other before collifion. Thus the relative velocity, before and after collifion, is 5 in the first example, 13 in the fecond, and 40 in the third. And in all cafes, whether the impinging bodies are elastic or not, the fum of the motions in the fame direction, and the difference of the motions in contrary directions, are the fame both before and after collifion. If two equal elastic bodies move towards each other with equal velocities, they will recede from each other after collifion each with the fame velocity. If one of them, in motion, ftrike against the other at reft, it will communicate the whole velocity, and remain at reft itself. If one overtakes the other, they will interchange velocities, and continue to go on the fame way as before. If they meet each other with different velocities, they will interchange velocities, and fly off from each other in contrary directions. If an elaftic body ftrikes upon an immoveable elaftic obftacle, it will rebound with the fame velocity that it came. If one of the impinging bodies be hard, and the other elaftic, the laws of the communication of motion are the fame as if both the bodies were elaftic; for the fpring will give way, till the force of elasticity becomes equal to the force of compreffion, that is, double to the quantity of the ftroke in each body; and the re-action of a hard body against double the quantity of elafticity, will produce the fame effect as a fingle quantity of elafticity in each body acting in contrary directions. the impulfe is oblique, it must be refolved into two impulfes, one direct, and the other parallel to the tangent at the point of collifion. The effect of the direct impulfe must be computed according to the laws before-mentioned: the parallel impulfe will continue after the collifion the fame fame in all refpects that it was before; nor will it produce any other effect, except by means of the friction to make the bodies revolve each about it's own center of gravity. It often happens that the communication of motion is the indifpenfable means of obtaining fome other effect; thus it is ufed to nail and flatten bodies; in thefe cafes it is not fufficient that the ftriking body has a certain quantity of motion, but the mafs or quantity of matter must be fo proportioned with the velocity, as to produce the required effect without fplitting or deftroying the body ftruck. In architecture there are many occafions where it is neceffary to drive piles; if the mafs which ftrikes the pile is fmall, it will not have force fufficient to drive it; and if it be moved with confiderable velocity, it will split the head of the pile; a large mafs must therefore be ufed moving with lefs velocity. If fmall hammers and a great velocity are used to drive pivots of iron into large pieces of wood, the head of the pivot will yield, and yet not be driven into the wood; whereas the effect will be answered by using hammers of confiderable weight moving with lefs velocity. Gold-beaters, and other workmen who flatten metals, make use of heavy hammers, and move them flowly; if they ufed fmall hammers and moved them fwiftly, the parts of the metal would be broke and divided by the ftrokes. To prevent the propagation of motion, and to deaden the blow, thofe that work in their chambers and are obliged to ufe anvils, place the blocks that hold the anvil upon a roll of matting, or upon fprings; without this precaution great part of the force force impreffed by the hammer would be tranfmitted to the floor, and would create fhaking to the prejudice of the building. The principles above laid down will affift you in explaining the recoil of cannon, fufees, and other fire-arms; for you may confider the gunpowder as a spring which unbends or expands itfelf in every direction, but which can only act efficaciously against the breech of the cannon and the ball. The action of the powder is that of two equal forces against two unequal powers of refiftance, the ball and the cannon; it may therefore be fuppofed, cæteris paribus, to imprefs them both with an equal quantity of motion, but with different degrees of velocity; that of the ball being as much greater as it's mafs is lefs than that of the cannon, &c. The cannon, the mufquet, &c. especially if you take into the account the obftacles which retain them, are much more difficult to move than the ball with which they are charged, which of courfe receives from the inflamed powder a much greater degree of velocity. There are other circumftances which contribute to augment the velocity of the ball, as the length of the piece, &c. which do not come properly before us. As to the recoil in general, fuppofing the quantity and quality of the powder the fame, a gun recoils fo much the more as the bullet makes more refiftance either by it's weight or the wadding. A rocket flies up, becaufe it's lower part, which is fired, performs the office of a fpring, which acts one way against the body of the rocket, and the other way against a volume of air; and as this fpring is continually renewed by the fucceffive inflammation of all the parts of the rocket, it's motion is accelerated, firft, because it is contained in in the body itself, and is therefore continually adding to it's velocity; and fecondly, because the weight or refiftance of the rocket is diminishing every inftant by the diffipation of the parts as they burn away. GENERAL OBSERVATIONS ON MOTIÓN. If you take only a curfory view of the opera tions in nature, you must be convinced that there is fomewhere an inexhaustible fource of impulfe, though undifcernible by our fenfes confider the diffolving power of menftruums, the violence of fire, the strong contraction of our heart and arteries, the ftability of heavy maffes held down by the force of gravitation to the earth, the firm cohesion of bodies, and you must own all these must have fome prodigious fund, though you know not whence to derive the force they exert. The heavens, the earth, and all the elements are in conftant motion; the matter of the earth, &c. is constantly paffing into the fubftance of trees and plants, and as conftantly returning from them again in their diffolution; the fea is moved with tides and currents; the air is agitated with winds and ftorms; and light is continually flowing from the fun, ftars, &c. to the utmost boundaries of the universe. Wherever the fources of this fund may be, or however copious the fupplies, they cannot answer' all the demands made upon them by the conftant collifion and other fources of decay. Every time you clap your hands together, you take fomething. from the ftock of motion which is to carry on the operations See Jones's Effay on the First Principles of Philofophy Tucker's Light of Nature. operations of nature; but the collifion occafioned by human actions are very trifles in comparison with that great quantity of force which is fpent in the workings of nature. The bearing of rivers against their winding banks; the dafhing of feas against the fhore; the oppofition of winds one against another, or from mountains; the fyftole, or contraction of circulating veffels in plants and animals; but above all, the gravitation of bodies to earth and funs; the cohefion of compounds; the oppofition of centripetal and centrifugal forces; the various repulfions, &c. which must all occafion every moment an immenfe confumption of force, and require things to be fo conftructed, that there may be continual recruits to fupply the perpetual diminution. We have no knowledge of fubftances, or of any being, or of any thing, abftracted from the action of that thing or being. All our knowledge of things confifts in the perception of the power, or force, or manner of acting of that thing; that is, of the action of that thing on our fenfes, or of the effects of that thing on fome other thing, whose action affects or is the object of our fenfes, and in the perception of the relations or ratios of these actions to each other: for if they produce no alteration on the fenfes, if no change is perceived by the mind through the medium of the fenfes, we can have no evidence of their existence; every effect must be produced by fome caufe or action. Every thing that you know is an agent, or has a power of acting, for you know nothing of any being but it's action, and the effects of that action; the moment it ceafes to act. it is annihilated as to you, you can form no notion of it's exiftence. Whatsoever produces any effect or alteration VOL. III. R on |