Application of the Pendulum to Time-Keepers. 255 



two years' trial to vary only j of a second in 24 hours from its 

 mean rate of going. A clock of the same construction owned by 

 W. C. Bond of Boston, though much less costly, has been found 

 by careful observation, to go with nearly the same accuracy. 



377. A watch or chronometer differs from a clock by hav- 

 ing a spring for its maintaining power, and a horizontal in- 

 stead of a vertical pendulum, in which a small, fine spring per- 

 forms the office of gravity. The pendulum or balance, in this Fig.184. 

 case also, is subject to irregularity from heat and cold, and re- 

 quires a distinct compensation. Considerable weights ra,w', are 

 attached to the balance by means of slips Cm, C' m', of brass and 

 steel, the brass slip in each being outermost. While, therefore, 

 the general expansion of the wheel tends to throw the weight 

 to a greater distance, the superior expansion of the brass slip 

 over the steel brings the weight nearer to the centre, and the 

 length of the slip being properly adjusted to the weight, the cen- 

 tre of oscillation, or rather of gyration, will be preserved always 

 at the same distance from the axis. 



273. We have found formulas for the difference in the rate 

 of going of a clock answering to small changes in the length of 

 the pendulum, the position with respect to the centre of the earth, 

 and consequently the force of gravity, being supposed to remain 

 the same. It will be easy also to find formulas for the vari- 

 ation in the force of gravity and in the rate of the going of a 

 clock, depending upon small changes of distance from the centre 

 of the earth, w, n', for example, being the number of vibrations 

 of the same pendulum at the two stations respectively, the pen- 

 dulum being supposed to vibrate seconds at the first ; from the 

 proportion, 



' 348. 



^15 ^16 



when a' = a, we have 



s n' 2 



n 2 



If the second station be below the first, or that at which the 

 pendulum vibrates seconds, g f will exceed g, and the clock will 



