256 Dynamics, 



gain ; on the contrary supposition it will lose. Let 



> = g (i *), 



and let y denote the daily gain or loss in seconds ; we shall have 



T \ -- 



" 



n 2 n* 



nearly. Whence, 



Thus, if a pendulum fitted to vibrate seconds at the equator, 

 would, upon being carried to the pole, gain 5' or 300" a day, we 

 should have 



_ 2 x 300 1 



86400 144' 



that is, the force of gravity at the equator is to that at the pole, 

 on this supposition, as 144 to 145. 



Let the difference h in the distances of the two stations from 

 the centre of the earth be given, gravity being supposed to vary 

 inversely as the square of the distance, the gain or loss of the 

 clock might be readily found as follows. 



If we call R the distance of the centre of the earth from the 

 first station, and g the force of gravity at this station, the pendu- 

 lum being supposed to vibrate seconds, we shall have for the 

 distance of the second station R /i, and for the force of grav- 

 ty at this station, 



Ra (\ - - 



7J g V* ^F ~n 



> (* 



nearly. Hence, putting-^- for x in the above formula, we obtain 



Thus, if the second station be above the first, as 1 mile for in- 

 stance, the radius of the earth being 3956, or 4000 nearly, the 



