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STR Strength of TRENGTH OF MATERIALS, in mechanics, is a fubMaterials, Sject of fo much importance, that in a nation fo emiso
nent as this for invention and ingenuity in all fpecies Importance of manufactures, and in particular so distinguished for of the fub- its improvements in machinery of every kind, it is fomeject. what fingular that no writer has treated it in the detail which its importance and difficulty demands. 'The man of science 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 purpose of improvement and refinement which he fees in every workshop. Every cotton mill appears an academy of mechanical fcience; and mechanical invention is spreading from these fountains over the whole kingdom: But the philofopher is mortified to fee this ardent spirit fo cramped by ignorance of principle, and many of these 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 scientific education, this ignorance of principle, is so frequently observed as in the injudicious proportion of the parts of machines and other mechanical ftructures; proportions and forms of parts in which the ftrength and pofition are nowife regulated by the strains to which they are exposed, and where repeated failures have been the only
Strength of materials
It cannot be otherwife. We have no means of inftruction, except two very fhort and abftracted treatifes of the late Mr Emerson on the ftrength of materials. We do not We do not recollect a performance in our language from which our artifts 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 performauces. Who would imagine that PRICE'S BRITISH CAR PENTER, the work of the first reputation in this country, and of which the fole aim is to teach the carpenter to erect folid and durable ftructures, does not contain one propofition or one reafon by which one form of a thing can be thown to be stronger or weaker than another? We doubt very much if one carpenter in an hundred can give a reafon to convince his own mind that a joift is ftronger when laid on its edge than when laid on its broad fide. We fpeak in this ftrong manner in hopes of exciting fome man of fcience to publish a system of inftruction on this fubject. The limits of 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 fyftematic connection by which all the knowledge already poffeffed of this fubject may be brought together and properly arranged. This we shall now attempt in as brief a manner as we are able.
THE ftrength of materials arises immediately or ultimate arifes from ly from the cohesion of the parts of bodies. Our examinaVOL. XVIII. Part I.
tion of this property of tangible matter has as yet been very Strength of partial and imperfect, and by no means enables us to apply mathematical calculations with precifion and fuccefs. The various modifications of cohesion, in its different appearances of perfect softness, plafticity, du&ility, elasticity, hardnefs, have a mighty influence on the ftrength of bodies, but are hardly fufceptible of measurement. Their texture also, whether uniform like glass and ductile metals, crys crystallized or granulated like other metals and freeftone, or fibrous like timber, is a circumstance no less important; yet even here, although we derive fome advantage from remarking to which of these forms of aggregation a substance belongs, the aid is but small. All we can do in this want of general principles Experiis to make experiments on every class of bodies. Accord-ments to ingly philofophers have endeavoured to inftruct the public in this particular. The Royal Society of London at its very first institution made many experiments at their meetings, as may be seen in the first registers of the Society t.† See Several individuals have added their experiments. The mott Birche's numerous collection in detail is by Muschenbroek, profeffor of Hiftery, and natural philofophy at Leyden. Part of it was published by Mathemahimself in his Effais de Phyfique, in 2 vols 4to; but the full tie Coller collection is to be found in his Syftem of Natural Philofo-tions. phy, published after his death by Lulofs, in 3 vols 4to. This was tranflated from the Low Dutch into French by Sigaud de la Fond, and published at Paris in 1760, and is a prodigious collection of phyfical knowledge of all kinds, and may almoft fuffice for a library of natural philofophy. But this collection of experiments on the cohefion of bodies is not of that value which one expects. We presume that they were carefully made and faithfully narrated; but they were made on fuch small specimens that the unavoidable natural inequa lities of growth or texture produced irregularities in the refults 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 absolute measures which may be employed with confidence; and there is nothing in the English language except a fimple lift by Emerfon, which is merely a set of affirmations, without any narration of circumstances, to enable us to judge of the validity of his conclufions: but the character of Mr Emerfon, as a man of knowledge and of integrity, gives even to these affertions a confiderable value.
But to make ufe of any experiments, there must be employed Rendered fome general principle by which we can generalize their re- ful by fults. They will otherwife be only narrations of detached generalizas facts. We must have some notion of that intermedium, by the intervention of which an external force applied to one part of a lever, joift, or pillar, occafions a train on a diftant part. This can be nothing but the cohesion between the A OF parts,
Strength of parts. It is this connecting force which is brought into Materials. action, or, as we more fhortly exprefs it, excited. This action is modified in every part by the laws of mechanics. It Strength is this action which is what we call the strength of that part, and its effect is the ftrain on the adjoining parts; and thus it is the fame force, differently viewed, that conftitutes both the ftrain and the ftrength. When we confider it in the light of a refiftance to fracture, we call it frength.
We call every thing a force which we obferve to be ever accompanied by a change of motion; or, more ftrictly speaking, we infer the prefence and agency of a force where ver we obferve the state 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 act 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 confi. dence as when we observe it drag the body along the ground. The immediate action of this force is undoubtedly exerted between the immediately adjoining parts of the rope. The immediate effect the keeping the particles of the rope to gether. They ought to feparate by any external force drawing the ends of the rope contrarywife; and we afcribe their not doing so to a mechanical force really oppofing this external force. When delired to give it a name, we name it from what we conceive to be its effect, and therefore its characteristic, and we call it COHESION. This is merely a name for the fact; but it is the fame thing in all our denominations. We know nothing of the caufes but in the ef. fects; and our name for the cause is in fact the name of the effect, which is COHESION. We mean nothing elfe by gravitation or magnetism. What do we mean when we fay that Newton understood thoroughly the nature of gravitation, of the force of gravitation; or that Franklin understood the nature of the electric force? Nothing but this: Newton confidered with patient fagacity the general facts of gravi. tation, and has defcribed and claffed them with the utmost precition. In like manner, we thall understand the nature of cohesion when we have difcovered with equal generality the laws of cohefion, or general facts which are obferved in the appearances, and when we have defcribed and claffed them with equal accuracy.
Let us therefore attend to the more fimple and obvious
long; fix one-end firmly to the ceiling, and let the wire Strength of
This What is
2dly, 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 ftops in a pofition almost two revolutions removed from its original pofition. It has now acquired a new arrangement of parts, and this new arrangement is permanent like the former; and, what is of particular moment, it is perfectly elaftic. change is familiarly known by the denomination of a ser, meant by The wire is faid to have TAKEN A SET. When we attend aet. minutely to the procedure of nature in this phenomenon, we find that the particles have as it were flid on each other, ftill cohering, and have taken a new pofition, in which their connecting forces are in equilibrio and in this change of relative fituation, it appears that the connecting forces which maintained the particles in their first fituations were not in equilibrio in some position intermediate between that of the firft and that of the latt form. The force required. for changing this firft form augmented with the change, but only to a certain degree; and during this procefs the connecting forces always tended to the recovery of this first form. form. But after the change of mutual pofition has paffed a certain magnitude, the union has been partly destroyed, and the particles have been brought into new fituations fuch, that the forces which now connect each with its neighbour tend, not to the recovery of the firft arrange ment, but to push them farther from it, into a new fitua tion, to which they now verge, and require force to prevent them from acquiring. The wire is now in fact again perfectly elaftic; that is, the forces which now connect 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 facts, on which a theory is to be founded. What we have been juft now faying is evidently a defcription of that fenfible form of tangible matter which we call ductility. It has Ducility, every gradation of variety, from the foftnefs of butter to the firmnefs- of gold. All thefe bodies have fome elafticity; but we lay they are not perfectly elaftic, becaufe they do not completely recover their original foim when it has been
Strength of greatly deranged. The whole gradation may be most difinetly obferved in a piece of glass or hard fealing wax. In the ordinary form glass is perhaps the most completely elaftic body that we know, and may be bent till juft ready to fnáp, and yet completely recovers its first form, and takes no fet whatever; but when heated to fuch a degree as juft to be visible in the dark, it lofes its brittleness, 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 1emarkably diftinguished from clay by a quality which we may Vifcidity call VISCIDITY, which is fomething like elafticity, of which clay and other bodies purely plaftic exhibit no appearance, This is the joint operation of ftrong adhesion and softness. When a rod of perfectly foft glafs is fuddenly stretched a little, it does not at once take the fhape which it acquires, after some little time. It is owing to this, that in taking the impreffion of a feal, if we take off the feal while the wax is yet very hot, the sharpness of the impreffion is deftroyed immediately. Each part drawing its neighbour, and each part yielding, the prominent parts are pulled down and blunted, and the fharp hollows are pulled upwards and alfo blunted. The fcal must be kept on till all has become not only stiff but hard.
Obferved tu all homogeneous
This vilcidity is to be observed in all plaftic bodies which are homogeneous. It is not obferved in clay, because it is plait:c bo. not homogeneous, but confifts of hard particles of the argillaceous earth fticking together by their attraction for water. Something like it might be made of finely powdered glass and a clammy fluid fuch as turpentine. Vifcidity 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 most perfect fluid that we are acquaint ed with, as we observed in the experiments for ascertaining specific gravity.
There is in a late volume of the Philosophical Transactions a narration of experiments, by which it appears that the thread of the spider is an exception to our firft general law, and that it is perfectly ductile. It is there afferted, that a long thread of goflamer, furnished with an index, takes any position whatever; and that though the index be turned round any number of times (even many hundreds), it has no tendency to recover its first form. The thread takes completely any fet whatever. We have not had an opportunity of repeating this experiment, but we have di linctly 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 flender flip of whalebone or a hair. If totally devoki 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 immense variety of sensible modes of aggregation may be produced. Some degree of both are probably to be observed in all bodies of complex conftitution; that is, which confift of particles made up of many different kinds of atoms. Such a constitution of a body must afford many fituations permanent, but eafily deranged.
In all these changes of difpofition which take place among the particles of a ductile body, the particles are at fuch distance that they ftill cohere. The body may be stretched a little; and on removing the extending force, the body shrinks into its first form. It alfo refifts, moderate compreflions; and when the compreffing force is removed, the body fwells out again. Now the corpufcular fad here is, that the particles are acted on by attractions and repullions, which balance each other when no external force is acting on the body, and which augment as the particles are made,
by any external caufe, to recede from this fituation of mutu. Strength of al inactivity; for fince force is requifite to produce either Aaterials. the dilatation or the compreffion, and to maintain it, we are obliged, by the conftitution of our minds, to infer that Particles it is oppofed by a force accompanying or inherent in every acted on particle of dilatable or compreffible matter and as this by actrec neccffity of employing force to produce a change indicates repulious. the agency of thefe corpufcular forces, and marks their kind, according as the tendencies of the particles appear to be toward each other in dilatation, or from each other in compreffion; fo it alfo measures the degrees of their intensity. 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 infances. We fee from all this that the phenomena of cohefon indicate fome relation between the intenfity of the force of cohesion and the diflance between the centres of the particles. To The great discover this relation is the great problem in corpufcular problem in mechanifm, as it was in the Newtonian investigation of the corpufcular force of gravitation. Could we difcover this law of action between the corpufcles with the fame certainty and diftinctnefs, we might with equal confidence fay what will be the refult of any position which we give to the particles of bodies; but this is beyond our hopes. The law of gravitation is fo fimple that the difcovery or detection of it amid the variety of celestial phenomena required but one ftep; and in its own nature its poffible combinations Aill do not greatly exceed the powers of human relearch. One is almoft difpofed to fay that the Supreme Being has exhibited it to our reafoning powers as fufficient to employ with fuccefs our utmost efforts, but not fo abftrufe as to difcourage us from the noble attempt. It seems to be otherwife with respect to cohesion. Mathematics informs us, that if it de viates fenfibly from the law of gravitation, the fimpleft com. binations will make the joint action of several particles an almoft impenetrable myftery. We must therefore content ourfelves, for a long while to come, with a careful obfervation of the fimpleft cafes that we can propofe, and with the dif covery of fecondary laws of action, in which many particles combine their influence. In pufuance of this plan, we observe,
3dly, That whatever is the fituation of the particles of a Particies body with refpect to each other, when in a quiefcent ftate, kept in their pla they are kept in these fituations by the balance of oppofite ce- by a forces. This cannot be refufed, nor can we form to our balance felves any other notion of the ftate of the particles of a ef forces. body. Whether we fuppofe the ultimate particles to be of certain magnitudes and thapes, touching each other in fingle points of cohesion; or whether we (with Bolcovich) confider them as at a distance from each other, and acting on cach other by attractions and repulfions-we muft acknowledge, in the first place, that the centres of the particles (by whofe mutual distances we must eftimate the distance of the particles) may and do vary their distances from each other. What elle can we fay when we observe a body increafe in length, in breadth, and in thickness, by heating it, or when we fee it diminish in all these dimenfions by an external compreffion? A particle, therefore, fituated in the. midst of many others, and remaining in that situation, must be conceived as maintained in it by the mutual balancing of all the forces which connect it with its neighbours. It is Illuftralike a ball kept in its place by the oppofite action of two tion of fprings. This illuftration merits a more particular applica- this pro tion. Suppose a number of balls ranged on the table in the angles of equilateral triangles, and that each ball is connected with the fix which lie around it by means of an elastic wire curled like a cork-fcrew; fuppofe fuch another ftratum of balls above this, and parallel to it, and fo placed that A 2