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A similar result will be obtained, whatever proportion may subsist between the masses A and B. Suppose B to be ten times A; then the whole motion of A must, after the impact, be distributed among the parts of the united masses of A and B: but these united masses are, in this case, eleven times the mass of A. Now, as they all move with a common motion, it follows that A’s former motion must be equally distributed among them; so that each part shall have an eleventh part of it. Therefore the velocity after impact will be the eleventh part of the velocity of A before it. Thus A loses by the impact ten-eleventh parts of its motion, which are precisely what B receives.

Again, if the masses of A and B be 5 and 7, then the united mass after impact will be 12. The motion of A before impact will be equally distributed between these twelve parts, so that each part will have a twelfth of it; but five of these parts belong to the mass A, and seven to B. Hence B will receive seven-twelfths, while A retains five-twelfths.