truth of the thing before the Royal Society by the experiment of pendulums, which Mr. Mariotte ſoon after thought fit to explain in a treatiſe entirely upon that ſubject. But to bring this experiment to an accurate agreement with the theory, we are to have a due regard as well to the reſiſtance of the air as to the elaſtic force of the concurring bodies.
Let the ſpherical bodies A B be ſuſpended by the parallel and equal ſtrings AC, BD, Fig. 4. from the centres C, D. About theſe centres, with thoſe intervals, deſcribe the ſemicircles EAF, GBH, biſected by the radii CA, DB. Bring the body A to any point R of the arc EAF, and (withdrawing the body B) let it go from thence, and after one oſcillation ſuppoſe it to return to the point V: then RV will be the retardation ariſing from the reſiſtance of the air. Of this RV let ST be a fourth part, ſituated in the middle, to wit, ſo as RS and TV may be equal, and RS may be to ST as 3 to 2: then will ST repreſent very nearly the retardation during the deſcent from S to A. Reſtore the body B to its place: and ſuppoſing the body A to be let fall from the point S, the velocity thereof in the place of reflexion A, without ſenſible error will be the ſame as if it had deſcended in vacuo from the point T. Upon which account this velocity may be repreſented by the chord of the arc TA. For it is a propoſition well known to geometers, that the velocity of a pendulous body in the loweſt point is as the chord of the arc which it has deſcribed in its deſcent. After reflexion, ſuppoſe the body A comes to the place s, and the body B to the place k. Withdraw the body B, and find the place v, from which if the body A, being let go, ſhould after one oſcillation return to the place r, ſt may be fourth part of rv, ſo placed in the middle thereof as to leave rs equal to tv, and
