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

let the chord of the arc tA repreſent 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 ſhould have aſcended, if the reſiſtance of the air had been taken off. In the ſame way we are to correct the place k to which the body B aſcends, by finding the place l to which it ſhould have aſcended in vacuo. And thus everything may be ſubjected to experiment, in the ſame manner as if we were really placed in vacuo. Theſe things being done, we are to take the product (if I may ſo ſay) of the body A, by the chord of the arc TA (which repreſents 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 ſo 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 ſame 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 themſelves, 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 deſcent through large ſpaces, 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 conſequence, that the action and reaction were always equal. As if the body A impinged upon the body B at reſt with 9 parts of motion, and loſing 7, proceeded after reflexion with 2, the body B was carried backwards with thoſe 7 parts. If the bodies