250 Dynamics. 



in which g represents the velocity acquired by a heavy body 



at the end of the first second of its fall, and which is double the 



height or space through which it would descend in a second from 



266. a state of rest ; a is the length of the pendulum each of whose 



vibrations is performed in the time t'. Accordingly, if for t' we 



put one second, a must be 39,1386 inches for the latitude of Lon- 



don.* Moreover ^, the ratio of the circumference of a circle 



Geom. to its diameter, is equal to 3,1416 nearly ; hence 



g = (3,1416) 2 X 39,1386. 

 Accordingly, 



3,1416....2 log.... 

 39,1386 ....... log....l,59260 



386,28 2,58690 



The value of g, therefore, is 386,28 inches, or 32,1 9t feet, equal 

 to 32,2 nearly ; and half this quantity or 16,1 is the space des- 

 cribed by a heavy body in an unresisting medium at the surface 

 of the earth in one second from the commencement of its motion. 

 273. We have thus fulfilled our promise. 



'Application of the Pendulum to Time-Keepers. 



372. The pendulum attached to clocks for the purpose of reg- 

 Fig.iso.ulating their motions, is ordinarily a rod of metal or wood loaded 



*The length of the seconds pendulum, and consequently the val- 

 ue of g, is referred to the latitude of London on account of the great 

 accuracy of the observations that have been made at this place. The 

 difference, however, in the length of the pendulum in different lati- 

 tudes, at the level of the sea, is so small as to amount only to about 

 J of an inch at the extreme, or when the places to which the obser- 

 vations relate are the equator and the pole ; and the difference in 

 the value of g at these places, is only about two inches, as may be 

 easily shown by the above formula. 



f The most accurate observations on the length of the seconds 

 pendulum at Paris in latitude 48 51' give for the value of g 32,182 ft. 



