MECHANICS. 



Let I be the length of a pendulum, w the number that 

 denotes the circumference of a circle, of which the 

 diameter is 1, and t = the time of one vibration of 

 the pendulum in seconds, 



t = 



As the weight of the body does not enter into the ex^ 

 pression of the time, the vibrations of a pendulum 

 are the same whatever be its weight. 



Hence the times of the vibrations of pendulums are 

 as the square roots of their lengths. 



If tf = 1, I' = length of the seconds pendulum, and 



1 TT i / - ; therefore g^iP^l', or V = -^ 



? "^ 





 If it be required, having /', to find g, g 7^ x I'. 



By help of this last formula, g is found more exactly 

 than can be done by direct experiment. In London, 

 Lat. 51 31' 8", by Captain KATER'S experiments, 

 the length of the seconds pendulum =39.1386 

 inches. Hence g = 32.193 feet. 



SIMPSON'S Fluxions, 460. ; SAUNDEKSON'S Fluxions, 

 p. 207. ; and CAVALLO, vol. i. p. 190. 



The values both of g and /' are somewhat different 

 in different latitudes, as will be explained in Phy- 

 sical Astronomy. 



In this proposition, the arch over which the pendu- 

 lum vibrates, is supposed to be very small ; if the 

 arch is considerable, let its versed sine (to the ra- 

 dius 1) be v, and t the time of an entire vibration, 



VOL. I. I * = 



