Theory of Electric Inertia. 249 



And substituting this value of -, in the integral A, we get 

 for that integral 



a- o af'o o* sin 2 cos sin 0' ,, ,, a 





. a a f*sin 3 0cos0d0 7/1 



Jo ''" 



o27T- Ki'irdt 

 = 5 rV 



And the integral of this force for the whole course of the 

 sphere beginning at S is 



32tt S dt 16tt 2 . 1 



2 r a 



5 ^.liv- — r^w 



if Ave neglect the value at the upper limit, which for any 

 considerable value of t must be inappreciable. This may 



also be put in the form — - — — ~. It may be appreciable if 



r o t u - - L 



t can be made small enough. 



14. Case II. — Suppose that when at S the sphere receives 

 a change of velocity d?/, that is that its velocity is ?/ — ~dti 

 before it reaches S, and there becomes u, and is thereafter 

 maintained constant. Then, due to the change of velocity ~du 



at 8 considered by itself, -r- =e~du — s— . And using this in 



dt r* ° 



the expression for the electric force E at S', we get for X 



X=- f%d« sil ^27rVsin 0d0*~vdt{l + *ccos0) 



« o 



= - W \\-bn Z^PI vdt(l +KCOS 0) 



c- 



, ,f« _ (l+5iccos6)awL 3 0d0 



«. 



.Stt- _ 1 

 k now disappearing along with the first power of cos 0. 



