Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/77

Rh truth of the thing before the Royal Society by the experiment of pendulums, which Mr. Mariotte oon after thought fit to explain in a treatie entirely upon that ubject. But to bring this experiment to an accurate agreement with the theory, we are to have a due regard as well to the reitance of the air as to the elatic force of the concurring bodies. Let the pherical bodies A B be upended by the parallel and equal trings AC, BD, Fig. 4. from the centres C, D. About thee centres, with thoe intervals, decribe the emicircles EAF, GBH, biected 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 ocillation uppoe it to return to the point V: then RV will be the retardation ariing from the reitance of the air. Of this RV let ST be a fourth part, ituated in the middle, to wit, o as RS and TV may be equal, and RS may be to ST as 3 to 2: then will ST repreent very nearly the retardation during the decent from S to A. Retore the body B to its place: and uppoing the body A to be let fall from the point S, the velocity thereof in the place of reflexion A, without enible error will be the ame as if it had decended in vacuo from the point T. Upon which account this velocity may be repreented by the chord of the arc TA. For it is a propoition well known to geometers, that the velocity of a pendulous body in the lowet point is as the chord of the arc which it has decribed in its decent. After reflexion, uppoe 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, hould after one ocillation return to the place r, t may be fourth part of rv, o placed in the middle thereof as to leave rs equal to tv, and Rh