Pendulums. 223 



t : I 1 : : \/~a~ : \TcT ; 



that is, in the same place the durations of the oscillations are as the 

 square roots of the lengths of the pendulums. 



347. But if the same pendulum be successively exposed to 

 the action of two different gravities, a being equal to a', the pro- 

 portion 



*:*> :: V^ : V? 



g 8 



becomes 



8 



in other words, the durations of the oscillations of the same pendulum 

 in different places are inversely as the square roots of gravity. 



348. Let n be the number of oscillations or vibrations made 

 by the pendulum a in a given time, as one hour or 3600'', we 



3600" 

 shall have t = - For the same reason, if we represent 



by n' the number of vibrations made by the pendulum a/ in the 



3600" 

 same time, we shall have r = - ; ; 



accordingly, 



I if 360Q " . 3600" '\ 



n n' ' ' T ' n ' 



that is, the number^ of vibrations made in the same time by two 

 pendulums of different lengths are inversely as the durations of 

 their respective vibrations. Consequently, since 



n : n' : : \f- : V -, 

 g' g 



that is, the number of vibrations made in the same time by two pendu- 

 lums of different lengths, and which are urged by different gravities, 

 are in the inverse ratio of the square roots of the lengths of the pen- 



