224 Dynamics. 



dulums divided by the square roots of the gravities ; so that if the 

 gravities are the same, the number of vibrations will be recipro- 

 cally as the square roots of the lengths of the pendulums ; and if 

 the lengths are the same, the number of vibrations will be direct- 

 ly as the square roots of the gravities. 



349. Hence if the same pendulum, carried to different parts 

 of the earth, does not make the same number of vibrations in the 

 same interval of time, it is to be inferred that gravity is not the 

 same in these places, and the number of vibrations actually 

 made in the same time by the same pendulum in two different 

 places, will furnish the means of ascertaining the relative inten- 

 sities of gravity at these places. It is by experiments of this 

 kind, taken in connection with the foregoing proposition, that we 

 are now assured of the diminution of gravity as we approach 

 toward the equator, and on the other hand of its augmentation 

 as we proceed from the equator toward either pole. 



350. If we call t the time employed by a heavy body, falling 

 freely, in describing the diameter ED or 2 , we shall have 



gt* a t* 

 273 2a = *_ or - = T ; 



Fig.164. whence 



g 



Substituting this value in the equation, 



we obtain, 



i' = i 7i t or | t' = i n /, 

 which gives 



that is, the duration of the descent through any small arc AE is 



to the time of falling through the diameter, as the fourth of the 



circumference of a circle is to its diameter. But the fourth of 



2$a. ' the' circumference is less than the diameter; consequently a 



