And here we would beg leave to object to Bos covich, that since lie has admitted that all the par ticks of matter may be formed upon the supposition only of one limit of distance, what good reason can be given for supposing, as he has done, that there are a succession of changes from attraction to repul sion, and vice versa, according to the change in the distance of his primary points. Surely this is to con tradict one of the first rules of philosophising, and to multiply causes without necessity. Would it not have been infinitely preferable, to have proceeded at once upon that supposition, for the existence of which lie appears to have brought forward such abundant proof? In sd doing, his 'theory would have appeared abundantly more simple, and equally satisfactory.; We can see no use whatever for,that vague and Pro teus-like law of forces which he has just been esta blishing, unless it be to use a favourite phrase of his own, to exhibit the itilinita fcecunditas thcoricc. How different from, we had almost said how unsatisfac tory in comparison to, the beautiful law of Newton ian gravity, by which the infinite variety of physical astronomy, the more generally it is applied, is the more completely explained ! Compared to this, in deed, the theory of Boscovich, is like the orbs, the deferents; and the epicycles of our forefathers, which, instead of explaining, only tended to multiply the difficulties of our prOgress in science. But we defer this, and some other remarks, until we have com pleted our account of the theory, and in the mean time return to its application to -mechanics, perhaps the most valuable part of his work, and which is, in reality, little dependent upon this peculiar law of forces.
In proceeding to the consideration of masses, the first subject which offers is, the numerous and import ant properties of the centre of gravity. These are readily.derived and demonstrated from our theory ; but are of such importance, that we shall make them the subject of a separate article. (See Centre of GAAVITY. ) In the mean time we shall only observe, that our author has demonstrated generally, that in every mass there must be some, and only one centre ; he shows by what means it may be generally deter mined; lie points out and supplies the defect of proof ip the common way of finding the centre of seve ral bodies ; illustrating the subject by the multiplica tion of numbers, and the composition of forces ; and he demonstrates the celebrated theorem of Newton, that the centre of gravity is undisturbed by mutual internal forces ; consequently, that the quantity of motion in the universe is preserved always the same, when computed in the same direction, and therefore that action and reaction arc always equal and con trary.
From this law of the equality of action and re action, readily flow the laws of collision, discovered at the same time by Wren, Huygens, and Wallis, as is mentioned by Newton, when treating of this very law. ,(Prin. lib. i. Cor. 4. Ax.) Boscovich derives then-1'in this way. Suppose a soft globe or ball goes forward with a less velocity, and followed by another soft globe with a greater velocity, so that their centres be always carried in the line which joins them, and that the one at length hits the other, which is called a direct collision ; this hitting, according to our au thor, is not done by an immediate contact, but be fore they come in contact, the after parts of the first and the fore parts of the last are compressed by the mutual repulsive force ; and this compression goes on increasing until they come to have equal veloci ties, then all further access ceases, and, conseepiently, all further compression ; and since the bodies are soft, they exert no mutual force after compression, but continue to go on with equal velocity. And
since the• quantity of motion will be the same in the same direction, we must, in order to find the com mon velocity ;fter collision, multiply each mass into its velocity, and divide the sum of these products by the sum of the masses. If one of the globes were at rest, its velocity might be made = 0, and, if moving in the opposite direction, it might be taken with a negative value.
From soft bodies, the transition is easy to those which are elastic. In these, after the greatest com pression and change' of figure, the two globes con tinue to act on each other, until they recover their first shape, and this action doubles the effect of 'the former. If the elasticity be imperfect; and the force in losing shape be to the force in recovering it in any given ratio, the effect of the former to that of the latter will also be in a given ratio, (See COLLISION) the deductions of Boscovich being no way different from those given in other elementary treatises.
Proceeding now to oblique concourse, let the two globes A and C in Fig. 8. come in a given time, by the right lines AB, CD, which measure their velo cities into physical contact at B and D. By the common mode, the effect of the contact is thus ex plained : Join the centres by the straight line BD, to which, produced if necessary, draw the perped diculars AF, CH ; and completing the rectangles, AFBE, CHDG, each of the motions AB, CD is resolved into two, the one into AF, AE, or BE, BF, the other into CH, CG, or GD, DH. The first of these on tack side remains entire ; the second, FB and HD, make a direct collision. We must there fore find, by the law of direct collision, the velocities DK, DI, which, according to that law, will be dif ferent for different sorts of bodies ; and we must compound these with the forces or velocities expreic sed by the straight lines BL, DQ lying in the same straight lines with BE and GD, and equal to them ; therefore BM and DP will express the velocities and direction of the motions after collision. The reso lution of motions in this way is considered as a real and actual resolution, the one of which continues un: altered, the other undergoes a change; and in the case which this figure expresses, is altogether ex tinguished, and then another is produced again. But the thing takes place, in fact, without any real resolu tion, in the following manner : The mutual force which acts upon the balls B, D, gives to them, du ring the whole time of the collision, the contrary ve locities BN, DS, equal, in this case, to those two, of which the one is commonly supposed destroyed and the other reproduced; these forces, compounded with BO and DR, equal, and in the same direction with AB, CD, and therefore expressing the entire effect of the preceding velocities, exhibit the very Same re BM, DP. For it is evident, that LO will be equal to AE or BF, and therefore MO =BN, and BMNO a parallelogram. In like manner', DRPS is a parallelogram. Wherefore there is no real resolution in this case, but merely a composition of motions ; namely, the former velocity persevering by the vas inertice, and that compounded with the new velocity which the forces produce that act in the collision.