If v be the velocity it has acquired when it comesto any angle p, v x vers, p is the velocity lost.
197. Any angle being given, it may be dividedinto angles, so small, that the sum of the versedsines of these angles shall be less tha any givenmagnitude.
Hence the number of planes may be so increased,and their inclination to one another so diminished,that though the change of direction between thefirst and the last be ever so great, the loss of velo-city in the descending body shall be less than anygiven quantity.
Hence, if the body descend in a curve, it suffers noloss of velocity.
D'Alembert , Traite de Dynamique, § 41.
This is true of the motion of a pendulum, that is, ofa body hanging by a thread, and swinging back-wards and forwards about a fixed point.
198. In a pendulum vibrating in a circle, theforce which accelerates it when it approaches thelowest point, is nearly proportional to its distancefrom that point.
Hence the small vibrations of the same pendulum arenearly isocronous.
199. If