Encyclopaedia Britannica [18, 3 ed.]

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B RITANNICA;

ENCYCLOPAEDIA O R, A

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DISCAN-F,

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EDINBURGH. PRINTED FOR A. BELL AND C. MACFARQU H AR>

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ENCYCLOP^D I BRITANNIC A.

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Strength of STRENGTH OF MATERIALS, in mechanics, is a fubi at^ria V3 of fo much importance, that in a nation fo emi! nent as this for invention and ingenuity in all fpecies Importance of mamifa&ures, and in particular fo diftinguifhed for of the fub- jts improvements in machinery of every kind, it is fomewhat fingular that no writer has treated it in the detail which its importance and difficulty demands. The man of fcience who vifits our great manufactures is delighted with the ingenuity which he obferves in every part, the innumerable inventions which come even from individual artifans, and the determined purpofe of improvement and refinement which he fees in every worklhop. Every cotton \ mill appears an academy of mechanical fcience ; and mechanical invention is fpreading from thefe fountains over the whole kingdom : But the philofopher is mortified to fee this ardent fpirit fo cramped by ignorance of principle, and many of thefe original and brilliant thoughts obfcured and clogged with needlefs and even hurtful additions, and a complication of machinery which checks improvement even by its appearance of ingenuity. There is nothing in which this want of fcientific education, this ignorance of principle, is fo frequently obferved as in the injudicious proportion of the parts of machines and other mechanical ftru&ures; proportions and forms of parts in which the ftrength and pofition are nowife regulated by the (trains to which they are expofed, and where repeated failures have been the only leffons. It cannot be otherwife. We have no means of inltrucV tion, except two very fhort and abftrafted treaties of the late Mr Emerfon on the Itrength of materials. We do not recoiled a performance in our language from which our artifis can get information. Treatifes written exprefsly on different branches of mechanical arts are totally filent on this, which is the bafis and only principle of their performances. Who would imagine that PRICE’S BRITISH CARPENTER, the work of the firfi; reputation in this country, and of which the foie aim is to teach the carpenter to eredt "x. folid and durable ftrudures, does not contain one -propofition or one reafon by which one form of a thing can be drown to be ttronger or weaker than another ? We doubt ver m 7 «ch if one carpenter in an hundred can give a reafon to convince his own mind that a joiff is ftronger when laid on its edge than when laid on its broad fide. We fpeak in this firong manner in hopes of exciting fome man of fcience ^s to publifli a fyftem of inftru&ion on this fubjed. The limits o( our Work will not admit of a detail : but we think it neceffary to point out the leading principles, and to give the traces of that fyHematic connedlion by which all the knowledge already poffeffed of this fubjed may be brought together and properly arranged. This we (hall now attempt m as brie( a manner as we are able.

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tion of this property of tangible matter has as yet been very Strength partial and imperfed, and by no means enables us to apply Matena^ v mathematical calculations with precilion and fticcefs. The ” various modifications of cohefion, in its different appearances of perfed foftnefs, plafticity, dudility, elafticity, hardnefs, have a mighty influence on the ftrength of bodies, but are hardly fufceptible of meafurement. Their texture alfo, whether uniform like glafs and dudile metals, cryftallized or granulated like other metals and freeftone, or fibrous like timber, is a circumftance no lef* important; yet even here, although we derive fome advantage from remarking to which of thefe forms of aggregation a fubftance belongs, the aid is ^ but fmall. All we can do in this want of general principles Experiis to make experiments on every clafs of bodies. Accord-ments ^ ingly philofophers have endeavoured to inftmd the public in this particular. The Royal Society of London at its very firft inftitution made many experiments at their meetings, as may be icen in the firft regifters of the Society f. f See Several individuals have added their experiments. The moft numerous colledion in detail is by Mufchenbroek, profeffor natural philofophy at Leyden. Part of it was publifhed by Mathem*. himfelf in his Effais de Phyfique, in 2 vols qto ; but the fulltlc.d ColUe* colledion is to be found in his Syftem of Natural Philofo-*,sw* phy, publifhed after his death by Lulofs, in 3 vols 4to. This was tranflated from the Low Dutch into French by Sigaud de la Fond, and publifhed at Paris in 1760, and is a prodigious colledion of phyfical knowledge of all kinds, and may almoft fuffice for a library of natural philofophy. But this colledion of experiments on the cohefion of bodies is not of that value which one expeds. We prefume that they were carefully made and faithfully narrated ; but they were made on fuch fmall fpecimens that the unavoidable natural inequalities of growth or texture produced irregularities in the rc« fults which bore too great a proportion to the whole quantities obferved. We may make the fame remark on the experiments of Couplet, Pitot, De la Hire, Du Hamel, and others of the French academy. In fhort, if we except the experiments of Buffon on the ftrength of timber, made at the public expence on a large fcale, there is nothing to be met with from which we can obtain abfolute meafures which may be employed with confidence ; and there is nothing in the Englifh language except a Ample lift by Emerfon, which is merely a fet of affirmations, without any narration of circumftances, to enable us to judge of the validity of ills epoclufions; but the charader of Mr Emerfon, as a man of knowledge and of integrity, gives even to thefe affertions a confiderable value. But to make ufe of any experiments, there muft be employed Rendered fome general principle by which we can generalize their reby fults. They will otherwife be only narrations of detached ®eiiera^zaa fads. We muft have fome notion of that intermedium, by 1 Strength of the intervention of which an external force applied to one materials THE ftrength of materials arifes immediately or ultimate- part of a lever, joift, or pillar, occafionsa (train on a diftaut 7 f m coheBan of the P"5 of WKS. Our esamiua. part. This can be nothing hut the cohelion between the , !° . XVIII, •ohefiM. ” Part I. Voi A parts.

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lead wire of ijth of

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long ; fix one end firmly to the ceiling, and let the wire Strertgtk ef hang perpendicular; affix to the lower end an index like the ^a'er‘ah. 1 hand of a watch ; on fome ftand immediately below let there -1 be a circle divided into degrees, with its centre correfponding to the lower point of the wire : now turn this index twice round, and thus twift the wire. When the index is let go, it will turn backwards again, by the wire’s untwifting itfelf, and make almoft four revolutions before it flops; after which it twifts and untwiils many times, the index going backwards and forwards round the circle, diminilhing however its arch ot twift each time, till at laft it fettles precifely in its original pofition. This may be repeated for ever. Now, in this motion, every part of the wire partakes equally of the twift. The particles are ftretched, require force to keep them in their ftate of extenfion, and recover completely their original relative pofitions. Thefe are all the charafters of what the mechanician calls perfed elafticity, This is a quality quite familiar in many cafes ; as in glafs, tempered Reel, &c. but was thought incompetent to lead, which is generally confidered as having little or no elafticity. But we make the affertion in the moil general terms, with the limitation to moderate derangement of form. We have made the fame experiment on a thread of pipe-clay, made by forcing foft clay through the fmall hole of a fyringe by means of a ferew ; and we found it more elaftic than the lead wire : for a thread of -ig-th of an inch diameter and 7 feet long allowed the index to make two turns, and yet completely recovered its firft pofition. 2d/y, But if we turn the index of the lead wire four times round, and let it go again, it untwifts again in the fame manner, but it makes little more than four turns back again ; and after many ofcillations it finally flops in a pofition aimoft two revolutions removed from its original po/ition. It has now acquired a new arrangement of paits, and this new arrangement is permanent like the former; and, g ! what is of particular moment, it is perfe&ly elaflic. This What is nie3 change is familiarly known by the denomination of a ntby The wire is laid to have When we attend3A** minutely to the procedure of nature in this phenomenon, we find that the particles have as it were Aid on each other, flill cohering, and have taken a new pofition, in which their connedling forces are in equilibrio : and in this change of relative fituation, it appears that the connefh’ng forces which maintained the particles in their firit fituations were not in equilibrio in fome oofition intermediate between that of the firft and that of the iaft form. The force required for changing this firft form augmented with the change, but only to a certain degree ; and during this procefs the connefting forces always tended to the recovery or this firft form. But after the change of mutual pofition has paffed a certain magnitude, the union has been partly deftroyed, and the particles have been brought into new fituations ; fuch, that the forces which now conneft each with its neighbour tend, not to the recovery of the firft arrangement, but to pufh them farther from it, into a new fituation, to which they now verge, and require force to prevent them from acquiring. The wire is now in fail again perfectly elaftic ; that is, the forces which now conned the particles with their new neighbours augment to a certain degree as the derangement from this new pofition augments. This is not reafoning from any theory. It is narrating fails, on which a theory is to be founded. What we have been juft now faying is evidently a defeription of that fen^ fible form of tangible matter which we call duBilhy. It has Duililitf every gradation of variety, from the foftnefs of butter to the firmnefs of gold.. All thefe bodies have fome elafticity ; but we fay they are not perfeilly elaftic, becaufe they do inch in diameter and ten feet not completely recover their original form when it has been 1 greatly

It is this connecting force which is brought into Materials. a&ion, or, as we more fiiortly exp refs it, excited. This action is modified in every part by the laws of mechanics. It 5 Stiength is this action which is what we call the firength of that part, tidiued. and its effeCt is the {train on the adjoining parts ; and thus it is the fame force, differently viewed, that constitutes both the {train and the ftrength. When we confider it in the light of a refiftance to fracture, we call it jlrength. We call every thing a force which we obferve to be ever accompanied by a change of motion ; or, more ftrictly fpeaking, we infer the prefence and agency of a force wherever we obferve the ftate of things in refpeCt of motion different from what we know to be the refult of the aCtion of all the forces which we know to a6t on the body. Thus when we obferve a rope prevent a body from falling, we infer a moving force inherent in the rope with as much confidence as when we obferve it drag the body along the ground. The immediate aftion of this force is undoubtedly exerted between the immediately adjoining parts of the rope. The immediate effeCl is the keeping the particles of the rope together. They ought to feparate by any external force drawing the ends of the rope contrarywife; and we aferibe their not doing fo to a mechanical force really oppofing this 6 Caufes external force. When defired to give it a name, we name known on- it from what we conceive to be its effett, and therefore its ly from charafteriiiic, and we call it COHESION. This is merely a their efname for the fadf; but it is the fame thing in all our denofects. minations. We know nothing of the caufes but in the effects ; and our name for the caufe is in faft the name of the effe£t, which is COHESION. We mean nothing elfe by gravitation or magnetifm. What do we mean when we fay that Newton underftood thoroughly/the nature of gravitation, of the force of gravitation; or that Franklin underftood the nature of the eledtric force? Nothing but this: Newton confidered with patient fagacity the general fads of gravitation, and has deferibed and claffed them with the utmoft precifion. In like manner, we fhall underhand the nature of cohefion when we have difeovered with equal generality the laws of cohefion, or general fa£ts which are obferved in the appearances, and when we have deferibed and claffed them with equal accuracy. Let us therefore attend to the more fimple and obvious phenomena of cohefion, and mark with care every circumflance of refemblance by which they may be claffed. Let us receive thefe as the laws of coheffon, charaderiftic of its fuppofed caufe, the force of cohefion. We cannot pretend to enter on this va!l refearch. The modifications are innumerable ; and it would require the penetration of more than Newton to deted the circumflance of fimilarity amidfl millions of diferrminating circumftances. Yet this is the only way of difeovering which are the primary fads characteriftic of the force, and which are the modifications. The lludy is immenfe, hut is by no means defperate; and we entertain great hopes that it will ere long be fuccefsfully profecuted : but, in our particular predicament, we mull content ourfelves with feleding fuch general laws as ieem to give us the moft immediate information of the circumftances that muft be attended to by the mechanician in his conftructions, that he may unite ftrength with fimplicity, economy, and energy. All bodies i/?,Then, it is a matter of fad that all bodies are in a cercl aide. tain degree perfedly elaftic ; that is, when their form or bulk is changed by certain moderate comtoreffions or diftractions, it requires the continuance of the changing force to continue the body in this new Rate ; and when the force is removed, the body recovers its original form. We limit the affertion to certain moderate changes : For inftance, take a

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by any ext cm til eaufe, to recede from this fituntlon of nwtu- Strength of al inactivity ; for fince force is requifite to produce either the dilatation or the compreffion, and to maintain it, we lz are obliged, by the conftitution of ogr minds, to infer that Particles it is oppofed by a force accompanying or inherent in every adtad on particle of dilatable or compreflible matter ; and as this neceffity of employing force to produce a change indicate|J.epUgjunf, the agency of thefefoorpufcidar forces, and marks their kind, according es the tendencies of the particles appear to bo toward each other in dilatation, er from each other in compreffion ; fo it alfo meafures the degrees of their intenfity. Should it require three times the force to produce a double compreffion, we muft reckon the mutual repulfions triple when the compreffion is doubled ; and fo in other inftances. We fee from all this that the phenomena of gohefion indicate feme relation between the inteniity of the force of cohefion j, and the diftance between the centres of the particles. TQ The great diicover this relation is the great problem in corpufcular Prcbleini11' mechanifm, as it was in the Newtonian invefligation of ^ niefharifni" force of gravitation. Could we diicover this law of aftion ‘ between the corpufcles with the fame certainty and diftimftnefs, we might with equal confidence fay what will be the refult of any poution which we give to the particles of bodies ; but this is beyond our hopes. The law of gravitation is fo fimple that the difeovery or detedtion of it amid the variety of eeleftial phenomena required but one ftep ; and in its owm nature its poffible combinations ftdl do not greatly exceed the powers of human refearch. One is almoft difpofed to fay that the Supreme Being has exhibited it to our reafoning powers as fufficient to employ with fuccefs our utmoft efforts, but not fo abftrufe as to difeourage us from the noble attempt. It feems to be otherwife with refpedl to cohefion. Mathematics informs us, that if it deviates fenfibly from the law of gravitation, the fimpieft combinations will make the joint action of feveral particles an almoll impenetrable myftery. We muft therefoie content ourfelves, for a long while to come, with a careful obfervation of the fimpieft cafes that we can propole, and with the difeovery of fecondary laws of a£tion, in which many particles combine their influence. In pufuance of this plan, we obferve, 3^/y, That whatever is the fituation of the particles of a Particles body with refpedl to each other, when in a quiefeent ftate, ^eP£ m they are kept in thefe fituations by the balance of oppofite forces. rJ'his cannot be refufed, nor can we form to our-j3a]ance felves any other notion of the ftate of the particles of a of forces* body. Whether we fuppofe the ultimate particles to be of certain magnitudes and lhapes, touching each other in fingle points of cohefion ; or whether we (with Bolcovich) confider them as at a dillance from each other, and adling on each other by attradlions and repulfions —we mull acknowledge, in the firft place, that the centres of the particles (by whofe mutual diftances we muft eftimate the dillance of the particles) may and do vary their diftances from each other. What elle can we fay when we oblerve a body increafe in length, in breadth, and in thicknefs, by heating it, or when we fee it diminilh in all thefe dimerifions by an external compreffion ? A particle, therefore, fit-uated in the midft of many others, and remaining in that lituation, muft be conceived as maintained in it by the mutual balancing of all the forces which connedt it with its neighbours. It is llluftralike a ball kept in its place by the oppofite adlion of two °f fprings. This illullration merits a more particular applica-^ tion. Suppofe a number of balls ranged on the table in the[ angles of equilateral triangles, and that each ball is connedled with the fix which lie around it by means of an elaftic wire curled like a cork-icrew ; fuppofe fuch another ftratum on the body, and which augment as the particles are made, of balls above this, and parallel to it, and fo placed that AZ each

itrengfh of greatly deranged. The whole gradation may fee moft du Materials, obferved in a piece of glafs or hard failing wax. In ordinary form glafs is perhaps the mod completely elaftic body that we know, and may be bent till juft ready to fnap, and yet completely recovers its firft form, and takes no Yet whatever ; but when heated to fuch a degree as juft to be vifible in the dark, it lofes its brittlenels, and becomes fo tough that it cannot be broken by any blow; but it is no longer elaftic, takes any fet, and keeps it. When more heated, it becomes as plaftic as clay : but in this ftate is remarkably diftinguilhed from clay by a quality which we may TO which is fomething'like dafticity, of wliich. Vifcidity call clay and other bodies purely plaftic exhibit no appearance. This is the joint operation of ftrong edhefion and foftnefs. When a rod of perfectly foft gla£ is fuddenly ftretched a little, it does not at once take the fhape which it acquires after feme little time. It is owing to this, that in taking the impreflion of a feal, if we takeoff the feal while the wax is yet very hot, the fharpnefs of the impreffion is deftroyed immediately. Each part drawing its neighbour, and each part yielding, the prominent parts are pulled down and bjunted, and the fharp hollows are pulled upwards and alio blunted. The feal muff be kept on till all has become not only ftiff but hard. IT Ohferved This vifeidity is to be obferved in all plaftic bodies wdiich in all ho- are homogeneous. It is not obferved in clay, becauie it is ^kXc bo*8 not homogent'ol,s> but confifts of hard particles of the arC Lts. gillaceous earth flicking together by their attraction for water. Something like it might be made of finely powdered glafs and a clammy fluid fuch as turpentine. Vifeidity has all degrees of foftnefs till it degenerates to ropy fluidity like that of olive oil. Perhaps fomething of it may be found even in the moft perfeft fluid that we are acquainted with, as we obferved in the experiments for aicertaining fpecific gravity. There is in a late volume of the Philofophical Tranfactions a narration of experiments, by which it appears that the thread of the fpider is an exception to our firft general law, and that it is perfeClly duftile. It is there afferted, that a long thread of goffamer, furnifhed with an index, takes any petition whatever ; and that though the index be turned round any number of times (even many hundreds), it has no tendency to recover its firft form. The thread takes completely any fet whatever. We have not had an ■opportunity of repeating this experiment, but we have di. flinCtly obferved a phenomenon totally inconfiftent with it. If a fibre of goffamer about an inch long be held by the end horizontally, it bends downward in a curve like a (lender flip of whalebone or a hair. If totally devoid of elafticity, and perfectly indifferent to any fet, it would hang down perpendicularly without any curvature. When duCtility and elafticity are combined in different proportions, an immenfe variety of fenfcble modes of aggregation may be produced. Some degree of both are probably to be obferved in all bodies of complex conftitution ; that is, which confift of particles made up of many different kinds of atoms. Such a conftitution of a body muft afford many fituations permanent, but eafily deranged. In all thele changes of difpofition which take place among the particles of a duCtile body, the particles are at fuch diftance that they ftill cohere. The body may be ftretched a little ; and on removing the extending force, the body {brinks into its firll form. It alfo refills moderate compreffions; and when the comprefling force is removed, the body fwells out again. Now the cerpufcular Jail here is, that the particles are aCled on by attractions and repulfions, which balance each other when no external force is aCting VISCIDITY,

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Strength of eneh ball of the upper rtratum is perpendicularly over the ^Materials. centJe 0f equilateral triangle below, and let thefe be v " ■ -' connected with the balls of the . under ftratum by limilar fpiral wires. Let there be a third and a fourth, and any number of fnch ftrata, all connedled in the fame manner. It is plain that this may extend to any fize and fill any fpace. —Now let this aflemblage of balls be firmly contemplated by the imagination, and be fuppofed to (brink continually in all its demenfions, till the balls, and their diftances from each other, and the connecting wires, all vanifh from the fight as difcrete individual objeCts. All this is very conceivable. It will now appear like a folid body, having length, breadth, and thicknefs; it may be comprefled, and will again refume its dimenfions ; it may be ftretched, and wall again (brink ; it will move away when (truck ; in (hort, it will not differ in its fenfible appearance from a folid elaftic body. Now when this body is in a (fate of compreffion, for inftance, it is evident that any one of the balls is at reft, in confequence of the mutual balancing of the aCtions of all the fpiral wires which connedt it with thofe around it. It will greatly conduce to the full under (landing of all that follows to recur to this illuftration. The analogy or refemblance between the effeCts of this conditutioirof things and the effeCts of the corpufcular forces is very great; and wherever it obtains, we may fafely draw conclufions from what we know would be the condition of the balls in par16 ticular circumftances to what will be the condition of a body 33y txam- of common tangible matter. We (hall juft give one in(truCtive example, and then have done with this hypothetical body. We can fuppofe it of a long (hape, refting on one point; we can fuppofe two weights A, B, fufpended at the extremities, and the whole in equilibrio. We commonly exprefs this (late of things by faying that A and B are in cquilibrio. '1 his is very inaccurate. A is ih faCt in equilibrio with the united aCtion of all the fprings which conneCt the ball to which it is applied with the adjoining balls. Thefe fprings are brought into aCtion, and each is in equilibrio with the joint aCtion of all the reft. Thus through the whole extent of the hypothetical body, the fprings are brought into aCtion in a way and in a degree which mathematics can eafily inveftigate. We need not do this : it is enough for our purpofe that our imagination readily difcovers that fome fpringsare ftretched, otheis are compreffed, and that a preffure is excited on the middle point of fupport, and the fupport exerts a reaCtion which precifely balances it; and the other weight is, in like manner, in immediate equilibrio with the equivalent of the aCtions of all the fprings which conneCt the laft ball with its neighbours. Now take the analogical or refembling cafe, an oblong piece of folid matter, refting on a fulcrum, and loaded with two weights in equilibrio. For the aCtions of the connecting fprings fubftitute the corpufcular forces, and the reiult will refemble that of the hypothefis. Now as there is fomething that is at lead analogous to a change of diftance of tire particles, and a concomitant change of the inteniity of the connecting j forces, we may exprefs this in the fame way that we are accuftomed to do Plate in fimilar cafes. Let A and B (fig. i.) reprefent the cenccccLxxxiv.tres of two particles of a coherent elaftic body in their quiefcent inaftive (late, and let us confider only the mechanical condition of B. The body may be ftretched. In this cafe the diftance A B of the particles may become A C. In this (late there is fomething which makes it neceffary to employ a force to keep the particles at this diftance.. C has a tendency towards A, or w.e may fay that A attraCts C. We may reprefent the magnitude of this tendency of C towards A, or this attraction of A, by aline Cc perpendicular to AC* Again* the body may be compreffed, and tire P’-c*

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diftance A B may become A D. Something obliges us to Strength of employ force to continue this compreffion ; and D tends Materials. from A, or A appears to repel I). The intenfity of this tendency or repulfion may be reprefented by another perpendicular T> d; and, to reprefent the different directions of thefe tendencies, or the different nature of thefe aCtions, i7 we may fet D on the oppofite fide of A B. It is in tin’s How Bof. cov ch re manner that, the Abbe .Bolcovich the aCtionsipreftntsths ; * ,. , has , .reprefented fm, f XT-.. r r ofr corpufcular forces in his celebrated Theory of Natural Philofophy. Newton had (aid, that, as the great movements corpufcular of the folar fyftem were regulated by forces operating at a forces, diftance and varying with the diftance, fo he ftrongly fufpeCted (valde fufpicor') that all the phenomena of cohefion, with all its modifications in the different fenfible forms of aggregation, and in the phenomena of chemiftry and phyffology, refulted from the iimilar agency o( forces varying with the diftance of the particles. The learned Jefuit purfued this thought; and has (hown, that if we fuppofe an ultimate atom of matter endowed with powers of attraction and repulfion, varying, both in kind and degree, with the diftance, and if this force be the fame in every atom, it may be regulated by fuch a relation to the diftance from the neighbouring atom, that a collection of fuch atoms may have all the fenfible appearances of bodies in their different forms of folids, liquids, and vapours, elaftic or unelaftic, and endowed with all the properties which we perceive, by whofe immediate operation the phenomena of motion by impulfe, and all the phenomena of chemiftry, and of animal and vegetable economy, may be produced. He (hows, that notwithftanding a perfeCt famenefs, and even a great fimplicity in this atomical conftitution, there will refult from this union all that unfpeakable variety of form and property which diverfify and embellifti the face of nature. We (hall take another opportunity of giving fuch an account of this celebrated work as it deferves. We mention it only, by the by, as far as a general notion of it will be of fome (ervice on the prefent occafion. For this purpofe, we juft obferve that Bofcovich conceives a particle of any individual fpecies of matter to confift of an unknown number of particles of fimpler conftitution ; each of which particles, in their turn, is compounded of particles (till more (imply conftkuted, and fo on through an unknown number of orders, till we arrive at the fimpleft pofiible conftitution of a particle of tangible ■ matter, fufceptible of length, breadth, and thicknefs, and neceffarily confiding of four atoms of matter. And ha (hows that the more complex we fuppofe the conftitution of a particle, the more muft the fenfible qualities of the aggregate refemble the obferved qualities of tangible bodies. In particular, he (hows how a particle may be fo conftituted, that although it aft on one other particle of the fame kind through a confiderable interval, the interpofition of a third particle of the fame kind may render it totally, or almoft: totally, inaftive; and therefore an affemblage of fuch particles would form fuch a fluid as air. All thefe curious inferences are made with uncontrovertible evidence; and the greateft encouragement is thus given to the mathematical philofo*pher to hope, that by cautious and patient proceeding in this way, we may gradually approach to a knowledge ot the laws of cohefion, that will not (hun a comparifon even with the Principia of Newton. Na ftep can be made in this inveftigation, but by obferving with care, and generalizing with judgment, the phenomena, which are abundantly nur merous, and much more at our command than thofe of the great and fenfible motions of bodies. Following this plan, we obferve, Eve/^b It is matter of faft, that every body has forae degree of comprefiibility and dilatability ; and when the changes of j.ireiiib!e dimenfiou are fo moderate that the body completely recovers and dilaits table.

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probably arifes from the difunion of fome particles, ^whofe Strength of ef its original dimcnlions on the ceffation of the changing force, Material*. the extenfions or comprefiions are fenfibly proportional to adion contributed to the whole or fenfible effed. And in — the extending or comprefiing forces ; and therefore the con- compreflions we may fuppofe fomething of the fame kind; for when we comprefs a body in one diredion, it common! " Inn ncRtn? hrcu are proportional to the dijlantet of the particlei ly bulges out in another; and in cafes of very violent adion ;™di'co from their quUfeent, neutral, or inohlive poftm,. fh.s feems fome particles may be difunited, whofe tranfverfe adion hadered by to have been ifirft viewed as a law of nature by the penetra)r Hocke, ti Robert Hooke, one of the moll eminent phi- formerly balanced part of the comprefling force. For the e 0f reader will fee on refledion, that fince the compreflion in lofophers of the laft centut7. He publilhed a cipher, which one diredion caufes the body to bulge out in the traniverfe he faid contained the theory of fpringinefs and ot the mo- diredion ; and fince this bulging out is in oppofition to the tions of bodies by the aftion of fprings. It was this, cct, tranfverfe forces of attradion, it muft employ fome part of inosssttu When explained in his differtation, publilhthe comprefling force. And the common appearances are ed feme years after, it was ut tenfiofic vis. Ihis is precife- in perfed uniformity with this conception of things. When ly the propofition juft now alferted as a general fadt, a law we prefs a bit of dryifh clay, it fwells out and cracks tranfof nature. This differtation is full of curious obfervations verfely. When a pillar of wood is overloaded, it fwells out, of faffs in fupport of his aflertion. In his application to and fmall crevices appear in the diredion of the fibres. After the motion of bodies he gives his'noble difeovery of the ba- this it will not bear half of the load. This the carpenters lance-fpring of a watch, which is founded on this law. 1 he fpring, as it is more and more coiled up, or unwound, by the call CRIPPLING ; and a knowledge of the circumftances which motion of the balance, aaS on it with a force proportional modify it is of great importance, and enables us to underftand' to the diflance of the balance from its quiefeent pofition. fome very paradoxical appearances, as will be fhown by and by. This partial difuniting of particles formerly cohering is, The balance therefore is a&ed on by an accelerating force, which varies in the fame manner as the force of gravity a&- we imagine, the chief reafon why the totality ot the forces ing on a pendulum fwinging in a cycloid. Its vibrations which really oppofe an external ftrain does not increafe in therefore mull be performed in equal time, whether they are the proportion of the extenfions and compreflions. But fufwide or narrow. In the fame diflertation Hooke mentions ficient evidence will alfo be given that the forces which would all the fails which John Bernoulli afterwards adduced in fup- conned one particle with one other particle do not augment port of Leibnitz’s whimfical db&rine of the force of bodies in the accurate proportion of the change of diftance ; that in motion, or the do&rine of the vires viva; a dodlrine which in extenfions they increafe more flowly, and in compreflions _ # m Hooke might juftly have claimed as his own, had he not feen more rapidly. But there is another caufe of this deviation perhaps equal-Du&ilityf its futulity. ao And conExperiments made fince the time of Hooke (how that ly effedual with the former. Moft bodies manifeft fome de-another Now what is this ? The fad is, that the firmed by this law is ftrictly true in the extent to which we have li- gree of dudility. the expe- mjted ^ viz. in all the changes of form which will be com- parts have taken a new arrangement, in which they again L nments of pjetely UIUj0ne by the elafticity of the body. It is nearly cohere. Therefore, in the paflage to this new arrangement, Lithers. true to a much greater extent. James Bernoulli, in his dif- the fenfible forces, which are the joint refult of many corfertation on the elaftic curve, relates fome experiments of his pufcular forces, begin to refped this new arrangement inown, which feem to deviate confiderably from it; but on ilead of the former. This muft change the Ample law of clofe examination they do not. The fineft experiments are corpufcular force, charaderiftic of the particular fpecies of thofe of Coulomb, publilhed in fome late volumes of the me- matter under examination. It does not require much reflecmoirs of the Academy of Paris. He fuipended balls by wires, tion to convince us that the pofiible arrangements which the and obferved their motions of ofcillation, which he found panicles of a body may acquire, without appearing to change their nature, muft be more numerous according as the paraccurately correfponding with this law. This we lhall find to be a very important fa& in the doc- ticles are of a more complex conftitution ; and it is reafontrine of the ftrength of bodies, and we defire the reader to able to fuppofe that the conftitution even of the moft Ample make it familiar to his mind. If we apply to this our man- kind of matter that we are acquainted with is exceedingly ner of exprefling thefe forces by perpendicular ordinates Cr, complex. Our microfcopes fhow us animals fo minute, that X) d (fig. i.), we mull take other fituations E, F, of the a heap of them muft. appear to the naked eye an uniform particle B, and draw E e, F/; and we muft have ~D f mafs with a grain finer than that of the fineft marble or ra— BD : BE, or C r : E r = BC : BE. In fuch a fuppo- zor hone; and yet each of thefe has not only limbs, but bones, fition Y dX> c e muft be a ftraight line. But we lhall have mufcular fibres, blood-veflels, fibres, and a blood confiding, abundant evidence by and by that this cannot be ftriftly in all probability, of globules organifed and complex like true, and that the line Bet which limits the ordinates exr our own. The imagination is here loft in wonder; and noprefifing the attractive forces becomes concave towards the thing is left us but to adore inconceivable art and wifdom, line ABE, and that the part B