128 OUTLINES QF NATURAL PHILOSOPHY. 



Hence the number of planes may be so increased, 

 and their inclination to one another so diminished, 

 that though the change of direction between the first 

 and the last be ever so great, the loss of velocity in 

 the descending body shall be less than any given 

 quantity. 



Therefore, if the body descend in a curve, it will suf* 

 fer no loss of velocity. 



D^ALEMBERT, Traite de Dynamique, 41. 



This is true of the motion of a pendulum, that is, of 

 *>;! a body suspended from a fixed point, and swinging 

 freely forwards and backwards about that point. 



. When a pendulum vibrates in a circle, the 

 force which accelerates it as it approaches the 

 lowest point, is nearly proportional to its distance 

 from that point. 



a. Hence the small vibrations of the same pendulunl 

 are nearly isochronous, or of the same duration. 



203. If a pendulum vibrate in a circle, and if g 

 be the velocity acquired by a heavy body de- 

 scending freely, in one second, the square .root of 

 g is to the square root of the length of the pendu- 

 lum; as the number which expresses the ratio of 

 the circumference of a circle to its diameter, is to 

 the time of. the least vibration of the pendulum, 

 expressed in seconds. 



Let 



