Theory of Electric Inertia. 



24' 



rfH 



10. Again, the electric force at S[ due to ^ at P is equal 

 to the electric force at S' due to tt, which can be found as 

 follows : — 



Fi-. 2. 



In the figure (2) the circle is the "a" circle described 

 about P. SP=r, PS'=r', zPSN = 0, zPS'N = 6>'. Q is 

 a point on the circumference of the a circle. Z_QPN = 7r— /3. 



Let S'Q=/o. 



Then p 2 = (r' cos 6" -a sin /3) 2 +{i J sin 0' + a cos /3) 2 



— . J2 



i + a 2 +2r , asm {&-&), 



and. a being very small compared with /•', 

 1_ 1 _ /asm {6' -j3) 



Again, the component parallel to the axis of the circular 

 current i at Q is — icos/3. And the electric force at S' in 

 direction SS* due to the variation of the circular current, 



denoted by T is 



dt) «co.^- a J «oo.^- ,,, }//3 



o rfi sin d' 



= — IT -j- 1" S 



at 



mOdOdfvdt (l + *cos0) 



sin 0' 



11. In order to effect the integration for tho ellipsoidal 

 shell, we shall have to express 6', r', and r in terms of 6. 

 ^Ye have first 



v 

 sio 0' = . ^in 0. 



/• 



Again, using the ordinary equation to the ellipse 1 , in which 

 £=rcos 6 — net, y=r sin 0. and remembering that the minor 



