Chap. 2 . PHILOSOPHY. 49

l. L e t us begin with the fubjedt, which concluded thelaft chapter. Although the body in motion be not equal tothe body at reft, on which it ftrikes; yet the motion afterthe ftroke is to be eftimated in the fame manner as above.Let A (in fig. 3.) be a body in motion towards another bodyB lying at reft. When A is arrived at B, it cannot proceedfarther without putting B into motion • and what motion itgives to B, it muft lofe it felf, that the whole degree of mo-tion of A and B together, if neither of the bodies be elaftic,fliall be equal, after the meeting of the bodies, to the fingleMotion of A before the ftroke. Therefore, from what hasbeen faid above, it is manifeft, that as foon as the two bodiesare met, they will move on together with a velocity, whichWill bear the fame proportion to the original velocity of A, asthe body A bears to the fum of both the bodies.

3• If the bodies are elaftic, fo that they ftiall feparate af-ter the ftroke, A muft lofe a greater part of its motion, andthe fubfequent motion of B will be augmented by this elafti-Clt y> as much as the motion of A is diminifhed by it. Theelafticity adting equally between both the bodies, it will com-municate to each the fame degree of motion; that is, it willfeparate the bodies by taking from the body A and adding tothe body B different degrees of velocity, fo proportioned totheir refpedtive quantities of matter, that the degree of mo-tlo n, wherewith A feparates from B, fhall be equal to the de-g* ee °f motion, wherewith B feparates from A. It followstherefore, that the velocity taken from A by the elafticitycars to the velocity, which the fame elafticity adds to B, the

II fame