let it be reprefented by b F. at a g’-eat difiance below the top ; fo that the legs of If we form the parallelogram FGC, the diagonal b G the arch being very long, a ftraight line may be drawn will reprefent the dirtftion and intenfity of the whole from the too of the keytlone of the arch through the preffure on the joint KL. Thus it appears that this whole arch ftones of the legs. By this difpofition the preffure is continually changing its direction, and that thrufts anting from the weight of thefe four pannelsare the line, which will always coincide with it, muft be a made to meet on the maffive mafonry in the middle of curve concave downward. If this be precifely the the fides of the tower, at a great diftance below' the curve of the dome, it will be an equilibrated vaulting ; fpringing of the fpire. This part, being loaded with but fo far from being the ftrongeft form, it is the the great mafs of perpendicular wall, is fully able to weakeft, and it is the limit to an infinity of others, which with ft and the horizontal thruft from the legs of thofe are all ftronger than it. This will appear evident, if arches. In many fpires thefe thrufts are ftill farther re- we fuppofe that b G does not coincide with the curve B, but paffcs without it. As we fuppofe the arch • lifted by iron bars which crofs the tower, and are hookftones to be exceedingly thin from infide to outfide, it is ed into pieces of brais firmly bedded in the mafonry o£ plain that this dome cannot {land, and that the weight of the fides. . # J* There is much nice balancing of this kind to be ob- the upper part will prefs it down, and fpring the vaultExamples ©ffuch con ■ferved in the highly ornamented open fpires ; iuch as ing outwards at the joint KL. But let us fuppofe, on ftrudlion. thofe of Bruftels, Mechlin, Antwerp, &c. We have the other hand, that b G falls within the curvelineal elenot many of this fort in Britain. In thofe of great ment b B. This evidently tends to pufti the arch ftone magnitude, the judicious eye will difcover that parts, inward, toward the axis, and would caufe it to Aide in, which a common fpedfator w'ould confrder are mere or- fince the joints are fuppofed perfectly fmooth and flipnaments, are neceflary for completing the balance of the ping. But fince this takes place equally in every tlonc whole. Tall pinnacles, nay, even pillars carrying eota- of this courfe, they muft all abut on each othet in the blatures and pinnacles', are to be feen {landing on the vertical joints, fqueezing them firmly together. Theremiddle of the {lender leg of an arch. On examination, fore, refolving the thruft b G into two, one of which is we find that this is neceffary, to prevent the arch from perpendicular to the joint KL, and the other parallel to fpringing upwards in that place by the prefiure at the it, we fee that this laft thruft is withftood by the verticrown. The fteeple of the cathedral of Mechlin was the cal joints all around, and there remains only the thrnft rr.oft elaborate piece of architecture in this tafte in the in the dire&ion of the curve. Such a dome muft therewot Id, and was really a winder ; but it was not calcu- fore be firmer than an equilibrated dome, and cannot lated to withftand a bombardment, which deftroyed it be fo eafily broken by overloading the upper part. When the curve is concave upwards, as in the lower in 1578. part of the figure, the line b C always falls below b B, Such frequent examples of irregular and whimfical buildings of this kind, {how that great liberties may be and the paint C below B. When the curve is concave taken with the principle of equilibration without rifle, downwards, as in the upper part of the figure, 'l O if we take care to fecure the bate from being thru ft paffes above, or without b B. The curvature may be outwards. This may always be done by hoops, which fo abrupt, that even b' G' {hall pafs without 'b B , and can be concealed in the mafonry ; whereas, in common the point G' is above B'. It is alfo evident that the arches, thefe ties would be vifible, and would offend the force which thus binds the Hones of a horizontal courfe together, by puffing them towards the axis, will be eye. It is now time to attend to the principle of equili- greater in fiat domes than in thofe that are more conbrium, as it operates in a fimple circular dome, and to vex ; that it will be ftill greater in a cone ; and greater determine the thicknefs of the vaulting when the curve ftill in a curve whofe convexity is turned inwards: for is given, or the curve when the thicknefs is given. in this laft cafe the line b G will deviate moft remarkPlate If. Therefore, let B £ A (fig. 17.) be the curve which pro- ably from the curve. Such a dome will ftand (having duces the dome by revolving round the vertical axis AD. poliffed joints) if the curve fprings from the bale with 39 Stability ofp We fhall fuDpofe this curve to be drawn through the any elevation, however fmall ; nay, fince the fi iftion of a dome de- middle of all the arch ftones, and that the courftng or two pieces of Hone is not lets than hah oi their mutual pends on horizontal joints are every where perpendicuar to the preffure, fuch a dome will ftand, although the tangent principles curve. We fhall fuppofe (as is always the cafe) that to the curve at the bottom fhould be horizontal, prothe thicknefs KL, HI, &c. of the arch ftones is very vided that the horizontal thruft be double the weight fmall in comparifon with the dimenfions of the arch. of the dome, which may eaffly be the cafe if it do not 40 If we confider any portion HA h of the dome, it is rife high. Thus we fee that the {lability of a dome depends on Different plain that it prefi’es on the courfe, of which HL is an arch ftene. in a direftion b C perpendicular to the joint very different principles from that of a common arch, n0 HI, or in the direttion of the next fuperior element and is in general much greater. It differs alio in a -mon arch (lb of the curve. As we proceed downwards, courfe af- ther very important circumftance, viz. that it may be ter courfe, we fee plainly that this direction mull open in the middle : for the uppernoit courfe, by tendArch.

ARC [2 7 1 arc ins* equally in every part to Aide in tov/ard tire axis, be, and complete the parallelogram MONT, and draw Arch. ' prefl'es all together in the vertical joints, and a&s on the GQ^perpendicular to the axis, and produce b F, cutting next courfe like the key Hone of a common arch. the ordinates in E and e. It is plain that MN is to Therefore an arch of equilibration, which is the weak- MO as the weight of the arch HA/j to the thruH b c eft of all, may be open in the middle, and carry at top which it exerts on the joint KL (this thruft being proanother building, luch as a lanthern, if its weight do pagated through the courfe HILK) ; and that MO , not exceed that of the circular feg men t of the dome that or its equal be, or id, may reprefent the weieht of the b is omitted. A greater load than this would indeed half AH. break the dome, by caufing it to fpring up in fome of Let AD be called and DB be called y. Then the lower courfes; but this load may be increafed if the be z= x, and eC=y (becaufe b c h in the dire&ion of curve, is flatter than the curve of equilibration : and any load whatever, which will not crufh the Hones to the qlement b). It is alfo plain, that if we make y powder, may be fet on a truncate cone, or on a dome conftant, BC is the fecond fluxion of *, or BC = x, formed by a curve that is convex toward the axis ; pro- and^e and BE may be confidered as equal, and taken vided always that the foundation be effedlually prevent- indiferimmateiy for *. We have alfo£ C= a/.v1 -f y\ ed from flying out, either by a hoop, or by a fufficient Let d be the depth or thicknefs HI of the arch Hones. xnafs of folid pier on which it is fet. We have mention1 2 ed the many failures which happened to the dome of Then d x + y will reprefent the trapezium HL ; and fince the circumference of each courfe increafes in St Sophia in ConHantinople. We imagine that the thruH of the great dome, bending the eaftern arch out- the proportion of the radius y, dys/ x1 y2 will exward as foon as the pier began to yield, deltroyed the half dome which was leaning on it, and thus, almoH in prefs the whole courfe. Ify' be taken to reprefent the an inflant. took away the eaHern abutment. We think fum or aggregate of the quantities annexed to it, the that this might have been prevented, without any change formula will be analogous to the fluent of a fluxion, and in the injudicious plan, if the dome had been hooped 2 with iron, as was pra&ifed by Michael Angelo in the fd$ «/ *> + y w'ill reprefent the whole mafs, and alfo the weight of the vaulting, down to the joint HI. vaftly more ponderous dome of St Peter’s at Rome, and ^ by Sir Chriflopher Wren in the cene and the inner Therefore we have this proportion f dy \/ x2 41 Excellency dome of St Paul’s at London. The weight of the : d y s/ x2 ~ b e : C G, rr $ d • C G atter con ofStPaui^ dderably exceeds 3000 tons, and they occa“fion a horizontal thruH which is nearly half this quand x tity, the elevation of the cone being c.bout 6oQ. This = x : C G- Therefore C G = A?JL-. l+jl. being diHributed round the circumference, occafions a ... . . fdy^+ J2 If the curvature of the dome be precifely fuch as Hrain on the hoop = —1— of the thruft, or nearlyJ puts it in equilibrium, but without any mutual preffure 2X 22 238 tons. A fquare inch of the worH iron, if well in the vertical joints, this value of OG muft be equal to forged, will carry 25 tons with perfeft fafety; therefore CB, or to x, the point G coinciding with B. This a hoop of 7 inches broad and inches thick will com•• • dy x 1~ pletely fecure this circle from burHing outwards. It is, condition will be expreffed by the equation —— however, much more completely fecured ; for befides a fdy a/ *3+/ hoop at the bafe of very nearly thefe dimenfions, there are hoops in different courfes of the cone which bind it = x, or, more conveniently, by d y \/ x '- + r into one mafs, and caufe it to prefs on the piers in a di/dy / x1 + y2 x reftion exactly vertical. The only thrufts which the But this form gives only a tottering equilibrium, indepiers fuftain are thofe from the arches of the body of pendent of the fridion of the joints and the cohefion of the church and the tranfepts. Thefe arc moH judi- the cement. An equilibrium, accompanied by fome firm cioufly direfted to the entering angles of the building, liability, produced by the mutual preflure of the vertiand are there reliHed with infuperable force by the whole lengths of the walls, and by four folid mafles of cal joints, may be exprefled by the formula mafonry in the corners. Whoever conflders with atJdy s/ x2jry2 tention and judgment the plan of this cathedral, will fee 2 2 tnat the thrufts of thefe arches, and of the dome, are * , dy /x -4- v x t . * t or by —1^ —f , where t is fome incomparably better balanced than in St Peter’s church x 2 , J dy v x -j-jy" x * at Rome. But to return from this fort of digrefiion. 41 variable pofitive quantity, which increafes when x inWe have feen that if 1/ G, the thruft compounded of Theory of This laft equation will alfo exprefs the equithe curves the thruft l C, exerted by all the courfes above HL.LK, creafes. proper for and if the force l> F, or the weight ot that courfe, be librated dome, if t be a conftant quantity, becaufe in domes. everywhere coincident with ^B, the element of the this cafe —is 0. curve, we fhall have an equilibrated dome ; if it falls t within it, we have a dome which will bear a greater r v X s/ X load ; and if it falls without it, the dome will break at Since a firm liability requires itN- fhall the joint. We muft endeavour to get analytical expref.. J dy +yz Hons of thefe conditions. Therefore draw the ordinates1 be greater than x, and C G muft be greater than C B : btb , BDB", Ce/C". Let the tangents at b and b' Hence we learn, that figures of too great curvature, meet the axis in M, and make MO, MP, each equal to v.hofe fidcs defeend too rapidly, are improper. Alio, I) 2 fmcc Arch.

28 ] ARC j dome, whofe outline is an undulated curve, may he made Arch, dy x kJ + y - abundantly firm, cfpecially if the upper part be convex fmce ftabllity requires that we have and the lower concave outwards. The chief difficulty in the cafe of this analyfis arifes greater than fdy s/x2 +/, we learn that the upper part from the neceffity of expreffing the wei yht of the inof the dome muft not be made very heavy. _ This, by diminilhinaj the proportion of 3 F to £ C, diminifhes the cumbent part, or /dy\^ x1 + y1- This requires the angle cbG, and may fet the point G above which meafurement of the conoidal furface, which, in mo:t will infallibly fpring the dome in that place. We fee cales, can be had only by approximation by means of here alfo, that the algebraic analyfis exjpreffes that pe- infinite feriefes We cannot expedt that the generality culiarity of dome-vaulting, that the weight of the up- of praftical builders are familiar with this branch of maper part may even be fuppreffed thematics, and therefore will not engage in it here ; but content ourfelves with giving fuch inftances as can be dy \/ x* + y* __ The fluent of the equation 2 r +7 underftoad bv fuch as have that moderate mathematical J'dy \f x + y knowledge which every man fhoutd poffeis who take* the name of engineer. 1 2 L x -fIs moll eafily found. It is LJ'dys/X -f y The furface of any circular portion of a fphere is veL /, where L Is the hyperbolic logarithm of the quan- ry eafily had, being equal to the circle deferibed with a tity annexed to it. If we confidei y as conilantj and radius equal to the chord of half the arch. This racorrect the fluent fo as to mahe it nothing eft the vertexj dius is evidently — \/x2 y2. In order to difeover what portion of a hemifphere it may be expreffed thus, \,fdy s/ x1 4~y2 ' —Lx fdy f ^ 4 T-I,f t> may be employed (for it is evident that we cannot emL J 4- L A This give us Lr' ploy the whole) when the thickneis of the vaulting is a y uniform, we may recur to the equation or formula and therefore/V^^l±2l= / ^ -r.—— —Jdyf x' + y1. Let a be the radius a y. This laft equation will eafily give us the depth of a yy and vaulting, or thicknefs d of the arch, when the curve is of the hemifphere. We have 1 a 2 2 . ^ . . d v v/ x 4- v* ^ x -}- t x ‘y given. For its fluxion is 7.y. > Subftituting thefe values in the formula, : a y a ~y\ n2 2 d t —T— & t X we obtain the equation y V a — = /— y y ..We andr/ = —7— t—^ - , which is all expreffed in known J \/ a"—y yy v xM-y1 eafily obtain the fluent of the fecond member = at quantities ; for we may put in place of t any power or 2 Therefore fundlion of x or of y, and thus convert the expreffion —■ ‘V^a —- y-, and y ■=: a s/ if the radius of the Iphere be 1, the half breadth of the into another, which will ftill be applicable to all forts of curves. 4- V' or 0,786, and dome muft not exceed n/X t * the height will be 618. The arch from the vertex is Inftead of the fecond member—+ - we might em- about 5 10 49'. Much more of the hemiiphere cannot x *» Hand, even though aided by the cement, and by the ploy , where p is fome number greater than unity. friftion of the courfinjz joints. This laft circumftancc, by giving connexion to the upper parts, caufes the x This will evidently give a dome having {lability ; be- whole to prefs more vertically on the courfe below, and thus diminifhes the outward thruft ; but it at the fame 1 v/ x time diminifties the mutual abutment of the vertical will then be caufe the original formula lojoints, which is a great caufe of firmnefs in the vaultfdy f x* + y* ing. A Gothic dome, of which the upper part is a .. ^ pax1 x portion of a fphere not exceeding 45° from the vertex, greater than x. This will give d ~ — * Each and the lower part is concave outwards, will be very yyW x2 4 y2 ftrong, and not ungraceful. 43 of thefe forms has its advantages when applied to parBut the public tafte has long rejefted this form, and Dome’of ax feems rather to feledt more elevated domes than this por-St peters ticular cafes. Each of them alfo gives r/— . — tion of a fphere; becaufe a dome, when feen from a, sat Rome. yy v^M-y* fmall diftance, always appears flatter than it really is. ^ when the curvature is fuch as is in precife equilibrium. The dome of St Peter’s is nearly an ellipfoid externally, And, laftly, if d be conftant, that is, if the vaulting be of which the longer axis is perpendicular to the horizon. of uniform thicknefs, we obtain the form of the curve, It is very ingenioufly conftruded. It fprings from the becaufe then the relation of x to x and toy is given. bafe perpendicularly, and is very thick in this part. The chief ufe of this analyfis is to difeover what After rifing about 50 feet, the vaulting feparates into curves are improper for domes, or what portions of two thin vaultings, which gradually feparate from each given curves may be employed with fafety. Domes are other. Thefe two fhells are connedled together by thin generally built for ornament ; and we fee that there is partitions, which are very artificially dovetailed in both, great room for indulging our fancy in the choice. All and thus form a covering which is extremely ftiff, while curves which are concave outwards will give domes of it is very light. Its great fttffneis was neceflary for engreat firmnefs.: They are alio beautiful. The Gothic abling the crown of the dome to carry the elegant ftone lan them ARC

Arch.

ARC [ 29 ] ARC lantTiern with fafcty. It is a wonderful performance, hemifphere, and may be broken off at any horizontal Arch, and has not its e^ual in the world ; but it is an enor- courfe, and then a fimilar or a greater portion of a imalv mous load in companion with the dome oi St Paul’s, ler fphere may fpring from this courie as a bale. It and this even independent of the difference of ftze. If alfo bears being interfe&ed by cylindrical vaultings in they were of equal dimenfions, it would be at leaft five every direction, and the interfeftions arc exaft circles, times as heavy, and is not fo firm by its gravity ; but and always have a pleating effeft. It alio fprings moft as it is connefted in every part by iron bats (lodged in gracefully from the heads of mall piers, or from the the lolid mafonry, and well fecuied from the weather hv corners of rooms of any polygonal fhape; and the arches having lead melted all round them), it bids fair to laft formed by its interfetfions with the walls are always cirfor ages, if the foundations do not fail. cular and graceful, forming very handfome Ipandrels in It a circle be delcribed round a centre placed any- every pofition. For thele realons Sir Chriftopher Wren platell. where ii^the tranfverfe axis AC (fig. 18. N° i.) of an employed it in all his vaultings, and he has exhibited ellipfe, fo as to touch the ellipfe in the extremities B, many beautiful varieties in the tranfepts and the aifles of an ordinate, it will touch it internally, and the circu- ol St Paul’s, which are highly worthy of the obiervalar arch ab will be wholly within the elliptical arch tion o* architects. Nothing can be more graceful than B A b. Therefore, if an elliptical and a fphtrical vault- the vaultings at the ends of the north and ibuth traning fpring from the fame bale, at the fame angle with fepts, elpecially ?.s firnfhed off in the fine mfide view the horizon, the fpherical vaulting will be within the el- publifhed by Gwynn and Wale, 46 ct c liptical, will be flatter and lighter, and therefore the We conclude this article with oLferving, that the^^' ‘ ^" f weight of the next courfe below will bear a greater pro- connection of the parts, arifing from cement and fromjieAent portion to the thruft in the direftion of the curve ; fridion, has a great efPCt on dome vaulting. In the valSttherefore the fpherical vaulting will have more liability. iame way as in common arches and cylindrical vaulting, ing. On the contrary, and lot fimilar reafons, an oblate el- it enables an overload on one place to break the dome liptical vaulting is preferable to a fpherical vaulting in a diftant place. But the refiftance to this effea is fpringing with the fame inclination to the horizon. much greater in dome-vaulting, becaufe it operates all (tig. 18. N° 2.) round the overloaded part. Hence it happens that domes Dimenfions Pcrfuaded, that what has been faid on the fubjeft are much lefs {battered by partial violence, fuch as the of the btf| convinces the reader that a vaulting perfectly equilibra- falling of a bomb or the like. Larje holes may be broforni of a ted throughout is by no means the befl form, provided ken in them without much affeding the reft. ; but, on dome. that the bafe is fecured from feparating, we think it un- the other hand, it greatly dimimfhes the ftrength which neceflary to give the inveftigation of that form, which fhould be derived from the mutual preffure in\he vertihas a confiderable intiicacy ; and fhall content ourfelves cal joints. FriCIion prevents the Aiding in of the arch with merely giving its dimenfions. The thickncfs is ftones which produces this mutual preffure in the vertifuppofed uniform The numbers in the firft column of cal joints, except in the very higheit courfes, and even the table exprefs the portion of the axis counted from there it greatly diminifhes it. Thefe caufes make a the vertex, and thofe of the fecond column are the great change in the form which gives the greatefl lengths of the ordinates. ftrength ; and as their laws of action are but very imperfeClly underftood as yet, it is perhaps impofiible, in the prefent Hate o’- our knowledge, to determine this AD DB AD DB AD DB form with tolerable precifion. We fee plainly, howtoo 610,4 1080 °;4 2990 1560 ever, that it allows a greater deviation from the beft 200 1140 3 >4 744 3442 1600 form than the other kind of vaulting, and domes may n,4 300 1200 9°4 3972 1640 be made to rife perpendicular to the horizon at the 26,6 400 1 r 00 1260 4432 1670 bafe, although of no great thicknefs; a thing which 500 1320 49^2 1700 52,4 muft not be attempted in a plane arch. The immenfe 600 1522 1360 5336 1720 9',4 addition of ftrength which may be derived from hoop146,8 700 1738 1400 SI 5^ 1740 ing, largely compenfates for all defeCts; and there is 800 1984 223,4 1440 6214 1760 hardly any bounds to the extent to which a very thin 3 26,6 900 2270 1480 6714 f 780 dome-vaulting may be carried, when it is hooped or 1000 2602 1520 4^5,4 7260 1800 framed in the direction of the horizontal courfes. The roof of the Halle du Bled at Paris is but a foot thick, I he curve delineated in fig. 19. is formed according and its diameter is more than 200, yet it appears to to thefe dimenfions, and appears deflitute of graceful- have abundannt ftrength. It is, on the whole, a noble nels ; becaufe its curvature changes abruptly at a little fpecimen of architecture. diftance from the vertex, fo that it has fome appearance 47 of being made up of different curves pieced together. We muft not conclude this article without taking Tht iron But if the middle be occupied by a lanthern of equal, notice of that magnificent and elegant arch which has^ridSe at or of fmaller weight, this defeft will ceaie, and the whole been ereCted in catt iron at Weremouth, near Sunderwill be elegant, nearly relembling the exterior dome of land, in the county of Durham. The inventor and ar^ St Paul’s in London. chiteCt is Rowland Burdon, Elq; one of the repre45 Advantages It is not a fmall advantage of dome-vaulting that it fentatives of that county in rhe prefent Parliament. of dome- is lighter than any that can cover the fame area. If, This arch is a fegment of a circle whofe diameter is au moreover, it be fpherical, it will admit confiderable va- about 444 feet. The tpan or cord of the arch is 236 rieties of figure, by combining different fpheres. Thus, feet, and its verfed fine or fpring is 34 feet. It iprings a dome may begin from its bale as a portion of a large at the elevation of 60 feet from the furface of the river Arch. — »

ARC -ARC [3° ] The rib having been all trimmed and put together. Arch.' ver at low water, fo that veflels of 200 ot* pethaps 300 V"—tons burden may pafs under it in the middle of the fo as to form the exad curve, the bolts are all taken out, and the horizontal bridles are theri fet on in their ftream,-and even 50 feet on each fide ot it. The fweep of the arch confifts of a feries of frames of places, and the bolts are again put in and made fait by caft iron, which butt on each other, in the fame man- the forelocks. The bolts now pafs through the {boulner as the vouffoirs of/a ftone arch. One of thele ders of the bridles, through the wrought iron bars, and frames pr blocks (as we fhall call them in future) is repre- through the caft iron arm that is between them, and forelocks bind all fail together. The manner in Fiate IV. fen ted in fic. 1. as feen in front. It is caft in one piece; the and confifts of three pieces or arms BC, BC, BC, the which this connection is completed is diftindly feen in middle one of which is two feet long, the upper being fio-. 2. which {hows in pertpedive a double block in fomewhat more, and the lower fomewdiat lefs, becaufe front, and a (ingle block behind it The butting joints their extremities are bounded by the radius drawn from of the two front blocks are at the letters E, F, E; the the centre of the arch. Thefe arms are four inches fquare, holes in the fiioulders of the horizontal crofs pieces are 4S and are connected by other pieces KL, of inch length at FI. This conftrudion is beautifully Ample and very judi- |ts cnthat the whole length of the block is five feet in the direction of the radius. Each arm has a fiat groove on each cious. A vaft addition of ftrength and of ftiffnefs fide, which is exprefied by the darker fhading, three inches procured by lodging the wrought iron bars in grooves judfciouSj broad and three fourths of an inch deep. A iedtion of formed in the caft iron rails; and for this purpofe it is of this block, through the middle of KL, is reprefented great importance to make the wrought iron bars fill the by the light-ftiaded part BBB, in which the grooves are grooves completely, and even to be lo tight as to remore diltindtly perceived. Thefe grooves are intended quire the force of the forelocks to draw them home to for receiving fiat bars of malleable iron, which are em- the bottom of tl e grooves. There can be no doubt but ployed for connedting the different blocks with each that this arch is able to and currently employed, in working it; fuch as ftraight pointed arches being thus produced, Handing oppofite lines, plain furfaces, fquate angles, and various mould- to each other in pairs, let each pair be hound by a hoings ufed to (often the effefl of abrupt terminations: rizontal pole lying on the oppofite forks, and crofling all of which, origination in motives of mechanical con- the longitudinal pole deferibed above. “ Two of the rods of each corner pod, and three of venience, and of Ample ornament, had. in very early times, been appropriated to mafonry, and confidered as thofe of each of the others, being thus difpofed of, we eftential in every finifhed work of ftone ; fo that, when have one of each corner poll and two of each middle the imitation of nature was introduced, thefe mafonic poll ilill to employ, which is done as follows : A pair forms Hill maintained their ground, and, being blended of thefe unoccupied rods being brought from any two with the forms of nature, the two claffes reciprocally pods which Hand diagonally to each other, and made to meet in the middle, not as in the firft cafe crofting modified each other. “ This combination of art with nature, of which we in an angle, but fide by fide, forming a femicircle, and fee the moft perfect example in the Corinthian capital, joined together after the manner of a hoop ; and the produces what are called architeiftonic forms, in which fame being done with every pair of diagonal polls (fig. the variety of nature, being fubje&ed to the regularity 3.), the whole rods will have been employed. “ In this manner a frame would be conftrudled fit to of art, the work acquires that peculiar character which, in a natural objefl, we confider as offenfive, under the fupport thatch or other covering; and fuch a one has name oi formality ; but which, in architedfture, we ad- probably been often ufed. It would feem, however* mire as a beauty, under the name of fymmetry : thus, that, for the fake of ftrength, the number of rods has ^ j we reprobate the fonnality of an avenue, and praile the been increafed in each duller, by the introdu&ion, between every two of them, of an additional rod, which fymmetry of a colonnade. “ Such is the nature of archite&onic imitation ; a rifing with them to the roof, Hill continues its middle device which probably originated in accident, but to pofition, as they fpread afunder, and meets the 1 , which aichitedture is indebted for its highefl attain- zontal pole at an intermediate point. This is ftiown in fig. 6. which is drawn with its covering of thatch ; ments.” As the ftone edifices of ancient Greece were con- and, from the imitation of a dwelling fo conftrudted, ftrudted in imitation of a wooden fabric, compofed of we may eailly trace the three leading charafterillics of fquare beams laid at right angles on round polls or Gothic archite&ure, the pointed arch, the cluflered coftems of trees. Sir Ja es conceives that the Gothic fa- lumn, and the branching rbof, as exhibited in fig. 7.” Upon the lame principles Sir Jams Hall, with much brics with pointed arches have been executed in imitaingenuity, accounts for the peculiar forms of the Gotion of a ruftic dwelling, condrufled in the following manner : Suppofe a let of round polls driven firmly in thic door, the Gothic window, and the pointed fpire: to the ground in two oppofite rows, the interval be- but it is not our intention to fuperfede the necefiity of tween the neighbouring pulls in the fame row being having recomie to his memoir, but to excite the defire of

ART [ 33 1 ART Arch'tec* of our readers to perufe as well that paper as a larger nietic, however, or logifiics, has been ufed by Vieta and Arithmetic tu e ' work which he promifes on the fame fubjedt, and in which others (or the rnles of computations in algebra. I! Political Arithmetic. Bee Political Arithmetic,, Ar edl, i Arithmetic wc ^ou^f: not but they will find both entertainment and < 1 iiiilrndVion. Wefijall conclude this article, therefore, Encycl. with an experimental proof of the juftnefs of his hypoStxagefimal Arithmetic. See Ar.it k me tic I Hid ) thefis. Encycl. ' J ' In the greater part of our late attempts at Gothic Tetraaic Arithmetic, is that in which only the four archite&ure, it is allowed by every man ot talle that we characteis o, 1, 2, 3> are uied. A treatile o[ this kind have failed. The failure is to be accounted for by the of arithmetic is extant by Erhard or Echard Weigel. buildings havingbeen conftrudtedupon no confident prin- But both this and binary arithmetic are little better ciple, applicable to every part of them, but upon a fervile tnan curiofittes, efpccially with regard to praCtice; as copying of ancient edifices, of which the ilru&ure was ail numbers are much more compendioufiy and convelittle underftood by the copiers. Sir James Hal!, how- niently exoreffed by the common decuple feale. ever, by applying his theory to praftice, has conftru&eda Univerfal Arithmetic, is the name given by Newbuilding in this ftyle, which has far furpaffed, he fays, his ton to the fcience of algebra; of which he lef t at Camown expectation, and has certainly gained the approba- bridge an excellent treatife, being the text-book drawn tion of every man of tafte and fcience by whom we up for the ufe of his leCtures, while he was profeflor of have had occalion to hear it mentioned. “ A fet of mathematics in that univerfity. polls of afh, about three inches in diameter, were placed ARIi'HMETICAL complement, of a logain two rows, four feet afunder, and at tfi^ interval of rithm, is what the logarithm wants of jo-ocqoo, &c. four feet in the rows ; then a number of (lender and ta- and the ealied way to find it is, beginning at the pering willow rods, ten feet in length, were applied to left hand, to iubtraCl every figure from y, and the lalt. the polls, and, in the manner which we have deferibed, from to. formed into a frame, wdiich being covered with thatch, ■ARTi^DI (John), was born in the year 1705, in produced a very fubdantial roof, under which a perfon the province of Angermania, in Sweden. From nacan walk with eafe. ture he inherited an ardenr paffion for all branches of “ This little fttuCture exhibits, in miniature, all the natural hiftory, but he excelled moll in that branch of •characteriftic features of the Gothic (lyle. It is in the it which is termed ichthyology. In 1724 he went to ^form of a crofs, with a nave, a choir, and a north and Itudy at the univerfity of Upfal, where fome years afterfouth tranfept. The thatch, being fo difpofed on the wards he gained the f riendfliip of the immortal Linnteus, frame as not to hide the rods of which it is compofed, who narrates the principal events, of his life in the folthey reprefent accurately the pointed and femicircular lowing animated terms. arches, and all the other peculiarities of a groined roof.” “ In 1728 (fays Linmsus) I came from Lund to ARCTUS, a name given by the Greeks to two con- Upfal. I wifhed to devote myfelf to medicine. I inftellations of the northern hemifphere, by the Latins quired who, at that univerfity, excelled mod for his called Ursa Major and Minor, and by us the Greater knowledge : every one named Artedi. 1 was impatient to fee him. I found him pale, and in great diand Lejfer Bear. Binary ARITHMETIC. See Binary Arithmetic, flrefs for the lofs of his father, with his thin hair neEncycl. glected. He refembkd the portrait of Ray the natuDuodecimal Arithmetic, is that which proceeds from ralift. His judgment was ripe, his thoughts profound, 12 to 1 z, or by a continual fubdivifion according to 12. his manners fimple, his virtues antique. The converfaThis is greatly ufed by mod artificers in calculating the tion turned upon (tones, plants, animals. I was enchantquantity of their work; as bricklayers, carpenters, pain- ed with his obfervations, equally ingenious and new ; for at the very firll he was not afraid to communicate ters, tilers, &c. Harmonical Arithmetic, is fo much of the doCtrine them to me with the utmoft franknefs. I defired his of numbers as relates to the making the comparifons, friendlhip, he alked mine. From that moment we formed a friendlhip; which we cultivated .with the greateft reductions, See. of mufical intervals. Arithmetic of Infinites, is the method of dimming ardour for feven months at Upfal. I was his bed friend, up a feries of numbers, of which the number of terms and I never had any who was more dear to me. How is infinite. This method was fird invented by Dr Wal- fweet was that intimacy 1 With what pleafure did we lis, as appears by his treatife on that fubjeCt; where fee it increafe from day to day ! The difference, even he fiiows its ufes in geometry, in finding the areas of of our characters, was uleful to us. His mind was more luperficies, the contents of folids, &c. But the method fevere, more attentive ; he obferved more (lowly, and ot fluxions, which is a kind of univerfal arithmetic of v/ith greater care. A noble wnulation animated us. infinites, performs all thefe more eafily, as well as a As I defpaired of ever becoming as well indruCted in great many other things, which the former will not chemidry as he, 1 abandoned it ; he alfo ceafed to dudy botany with the fame ardour, to which I had devoreach. Logiflical Arithmetic, & uzme fometimes employed ted myfelf in a particular manner- We continued thus for the arithmetic of iexagefimal fractions, ufed in agro- to dudy different branches of fcience; and when one of nomical computations. Shakerly, in his Babula Bri- us excelled the other, he acknowledged him for his tannica, has a table of logarithms adapted to fexagefi- mader. We difputed the palm in ichthyology ; but mal fractions, which he calls logifiical logarithms ; and foon I was fotced to yield, and I abandoned that part the expeditious arithmetic, obtained by means of them, ©f natural hidory to him, as well as the amphibia. I he calls logijlical arithmetic. The term logijlical arith- fucceeded better than he in the knowledge of birds and E infeCts, Suppl. Vol. I. Part I.

ART F 34 1 ART Artedi. infe&s, and he no longer tried to excel in thefe branch- this great ichthyologift, who had ever, delighted in that Artedi. es. We marched together as equals in lithology, and element.” Of the works of this eminent naturalift there have been the hiftory of quadrupeds. When one of us made an ebfervation, he communicated it to the other: fcarce a two editions, of which the former was publilhed by day paffed in which one did not learn from the other' Linnaeus in 1738, and the latter by Dr Walbaum of fome new and interefting particular. Thus emulation Lubeck, in the years 1788, 1789, and 1792. This excited our induftry, and mutual afllftance aided our ef- edition, which is by much the molt valuable, is in three forts. In fpite of the didance of our lodgings, we faw volumes qto ; of which the lirll contains the hiftory of each other every day. At lall I fet out for Lapland ; the fcience of ichthyology, commencing feveral years he went to London. He bequeathed to me his manu- before the Chriftian era, and coming down to the prelent times. The fecond prefents to the reader the fcr'pts and his books. “ In 1735 I went to Leyden, where I found Ar- Philofophia Ichthyologica of Artedi, improved by Waltedi. I recounted my adventures ; he communicated his baum, who was benefited by the writings of Monro, to me. He was not rich, and therefore was unable to Camper, Kaetfeuter, and others. Here alfo are added be at the expence of taking his degrees in phyfic- I tables containing the fyftem of fifties by Ray, Dale, recommended him to Seba, who engaged him to publifh Schaeffir, Linnaeus, Gowan, Scopola, Klein, and Grohis work on hikes. Artedi went to join him at Am- novius. The third volume, which completes the colle&ion of Artedi’s works, contains the technical definifterdam. “ Scarcely had I finilhed my Funclamenia Bctanica. tions of the fcience. After the generic and individual I communicated it to him; he let me fee his Philofophia chara&ers, come the names and Latin phrafes of ArIchthyologic a He prcpofed to hnifh as quickly as pol- tedi ; the fynonymes of the belt naturalifts; the vulgar hble the work of Seba, and to put the laft hand to it. names in Englilh, German, Swedifh, Ruffian, Danilh, He {bowed me all his manufcripts which I had not feen: Norwegian, Dutch, and Samoyed ; the feafon and the I was preffed in point of time, and began to be impa- countries where every kind is found their varieties, tient as being detained fo long. Alas! if I had known their defeription, and obfervations. The modern difeothis was the laft time I fhould fee him, how Ihould I veries, even to our own times, are added ; fo that in this part is collected the obfervations of Gronovius, have prolonged it! “ Some days after, as he returned to fup with Seba, Brunich, Tenant, Forfter, Klein, Bloch, Gmelin, Hafthe night being dark, he fell into the canal. Nobody felquift, Brouftbnet, Lelke, Builh, Linnaeus, and other perceived it, and he perifhed. Thus died, by water, great examiners of nature.. ASTRONOMY IS a fcience which has been cultivated from the earlieft ages, and is converfant about the moft fublime obiefts of inquiry which can employ the mind of man; It has accordingly been treated at great length in the Encyclopaedia Britannica ; but, in the opinion of fome of the moft judicious readers of that work, the compiler of the fyftem which is there delivered has failed in his attempt to give a penpicuous and conne&ed view of the t fcience in its prefent ftate of improvement. This defeCb Objedt of it is our duty to remedy. Our object, therefore, in this this articie. ffipplementary article, will be to bring into one point of view the phyfical fcience which may be derived from the confideration of the celeftial motions ; that is, to deduce from the general laws of thofe motions the inferences with refpeft to their fuppofed caufes, which conftitute the philofophy of the aftronomer. The caufes of all phenomena are not only inferred from the phenomena, but are charafterifed by them ; and we can form no notion of their nature but what we conceive as competent to the phenomena themfelves. The aftronomical phenomena are aflumed to be the motions of the bodies, which we call the fun, \\\e planets, the comets, &c. The notion which we exprefs by the word body in the prefent cafe, is fuppofed to be the fame with that which we form of other obje&s around us, to which we give the fame name ; fuch as (tones, (ticks, the bodies of animals, &c. Therefore the notion which we have of the caules of the celeftial motions muft be the fame with that which we have of the caufes of motion

in thofe more familiar bodies. All men feem to have Metaphor! agreed in giving the name forces, or moving forces,cal ufe of to the caufes of thofe familiar motions. This is a ft- tenu gurative or metaphorical term. The true and original meaning of it is, the exertion which we are confciousof making when we ourfelves put other bodies in motion. Force, when ufed without figure, always fignifies the exertion of a living and afting tiring. We are more interefted in thofe productions of motion than in any other, and our recolleftions of them are more numerous. Hence it has happened that we ufe the fame term to exprefs the caule of bodily motion-in general, and (ay that a magnet has force, that a fpring has force, that a moving body has force. Our own force is always exerted by the intervention of our own body ; and we find that the fame exertion by which we move a (tone, enables us to move another man ; therefore we conceive his body to refemble a ftone in this refped, and that it alfo requires the exertion of force to put it in motion. But when we refleCb on our employment of force for producing motion in a. body, we find ourfelves puzzled how to account for the motion of our own bodies. Here we perceive no intervening exertion but that of willing to do it; yet we find that we cannot move it as we pleafe. We alfo find that a greater motion requires a greater exertion. It is therefore to this exertion that the reflecting man reftrains the term force ; and he acknowledges that every other ufe of it is metaphorical, and that it is a refemblar.ee

ASTRO N O M Y. 3J blsrice in the ultimate effe£l alone which difpofes us to We can conceive a force aCting equally or unequally. Employ the term in fuch cafes : but we find no great If we fuppofe it to aft equally or uniformly, we fupinconvenience in the want of another term pole that in equal times it produces equal effeCts ; that We farther find, that our exertion is necefiary, not is, equal determinations, or equal changes of determinaonly for producing motion where there was none be- tion. W e have no other notion of equality or uniforfore, but alfo for producing any change of motion ; mity of aCtion. Therefore it mufl produce equal augand accurate obfervation fhows us, that the fame force mentations or diminutions of velocity in equal times ; is required for changing a motion by any given quan- theiefore it muft produce an uniformly accelerated or retity, as for producing that quantity where there was tarded motion. Uniformly accelerated or retarded mo-Acrtferanone before. tion is, therefore, the mark of uniform or unvaried ac- e< moion Laftly, we are confcious of exerting force when we tion. In fuch a motion, the changes of velocity arerhi;R,ail10^ refill the exerted force of another; and that an exertion, proportional to the times from the beginning of the ac-adiV^ perfectly limilar to this, will prevent fome very familiar tion ; and if the motion has begun from reft, the whole^ 1 ^ tendencies to motion in the bodies around us: thus an acquired velocities are pn portional to the times irofn exertion is necelfary for carrying a weight, that is, for the beginning of the motion In this cafe, the fpaces preventing the fall of that weight. deferibei are as the fquares of the times from the beAll thei’e refemblances between the effecls of our for- ginning ©f the motion ; and thus we arrive at an oftencible exertions and the changes of motion which ac- fible mark of the unvaried adion of a moving force, company the meeting, and fometimes the mere vicinity viz. ipaces increafing in the duplicate ratio of the times: of other bodies, juftify us in the ufe of this figurative for fpaee and time are all that we can immediately obi language The refemblance is found to be the more ferve ia any motion that is continually varying ; the perfedl as we obferve it with more care, and, in fhort, velocity or determination is only an inference, on the appears to be without exception. Bodies are therefore fuppofition that the motion continues unchanged for faid to on each other, to rejiji each other, to rejijl a fome time, or that all adlion ceaies for fome time. change of motion, 8cc. This abftradl reafoning is perfedly agreeable to every Therefore, wherever we obferve a change of motion, phenomenon that we can obferve with diftindlnt we infer the exiftence and exertion of a changing force; Thus we cannot, or at kaft we do not, conceive the and we infer the diredlion of that exertion from the di- weight of a body to vary its adion during the fall. rection of the change ; and the quantity of the exer- We confider this weight as the caufe of the fall—as the tion, or intenfity of the force, from the quantity of the moving force - and we conceive it to ad uniformly. change. And, in tad, a body falling freely, defcribes Ipaces The fiudy of the caufes of the celeftial motions is which are proportional, not to the times, but to the therefore hardly different from the fiudy of the motions fquares of the times, and the fall is a motion uniformly themfelves ; fince the agency, the kind, and the degree accelerated. In like manner, the motion of a body of the moving force, are immediate inferences from the riling in the air, in oppofition to gravity, is uniformly exiftence, the kind, and the quantity of the change of retarded. g motion. 1 his kind of motion alfo gives us a certain meafure And pives d rneafure lur .... nrces. refpeft. Therefore thefe determinations are the only the moving force continued to aft on it, and made it mealures of thefe two forces ; that is, moving forces are really deferibe 60 feet with an accelerated motion. Becaufe halves have the fame proportions with the conceived by us as having the proportion of the velocities which they produce in a body by aCting in a man- units of which they are the halves, it is plain that we may take the fpaces, deferibed in equal times with moner perfectly fimilar. E2 tiong

rce. the ipaces through which the defleding forces would Mathematicians are farther able to demonftrate, that if have impelled the bodies from a irate of reft in the time forces vai*y their coi 'med adion in any manner what- of deferibing the arches AC, a c. Therefore, when ever, the propc1 t on ot the fpaces delcnbed by two bo- thde times are diminilhed without end, the ultimate radies in equal times approaches nearer and nearer to the tio of AD and ad\% the ratio of the forces which deproportion of the fpaces which they would deferibe in fied the bodies in the points A and a. But it is evithofe times by the until m adion of the forces, as the dent that the ultimate ratio of AC to « d is the ratio of times thernlelves are fmalier ; and therefore \vhenever the velocity in/the point A to the velocity in the point we can point out the ultimate ratio o; the {paces, de- a ; becaufe thefe arches are fuppofe d to be deferibed in scribed in eoual t: les, thefe times being diminifhed the fame or equal times. Therefore the defleding forwithout end, we obtain the ratio of the forces. ces, by which bodies are made to deferibe arches of Motions may be changed, not only in quantity, by circles, are to each other as the fquares of the velocities acceleration or retardation, but alfo in diredion, by de- diredly, and as the defledive cords of thofe circles infleding a body from its former diredion. When a .verfely. This ratio may be expreffed fymbolically thus* riateVI body, moving uniformly in the diredion AB.(hg. I.), F Y : or thus, in a proportional equatior,9 has its motion changed in the point 13, and, inkead of C c defcribmg BO uniformly in the next moment with the former velocity, defenbes BD uniformly in that mo- f-r ment, it is plain that the motion BO will be the fame, It is eafy to fee that in this laft formula/ exprefles ■whether the body had begun to move in A, or in F, diredly the line b e, or the fpace through which the or in G, or in B, provided only that its determination body is adually made to deviate from r.edilineal motion to move, or its velocity, be the lame in all thofe points. in the time of deicribirg the arch a c. It is a third Complete the parallelogram BCDE. It is well known, proportional to ae the defledive chord, and ac the arch that if one force ad on the body which would make it of the circumference deferibed in a fmall moment ot deferibe BC, and another which would make it deferibe time. This is the meafure afforded immediately by obIntenfuy the body will deferibe BD. Hence we learn, fervation. We have obferved the arch AC that is deand direc- that when a body has the motion BC changed into the feribed, and know the diredion and the length of AE tion of de- motion BD, it has been aded on in the point B by a iledirg force w^-ch woay have cauied a body at tell in B to from fome circumftances of the cafe. The formula which treating this queftion by the help of *orces* deferibe BE. Thus we can difeover the intenfity comes to us, when 2 “U1 and diredion of the tranfverfe force which produces fluxions, is/= -y. This is perhaps a more proper any defledion from the former diredion. In general, the force is that which would have produced in a body expreffion of the phyfical fad ; for it expreffes twice at reft that motion BE, which, when compounded with the line be, or the meafure of the velocity which the defleding force would have generated in the body by the former motion BC, proauces the new motion BD. Thefe two principles, viz. ift, that forces are pro- ading on it during the time of its deferibing the arch portional to the velocities which they produce in the a c. But it is indifferent which meafure we take, profame circumftances, and, 2d, the compoiition of mo- vided we always take the fame meafure. Thetfirft mation or forces, will ferre for all the phyfical inveftiga- thematicians, however, have committed miftakes by mixtrons in aftronomy. All the celeftial motions are curvi- ing them. The planets, however, do not deferibe circles: but h'neal, and therefore are inftances of continual deflection, and of the continual adron of tranfverfe or defled- all the curves which can be. deicribed by the adion oi ing forces. We muft therefore endeavour to obtain a finite defleding forces are of fuch a nature, that we can deferibe a circle through any point, having the fame general meafure of fuch continual defleding forces. Meafjre of ^ Let two bodies A and a (fig. 2.) deferibe in the fame tangent, and the fame curvature which the planetarythtfeforces time the arches AC, ac of two circles. They are de- curve has in that point, and which therefore ultimately ebtained. from the tangents AB, ab. Let us fuppofe that coalefces with it. T his being the cafe, it is plain that the diredion of the defleding forces is known to be the planet, while paffmg through a point of the curve, that of the chords AE, ae of thefe circles. Let thefe and deferibing an indefinitely Imall arch of it, is in the be called the deflective chords. Draw CB, r pa- fame condition as if deferibing the coincident arch of rallel to AE, ae, and CD, cd parallel to AB, ab. the eqnicurve circle. Hence we obtain this moft geneJoin AC, a c, CE, and c e. It is plain that the angle ral propofition, that the tranfverfe force by ‘which a plaBAG is equal to the angle CEA in the alternate feg- net is made to deferibe any curve, is diredly as the fquare ment. Therefore ACD is alfo equal to it; and, be- of its velocity, and inverfely as the dfie hive chord of the caufe the angle CAD is common to the two triangles equicurve circle. Farther: The velocity of a body in any point A CAD and EAC, thefe two triangles are fimilar, and (fig.

ASTRO N O M Y. 37 (fU'. 2.) of the curve, is equal to that which the deflec- minute deviations which muft refult from the phyfical tive force in that point would generate in the body by law, but which the art of obfervation was not then fufadting uniformly on it along A.F, one-fourth part of ficiently advanced to difeover in the phenomena. This the defledive cord AE or the equicurve circle. It is excited the efforts of men of fcience to improve the art the fame which the body would acquire at F, after a of aftronomical obfervation ; and not only have the inti- iii3 *3 His followuni ormly accelerated motion along AF, mations of Newton been verified by moder n obfervation, ers. For it is certain that there is fome length AF, fuch but other deviations have been difeovered, and, in prothat the velocity acquired at F is the fame with the ve- ce.s of time, have alfo been fhown to be confequences locity in the point A of the curve. Draw FG parallel of the fame general law of agency : And, at this preto the tangent, and join AG. Make the arch ACI fent day, there is not a fingle anomaly of the planetary — 2AF. Then, becaufe the fpace defcribed with a motion's which has not been fliown to be a modification uniformly accelerated motion is one half of the fpace of one general law which regulates the aftion ; and which would be uniformly defcribed with the final ve- therefore charafterifes the nature of that Angle force locity, the arch ACI would be uniformly defcribed which actuates the whole fyftcm of the fun, and his atwith the velocity which the body has at A in the time tending planets and comets. that AF is defcribed with the uniformly accelerated moIt was a moft fortunate circumftance that the conftition ; and the arch AB will be to the arch AJ as the tut’on of the folar fyftem was fuch that the deviations time of defcribing AB to that of defcribing AI ; that from the general law are not very confiderable. The is, as the time of falling through AD to that of falling cafe might have been far otherwife, although the law, through AF. But the motion along AF being uni- or nature of the planetary force, were the fame, and formly accelerated, the fpaces are as the fquares of the the lyftem had been equally harmonious and beautiful. times. Therefore AD is to AF as the fquare of the Had two or three of the planets been vaftly larger than arch AC to the fquare of the arch AI. But AD is they are, it would have been extremely difficult to difto AF as the fquare of the chord AC is to the fquare eover any laws of their motion fufficiently general to ot the chord AG, Therefore the arch AC is to the have led to the fufpicion or the difeovery of the univerchord AC as the arch AI is-to the chord AG. But the fal law of action, or the fpecific circumftance in the plaarch and chord AC are ultimately in the ratio of equa- netary force w’hich diftinguiflies it from all others, and lity. Therefore the chord AG is equal to the arch A I. chara&erifes its nature. But the three laws of the plaTherefore AG is double of AF. But becaufe the tri- netary motions difeovered by Kepler were lo nearly angles FAG and GAE are fimilar, AF is to AG as true, at leaft w’ith refpeft to the primary planets, that AG to AE ; and therefore AE is double of AG and the deviations could not be obferved, and they w’ere quadruple of AF. Therefore the vefocity at A in the thought to be exaft. It was on the fuppofition that curve is that, which would be produced by the uniform they were exalt, that Newton affirmed that they w’ere impulfe of the defle&jng fogee along the fourth part of only modifications of one law ftill more general, nay 10 the deflective chord of the equicurve circle. univerfal. Two tfeful Thefe two afFe6xions or properties of curvilineal moWe fhall follow in order the fteps of this inveftigaaffedhons oftJong are 0f tj,e extenf1VTe ufe ancJ fr{ve an eafier f0. tion. r rnrui lir-w»a! » # % curvilineal Sir Ifaac Newton took it for granted, that the fun The fteps Biodocs. lutron of moft quefhons than we ebtain by the more ufual methods, and deferve to be kept in remembrance and planets confifted of matter which refembled thofeby which by fuch as engage much in the difeufiion of queftions bodies which we daily handle, at leaft in reipeft ofthe^Pr0~ of this kind. their mobility; and that the forces which agitatecceiiei’ Thus the invefligation of the forces which regulate them, confidered merely as moving forces, but without the planetary motions, is reduced to the talk of difeo- confidering or attending to their mode of operavering the velocity of the planet in the different points tion, were to be inferred, both as to their direction of its mbit, and the curvature in thofe points, and the and as to their intenfity, from the changes of motion pofition of the deflective chords. II v/hich were aferibed to their agency. He firft endeaPhyfical The phyfical fcience of aftronomy muft confift in the voured to difeover the direliion ©f that tranfverle force i'cience of difeovery of the general laws which can be affirmed with by w’hich the planets are made to deferibe curve lines. aflrouomy refpedt to the exertion of thofe forces, whether with re- Kepler’s fiift law furnifhed him with ample means for fpeft to their direction or the intenfity of their aCtion. this difeovety. Kepler had difeovered, that the right If the mechanician can do more than this, and fhow that line joining the fun and any planet defcribed areas proporevery motion that is obferved is an immediate 01 remote tional to the times. Newton demonllratcd, that if a bocenfequence of thofe general laws, he will have comple- dy was fo carried round a fixed point fituated in the 12 plane of its motion, that the right line joining it with Completed ted the fcience, and explained every appearance. by Newtoft This has accordingly been done by Sir Ifaac Newton that point defcribed areas proportional to the times, and his followers. Sir Ifaac Newton has difeovered the the force which deflected it from an uniform reftilineal nd general law’s which regulate the exertions of thofe forces motion w’as continually direfted to that fixed point. which produce the planetary motions, by reafening from This makes the 2d propofition of his immortal work general phenomena which had been obferved with a cer- The Mathematical Principles of Natural Philofophy, and tain precifion before his time; and has alfo fliown that it is given in the article Astronomy of the Encyclocertain confiderable deviations from the generality w’hich patdia Britannica, $ 260. he iuppofed to be perfeft were neceffary confequences Hence Sir Ifaac Newton inferred, that the primarycf the very univerfality of the phyfical law, although the planets were retained in their orbits by a force contiphenomenon was not fo general as was at fir ft imagined. nually dire&ed to the fun ; and, becaufe Kepler’s law He has gone farther, and has pointed out feme other of motion wras alfo obferved by the fecondary planets

38

ASTRO NOM Y. in their revolutions round their refpeftive primary pla- perfon almoft ignorant of mathematics may fee the truth I? nets, this inference was extended to them. of this by looking into a table of natural verfed fines. Centripetal From the circumftance that the planetary defle&ing He will obferve, that the verfed fine of one degree is forces. forces in the different points of the mbit are always di- quadruple the verfed fine of half a degree, and lixteen refted toward one point as to a centre, they have been times the verfed fine of a quarter of a degree ; in fhort, that the verfed fines of fmall arches are in the propor16 ca'led CENTRIPETAL FORCES. Velocity of From this propolition may be deduced a corollary tion ©f the fquares of the arches. Now lince the arches deferibed in equal times are inverfely as the diftances, tV *n ^ich eftablifhes a general law of the motion of any re 11 (-nts planet in the different parts of its orbit, namely, that their verfed fines are inverfely as the fquares of the di©fitsorbit, the velocity which a planet has in the different points ftances. But t-hefe verfed fines are the fpaces through of its path are inverfely proportional to the perpendi- which the centripetal forces at the aphelion and periculars drawn from the fun on the tangents to the orbit helion ddledft the planet from the tangent. Therein thofe points refpe&ively. For, let AB, ab (fig. 3.) fore, &c. Thus we have found, that in the aphelion and peribe two arches (extremely fmall), deferibed in equal times, thefe arches mull be ultimately proportional to the ve- helion the centripetal force a&s with an intenfity that locities with which they are deferibed. Let SP, S/ is proportional to the fquares of the diftances inverfely. be perpendicular to the tangents AP, ap. The tri- As thefe are the extreme fituations of a planet, and as -angltrs A SB, & Q b are equal, becanfe equal areas are the proportion of the aphelion and perihelion diftances defciibed by the radii vefiores SA, S «, in equal times: are confiderably different in the different planets, and but in equal triangles, the bafes AB, a b, are recipro- yet this law of adlion is obferved in them all, it is reafonable to imagine that it holds true, not in thofe fituacally their heights SP, S or AB : a b — Sp : SP. This corollary gives us another expreffion of the ra- tions only, but in every intermediate fituation. But a tio of the centripetal forces in different points A and a of conjecture, however probable, is not lufficient, when a curve.- We faw by a former propofition, that the force we aim at accurate Icience, and it is needfary to exaat A (fig. 2.) is to the force at a as A.C2 X a e to mine whether this law of adlion is really obferved in ,g a c- ;< AE, which we may exprofs thus : F = V2 every point of the elliptical orbit. For this purpofe it is necefiary to mention fome geo-Dm nftraX c : •a2 X C If we exprtfs the perpendiculars SP, Sy> (in fh?. 3.) by the fymbols P,/, we have V2 : v1 zz p1: P2, metrical properties of the ellipfe. Therefore let ADBEted withreto thc and therefore F : / =z px X c : F2 X C. 'The centripetal (fig. 4.) be the elliptical orbit of a planet or comet, forces in different points of an orbit are in the ratio com- having the fun in the focus S. Let AB be the tranf-^ ' ’ pounded of the inverfe duplicate ratio of the perpendiculars verfe axis, and DE the conjugate axis, and C the centre. drawn to the tangents in thofe points from the centre of Let P be any point of the ellipfe. Draw PS through forces, and the inverfe ratio of the defective chords of the the focus. Draw the tangent PN, and SN from the focus, perpendicular to PN\ Draw PQ^perpendicular equicurve circles. are now a Draw QG Law*of condition to determine the law of to PN, meeting the tranfverfe axis in a difeovered, as he thought, the prod'u&ion of a preffure, may the weight of a heavy body. But we do not conlike gravity, irom motion, fays, “ as motion may a tile O„rSkn0w cern oorfelvcs with this queftion. We g?in a rroft ex- from preffing powers, fo we have feen that preffing 1’dge of tenfrve and important knowledge by our knowledge ot that law fa- t^-s ur;verfal law ; for we can now explain every phe- powers may anfe from motion.c Nit lee teat botli exnc ri-factory. pointing out how it is contained in this in the univtrfe. It is the bu fs of a philofopher to difeover, hy reafon and cbfervation,-which is the onmn law; and we can predift the whole events of the folar the other. It is incompatible with reafon, that bofyltem with unerring exadnefs. This fhould fatisfy tue of dies {hould be pofteffed of inherent tendencies ; much ? moft inquifitive mind. But, nilimur in vet hum, femper cupmufque negata. more that powers /hould exift independently. Farther, There feems to be a fatal and ruinous difpofitton in the that philofopher muff be reckoned to have affigned the human mind, a fort of priapifm of the underftandmg, true caufes of phenomena, who demouftrates that they arife from motion ; tor motion, once exi/ting, muft. be that is irritated by every interdid of natural imperfec- preferved for ever. In the.prefent inftance (a certain tion. We would take a microfpope to look at light ; whimfical fad of a ball running round the infide of a we would know what knowing is, and we would weigh hoop) we fee how a preffing power may be derived from heavinefs. , . . . All who are acquaintedxvith the writings of Anitotle motion; but we cannot fee how powers can exert themor be preferved, without motion. Wherefore we have fome notion of his whimflcal opinions on this fub- felves, may conclude that gravity, and all other powers, are ied. He imagines that the planets^ate conduded m derived from motion ; and it is our bufinefs to invetlitheir orbits by a fort of intelligences, ^xai, which animate the orbs that wheel them round. Although g’^te from what motions of what bodies each obfetvccl derives its origin.” 1 5 this crude conception met with no favour in later times, power Accordingly many attempts have been made to trace Vaio at- anoti)erj not more reafonable, was maintained by Leibthe planetary defledions to their origin in the motion account0 nitz, who called every particle of matter a monad, and of finite impelling matter; but thefe attempts could not for it. gave it a perception of its fituation/in the univerfe, ot fuccefsful, becaufe they are all built on hypothecs. its diflance and diredion from every other, and a power be It has been aftiimed, that there is a matter diffufed and will to move itfelf in conformity to this ikuatioit, through the ceieftial fpaces ; that this matter is in moby certain conftant laws. This in the Mo- tion, and by its impulfe moves the planets: but the onnad is nothing but an aukward fnbftitute for the pnn- ly reafon that can be given for the exigence of this cide of gravitation, which tlie learned infilled that_New- matter is the difficulty we find in explaining the planeton placed in every particle of matter as an innate defle&ions without it. Even if the legitimate conpower, and which they reprobated as unphdofophical. tary fequences of this hypothefis were confiftent with the But in what refped this perception mid adive propenfity is better, we do not perceive. It is more com- phenomena, we have not advanced in our knowledge, plex, and involves every notion that is reprehenGble m nor obtained any explanation. We have only learned, the other; audit offers no better explanation of the that the appearances are fitch as would have obtained had fuch a matter exifted and a&ed in this mariner. phenomena. # r But Newton is equally anxious with otner philoio- The obferved laws of the phenomena are as extenfive ■ phers not to aferibe gravity to matter as an innate in- as thofe of the hypothefis; therefore it teaches us noherent property. In a letter to_Dr Bently, he earnell- thing but what we knew without it. S But this is not all that can be faid againft thofe *fta Iv requefts"him not to charge him with fuch an abfurd tempts ; their legitimate confequences are iticonflftent with (nco y f finu C 0 opinion. It is an avowed principle, that nothing can aS the phenomena. By legitimate confequences We mean of thefe on any thing that is at a diftance; and tips is confiderlaws of motion. _ Thefe muft be admitted, and are ed as an intuitive axiom. But it is furely very obfeure; the admitted, by the philofopher who attempts to explain for we cannot obtain, or at leaft convey, clear notions of the terms in which it is expreffed. _ The word a£l is the planetary motions by impulfe. It would be ridicuentirely figurative, borrowed from animal exertions ; it lous to fuppofe a matter to fill the heavens, having laws is therefore unlike the expreffion of anything itititled of impulfe" different from thofe that are obferved by io thTapplliation of If we hy tottpref. it common matter, and which laws rnt.ft be ewJrtW fo & without ugnit, feme, we find our confidence as to anfwer the thofe purpofe. would be more at Wltnoui j- • — once -- *-- , in . .1its certainty to afii^n pro reItnata laws to theftmple planets 'Trearly dimrnifhed. Should we fay that the condition N of a body A cannot depend on another body B that is themfelves. Yet fuch was the explanation which the celebrated nt diftance from it, we believe that no perton will % Defcartes offered by his hypothefis of vertices, in which that he makes this affertion from perceiving the abfardity of the contrary propofitkm. In the demon ft rat ion, the planets were immtrfed and whirled round the fun. It

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ASTRO N O M Y. 49 ys Tt U aftonl/Ki'ng that fo crude a conception ever obtain- net follows its motion, non alrepta tmm, fed trdnquilli‘/o ticesof etj pn^. partifans ; yet it long maintained its authority, ter quaji natanie. The planet therefore has no tendenDebits and (till has zealous defenders. Till Sir Ifaac Newton cy to perfevere in its former (late of motion. Why faw the indifpenhble necefiity of mathematical invdliga- -therefore does it not follow this harmonic motion extion in every queftion of matter in motion, no perfon aftly, and deferibe a circle trtinquilliter natans ? This is had taken the trouble of giving any thing like a diilinct owing, fays Leibnitz, to its centrifugal force, by which defeription of thofe vortices, the circumftances of their it perieveres in a ftate of redlilineal motion. It has no motion, and the manner of their action ; all determined tendency to preferve its former velocity, but it perfewith that precilion that is required in the explanation : veres in its former direction. The planet there‘ore is for this mull always be kept in mind, that we want an not like common matter, and has laws of motion pecuexplanation of the prec.fe motions which have been ob- liar to itfeli ; it was needtefs therefore to employ any Jerved, and which will enable us to predict thofe which impulfe to explain its motions But to proceed: This are yet to happen. Men were contented with fome centrifugal force muft be countera&ed in every point of vague notion of a fort of firrularity between the effefts the orbit. Leibnitz therefore fuppoles that it is alfo of fuch vortices and the planetary motions in a few ge- urged toward the centre by a felicitation like gravity neral circumftances ; and were neither at the trouble to or attraction. He calls it the paracentric force. He confider how thefe motions were produced, nor how far computes what mnft be its intenfity in different parts of they tallied with the phenomena. Their account of things the orbit, in order to produce an elliptical motion, and was only fit for carelefs chat, but unworthy of the at- he finds that it muft be inverfely as the fquare of the tention of a naturalift. But fince this explanation came diftance from the centre (for this reafon he is frequent^ from a perfon defervedly very eminent, it was refpeCled ly quoted by Bernoulli, Wolff, and others, as the difeoBut Leibnitz arrives Examined hy Newton, and he honoured it with a ferious exami- verer of the law of gravitation). by Newton.nation. It is to this examination alone that we are in- at this refult by means or feveral mathematical blunders, debted for all the knowledge that we have of the con- either avifing from his ignorance at that time of fluxioft’^tion of a fluid vortex, of the motions of which it nary geometry, or from his perceiving that an accurate is lufceptible, of the manner in which it can be produ- procedure would lead him to a conclufion which he did ced, the laws of its circulation, and the effeffs which it not wiffi : for we have feen (and the demonftration is can produce. We have this account in Sir Ifaac New- adopted by Leibnitz in all his pofterior writings of this ton’s Principles of Natural Philofophy; and it contains kind), that if the ordinary laws of motion are ohferved, many very curious and intereiling particulars, which a body, aftuated by this paracentric force alone, will have been found of great fervice in other branches of deferibe an ellipfe, periorming both its motion of harmechanical philofophy. But the refult of the examina- monic circulation, and its motion of approach to and retion was fatal to the hypothclis ; (hewing that the mo- cefs from the centre, without farther help. Therefore, tions which were poffible in the vortices, and the effects if the harmonic circulation is produced by a vortex, a which they muft produce, are quite incompatible with force inverfely as the fqnare of the diftance from the the appearances in the heavens. We do not know one centre, combined with the harmonic circulation, will perion who has acquired any reputation as a mechani- produce a motion entirely different from the elliptical. cian that now attempts to defend it ; nor do we know It is demonftrated, that the force which is neceffary for of any other perfon belides Newton who has attempted deferibing circles at different diftances, with the anguto explain mathematically how the circulation or a fluid lar velocity of the different parts of the orbit, is not in can produce the revolution of a planet, if we except Mr the inverle duplicate, but in the inverfe triplicate, ratio ^ Leibnitz, the celebrated rival of the Britifti philofopher. of the diftances This muft have been the nature of L c,6 I P th fi- This gentleman publilhed in the Leipfic Review in his paracentric force, in order to counteract the centri Iff Leibnitz. 1689, three years after the publication of the Principiat fugal force arifing from the harmonic circulation. There- Difincemil an attempt to explain the elliptical motion of the pla- fore Leibnitz has not arrived at his conclufion by juftTT pf ^ nets, and the defeription of areas proportional to the reafoning, nor can be faid to have difeovered it. ]-jeauthur. times by the impulle ot a vortex. It muft not be paffed fays, Video hanc propqjitionem innotuijfe viro celiberrimo over in this place, becaufe it acquired great authority Ifaaco Nezutono, licet non pofjim judicare quomodo ad earn in Germany, and many of that country ftill affirm that pervemrit. This is really fomewhat like impudence. Leibnitz is the difeoverer of the law of planetary gra- The Principia were publifhed in 1686. They were revitation, and of the mechanical conftitution of the folar viewed at Leipiic, and the Review publifhed in 1687. fyflem. We cannot help thinking this explanation the Leibnitz was at that time the principal manager of that rnoft faulty of any, and a moft difingenuous plagiarifm Review. When Newton publifned, Leibnitz was living at Hanover, and a copy was lent him, within two from the writings of Newton. Mr Leibnitz luppofes a fluid, circulating round the months of its publication, by Nicholas Facio, long befun in luch a manner that the velocity of circulation in fore the Review. The language of the Review has every part is inverfely as its diftance from the fun. (everal Angularities, which are frequent in Leibnitz’s (iV. B. Newton had ihown that fuch a circulation was own compofrtion ; and few doubt or its being his wripoffible, and that it was the only one which could be ting. Befides, this propofition in the Principia had generated in a fluid by an action proceeding from the been given to the Royal Society feveral years before, centre). Leibnitz calls this harmonical circulation. He and was in the records before 1684. Thefe were all fuppofes that the planet adopts this circulation in every feen by Leibnitz when in England, being lent him by part of its elliptical orbit, obeying without any refift- his friend Collins. We think that the opinion which a candid perfon ance the motion of this fluid. He does not aferibe this to the impulfeof the fluid, faying exprefsly that the pla* muft form of tht whole is, that Leibnitz knew the proG pofttion, Suppl. Vol. I. Part I.

ASTRONOMY, portion, and attempted to demonftrate it in a way that under the name of Lucrecc' Newtonlcn ; and there are • would make it pafs tor his own difcovery ; or that he many who confider it as a good explanation of gravitaonly knew the enunciation, without underftanding the tion : for our part, wc think it inconceivable. The principles. His harmonic circulation is a clumfy way motions of the planets, with undiminifhed velocity, for of explaining the proportionality of areas to the times ; more than four thoufand years, appears incompatible and even this circulation is borrowed from Newton’s dif- with the impelling power ‘of this fluid, be its velocity fertation on the Cartefian vortices, which is alfo con- what It will. The abfokite precifion of the law of gratained in the Leipfic Review above mentioned. Leib- vitation, v/hich does not {how the fmalleft error during nitz was by this time a competitor with Newton for that time, is incompatible with an impulfe which cannot the honour of inventing the fluxionary mathematics, and be exaff/y proportional to the quantity of matter, nor was not guiltlefs of a£ts of difmgenuity in afferting his to the reciprocal of the fquare of the diftance, nor the claim. He publifhed at the fame time, in the fame Re- fame on a body moving with the rapidity ot the comet view, an almoft unintelligible differtation on the rehfl- of 1680 in its perihelion, as on the planet Saturn, ance of fluids, which, when examined by one who has whofe motion is almoft incomparably flower. What is learned the fubjeft by reading the Principia of Newton, the origin of the motion of this fluid ? Why does it affords an enigmatical defcription of the very theory not defiroy itfelf by mutual impulfe, flnce it is conti58 publifhed by Newton, as a neceflary part of his great nually paffing through every point ? &c. We have already obferved that Newton expreffed the Ether of work. But befides all the above objedtions to Leibnitz’s theo- fame anxiety to avoid the fuppofition of adtion among ry of elliptical motion, we may afk. What is this paracen- bodies at a diftance. lie alfo feemed to flrow fome dif- diflicup. tric force ? He calls it like gravity. This is precifely pofition to account for gravitation by the adlior. of a ties, Newton’s dodlrine. But Leibnitz fuppofes this alfo to contiguous fluid. This is the fubterfuge fo much rebe the impulfe of a fluid. It would have been enough curred to by precipitate fpeculatifts, by the name of had he explained the adfion of this fluid, without the the ether of Sir Ifaac Newton. He fuppofes it highly other circulating harmonically. He defers this expla- elaftic, and much rarer in the pores of bodies and in nation, however, to another opportunity. It muft have their vicinity than at a diftance ; therefore exceedingly very Angular properties: it muft impel the planet with- rare in the fun, and denfer as we recede from him. Beout difturbing the other fluid, or being difturbed by it. ing highly elaftic, and repelled by all bodies, it muft He alfo defers to another opportunity the explaining impel them to that Ade on which it is moft rare; therehow the fquares of the periodic times of different pla- fore it muft impel them toward the fun. This is enough nets are proportional to the cubes of the mean diftances; of its general conftitution to enable us to judge of its for this is quite incompatible with the harmonic circu- Atnefs for Newton’s purpofe. It is wholly unAt; for" lation of his vortex. This would make the fquares of fip.ce it is fluid, unequally denfe and elaftic, its particles the periods proportional to the diftances. He has per- are not in contact. Particles that are elaftic, and in a formed neither of thefe promifes. Several years after ftate of compreffion, and in contact, cannot be fluid ; this he made a corre&ion of one of his mathematical they muft be like fo many blown bladders compreffed in a blunders, by which he deftroyed the whole of his de- box ; therefore they are not in contaft; therefore they monftration. In fhort, the whole is fuch a heap of oh* are elaftic by mutual repulfion ; that is, by adting on fcure, vague, inconfiftent affumptions, and fo replete with each other at a diftance. It is indifferent whether this mathematical errors, that it is aftonifhing that he had diftance is a million of miles, or the millionth part of a hair’s breadth; therefore this fluid does not free Newton the ignorance or the effrontery to publifh it. Hypethefis There is another hypothefis that has acquired fome from the fuppofition which he wifhes to avoid. Nay, it «£ Ze Sage, reputation. M. le Sage of Geneva fuppofes, that there can be demonftrated, that in order to form a fluid paffes through every point of the univerfe a ftream of which fhall vary in denfity-from the fun to the extrefluid, in every direffion, with aftonifhing velocity. He mity of the folar fyftem, thete muft be a mutual repulfuppofes that, in the denfeft bodies, the vacuity is in- fion extending to that di/lance. This is introducing milcomparably more bulky than the folid matter; fo that a lions of millions of the very difficulties which Newton, folid body fomewhat refembles a piece of wire cage- wifhed to avoid; for each particle prefects the fame work. The quantity of fluid which paffes through will difficulty with a planet. We would now afk thefs atomical philofophers, why be incomparably greater than that of the intercepted fluid ; but the impulfe of the intercepted fluid will be they have, in all ages, been fo anxious to trace the cefenfibly proportional to the quantity of folid matter of leftial motions to the effedls of impulfe ? They imagine the body. A Angle body will be equally impelled in that they have a clear perception of the communication every direction, and will not be moved ; but another of motion by impulfe, while their perception of the probody will intercept fome fluid. Each will intercept duction of it in any other way is obfcure. Seeing, in fome from the other; and the impulfe on B, that is in- a very numerous and familiar collection of fadts, that tercepted by A, will be nearly proportional to the mat- motiongk communicated by impulfe, they think that it ter in A, and inverfely proportional to the fquare of is communicated in no other way, and that impulfe is * ^ its diftance from B ; and thus the two bodies will ap- the only moving power in nature. But is it true that our notion of impulfe is more clear Our nodor pear to tend toward each other by the law of gravitathan that of gravitation ? Its being more familiar is no°^in^“^e tion. exertec C C l ”| ar, 0rKia M. le Sage publifhed this in a work called Chmie argument. A caufe may be real, though it has Mechanique, and read leftures on this do&rine for many itfelf but once fince the beginning of time. In no cafe years in Geneva and Paris to crouded audiences. It is do we perceive the exertion of the caufe ; we only peraifo publiihed by Mr Prevail in the Berlin Memoirs, ceive the change of motion. The conftitution of our mind

\ A S T R O N O M Y. 5* r^ind rrak«s us confider this as an effeft, indicating a impulfe, without the aft’on of forces at a diftanee ? caufe which is inherent in that body which we always This appeals to us very doubtful. Eveiy one acquaintlee affociated with that change. Granting that our per- ed with Newton’s difeoveries in optics will grant, that ception of the perfeveranee of matter in its ftate of mo- the colours which appear between two objed-glafles of tion is intuitive, it by no means follows that the body long telefcopes, when they are prefled together, deA in motion muft move the body B by ftriking it. monftrate, that the glades do not touch each othe’*, exThe moment it ftrikes B, all the metaphylical argu- cept in the place where there is a black fpot. It rements for A’s continuance in motion are at an end, and quires more than a thoufand pounds to produce a fquare thev are not in the leatl affedied by the fuppohtion that inch of this fpot. Therefore every communication of A and B (hould continue at reft after the firoke ; and motion between two pieces of glafs, which can be pronve may defy any perfon to give an argument which will duced by one of them ftriking' the other, is produced prove that B will be moved ; nay, the very exiftence of without impulte, unlefs their mutual preffiire hasexceeded B may, for any thing we know to the contrary, be a 1000 pounds on the fquare inch of the parts which ad fufficient reafon for the ceflation of the motion of A. on each ether. Nay, fince we fee that a black fpot apThe production of motion in B, by the impulfe of A, pears on the top of a foap bubble, in the -middle of the muft therefore ftand on the fame foundation with every coloured rings, we learn that there is a certain thickother production of motion. It indicates a moving nefs at which light ceafes to be vifibly rcfled'ed'; therepower in A ; but this inherent power feems to have no fore the black fpot between the glafles does not prove dependence on the motion of A: (See what is con- that they touch in that part; therefore we cannot fay tained in n°8i. of the article Physics, and n° 67. of that any force whatever can make them touch. The Optics of the Encycl.) We fee there a motion pro- ultimate repulfion may be infuperable. If this be the duced in B without impulfe, and taken from A, fimi- cafe, the produdion of motion by impulfe is, in every lar in every refpeCt to every cafe of impulfe ; and we inftance, like the produdion of motion between the fee that the motion of A is necefl'ary for producing fuch magnets in n° 81. of the article Physics in the Encycl. a motion in B as is obferved in all cafes of impulfe, and is of the fame kind with the produdion of motion merely in order that the moving power, which is inhe- by gravity. _ 61 rent, in A, whether it be in reft or in motion, may ad "i herefore no explanation of gravitation can be de- fntei-vening during a fufficient time. Our confidence in the com- rived from any hypothefis whatever of intervening fluids. munication of motion, in the cafe mentioned there, is They only fubftitute millions of bodies for one, and ftillcultles.' ** derived entirely from experience, which informs us that leave the adion e dijlahti the fame difficulty as before. A poffdTes a moving power totally different from im- It is not in the leaft neceflaiy that we fhall be able to -pulfe. Our belief of the impelling power of matter conceive how a particle of matter can be influenced by therefore does not neceflarily flow from our intuitive another at a diftance ; if we have difeovered in every knowledge of the perfeverance of matter, although it inftance the precife degree and diredion of the effed gives us the knowledge of this perfeverance. It is like of this influence, we have made a moft important addia mathematical demonftration, a road to the dilcovery tion to our knowledge of nature ; and our fuccefs in of the property of figure, but not the caufe of that the cafe of the power of gravity fhould make us affiduproperty. The impulfion of matter is merely a fad, ous in our endeavours to difeover, from the phenomena, like its gravitation, and we know no more of the one the laws which regulate the other ad ions e dijlantiy than of the other. which obfervation is daily finding out. A knowledge It is not a clearer perception, therefore, which has equally accurate of the law of magnetic and ele£iric acprocured this preference of impulfion as the ultimate tion may enable us to give theories of magnetifm and explanation of motion, and has given rife to all the fool- eledricity equally exad with the Newtonian theory of ifh hypothefes of planetary vortices, ethers, animal fpi- gravitation. rits, nervous fluids, and many other crude contrivances Having, we hope, evinced the truth of this theorv, for explaining the abftrufe phenomena of nature. by following out the inveftigations to which Newton 6o Nor does it deferve any preference on account of its was gradually led, we might proceed to confider, in ormpulfe arely tb' greater familiarity. Juft the contrary : for one fad of der, the complicated and fubordinate phenomena which ;rved. undoubted impulle, we lee millions where no impulfe is depend on it. 1'he lunar and planetary inequalities are obferved. Confider the motion produced by the explo- the fubjeds that naturally come firft in our wav ; but fion o^ gunpowder. Where is the original impulfe? Sup- they have already been explained in all the detail that pofe the impulfe of the firft fpark of lire to be immenfe, this concife account will admit, as they occurred to how comes it that a greater impulle is produced by a Newton as tefts of the truth of his conjedure. If the greater quantity ©f gunpowder, a greater quantity of law be fuch as hefufpeded, its confequences muft be To quiefeent matter ? The ultimate impulfe on the bullet and fo; if the celeftial motions do not agree with them, fhould be lefs on this account. Here are plain exer- the law muft; be rejeded. We (hall not repeat any thing tions of moving powers, which are not reducible to im- therefore on this head, but confine our obfervations to pulfe. Confider alfo the fads in animal motion. Re- fuch applications of the theory of umverfal gravitation lied alfo, that there has been more motion, without any as newly difeovered objeds, or the improvement of afobferved impulfe, produced in the waters of a river fince tronomical obfervation and of fluxionary analylis, have the beginning of the world, than by all the impulfe that enabled us to make fince the time of Newton. man has ever obferved. Add to thefe, all the motions The fubferviency of the eclipfes of Jupiter’s fatelin magnetiim, eledricity, &c. Impulfe is therefore a lites to geography and navigation had occafioned their phenomenon which is comparatively rare. motions to be very carefully obferved, ever fince thefe Have we ever obferved motion communicated by pure • ufes of them were firft fuggefted by Galileo, and their G 2 theory

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ASTRO theory is as far advanced as that of the primary planets. Jt has peculiar difficulties. BeiH.T very near to Jupiter, the great deviation of his figure from perfedt fphericity makes the relation between their diftances from his centre and their gravitations toward it vaftly complicated. But this only excited the mathematicians fo much the more to improve their analyfis ; and they faw, in this little lyitem of Jupiter and his attendants, an epitome of the folar fyftem, where the great rapidity of the motions muft bring about in a {hort time every variety of configuration or relative pofition, and thus give us an example of thofe mutual difturbances of the primary planets, which require thoufands of years for the difcovery of their periods and limits. We have derived gj fome very^ remarkable and ufeful pieces of informaiiion Eternal du-from this inveftigation ; and have been led to the difrability of Covery of the eternal durability of the folar fyflem, a the folar tp^ng which Newton greatly doubted of. Mr Pound had oblerved long ago, that the irregularities of the three interior fatellhes were repeated in a period of 437 days ; and this obfervation is found to be juft to this day. 247 revolutions of the firft occupy 437^' 3^ 44' 123 fecond 437 3 42 61 third 437 3 36 26 fourth 435 14 16 This naturally led mathematicians to examine their motions, and fee in what manner their relative pofitions or configurations, as they are called, correfponded to this period : and it is found, that the mean longitude of the firft fatellite, minus thrice the mean longitude of the fecond, plus twice the mean longitude of the third, always made 180 degrees. This requires that the mean motion of the firft, added to twice that of the third, {hall be equal to thrice the mean motion of the fecond. This correfpondence of the mean motions is of itfelf a fingular thing, and the odds againft its probability feems infinitely great; and when we add to this the particular pofidons of the fatellites in any one moment, which is neceffary for the above conftant relation of their longitudes, the improbability of the coincidence, as a thing quite fortuitous, becomes infinitely greater. Doubts were firft entertained of the coincidence, becaufe it was not indeed accurate to a fecond. i he refult of the inveftigation is curious. When we follow out the confequences of mutual gravitation, we find, that although neither the primitive motions of projection, nor the points of the orbit from which the fatellites were projected, were precifcly fuch as iuited thefe obierved relations of their revolutions and their contemporaneous longitudes; yet, if they differed from them only by very minute quantities, the mutual gravitations of the fatellites would in time bring them into thofe pofitions, and thofe flates of mean motion, that would induce the obferved relations; and when they are once induced they will be continued for ever. There will indeed be a {'mall equation, depending on the degree of unfuitableneis of the fitft motions and pofitions ; and this caufes the whole fyltem to ofcillate, as it were a little, and but a very little way on each fide of this exaft and permanent ftate T he permanency of theie relations will not be deftroved by any fecular equations arifing from external caufes ; fuch as the aftion of the fourth fatellite, or of the fun, or of a refilling medium;

52

N O M Y. becaufe their mutual aftions will diftribute this equa* tion as it did the original error. T his curious relult came into view only by degrees,, as analyfis improved and the mathematicians were enabled to manage more complicated formulas, including more terms of the infinite feriefes that were employed to eyprefs the different quantities. It is to M. de la Grange that we are indebted for the completion of the difcovery of the permanency of the fyftem in a ftate very little different from wdiat obtains in any period of its exiftence. Although this required all the knowledge and addrefs of this great mathematician, in the management of the moft complicated analyfis, the evidence of its truth may be perceived by any perfon acquainted with the mere elements of fluxionary geometry. The law of the compofition of forces enables us to exprefs evcmy aftion of the mutual forces of the fun and planets by the fines and cofmes of circular arches, which increafe with an uniform motion, like the perpetual lapfe of time. The nature of the circle fhows, that the variations of the fines and cofines are proportional to the cofints and lines of the fame arches. 1 he variations of their fquares, cubes, or other powers, are proportional to the fines or cofines of the doubles or triples, or other multiples of the fame arches. Therefore fince the infinite feriefes which expreis thoie aftions of forces and their variations, include only Unes and cofines, with their powers and fluxions, it follows, that all accumulated forces, and variations of forces, and variations of variations, through infinite orders, are (till expreffible byrepeated fums of fines or col'mes, correlponding to arches which arc generated by going round and round the circle. The analyft knows that thefe quantities become alternately pofitive and negative; and therefore, in whatever way they are compounded by addition of themfelves, or their multiples, or both, we muft always arrive at a period after which they will be repeated with all their intermediate variations. It tpay be extremely difficult, it may be impoffible, in our prefent ftate of mathematical knowledge, to afeertain all thofe periods. It has required all the efforts of all the ijeniufes of Europe to manage the formulas which include terms containing the fourth and fifth powers of the eccentricities of the planetary orbits. Therefore the periods which we have already determined, and the limits to which the inequalities expreSed by fecular equations arrive, are ftill fubjefted to fmaller correftions of incomparably longer periods, which arife from the terms negiefted in our formulas. But the correftion arifing from any nt lefted term has a period and a limit ; and thus it will haopen that the fyftem works itfelt into a ftate of permanency, containing many intervening apparent anomalies. The elliptical motion of the earth contains an anomaly or deviation from uniform circular motion; the aftion of Jupiter produces a deviation from this elliptical motion, which has a period depending on the configuration of the three bodies; Saturn introduces a deviation fiom this motion, which has alfo a period; and fo on. There is another accurate adjuftment of motions which has attrafted attention, as a thing in the higheft degree improbable, in events wholly independent on each other. This is the exaft coincidence of the period of the moon’s revolution round the earth with that of her rotation round her own axis. The dlipticity or oval fhape of the moon differs fo infenlibly from a fphere, that

ASTRO N O M Y. 53 tion of its effeds after a longtime. It is only thus that that if the onpinal rotation had differed confiderably from the period of revolution, the pendular tendency to the effeds of the oblate figure ot Jupiter are perceived the earth could never have operated a change : but if in the motion of his fatellites. The boafied found phithe difference between thofe two motions was fo fmall, lofophy which fees fatal necefftty where the mojl Juccefsthat the pendular tendency to the line joining' the cen- fuljludents of nature favv moral excellence, has derived tres ot the earth and moon was able to overcome it af- yery little credit or title to the name of nuijdom, by letter fome time, the pole of the lunar fpheroid would de- ting loofe all thofe propenfities of the human heart 64 viate a little from the line joining the earth and moon, which are effentially deftrudive of foeial happinefs. and then be brought back to it with an accelerated Thete propenfities were always known to lurk in the A"devin,_ motion ; would pafs it as far on the other fide, and heart of man ; and thofe furely were the vviieft who lathen return again, vibrating perpetually to each fide o‘ boured to keep them in check by the influence of moral greatGr, the mean pofition of the radius veBor. The extent of principles, and particularly by cherifhing that difpofition this vibration would depend on the original difference of the human heart which prompts us. to fee contrivance between the motion, of rotation and the mean motion of wherever we fee nice and refined adjuftment of means revolution. i'his difference muff have been very Imall, to ends ; and, from the admirable beauty of the folar becaufe this pendular vibration is not ienfible from the fyftem, to cry out, earth The obierved libration of the moon is pre“ Thefe ate thy glorious works, Parent of good ! cifely what arifes from the inequality of her orbital mo“ Almighty, thine this univerfal frame, tion. For the fame reafons, the effeds of the fecular “ Thus wond’rous fair; thyfelf how wnnd’rous then! equations of the moon (which would, in the courfe of “ Unlpeakafcle, who fitt’ft above thefe heavens, ages, have brought her whole furface into our view, had “ To us invifible, or dimly feen her rotation been ftridly uniform) are counteraded by “ In thefe thy loweft works 3 yet thele declare her pendular tendency, which has a *orce fufficient to “ ] hy goodnefs beyond thought, and power divine. alter her rotation by nearly the fame flow and infenfible Par. LoJli b. v. charges that obtain in her mean motions. The fame “ But wandering oft, with brute unconfcious gaze, caufes alfo preferve the nodes of her equator and of her “ Man marks not Thee, marks not the mighty hand M orbit in the fame points of the ecliptic. The complete That, ever bufy, wheels the lilent fpheres.” demonflration of this is perhaps the moft delicate and Thomson. elegant fpecimen that has been given of the modern anThe moft important addition (in a philofophical view) alyfis. We owe it to M. de la Grange ; and he makes it appear that the figure of the moon is not that which that has been made to aftronomical fcier.ce fince the a fluid fphtre would acquire by its gravitation to the difeovery of the aberration of light and the nutation of ^ earth ; it muff be the effed of a more confiderable el- the earth’s axis, is that of the rotation of Saturn’s ring. The ring itfelf is an objed quite fim'ular; and when it Saturn’slipticity, or internal inequality ot denfity. rin Depenchon 'i bis permanency or the lyflem, within very narrow was dilcovered that all the bodies which had any imme- S* the law of limits of deviation from its prefent Hate, depends entire- d ate connection wuth a planet were heavy, or gravitaplanetary pianetary defledion. Had it been di- ted toward that planet, it became an interefting quefon ^ aefledion, Qr ,nvcr{ely as the diftance, the deviations would tion, what was the nature of this ring ? what iupporthave been iuch as to have quickly rendered it wholly ed this immenfe arch of heavy matter without its reftunfit for its prefent purpofes. They would have been ing on the planet ? what maintains it in perpetual convery great, had the planetary orbits differed much from centricity with the body of Saturn, and maintains its circles ; nay, had fome of them moved in the oppofite furface in one invariable pofition ? The theory of univerfal gravitation tells us what diredion The feledion of this law, and this form of the orbits, ftrikes the mind of a Newton, and indeed things are poffible in the folar fyftem ; and our conjecany heart poffefied of lenfibility to moral or intelledual tures about the nature of this ring muft always be reexcellence, as a mark of wifdom prompted by benevo- gulated by the circumftance of its gravitation to the lence. But De la Place and others, infeded with the planet. Thilofophers had at firft fuppofed it to be a Thecphobia Gailica engendered by our licentious de- luminous atmoiphere, thrown out into that form by the fires, are eager to point it out as a mark of fatalifm. great centrifugal force arifing from a rotation : but its They fay, that it'is effential to all qualities that are dif- well defined edge, and, in particular, its- being two very fufed from a centre to dimimfh in the inverfe duplicate narrow rings, extremely near each other, yet perfedly ratio of the diftance. But this is falfe, and very falfe .• ieparate, rendered this opinion of its conftitution more _ 6 Surgite mortales, terrenas mittete curas, Atque hlnc cddigena vires dignofcite Mentis} A pecudum vita longe latequs remote.

A S Y called incommenfurability, or the relation of two quanti- Afymp ties which have no common raeafure, as between 1 and totea. 4/2, or the fide and diagonal of a fquare. ASYMPTOTES (fee Encycl.) are, by fome, diftinguifhed into various orders. The afymptote is faid to be of the firft order, when it coincides with the bafe of the curvilinear figure ; of the fecond order, when is is a right line parallel to the bafe ; of the third order, when it is a right line oblique to the bafe; of the fourth order, when it is the common parabola, having its axis

A^U T t 56 ] A U T ^tfar HX18 perpendicular to the bafe; and, in general, of the nor and all the officers with whatever wood they have I! order it is a, parabola whofer ordinate ah occafron and it rs delivered to themtherefore at their has houfes r r Aiue- iqua. n 4-2 - n when .bafe. . -T n-, - isis oo -rwithout for any ; expence. The governor no —v*—* ways as the power ot- the he afymptote lique to the bafe, when the r?tio of the In ft fluxion df perfonal intereft to extend his views to this part of the the ordinate to the fluxion of the bafe approaches to an adminiftration, and to abolifti an abufe fo prejudicial to nffignable ratio, as its limit; but it is parallel to the the colony.” But the colonifts themfelves mull be a very indolent bafe, or coincides with it, when this limit is not affignand ftupid kind of people ; fince, if our traveller deable. ATTAR of roses. See Roses, Otter of, both in ferves credit, they negleft advantages with which the perfonal intereft of the governor cannot poflibly interthe Encyclopaedia and in this Supplement. AVANT-foss, or Ditch of the Counterfcarp, in for- fere. “ 1 was filled with indignation (fays M. Vailtification, is a wet ditch furrounding the counterfcarp lant’ to fee people, who have wood within their reach, on the outer fide, next to the country, at the foot of employ it in commerce, and not have the courage to the-glacis. It would not be proper to have fuch a build for themfelves habitable houfes. They live in ditch if it could be laid dry, as it would then ferve as a wretched hovels, confttlifted of wicker-work, daubed over with clay ; the fkin of a buffalo, fixed at the four lodgment for the enemy. corners to as many ftakes, ferves them for a bed ; and AUB1GNE. See Stuart in this Supplement. AUMIL, in Bengal, a native colkftor or manager the door, which is at the fame time a window, is ftmt by a mat; while two or three mutilated chairs, a tew of a diftrift on the part of government. AUTENIQUA, a large and beautiful country in pieces of plank, a kind of table, and a pitiful box of Africa, lying to the eaft of the Cape of Goad Hope, two feet fquare, form all the furniture of thefe colonial and inhabited, part of it, by Hutch colondls. 1 he habitations. Thus is the pifture or the moll profound word Auteniqua fignifies, in the Hottentot language, mifery contraftcd with the charms of this terrellrial pa« a man loaded with honey a name which is not radife ; for the beauties of thefe regions extend even improperly given to the country, fince, as you enter it beyond Auteniqua. The people, however, though from the Cape, you cannot proceed a fttp without fee- their houfes be bad, live well. They have game and ing a thoufand fwarms of bees. The flowers on which fait water fifh in abundance ; and enjoy exclunvtly, they feed faring up in myriads; and your attention is over all the other cantons of thefe colonies, the advanengaged, and your courfe fufpended, by the mixed tage of having, for the whole year without interruption, odours which exhale from them, by their colours and vegetables of every kind in their gardens. For this -variety, and by the pure cool air which you breathe. they are indebted to the excellence of the foil, and to Nature has made thefe enchanting regions like fairy its being naturally watered by f nail ftrearns, which crofs land. The calyxes of all the flowers abound with ex- each other in a thoufand different direftions, and, as cellent juices, from which the bees extraft the honey one mav fay, lay the four feafons under contribution to that they everywhere depofit in hollow rocks and trees. fertilize uteniqua. Thefe ftreams, which frequently This country was vifited in [782 by M. Vaillant, overflow their banks, but never dry up, proceed from a who calls it the moil delightful region in the univerfe ; caufe well known ; the high mountains towards the and fays, that, as he approached it, he beheld, from the eaft, which are covered with forefts, ftop the clouds top of a very high mountain, an immenfe valley, adorn- and the fogs carried from the fea, and this occaiions ed with agreeable hills, variegated in an infinite num- very abundant rains.” In thefe mountainous regions, which, as well as the ber of ftiapes, and extending in an undulating manner as far as the fea ; whilft enamelled meads, and the moil plain, our author comprehends under the denomination beautiful paftures, ftill added to the magnificent feene. of Auteniqua, there are multitudes of elephants, buffaIt abounds with fmall rivulets, which, flowing down loes, panthers, hyenas, and antelopes of every fpecies from the mountains, run inro the fea through an hun- and all thefe antmals are hunted and killed by the nadred different channels. The water of thefe rivulets has tives, as well for food as for the proteftion of their the colour ot Madeira wine, and a ferruginous tafte ; flocks and herds from fuch of them as are beafts of but our traveller did not examine whether this tafte and prey. Our author has eaten the flefh of every one of colour proceed from their flowing through foine mine them except the hyena ; and declares, that the foot of in their paffage, or from the roots and leaves of trees an elephant, baked after the Hottentot manner, is one of the mod delicious morfels that he ever tailed. He which they carry along with them. The whole of Auteniqua, from the chain of moun- gives direftions for hunting them all; but warns his tains which divides it from the country of that race of readers from attacking elephants when he finds them in Hottentots called Gonaquas to the fea, is inhabited by droves, for then, he fays, they are invincible. He even feveral planters, who rear a number of cattle, make but- thinks it exceedingly dangerous for one rnan, however ter, cut down timber, and coileft honey ; all of which well armed, to attack a Tingle elephant in the plain. they tranfport to the Cape : but it appears that they The buffalo he deferibes, contrary to moll ocher travelmake not the moft of their fituation. “ Can it be be- lers, as a timid animal, which never refills till his fitualieved. (fays M Vaillant), that the direftors'of the Com- tion becomes defperate; and he thinks that there would pany, for their own ufe, fhould order (hips to be fent be no difficulty in training him, if caught when a calf, every year from Amfterdam, loaded with planks and to the yoke like the bullocks ot Europe. The kites and vultures of this country, our traveller boards of every kind, whilft in this country there are immenfe fovefts, and the moft beautiful trees in the reprefents as in the highett degree voracious and fierce, inworld ? This abfurdity, however, is not at all aftonifti- fomuch that it is hardly poffible to fright them from their ing. The Company gratuitoufly furniihes the gover- prey. He had on one occafion killed two buffaloes, which

A U T r 57 3 A U T jtemqua. which he ordered to be cut into very fmall pieces, that dred groves, which are naturally variegated, and each Auten«u». 1 —’V”*-' they might be more eafily faked, and expofed after- more agreeable than another. —~ 1 wards to the air and the fun. His waggons, as well as . -^e author proceeding forwards about two days the bulhes and trees which furrounded him and his peo- journey, arrived at a bay known to navigators by the ple, were loaded with the bloody fragments of thefe two name of the Bay of Agoa, but called by the colonifts animals, and they had begun their operation of faking; £ letter? berg’s Bay, from its having been vifited fome but on a fudden, while they were not expecting it, time before by a Governor Blettenberg, who ordered they found themfelves attacked by flights of kites°and his name, together with the year and day of his arrival, vultures, which, without exhibiting the lead fymptoms to be engraven on a ftone column. This bay is a little of Fear, perched in the midft of them. The kites were beyond the limits of the country called Auteniqua; but above all the moft impudent. They feized upon the it is not foreign from the purpofe of this article to inmorfels of flefh, and even contended furioufly with his fert in this place our traveller’s account of it, and of the people. “ When they had each carried away (fays he) country around it. a pretty large piece, they retired to fome branch, at The bay itfelf, he fays, is very fpacious, and has a the diltance of ten paces from us, and devoured it before fufficient depth of water for the largefl veffels. The our eyes. Though we fired our fufees they were not anchoring ground is fure, and boats can fail to a beaufrightened, but returned inceflantly to the charge ; fo tiful part of the fhore, which is not confined by the that finding our powder wafted in vain, we refolved to rocks, as they are all there detached from one another. keen them off with large poles until our provifions By advancing a league along the coaft, the crews would ftould be quite dry. This manceuvre, which for a arrive at the mouth of a conliderable river called the long time harafled my people, did not prevent us .from Queiir-Bocm, where they would find water. Refrefhbeing plundered without mercy ; but had we not em- ments might be procured from the inhabitants of the ployed it, nothing would have remained to us of our environs ; and the bay would fupply them with exceltwo buffaloes.” lent fifh, with which it abounds. This battle with the kites took place on the confines Ibis bay is one of thofe places where government of the Dutch fettlements; but when M. Vaillant had might eftablifh warehoufes and repolitories for timber; with difficulty pafled over the mountains which bound and it is for this reafon that we have introduced it to them, the profpe&s became more magnificent, the foil notice in this article. The forefts around it, fays M. feemed to be more fruitful and rich, nature appeared to Vaillant, are everywhere magnificent, and the trees be more majeflic and grand, and the lofty mountains could be more ealily cut down than anywhere elfe; for prefented on all fides more charming and delightful it is not to fleep mountains that one muft go for wood, points of view than any that he had ever before met as at Auteniqua ; it is here ready at hand ; and during with. 'I hefefeenes, contrafted with the dry and parch- the fine monfoon might be tranfported to the Cape with ed fields of the Cape, made him exclaim, he fays, in little trouble and no rifle. The inexhauftible and ferecftacy, “ W^hat! fhall thefe fuperb regions be eternally tile lands in the neighbourhood of the bay, if once culinhabited by tygers and lions ? What fpeculator, with tivated, would produce abundant crops, and draw togethe fordid view only of eftablifhing a kind of centre for ther a great number of intelligent planters, on account commerce, could have preferred the ftormy Table Bay of the ready communication which they would have to the numberlefs roads and commodious harbours which with the Cape. In a word, the Company, continues are to be found on the eaftern coafts of Africa ? Thus he, have nothing to do fo much for their own intereit (continues he) was I reflefting within myfelf, whilfi: I as to form here a proper eftablifhment. To the general was climoing the mountain, and forming vain wifhes for profits of fuch an inftitution, would be added thofe of the conqueft of this beautiful country, which the indo- individuals, which could not fail to be of great importlent policy of the European nations will perhaps never ance. They might, for example, cut down a certain gratify.” tree called Jlinking wood, and export it to Europe, If his defeription of its beauties and fertility be not where it would undoubtedly be foon preferred to mahogreatly exaggerated, it is indeed wonderful that either gany and every other kind of wood employed by cabithe Dutch or fome other maritime power of Europe has net makers. not long ago taken pofieffion of it. After he had palled The Hottentots, who in fcattered kraals inhabit this the mountain, one could not, he fays, choofe a more delightful country, our author deferibes as a faithful, agreeable ©r advantageous fpot than that upon which he gentle, and rather timid race. He affirms, that they then was for cftabliflung a thriving colony. The fea have no religious impreffions w’hatever, nor any notion advances through an opening of about a thoufand paces of fuperior powers who govern the world. But this, if in breadth, and penetrates into the country to the dt- not a wilful falfehood dictated by the philofophy of ftance of more than two leagues and a half. The bafon France, is probably a miftake arifing from his fcanty which it forms is more than a league in extent (he knowledge of their language, and total ignorance of the does not fay whether in breadth or in circumference) ; meaning of their religious ceremonies. His great maand the whole coaft, both on the right and the left, is iler, as well as the mafter of his fed, Lucretius, might bordered with rocks, which intercept all communication have taught him, that fear, if not a better principle, will with it. The land is watered by limpid and refrefhing generate the notion of fuperior beings in the minds of ftrearns, which flow down on all fides from the eaftern of favages ; and from fear, by his own account, the inmountains ; and thefe mountains, crowned with majef- habitants of Auteniqua are tar from being free. He tic woods, extending as far as the bafon, and winding likewife affirms, and feems to confider it as much to round it with a number of finuofities, exhibit a hun- their credit, that this race of gentle beings, fo far from Suppl. Vot. I. Part I. H being

A U T [58 Automa- being a prey to the paflion of jealoufy (as other traveltor ’^ krs have reprefented.the Hottentots in general), are fo 'r~~~ obliging, as to lend their wives to travellers who vifit them, and that they aftually accommodated his Hot'tentots in this way. Auteniqua, as laid down in M. Vaillant’s map, lies between 330 30' and 340 50' of fouth latitude, and between 2oQ and 230 40' of eaft longitude; and his rout through the country was from fouth-well to north-ead, or nearly fo. AUTOMATON. Under this title and that of An oroides full credit was allowed in the Encyclopedia Britannica to the ftory of M. de KernpelPs mechanical chefs-player, and a detail at fome length was given of the feats of that figure, as well as of fome other furprifing automata. No man more readily admits the powers of the fkilful mechanician than the writer of this fhort article ; but having many years ago dete&ed the impohtion which wms pratfifed on the public in fome parts of Scotland by a circumferaneous mountebank, who exhibited a figure apparently capable of writing a certain number of words, he has ever fince fufpe&ed impofture in all automata which appear to have the power of varying their motions according to circumftances. With refoeft to the chefs-play er^ there is now fufficient evidence that his fufpicions were well founded. In the defcription of this figure (Encycl. Vol. I. p. 787.), “ it is faid, that the automaton could not play unlefs M. de Kempell or his fubftitute was near it to direft its moves. A fmall box during the game was frequently confulted by the exhibiter; and herein confifted the fecret, which he faid he could in a moment communicate.” The fecret was indeed fimple ; “ A well taught boy, very thin and fmall of his age, was concealed in this box almoll immediately under the chefs-board, and agitated the whole machine.” This we learn from Thomas Collinfon, Efq; who wras let in-

1 A X I to the fecret at Drefden by a gentleman of rank and ta- Automa. Icnts, named jfofeph Freidrick Frey her by whom the t0Ib 'vitality and foul of the chefs-playing figure had fome . Axi'‘ time before been completely diicovered. Mr Collinfon, finding that Dr Hutton had given the fame credit with us to the reality of mechanical chefs-playing, undeceived his friend, by communicating the difcovery of Freyhere in a letter, which the Dodlor has with great propriety publifhed in the Addenda to his Mathematical Diftionary. Mr Collinfon adds, and we doubt not with truth, that, “ even after this abatement of its being ftriftly an automaton, much ingenuity remains to the contriver.” This was in fome degree true of the me- ' chanifm of the writing figure, of which the compiler of this article detefted the bungling impofture of the two exhibiters. The figure itfelf, with all the principles of its motion, w^ere very ingenioufiy conftrufted ; but the twro men who exhibited it were ignorant and aukwrard, and could not conceal from a ferutinizing eye, that the automaton wrote fometimes well and fometimes ill, and never wrote at all w-hen they w’ere both prefent to the company. It was by infilling upon feeing them both together, and threatening to expofe the cheat to the whole town, that the prefent writer prevailed upon him who appeared to be the principal exhibiter, to confefs in private that his companion was concealed behind a fereen, and to fhow how, from thence, he directed the movements of the figure. Conjugate AXIS, or Second Axis, in the elh’pfe and hyperbola, is the diameter palling through the centre, and perpendicular to the tranfveife axis; and is the Ihorteft of all the conjugate diameters. ‘Tranfverfe Axis, in the ellipfe and hyperbola, is the diameter palling through the two foci and the two principal vertices of the figure. In the hyperbola it is the fhorteft diameter, but in the ellipfe it is the longeft.

B. Bahrdt. BAHRDT (Dr Carl Fnedlrich) was fo deeply concerned in a combination of philofophers formed, as they faid, for the advancement of fcience and virtue, that an account of his life muft be interefting, if it were only to Ihow the effe&s of this philofophic culture on his own morals. We trull therefore that our readers will be pleafed, perhaps improved, by the following narrative, taken from documents the moll authentic, by a * See Pro- man* whofe communications on other fubje&s do crefeffor Robi dit to this volume. fon of Edin- Carl Friedirich Bahrdt was, in 174', born at Leipburgh’s Profs of a fig, where his father, then a parilh minifter, and afterConj piracy wards profeffor of theology, died in 177 5. It is natuacratrip all ral to fuppofe that fuch a parent would be at due pains the Religions to inftil into the mind of his fon the principles of piety, and Go-vernments of Eu- virtue, and patriotifm, v/hich is indeed a branch of virtue ; but if fo, he lived to fee that his labour had been rope.

/

in vain. While yet at college, where the courfe of his ®ahrdt. ftudies was calculated to fit him for the important office of preaching the gofpel, the young man enlifted as a huflar in the Pruflian fervice ; but being bought off, he returned to the univerfity, where, in 1761, he was admitted to the degree of M. A. Soon afterwards he became catechift in his father’s church, was a popular preacher, and in 1765 publilhed fermons, and fome controverfial writings, which evinced that he pofielfed both learning and genius. Neither learning nor genius, however, nor both united, could attach him to the caufe of virtue, or make him obferve even the common rules of decorum ; for immediately after this publication he began to indulge in conviviality, and to give fcope to his refentments in anonymous pafquinades, in thehigheft degree bitter and oftenfive. From the ftiafts of his malice no perfon was fafe. Profeflbrs, magiftrates, and

B A H B A H Bahrdt. and clergyman, had indeed Ills chief notice ; butf he 59 1 how beer-, made acquainted with this nefarious tranfaccondefcended occafionally to attack ftudents, and fpared tion, anc. brought it into court on the day that our BahrdC. not even his own comrades or his friends. hero was to make fome very reverend appearance at Whilft he was thus labouring to make enemies of all church. 1 he cafe of Bahrdt was now hooelefs; for to whom he was known, unfortunately, for his own chatome uniuccefsful attempts of his poor father to rader, his temperament was what the atomical philofo- after lave him, he was obliged to give in his gown and band, phers (who can explain every thing by ethers and vi- and to quit Leipfig. & & u* m. brations) call fanguine ; and he was, as he himfelf acTo a parent the public difgrace of a child is one of knowledged, a paffionate admirer of the ladies. Coming the levereft calamities to which human nature is liable; home from his midnight revels, he frequently met in but for this calamity the father of Bahrdt muft have his way a young girl neatly dreffed in a rofe coloured been long prepared, as bis fon appears to have been refilk jacket and train, and a coftly fable bonnet; and markably undutiful. Of this we have one memorable one evening, after having, as he fays, indulged freely in in fiance recorded by himfelf. His father, he fays, was feme old Rhenifh, he faw her home to her lodgings. Some time after this interview, the miftrefs of the houfe levele, and his own temperament hafty, fo that he fomeforgot himfelf. “ One day (continues he) I laid (a Madam Godfchulky) came into his room, and faid atimes loaded piftol on the table, and told him that he fhould that the poor maiden whom he had debauched was preg- meet with that if he went on fo ; but I was then only nant. This was a misfortune which he could not help ; 1 but as it would ruin his charafter if known, he gave to seventeen!” n his bein .° g obliged to leave the place of his natithe old lady a bond for 200 dahlers (about L.40 fter- vity, the friends of Bahrdt, and in particular 8emler, Img), to be paid by inftalments of twenty-five, to keep an eminent theological wiiter, who had formed a very the matter fecret. “ The girl (he fays) wnfenfible and good; and as her converfation, for which "he had al- favourable opinion of his talents, were affiduous in their endeavours to procure an eftablifhment for him elfeready paid, was agreeable, he did not difeontinue his w ere ; but his high opinion of himfelf, his impetuous acquaintance.” and precipitant temper, and that fatirical habit which It could not be fuppofed that fuch vifits, by a cler- he had fo freely indulged in his outfet in life, made gyman, would pafs unobferved, however cautioufly their endeavours long ineffeaual. At laft he got a made, in the rnidll of a town, of which the inhabitants profeftbrfhip at Erlangen, then at Erfurth, and in 1771 had been the mdifcrimmate objefts of his fatire; and he at Gieffen. But in each of thefe places he was no could haidly be furprifed when told by a friend, that fooner fettled than he got into difputes with his colone Bel, a magiftrate whom he had lampooned, was acquainted with the whole affair, and would bring it in- leagues and with the eftablifhed church; for he was a ftrenuous partizan of the innovations then attempted to to a comt of juftice, unlefs the bond was immediately be made in the do&rines of Chriftianity. In his publiJ retired. cations, which were generally anonymous, he did not This bond was the only evidence which could be pro- trufl to rational difeuffion alone, but had recourle to riduced agamft Bahrdt, but it was fufficient to blaft his dicule and perfonal anecdotes, and indulged in themoft characfer in Leipfig, and muft therefore by any means cutting farcafms and grofs feurrility. be removed out of the way. To accomplilh this, howHis love for convivial company continuing, his ineyer, was a matter of fome difficulty; for neither he nor come was infufficient for the craving demand. ' Finding his friend could raife the money. In this dilemma they therefore that anecdote and flander always procured readu on a . . P contrivance worthy of themfelves. They ers, and poffeffing a wonderful aftivity and facility in wriinvited Madam Godfchufky to meet them in another ting, he never ceafed from publifhing lampoons and fahoufe to receive the 200 dahlers due to her by Bahrdt; tires, in which he fpared neither friends nor foes. But but when fhe was uffiered into the room, and found no it was impoffible to prevent thefe publications from beperfon waiting for her but Bahrdt’s friend, fhe could ing traced to their author ; and his avowed theological not be prevailed upon to produce the bond till the mowritings being fuch as could not be iuffered in a proney mould be put into her hands, together with a pre- feffor of divinity, the hoft of enemies which he had been ient to herfelf. The Gentleman tried to intimidate her. at fo much pains to raife againft himfelf, were furnifhed e drew his fvvord; fhowed her how men fence; made with fufficient grounds for fubjefting his condudft to lepulhes at the wall and then at her: but finding that fhe gal cognizance ; even the very ftudents at Gieffen were could not be frightened out ofher fenfes, he threw away fhocked at fome of his liberties. his fword, and endeavoured to take the bond from her The confequence of all this was, that, after much by force. It was fome time before he prevailed ; but wrangling in the church judicatories, he was juft about at laft getting the paper out of her pocket, he tore it to be difmifted from his profeftorfhip, when he got an m pieces, opened the door of a clofet in which Bahrdt invitation to Marfchlins in Switzerland to fuperintend was concealed, and faid, « There, you b ; there is an academy. / the honourable fellow whom you and your whore have To Marfchlins he went about the year 1776, and bullied; but it is with me you have now to do, and you began his new career by forming the feminary after the know that I can bring you to the gallows.” model of an academy which had fome time before been Bahrdt, from whofe memoirs of himfelf this {lory is fet up in the principality of Anhalt Deffau by one Bataken, admits that there was a great fquabble on the fedbw, a man of talents and learning, who gave to it occafion ; bat he went home, comforting himfelf with the appellation of philanthropine. The plan of this the belief that he fhould now have no farther trouble academy was very different from thofe of the univerfifrom Madam Godfchufky or her girl. He chanced, ties ; for its author profeffed to confider languages, however, to be miftaken. The magillrate Bel had feme fciences, and the ornamental exercifes, as mere acctffoH2 ries.

BAH BAH [ 60 j ciples of thofe who have on the continent of Europe Bahrdt, Bahrdt. vies, kis aim being to form the young mind to the love v-™' 0f mankind and of virtue, by a courfe of moral educa- aifociated for the purpofe of enlightening the world. tion certainly fpecious, and apparently unexceptionable. This amiable man, whofe character is here fo jultly To make this novel inftitution the more extendvely ufe- drawn, was afterwards depifted by the monfter whom ful, the rules by which the education was to be con- he had faved from periftiing by hunger, as a wretch left ducted were framed in fuch a manner as, it was thought, to all fenfe of lhame and decency, as an apoftate from would remove from the minds of Catnolics, Lutherans, the Chriftian faith, and as a notorious frequenter oi the and Calvinifts, all uneaftnefs refpefting the faith of their London brothels ! Fortunately he was able to vindicate children, as it related to thofe particular tenets which his charsCter completely from this flanderous abule, and feparated them into different communions. It was even to convict Bahrdt of having publiihed what could not propofed to banifh from the philanthropine pojitivc pojfibly be true. This ungrateful liar returned from England, and carreligion whatever, and to inftruft the youth educated there in the principles only ot natural, or, as it was ried into execution his plan of the Philanthropine. i he cattle of Count Leining Hartzburgh at Heidefheim* called, philofcphical religion. This plan was peculiarly fuited to Bahrdt’s tafte, be- having gardens, park, and every hanfome accomrnoaafcaufe it left him at liberty to introduce into his academy tion, had been fitted up for it; and in 1778 it was any fyftem of religious or irreligious opinions that he confecrated by a folemn religious feltival. But lus old plea-fed ; a liberty of which he refotved to avail himfeU, misfortunes ourfued him. He had indeed no colleaguesandv though now a do&or in theology, to outftrip,- in with whom he could quarrel; but his avowed pubhealicentioufnefs, even the founder of the philanthropine, tions became every day more obnoxious; and when any who was not in orders. By meditating on the work- of his anonymous pieces had a great run, he could not to ings of his own mind, he had by this time formed his far Rifle his vanity as to conceal that he was the autheory of human nature, which was indeed very fimple. thor. Of thefe pieces fome were (hocking to decency, “ The leading propensities of the human mind (he fays) and others fo horribly injuiious to the characters ot the are three inftinftive liberty, infbnCtive aCfivity. and moft relpeCtable men in the ftate, that he was contiimimClive love.” By thefe exprcfiions we fuppofe he nually under the correction of the courts of juttice. It means, “ innate love of liberty, inilinft prompting to was hardly poffible tor a man of letters to be in hia aftion, and the fexual appetite and he immediately company, and not fuffer by it ; for it was his eonitant adds, that “ if a man is obftru&ed in the gratification praCtice to attribute every flep which he took towards of any of thefe propenfities, he fuffers an injury. The atheifm, to the force of the arguments urged by fome bufinefs therefore of a good education is to teach us of his friends. To be his friend, or to obtain bis applaufe, was inhow they are to be gratified in the higheft degree ” That fuch an education would be approved of by the deed fo great a misfortune, that when the leeder fees uncorrupted natives of Switzerland was hardly to be any perfon celebrated by Dr Bahrdt, in the beginning expefted; and Bahrdt foon found his iituation at ot a book, for found fenfe, profound judgment, accurate Matfchlins as uncomfortable as it had been at Giefien. reafoning, or praiftd for aCts of fiiendfliip to himfelf, “ The Grifons (he fays) were a itrong inftancc of the be may be affured, that before the clofe of the book immtnfe importance oi education. They knew nothing this man (hall be reprefented as having in private conbut their handicrafts ; and their minds were as coarfe veriation convinced the author, that fome do .tune, dieas their perfons.” He quarrelled with them all, and riihed and venerated by ail Chiiftians, is a piece of knawas obliged to abfeond after lying fome time in prifon. vifh fuperftition. Dr Bahrdt had married, while at Gieften, a woman From Marfchlins he went to Durkheim, a town in the palatinate, where his father had been mmifter, and with a fmail fortune : but fuch a ftranger was he to the. where his literary talents were well known. A fter fome delicacies of wedded love, fo loft indeed to all fenfe of little time he got an affociation formed for erecting and decency, that he contrived one day to entice his wife fupporting a Philanthropine or hotife of education. A naked into the bath in the garden of his Philanchropine, large fund was eolle&ed ; and he was enabled to travel where, in the water, he, being alio naked, toyed with into Holland and England to engage pupils, and was her in the fight of all his pupils. It was his boaft that he held his opinions independent of all mankind, and iurnifhed with proper recommendations. In London he gained the friendihip of a clergyman, was indifferent whether they procured him pvaile or rewhom he reprefents as a perfon in the higheft degree proach : but it appears from this fad, that he was accomplifhed. “ With found judgment (fays Bahrdt), equally regardlefs of the praife or ceniure which might great genius, and corrtCl tafte, he was perfeCtly a man be attached to his aCtions; tor furely the groffeft hog of the world. He was my iriend, and the only perlon that ever before him battened in the Epicurean fty who warmly interefted himielf for my inftitution. To would not have prefented fuch an exhibition to boys. t he confequence of all this was, that he was obi 1.red his earned and repeated recommendations I owe all the to fly from Hddeftieim, leaving his fureties in the Phi* pupils that I got in England, and many molt *refpeCt. able connections; for he was univerfally efteemed as a lanthropine to pay about 14,000 dahlers, befides debts i,van o* learning and of the moft unblemilhed character. without number to his friends. He was imprifoned at He was my friend, my conductor, and I may fay my Dienheim ; but being loon releafed, he fettled at Halle, preferver; for when I had not bread for two days, he where he funk to be the keeper of a tavern and billiardtable. His houte became of courfe the refort and the took me to his houfe, and fupplied all my wants.” For fo much kindnefs the reader doubtlefs fuppofes bane of the {Indents in the univerfity, and he was oblithat the heart of Babrdt overflowed with gratitude ; ged to leave the city. He had fome how got money but if iuch be his opinion, he is a itranger to the prin- fufikient to purchafe a little vineyard, pleafantly fitua ted

BAH [6 r T BAH Bakrdt. ted in the neighbourhood. This he fitted up with Dr Bahrdt affeAed to be the enlightener and reformer BaffrcJt; “■’V"—"- every accommodation tint could invite the {Indents, of the world; and affirmed, that all the evils of life ori/"-« and called it Bahrdt’s Ruhe ( Bahrdt’s repofe); where ginated from deipotifm and fuperftition. “ In vain he lived for two years, dire&ing the operations of a fe- (lays he) do we complain of the inefficacy of religion. cret fociety called the Gi- rman Union, for rooting All pofitive religion is founded on injuflice. No prince ©ut Superstition and Prejudices, and for advan- has a right to prefcribe or fanAion any fuch fyftem ; cing true Christianity. nor would he do it, were not the priefts the lirmeft oilWith Pnhrdt’s qualifications for advancing the inte- lars o! his tyranny, and fuperftition the llrongeft fetters refts of genuine Chriftianity, the Chriftian reader is al for his fubjeAs. He dares not ffiow Religion as fire is, ready fufficitntly acquainted ; but he will not wonder pure and undehled—ffie would charm the eyes and the at his appointment to this high office, when he is in- hearts ot mankind, would immediately produce true moformed that the German Union is nothing more than rality, would open the eyes of freeborn man, would a fpawn of the fecret fociety of Illuminati (fee Illu- teach him what are his rights and who are his opprefminati in this Supplement) ; and that its objedt is to iors, and princes would vanifh from the face of the earth.’* abolifh the religion of the gofpel, and to teach in its Therefore, without troubling ourfelves with the truth fltad the fatalilm of the Stoics. With this view Chri- or falfehood of his religion of nature, and affuming it as ftiauity is cor.fidered in the union as a myftical fociety, an indilputable point, that Dr Bahrdt has feen it in this and its Divine Founder as the grand mailer of a lodge! natural and ’o effeAive purity, it is furely a very pertiThe gpoitles Peter, James, ‘ohn, and Andrew, were the nent queftion. “ Whether has the fight produced on his elfct, brethren of the third degree, and initiated into mind an effeA fo far fuoerior to the acknowledged faintall the myfteries The remaining apoflles were only of nefs of the impreffion of Chriftianity on the bulk of the fecmd degree ; and the feventy-two, of the Jhjl: a mankind, that it will be prudent to adopt the plan of degree into which ordinary Chrillians may he admitted, the German Union, and at once put an end to the diand prepared for farther advancement. The great my- viftons which fo unfortunately alienate the minds ofproItery is, that J C was a naturalist, and ftffing Chriftians from each other?'’ The account here taught the dodlrine of a fupreme mind, the fpedlator given of Dr Bahrdt’s life Teems to decide the queiiion. hut not the governor of the world. But it will be laid that we have only related io maTo propagate theie impious and abfard notions, ny inftances of the quarrels of priefts and their flavifh Bahrdt publifhed many books of the moil antichriilian adherents with Dr Bahrdt. Let us view him in his tendency, and feme of them calculated to make their ordinary conduA, not as the champion and martyr of readers ihake off all moral obligation. But the labours illumination, but as an ordinary citizen, a hulband, a fa©t the fociety were not confined to religion ; it incul- ther, a friend, a teacher of youth, a clergyman. cated on its members the moft dangerous maxims of ciWhen Dr Bahrdt was a parifh minifter, and prefident' vil conduct : for, as we learn from Bahrdt himfelf, the of fome inferior ecclefiallical diftriA, he was empowered ©bjeAs at which the Union aimed were—Advancement to take off the cenfures of the church from a young woojfcience— a general interejl and concern fur arts and learn- man who had born a baftard child. By violence he ing—excitement of talents—check of fcrilbling—good edu- again reduced her to the lame condition, and efcaped cation — LIBERTY EQUALITY — hofpitality DELIVERY cenfure by the poor girl’s dying of a fever before her ©f many from misfortunes — union of the learned— pregnancy was far advanced, or even legally documentand at laf—perhaps—Amen. ed. On the night of the folemn farce of confecrating What the meaning of this enigmatical conclufion is his Philanthropine, he debauched the maid-Iervant, who* we can only guefs ; and we agree with the real philofo- bore twins, and gave him up for the father. The pher from whom we havg taken this account, that our thing was not judicially proved, but was afterwards conjeAares cannot he fayowrablt Bahrdt was a villain, made fufficiently evident by letters found among his and could be aflbciated only with villains, whofe affairs papers, and publiftied by one of his friends in the Union. he managed with the help of an old man, v/ho lived at Having lupported theie infants, in a pitiful manner, for bed and board in his houfe for about fix {hillings a week, little more than a year, he catifed them to be taken and d^fcharged the office of fecretary to the Union. aw'ay from their mother, during night, forae time in When he had toiled in this caufe near two years, the month of February 1780 ; and they were found, fome of the fecrets of the Union tranfpiied; his former expofed, the one at Ufftein, and the other at Worms, conduA and his conllant imprudence made him fufpeA- many miles diftant from each other, and almoft frozen «d; his afibciated friends lodged infor ations againfl to death. him ; his papers were teized ; and he himfelf was fent So much for the purity of his morals and his relito prifon, firtl at Halle and then at Magdeburg. After gion, as he appears in the charaAer of a father and of fomething more than a year’s confinement, he was fet a clergyman. His decency as a hufband, and his at liberty, and returned to his Ruhe, not, alas! to live gratitude to his friend, we have Already feen ; and at eafe, or to exhibit fymptorns ot repentance, but to we lhall now fee his kindneis and fidelity. Alter lie down on a fick-bed, where, after many months luf- wafting the greateft part ot his wife’s little fortune,, ftring of increafing pain, he died on the 2;d of April he was fo provoked becaufe her brother would nofc 179?, the moft wretched and loathfome viAim of uns give him up the remainder, amounting to about L. r 10, bridled fenfuality. that he ever afterwards treated her with the greateft: Such were the fruits of the German Union, and of cruelty, and exhibited her to contempt and ridicule in. that illumination which was to refine the heart of man, two intamous novels. At Halle he brought a miftrefs and bring to mat: rity the ieeds of native virtue, which into the houfe, and committed to her the care of his faare choaktd in the heart by iuperftition and defpotifm. mily, confining hig wile and daughter to their own apartment .3.

B A I B A I [ 6* 1 Bsnrdt, apartment; and the laft thinp- which he did was to formidable rival in La Grange, who already promifed to 'Ballly, Bailiy. £encj for a book feller, who had publifhed feme of his become the firft mathematician in Europe. The revile ft pieces, and, without a thought of his injured wife, fults of his inveftigations were colle&cd into a treatife recommend his ftrumpet and her children to his protec- publifhed in 1766, containing alfo the hiftory of that part of allronomy. In 1771 he gave a moft curious tion. “ Think not, indignant reader (fays Arbuthnot), and important memoir on the light of the fatellites, and that this man’s life is ufelefs to mortals.” It fhows in introduced a degree of accuracy till then unknown in a Itrong light the falhty of all his declamations in favour the obfervations of their eclipfes. His (Indies were not confined to the abftraft fciences ; of his fo much praifed natural religion and univerlal kindnefs and humanity. No man of the party writes for he cultivated letters with fuccefs. His eloges of with more perfuafive energy, and, though his petulance Charles V. of Corneille, of Leibnitz, of Moliere, and and precipitant felf-conceit lead him frequently altray, afterward thofe of Cook, La Caille, and Grefiet, were no man has occafionally put all the arguments of thefe ■much admired. Elis eloquence pointed him out as a philofophers in a clearer light; yet we fee that all is proper perfon tb fill the charge, vacant in 1771, of fefalfe and hollow. He is a vile hypocrite, and the real cretary to the Academy of Sciences ; and, under the aim of all his writings is to make money, by foftering patronage of Buffon, he flood candidate for that enthe fenfual propenfities of human nature, although he viable place. He failed: but it was the high birth and fees and feels that the completion of the plan of the promifing talents of the young Condorcet, joined to the German Union would be an event more deftruftive and adtive influence of D’Alembert, that carried the prize. In 177 s appeared the firft volume of the Hiftory of lamentable than any that can be pointed out in the annals of fuperflition. We will not fay that all the parti- Aftronomy, which indeed ftrews the path of fcience fans of illumination are hogs of the fty of Epicurus like with flowers, and in every reipedl is a moft valuable this wretch ; and it would be extremely unjuft to con- work—full of animated defeription, of luminous narrafider his vices as the effefts of his illumination. Ele tive, and interefting detail. His very peculiar ideas was fenfual, ungrateful, and profane, before he was ad- concerning the early flate of Upper Afia gave rife to mitted into the order of the Illuminati; but had the an ingenious correfpondence and difcufllon with the veviews of that order been fuch as were held cut to the teran philofopher Voltaire, the fubftance of which foon world at large, its fagacious founder would not have ini- appeared in two volumes, intitled, “ Letters on the Oritiated a wretch fo notorioufly profligate as Dr Bahrdt. gin of Sciences,” and “ Letters on the Atlantide of Their views, however, being to govern mankind thro’ Plato.” If imagination fhone forth in thefe efiays, eruthe medium of their fenfual appetites, and to reign in dition was no lefs conipicuous in a great work compohell, rather than ferve in heaven, they could not have led in the years 1781 and 1782, on the fables and reli■employed a better inftrument. Dr Bahrdt was a true gior.s creeds of antiquity ; which fliil exifts in manu•difciple of illumination; and though his torch was made feript, and the publication of which would afluredly exof the coarfeft materials, and ierved only to difeover tend the fame of its author and gratify the learned lights of woe, the horrid glare darted into every corner, world. His opinions on fome points happening to co*roufing hundreds of filthy vermin, and dire&ing their incide with the theories of Buffon, he contrafied with flight to the rotten carrion, where they could heft de- that celebrated naturalift a dole friendfhip, which was polit their poifon and their eggs. Whilft the more de- diffolved by Bailly’s uncourtly oppofition to the ele&ion cent members of the Union laboured to pervert the re- of the Abbe Maury into the Academic Frangaife. Of fined part of mankind, by declamations on the rights of that academy he had been chofen fecretary in 1784; man and the bleffings o!^ liberty, Bahrdt addreffed him- and he was admitted, in the following year, into the felf to readers of all deferiptions, and aflailed at once the Academy of inferiptions and Belles Lettres ; the only imagination and the appetites. Ele taught them, that inftance, fince Fontenelle, of the fame perfon being at religion is an impofture ; that morality is convenience ; once a member of all the three academies. In the meanand, with blafphemy peculiar to himfelf, that he and time, the other volumes of the Hiftory of Aftronomy his order, by their licentious doftrines, were to complete fucceffively appeared, and that capital work was completed in 1787 by the Hiftory of the Indian and Orienthe plan and aim of J — C . BA ILLY (Jean-Sylvian), who made fuch a figure tal Aftronomy; a produ&ion of Angular acutenefs, reduring the firft years of the French revolution, was born fearch, and nice calculation. In 1784 he made an elegant report to the Academy at Paris on the 15th of September 1736, of a family which had bees diftinguiflied painters during four fuc- of Sciences on the animal magnetifm of Mefmer; and cefiive generations. He was bred to the fame pr'ofef- in 1786 another report, which difplays the judgment fion, but (bowed an early tafte for poetry and the belles and humanity of its author, on a projedt for a new lettres. Chancing, however, to become acquainted with hoteldieu or infirmary. We now approach the eventful period which fumthe geometer La Caille, this circumfiance decided his genius, and he thenceforth devoted himfelf to the culti- rnoned Bailly from his retirement, to enter on a politivation of fcience. He calculated the orbit of the co- cal career, that was full of difficulty and danger, and met of 1759; and on the 29th of January 1763^35 for which his habits and itudies appear r.ot to have fitted received into the Academy of Sciences. In that year him. He had ften, as others faw, the defedls of the old he publifhed an ufeful and laborious compilation, being government of France. His heart panted for civil and the reduction of the obfervations made by La Caille in ecclefiaftical liberty; but unfortunately, like many other 1760 and 1761, on the zodiacal liars. He likewife be- philofophers both in his own country and in this, he gan to confider the theory of Jupiter’s fatellites, and, in had formed notions of that bleffing which experience rhe competition for this prize queltion of 1764, had a fhould have taught him can never be realifed among beings

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