CHANGES OF EARTH'S VERTICAL FORCE. 201 



the same value I will now apply to its moment of 

 inertia in horizontal vibration which formerly applied 

 in vertical vibration. The magnet being now inclined 

 to the meridian by the angle o>, and the force which 

 acts on it being the horizontal magnetic force H, we 



HB . sin &) H. B. co r , 



shall have - j or = for the angular mo- 

 ment: therefore 



H.B 



ft) 



and, if T be the time occupied by a complete double 

 vibration, 



.B T'\H.B 



T """" J A 2 * 



Substituting this in the last expression 

 SV_T* H.B 



. T' 2 H. B 



~ifiz cotan dip x ^r. 



This supposes that the unit by which 8 V is measured is 

 the entire vertical force. If we prefer to adopt for unit 

 the entire horizontal force, we have simply 



gy 2 1 ' 2 



