і ་ 1 Materials. Strength of each ball of the upper ftratum is perpendicularly over the centre of the equilateral triangle below, and let these be connected with the balls of the under ftratum by fimilar fpiral wires. Let there be a third and a fourth, and any number of fuch ftrata, all connected in the fame manner. It is plain that this may extend to any fize and fill any fpace. Now let this affemblage of balls be firmly contemplated by the imagination, and be supposed to shrink continually in all its demenfions, till the balls, and their diftances from each other, and the connecting wires, all vanish from the fight as difcrete individual objects. All this is very con ceivable. It will now appear like a folid body, having length, breadth, and thickness; it may be compreffed, and will again refume its dimenfions; it may be ftretched, and will again fhrink; it will move away when ftruck; in fhort, it will not differ in its fenfible appearance from a folid elaftic body. Now when this body is in a flate of compreffion, for instance, 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 connect it with thofe around it. It will greatly conduce to the full understanding of all that follows to recur to this illuftration. The analogy or refemblance between the effects of this conftitution of 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 particular circumftances to what will be the condition of a body of common tangible matter. We fhall just give one inftructive example, and then have done with this hypothetical body. We can fuppofe it of a long shape, refting on one point; we can fuppofe two weights A, B, fuspended at the ́extremities, and the whole in equilibrio. We commonly exprefs this ftate of things by faying that A and B are in equilibrio. This is very inaccurate. A is in fact in equilibrio with the united action of all the fprings which connect the ball to which it is applied with the adjoining balls. These springs 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 springs are brought into action in a way and in a degree which mathematics can easily investigate. We need not do this: it is enough for our purpose that our imagination readily difcovers that some springs are ftretched, others are compreffed, and that a preffure is excited on the middle point of fupport, and the fupport exerts a reaction which precisely balances it; and the other weight is, in like manner, in inmediate equilibrio with the equivalent of the actions of all the fprings which connect the last ball with its neighbours. Now take the analogical or resembling 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 result will refemble that of the hypothefis. 16 By exam ple Plate Now as there is fomething that is at leaft analogous to a change of distance of the particles, and a concomitant change of the intenfity of the connecting forces, we may exprefs this in the fame way that we are accuftomed to do in fimilar cafes. Let A and B (fig. 1.) reprefent the cenCCCCLXXXIV. tres of two particles of a coherent elaftic body in their quiefcent inactive ftate, and let us confider only the mechanical condition of B. The body may be ftretched. In this cafe the distance A B of the particles may become A C. In this flate there is fomething which makes it neceffary to employ a force to keep the particles at this distance. Chas a tendency towards A, or we may say that A attracts C. We may reprefent the magnitude of this tendency of C towards A, or this attraction of A, by a line Ce perpendicular to AC. Again, the body may be compreffed, and the Materials. 17 diftance A B may become A D. Something obliges us to Strength of employ force to continue this compreffion; and D tends from A, or A appears to repel D. The intenfity of this tendency or repulfion may be reprefented by another perpendicular Dd; and, to reprefent the different directions of these tendencies, or the different nature of these actions, we may set Dd on the oppofite fide of A B. It is in this How Bofmanner that the Abbé Bolcovich has reprefented the actions covich reof corpufcular forces in his celebrated Theory of Natural action of Philofophy. Newton had faid, that, as the great movements corpufcular of the folar fyftem were regulated by forces operating at a forces. diftance and varying with the distance, so 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 chemistry and phyfiology, refulted from the fimilar agency of forces varying with the distance of the particles. The learned Jefuit purfued this thought; and has shown, 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 such 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, elastic or unelastic, and endowed with all the properties which we perceive, by whose immediate operation the phenomena of motion by impulfe, and all the phenomena of chemistry, and of animal and vegetable economy, may be produced. He fhows, that notwithstanding a perfect fameness, 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 embellish the face of nature. We fhall take another opportunity of giving fuch an account of this cele brated work as it deferves. We mention it only, by the by, as far as a general notion of it will be of fome fervice on the prefent occafion. For this purpose, we just observe that Boscovich conceives a particle of any individual species of matter to confift of an unknown number of particles of fimpler conftitution; each of which particles, in their turn, is compounded of particles ftill more fimply conftituted, and fo on through an unknown number of orders, till we arrive at the fimpleft poffible conftitution of a particle of tangible matter, fufceptible of length, breadth, and thickness, and neceffarily confifting of four atoms of matter. fhows that the more complex we fuppofe the conftitution of a particle, the more mult the fenfible qualities of the aggre gate refemble the obferved qualities of tangible bodies. In particular, he fhows how a particle may be fo conftituted, that although it act 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 almost totally, inactive; and therefore an affemblage of such particles would form fuch a fluid as air. All these curious inferences are made with uncontrovertible evidence; and the greateft encouragement is thus given to the mathematical philofopher to hope, that by cautious and patient proceeding in this way, we may gradually approach to a knowledge of the laws of cohefion, that will not fhun a comparison even with the Principia of Newton. No ftep can be made in this inveftigation, but by obferving with care, and generalizing with judgment, the phenomena, which are abundantly numerous, and much more at our command than those of the great and fenfible mations of bodies. Following this plan, we observe, And he 18 Every bo 4thly, It is matter of fact, that every body has fome degree dy comof compreffibility and dilatability; and when the changes of preffible dimenfion are fo moderate that the body completely recovers and dila its table. ''' 19 And in Materials. Strer gth of its original dimenfions on the ceffation of the changing force, probably arifes from the difunion of fome particles, whofe Strength of Materials, the extenfions or compreffions are fenfibly proportional to action contributed to the whole or fenfible effect. the extending or compreffing forces; and therefore the con- compreffions we may fuppofe fomething of the fame kind; Lawf na nedling forces are proportional to the distances of the particles for when we comprefs a body in one direction, it commonhure dico from their quiefcent, neutral, or inadive pofitions. This feems ly bulges out in another; and in cafes of very violent actionwered by to have been first viewed as a law of nature by the penetra fome particles may be disunited, whose transverse action had For the Dr Hooke, ting eye of Dr Robert Hooke, one of the moft eminent phi- formerly balanced part of the compreffing force. lofophers of the last century. He published a cipher, which reader will fee on reflection, that fince the compreffion in he faid contained the theory of springiness and of the mo- one direction causes the body to bulge out in the tranfverfe tions of bodies by the action of fprings. It was this, ccii direction; and fince this bulging out is in oppofition to the inos ssttuu.—When explained in his differtation, publifh- tranfverfe forces of attraction, it must employ fome part of ed some years after, it was ut tenfio fic vis. This is precife- the compreffing force. And the common appearances are ly the propofition just now afferted as a general fact, a law in perfect uniformity with this conception of things. When of nature. This differtation is full of curious obfervations we prefs a bit of dryish clay, it fwells out and cracks trans of facts in support of his affertion. In his application to verfely. When a pillar of wood is overloaded, it fwells out, the motion of bodies he gives his noble discovery of the ba- and fmall crevices appear in the direction of the fibres. After This the carpenters lance-spring of a watch, which is founded on this law. The this it will not bear half of the load. 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, acts on it with a force proportional modify it is of great importance, and enables us to understand to the distance of the balance from its quiefcent pofition. fome very paradoxical appearances, as will be thown by and by. The balance therefore is acted on by an accelerating force, This partial difuniting of particles formerly cohering is, which varies in the same manner as the force of gravity act- we imagine, the chief reason why the totality of the forces ing on a pendulum fwinging in a cycloid. Its vibrations which really oppofe an external strain does not increase in therefore must be performed in equal time, whether they are the proportion of the extentions and compreffions. But fufwide or narrow. In the fame differtation Hooke mentions ficient evidence will also be given that the forces which would all the facts which John Bernoulli afterwards adduced in fup- connect one particle with one other particle do not augment port of Leibnitz's whimsical doctrine of the force of bodies in the accurate proportion of the change of distance; that in motion, or the doctrine of the vires viva; a doctrine which in extenfions they increase more flowly, and in compreffions Hooke might justly have claimed as his own, had he not seen more rapidly. its futulity. 20 And con. firmed by the expe riments of others. When a body is lated, a Ima 1 addition of Experiments made fince the time of Hooke fhow that this law is ftrictly true in the extent to which we have limited it, viz. in all the changes of form which will be completely undone by the elafticity of the body. It is nearly true to a much greater extent. James Bernoulli, in his differtation on the elaftic curve, relates fome experiments of his own, which feem to deviate confiderably from it; but on close examination they do not. The finest experiments are thofe of Coulomb, published in fome late volumes of the memoirs of the Academy of Paris. He fufpended balls by wires, and observed their motions of oscillation, which he found accurately corresponding with this law. This we fhall find to be a very important fact in the doctrine of the ftrength of bodies, and we defire the reader to make it familiar to his mind. If we apply to this our manner of expreffing these forces by perpendicular ordinates C, Dd (fig. 1.), we mufl take other fituations E, F, of the particle B, and draw Ee, Fƒ; and we muft have Dd: Ff = BD: BF, or Cc: Ee BC: BE. In fuch a fuppofition Fd Bce muft be a ftraight line. But we fhall have abundant evidence by and by that this cannot be frictly true, and that the line B ce which limits the ordinates expreffing the attractive forces becomes concave towards the line ABE, and that the part B df is convex towards it. All that can be safely concluded from the experiments hitherto made is, that to a certain extent the forces, both attractive and repulsive, are fenfibly proportional to the dilatations and compreffions. For, 5kly, It is univerfally obferved, that when the dilatations have proceeded a certain length, a lefs addition of force is much di fufficient to increase the dilatation in the fame degree. This is always obferved when the body has been so far ftretched that it takes a fet, and does not completely recover its form. force will The like may be generally obferved in compreffions. Moft perfons will recollect, that in violently ftretching an elastic cord, it becomes fuddenly weaker, or more eafily ftretched. But these phenomena do not pofitively prove a diminution of the corpufcular force acting on one particle: It more increase its dilatation. 22 deviation. But there is another caufe of this deviation perhaps equal-Ductility ly effectual with the former. Most bodies manifeft fome de-another gree of ductility. Now what is this? The fact is, that the caufe of parts have taken a new arrangement, in which they again cohere. Therefore, in the paffage to this new arrangement, the fenfible forces, which are the joint refult of many corpufcular forces, begin to refpect this new arrangement instead of the former. This must change the fimple law of corpufcular force, characteristic of the particular fpecies of matter under examination. It does not require much reflection to convince us that the poffible arrangements which the particles of a body may acquire, without appearing to change their nature, must be more numerous according as the particles are of a more complex conftitution; and it is reafonable to suppose that the conftitution even of the most simple kind of matter that we are acquainted with is exceedingly complex. Our microscopes fhow us animals fo minute, that a heap of them muft appear to the naked eye an uniform mafs with a grain finer than that of the finest marble or razor hone; and yet each of these has not only limbs, but bones, mufcular fibres, blood-veffels, fibres, and a blood confifting in all probability, of globules organifed and complex like our own. The imagination is here loft in wonder; and nothing is left us but to adore inconceivable art and wisdom, and to exult in the thought that we are the only ipectators of this beautiful feene who can derive pleature from the view. What is trodden under foot with indifference, even by the half-reafoning elephant, may be made by us the fource of the purest and most unmixed pleasure. But let us proceed to observe, 23 The forces 6thly, That the forces which connect the particles of tangible bodies change by a change of diftance, not only in de- which con gree, but also in kind. The particle B (fig. 1.) is attracted nect the by A when in the fituation C or E. It is repelled by it when particles of at Dor F. It is not affected by it when in the fituation B. The tangible reader is requested carefully to remark, that this is not an inte change by rence founded on the authority of our mathematical figure. The a change figure is an expreffion (to affift the imagination) of facts in na. of diftince. ture. It requires no force to keep the particles of a body in 2 their bodies ! . Strength of their quiefcent fituations: but if they are feparated by stretchMaterials. ing the body, they endeavour (pardon the figurative expreffion) to come together again.If they are brought nearer by compreffion, they endeavour to recede. This endeavour is manifefted by the neceffity of employing force to maintain the extenfion or condensation; and we reprefent this by the different pofition of our lines.. But this is not all: the particle B, which is repelled by A when in the fituation For D, is neutral when at B, and is attracted when at C or E, may be placed at fuch a diftance A G from A greater than AB that it fhall be again repelled, or at fuch a distance AH that it shall again be attracted; and thefe alterations may be repeated again and again. This is curious and important, and requires fomething more than a bare affertion for its proof. 2:4 Light alternately attracted and repelLed. 25 The fame tion and ticles of other bodies, as glafo. I TO In the article OPTICS we mentioned the most curious and valuable obfervations of Sir Ifaac Newton, by which it appears that light is thus alternately attracted and repelled by bodies. The rings of colour which appear between the object glaffes of long telescopes fhowed, that in the fmall interval of th of an inch, there are at least an hundred fuch changes obfervable, and that it is highly probable that these alternations extend to a much greater diftance. At one of these distances the light actually converges towards the folid matter of the glafs, which we exprefs fhortly, by faying that it is attracted by it, and that at the next diftance it declines from the glafs, or is repelled by it. The fame thing is more fimply inferred from the phenomena of light paffing by the edges of knives and other opaque bodies. We refer the reader to the experiments themselves, the detail being too long for this place; and we request the reader to confider them minutely and attentively, and to form diftinct notions of the inferences drawn from them. And we defire it to be remarked, that although Sir Ifaac, in his difcuffion, always confiders light as a fet of corpufcles moving in free fpace, and obeying the actions of external forces like any other matter, the particular conclufion in which we are just now interefted does not at all depend on this notion of the nature of light. Should we, with Des Cartes or Huygens, fuppofe light to be the undulation of an elastic medium, the conclufion will be the fame. The undulations at certain distances are difturbed by forces directed towards the body, and at a greater distance, the disturbing forces tend from the body. But the fame alternations of attraction and repulfion may alternations be obferved between the particles of common matter. If of attrac- we take a piece of very flat and well polished glass, fuch as repulfion are made for the horizon glaffes of a good Hadley's quaobfervable drant, and if we wrap round it a fibre of filk as it comes in the par- from the cocoon, taking care that the fibre nowhere cross another, and then prefs' this pretty hard on fuch another piece of glass, it will lift it up and keep it fufpended. The particles therefore of the one do most certainly attract thofe of the other, and this at a distance equal to the thickness of the filk fibre. This is nearly the limit; and it fometimes requires a confiderable preffure to produce the effect. The preffure is effectual only by compreffing the filk fibre, and thus diminishing the diftance between the glass plates. This adhesion cannot be attributed to the preffure of the atmo. fphere, because there is nothing to hinder the air from infinuating itself between the plates, fince they are feparated by the filk. Besides, the experiment fucceeds equally well under the receiver of an air-pump.. This moft valuable experiment was first made by Huygens, who reported it to the Royal Society. It is narrated in the Philofophical Tranfactions, no 86. Here then is an attraction acting, like gravity, at a ditance. But take away the filk fibre, and try to make the I ୪ glasses touch each other, and we fhall find a very great force Strength of neceffary. By Newton's experiments it appears, that unless Material. the prifmatic colours begin to appear between the glaffes, they are at least th of an inch afunder or more. Now we know that a very confiderable force is neceffary for producing these colours, and that the more we prefs the glaffes together the more rings of colours appear. It also appears from Newton's measures, that the difference of distance be tween the glaffes where each of thefe colours appear is about the 89,000th part of an inch. We know farther, that when we have produced the last appearance of a greasy or pearly colour, and then augment the preffure, making it about a thoufand pounds on the fquare inch, all colours vanish, and the two pieces of glafs feem to make one transparent undistin, guishable mass. They appear now to have no air between them, or to be in mathematical contact. But another fact fhows this conclufion to be premature. The fame circles of colours appear in the top of a foap bubble; and as it grows thinner at top, there appears an unreflecting spot in the middle. We have the greatest probability therefore that the perfect transparency in the middle of the two glaffes does not arife from their being in contact, but because the thickness of air between them is too fmall in that place for the reflection of light. Nay, Newton exprefsly found no reflection where the thickness was ths or more of the oth part of an inch. All this while the glaffes are ftrongly repelling each other, for great preffure is neceffary for continuing the appearance of thofe colours, and they vanish in fuccefion as the pressure is diminished. This vanifhing of the colours is a proof that the glaffes are moving off from each other, or repelling each other. But we can put an end to this repulfion by very ftrong preffure, and at the fame time fliding the glaffes on each other. We do not pretend to account for this ef fect of the fliding motion; but the fact is, that by fo doing, the glaffes will cohere with very great force, fo that we fhall break them by any attempt to pull them afunder. It commonly happens (at least it did fo with us), that in this fliding compreffion of two 'fmooth flat plates of glass they fcratch and mutually deftroy each other's furface. also worth remarking, that different kinds of glass exhibit different properties in this refpect. Flint glafs will attract even though a filk fibre lies double between them, and they much more readily cohere by this fliding preffure. It is 26 Here then are two diftances at which the plates of glafs attract each other; namely, when the filk fibre is interpofed, and when they are forced together with this fliding motion. And in any intermediate fituation they repel each other, We fee the fame thing in other folid bodies. Two pieces Lead and of lead made perfectly clean, may be made to cohere by iron. grinding them together in the fame manner. It is in this way that pretty ornaments of filver are united to iron. The piece is fcraped clean, and a small bit of filver like a fish scale is laid on. The die which is to ftrike it into a flower or other ornament is then fet on it, and we give it a fmart blow, which forces the metals into contact as firm as if they were foldered together. It fometimes happens that the die adheres to the coin fo that they cannot be fepara, ted and it is found that this frequently happens, when the engraving is fuch, that the raifed figure is not completely furrounded with a fmooth flat ground. The probable Probable caufe of this is curious. When the coin has a flat furface caufe all around, this is produced by the most prominent part of why the the die. This applies to the metal, and completely confines to the coin. the air which filled the hollow of the die. As the preffure goes on, the metal is fqueezed up into the hollow of the die; but there is ftill air compreffed between them, which cannot efcape by any paffage. It is therefore prodigiously condenfed, 27 die adheres Strength of condenfed, and exerts an elasticity proportioned to the 28 Repulfion of fome bodie fwimming in a fluid fpeTo fically lighter than themfelves. We have admitted that the glass plates are in contact when they cohere thus firmly. But we are not certain of this: for if we take thefe cohering plaffes, and touch them with water, it quickly infinuates itself between them. Yet they still cohere, but can now be pretty eafily feparated. It is owing to this repulfion, exerted through its proper the caufe fphere, that certain powders swim on the furface of water, and are wetted with great difficulty. Certain infets can run about on the surface of water. They have brushy feet, which occupy a confiderable furface; and if their steps are viewed with a magnifying glass, the furface of the water is feen depreffed all around, resembling the footsteps of a man walking on feather-beds. This is owing to a repulfion between the brush and the water. A common fly cannot walk in this manner on water. Its feet are wetted, because they attract the water instead of repelling it. A fteel needle, wiped very clean, will lie on the furface of water, making an impreffion as a great bar would make on a feather bed; and its weight is lefs than that of the displaced water. A dew drop lies on the leaves of plants without touching them mathematically, as is plain from the extreme brilliancy of the reflection at the pofterior surface; nay, it may be sometimes obferved that the drops of rain lie on the furface of water, and roll about on it like balls on a table. Yet all these fubftances can be wetted; that is, water can be applied to them at such distances that they at tract it. What we faid a little ago of water infinuating itself between the glass plates without altogether deftroying their cohesion, shows that this cohe fion is not the fame that obtains between the particles of one of the plates; that is, the two plates are not in the state of one continued mass. It is highly probable, therefore, that between these two ftates there is an intermediate ftate of repulfion, nay, perhaps many fuch, alternated with attractive ftates. It Materials. wetted with water. This distance is lefs, and not greater, Strength of 29 These are a few of many thousand facts, by which it is Particles unqueftionably proved that the particles of tangible matter of matter are connected by forces acting at a diftance, varying with connected by forces the distance, and alternately attractive and repulfive. If acting at z we represent these forces as we have already done in fig. 1. diftance.by the ordinates Cc, Dd, Ee, Tƒ, &c. of a curve, it is evident that this curve muft cross the axis at all those diftances where the forces change from attractive to repulfive, and the curve must have branches alternately above and below the axis. 03 All these alternations of attraction and repulfion take 30* A piece of ice is elaftic, for it rebounds and it rings. Its particles, therefore, when compreffed, refile; and when We shall juft mention one of thefe, which we confider Mathemaftretched, contract again. The particles are therefore in the as unanswerable. Suppofe two atoms, or ultimate particles tical con-tact impo ftate reprefented by B in figure 1. acted on by repulfive of matter A and B. acted on by repulfive of matter A and B. Let A be at reft, and B move up to tible.. forces, if brought nearer; and by attractive forces, if drawn it with the velocity 2; and let us fuppofe that it comes into further asunder. Ice expands, like all other bodies, by heat. mathematical contact, and impels it (according to the comIt abforbs a vast quantity of fire; which, by combining its mon acceptation of the word). mon acceptation of the word). Both move with the veloattractions and repulfions with thofe of the particles of ice, city 1. This is granted by all to be the final refult of the changes completely the law of action, without making any collifion. Now the inftant of time in which this commufenfible change in the distance of the particles, and the ice nication happens is no part either of the duration of the becomes water. In this new ftate the particles are again in folitary motion of A, ror of the joint motion of A and B : limits between attractive and repulfive forces; for water has It is the feparation or boundary between them. It is at been shown, by the experiments of Canton and Zimmerman, once the end of the firft, and the beginning of the fecond, to be elastic or compreffible. It again expands by heat. It belonging equally to both. A was moving with the again abforbs a prodigious quantity of heat, and becomes velocity 2. The diftinguishing circumftance therefore of elaftic vapour; its particles repelling each other at all di- its mechanical ftate is, that it has a determination (however ftances yet obferved. The diftance between the particles incomprehenfible) by which it would move for ever with of one plate of glafs and thofe of another which lies on it, the velocity 2, if nothing changed it. This it has during and is carried by it, is a distance of repulfion; for the force the whole of its folitary motion, and therefore in the lalt which fupports the upper piece is acting in oppofition to its inftant of this motion. In like manner, during the whole weight. This diftance is lefs than that at which it would of the joint motion, and therefore in the firit inftant of this fuffend it below it with a filk fibre interpoled; for no prif- motion, the atom A has a determination by which it would. matic colours appear between them when the filk fibre is move for ever with the velocity 1. In one and the fame interpofed. But the diftance at which glass attracts water inftant, therefore, the atom A has two incompatible deteris much less than this, for no colours appear when glafs is minations. Whatever notion we can form of this ftate, which Strength of which we call velocity, as a diftinction of condition, the Material fame impoffibility of conception or the fame abfurdity oc. curs. Nor can it be avoided in any other way than by faying, that this change of A's motion is brought about by infenfible gradations; that is, that A and B influence each other precifely as they would do if a flender fpring were interpofed. The reader is defired to look at what we have said in the article PHYSICS, § 82. 31 ticle con atoms. 'The two magnets there spoken of are good reprefentatives of two atoms endowed with mutual powers of re-mechanics. We fhall borrow as much as will fuffice for pulfion; and the communication of motion is accomplished in both cafes in precifely the fame manner. If, therefore, we shall ever be fo fortunate as to discover the law of variation of that force which connects one ATOM of matter with another atom, and which is therefore characteristic of matter, and the ultimate fource of all its fenfible qualities, the curve whose ordinates represent the kind and the intensity of this atomical force will be fomething like that sketched in fig. 2. The first branch an B will have AK (perpendicular to the axis AH) for its affymptote, and the laft branch Imo will be to all fenfe a hyperbola, having AO for its affymptote; and the ordinates /L, m M, &c. will be proportional to AL AM, &c. expreffing the univerfal gravitation of matter. It will have many branches B 6C, DdE, FƒG, &c. expreffing attractions, and alternate repulfive branches Cc D, E e F, Gg H, &c. All thefe will be contained within a distance A H, which does not exceed a very minute fraction of an inclı. I I The fimThe fimpleft particle which can be a conftituent of pleft exa body having length, breadth, and thickness, must confift tended par- of four fuch atoms, all of which combine their influence on fifts of four each atom of another fuch particle. It is evident that the curve which expreffes the forces that connect two fuch particles must be totally different from this original curve, this hylarchic principle. Suppofing the last known, our mathematical knowledge is quite able to discover the firft; but when we proceed to compose a body of particles, each of which consists of four fuch particles, we may venture to fay, that the compound force which connects them is almoft beyond our fearch, and that the difcovery of the pri mary force from an accurate knowledge of the corpufcular forces of this particular matter is abfolutely out of our power. All that we can learn is, the poffibility, nay the certainty, of an innumerable variety of external fenfible forms and qualities, by which different kinds of matter will be diftinguished, arifing from the number, the order of compofition, and the arrangement of the fubordinate particles of which a particle of this or that kind of matter is compofed. All thefe varieties will take place at those small and infenfible distances which are between A and H, and may produce all that variety which we obferve in the tangible or mechanical forms of bodies, fuch as elasticity, ductility, hardness, softness, fluidity, vapour, and all thofe unfeen motions or actions which we obferve in fufion and congelation, evaporation and condenfation, folution and precipitation, cryitallization, vegetable and animal affimilation and fecretion, &c. &c. &c. while all bodies must be, in a certain degree, elaftic, all muít gravitate, and all must be imcompene 32 nothing will be got by a hafty look at it. The reader will St-ength of be particularly pleafed with the facility and evidence with Material, which the ingenious author has deduced all the ordinary principles of mechanics, and with the explanation which he has given of fluidity, and his deduction from thence of the laws of hydrostatics. No part of the treatife is more valuable than the doctrine of the propagation of preffure through folid bodies. This, however, is but just touched on in the course of the investigation of the principles of our prefent inquiry into the ftrength of materials; and we truft that our readers are not difpleafed with this general sketch of the doctrine (if it may be fo called) of the cohefion of bodies. It is curious and important in itself, The doc and is the foundation of all the knowledge we can acquire of the prefent article. We are forry to say that it is as yet a new fubject of study; but it is a very promifing one, ject. and we by no means defpair of feeing the whole of chemitry brought by its means within the pale of mechanical fcience. The great and diftinguishing agent in chemistry is heat, or fire the caufe of heat; and one of its most ingular effects is the converfion of bodies into elastic vapour. We have the cleareft evidence that this is brought about by mechanical forces: for it can be oppofed or prevented by external preffure, a very familiar mechanical force. We may perhaps find another mechanical force which will prevent fufion. HAVING now made our readers familiar with the mode of action in which cohefion operates in giving ftrength to folid bodies, we proceed to confider the trains to which this strength is opposed. I. It trine of cohefion yet a new fub 33 A piece of folid matter is exposed to four kinds of ftrain, pretty different in the manner of their operation. may be torn asunder, as in the cafe of ropes, ftretch-Strains to ers, king-poits, tye-beams, &c. It may be crushed, as in the case of pillars, pofts, and trength is trufs-beams. 3. It may be broken acrofs, as happens to a joift or lever of of any kind. 4. It may be wrenched or twisted, as- in the cafe of the axle of a wheel, the nail of a prefs, &c. which oppofed. 34 I. IT MAY BE PULLED ASUNDER. This is the fimpleft of all strains, and the others are in- Matter To this the force of cohesion is may be deed modifications of it. pulled directly oppofed, with very little modification of its action afunder by any particular circumstances. . When a long cylindrical or prifmatic body, fuch as a rod of wood or metal, or a rope, is drawn by one end, it must be refifted at the other, in order to bring its cohefion into action. When it is faftened at one end, we cannot conceive it any other way than as equally ftretched in all its parts; for all our obfervations and experiments on natural bodies concur in fhowing us that the forces which connect their particles, in any way whatever, are equal and oppofite. This is called the third law of motion; and we admit its univerfality, while we affirm that it is purely experimental (fee PHYSICS). Yet we have met with differtations by perfons of eminent knowledge, where propofitions are maintained inconfiftent with this. During the difpute about the communication of motion, fome of the ableft writers have faid, that a spring compreffed or ftretched at the two ends was gradually lefs and lefs compreffed or stretched from the extremities towards the middle: but the fame writers acknow. ledged the univerfal equality of action and reaction, which is quite incompatible with this ftate of the fpring. No fuch inequality of compreffion or dilatation has ever been obfer- ved ; |