Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/78

34 let the chord of the arc tA repreent the velocity which the body A had in the place A immediately after reflexion. For t will be the true and correct place to which the body A hould have acended, if the reitance of the air had been taken off. In the ame way we are to correct the place k to which the body B acends, by finding the place l to which it hould have acended in vacuo. And thus everything may be ubjected to experiment, in the ame manner as if we were really placed in vacuo. Thee things being done, we are to take the product (if I may o ay) of the body A, by the chord of the arc TA (which repreents its velocity), that we may have its motion in the place A immediately before reflexion; and then by the chord of the arc tA, that we may have its motion in the place A immediately after reflexion. And o we are to take the product of the body B by the chord of the arc Bl, that we may have the motion of the ame immediately after reflexion. And in like manner, when two bodies are let go together from different places, we are to find the motion of each, as well before as after reflexion; and then we may compare the motions between themelves, and collect the effects of the reflexion. Thus trying the thing with pendulums of ten feet, in unequal as well as equal bodies, and making the bodies to concur after a decent through large paces, as of 8, 12, or 16 feet, I found always, without an error of 3 inches, that when the bodies concurred together directly, equal changes towards the contrary parts were produced in their motions, and, of conequence, that the action and reaction were always equal. As if the body A impinged upon the body B at ret with 9 parts of motion, and loing 7, proceeded after reflexion with 2, the body B was carried backwards with thoe 7 parts. If the bodies Rh