200 ON MAGNETISM. 



the moment of inertia of the magnet : and consider the 

 whole weight of the magnet, as assisted by the vertical 

 magnet-force of the earth as above mentioned (the petty 

 alteration of which will have no sensible effect on this 

 element) to be collected at a point which, when the 

 magnet is horizontal, coincides with K. Incline the 

 magnet through a small angle % : the angular moment 

 produced by its weight will be 



W. 0/r.sinv W. CK 

 _____ *or--^ % , 



(omitting the usual factor g, for the reason given in 

 Article 18) : hence 



df ~ 1 



The solution of this equation is, 



W.GK 



Let T be the time of a complete double vibration, in 

 which the variable term in the bracket increases by 



27r ; then T ' = 2?r, or CK= ~r* Hence 



V~ W.T 



To obtain a value for /, take the magnet off from its 

 bearings, and suspend it by a single cord, as a free 

 declination-magnet ; the side which, when mounted on 

 its bearings, is vertical, being now horizontal ; so that 



