Chap. 2. PHILOSOPHY.

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1. Let us begin with the subject, which concluded thelast chapter. Although the body in motion be not equal tothe body at rest, on which it strikes ; yet the motion afterthe stroke is to be estimated in the same manner as above.Let A (in fig. 3.) be a body in motion towards another bodyB lying at rest. When A is arrived at B, it cannot proceedfarther without putting B into motion ; and what motion itgives to B, it must lose it self, that the whole degree os mo-tion of A and B together, if neither os the bodies be elastic,shall be equal, aster the meeting os the bodies, to the singlemotion of A- before the stroke. Therefore, from what hasbeen said above, it is manifest, that as soon 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 sum of both the bodies.

3. If the bodies are elastic, so that they shall separate af-ter the stroke, A must lose a greater part of its motion, andthe subsequent motion of B will be augmented by this elasti-city, as much as the motion of A is diminished by it. Theelasticity acting equally between both the bodies, it will com-municate to each the same degree of motion; that is, it willseparate the bodies by taking from the body A and adding tothe body B different degrees of velocity, so proportioned totheir respective quantities of matter, that the degree of mo-tion, wherewith A separates from B, shall be equal to the de-gree of motion, wherewith B separates from A. It followstherefore , that the velocity taken from A by the elasticitybears to the velocity, which the same elasticity adds to B, the

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