connected with the Motion of Charged Spheres. 947 



or using the relation (2) above 



~s — / ~9i —92 • 



The tangential component of the electric force is 



sin 



z = -™(«r+/') 



and the total couple on the sphere is 



f <rZa sin 6ds= - ? ~(af" +f\ 



These results are quite general. Now let us try a solution 

 of the conditions when the sphere has a uniform angular 

 acceleration round the axis equal to co. The conditions to 

 determine/* cf>i and <j> 2 are then 



a/ r +/=a(*i'-*,') + *i+*s 



J — 9i -92 V' 



The particular solution of these conditions is found to be 



1 earn 

 3 7 





W"-') -48-^?- («*-»■)*. 



where K = -^ is the specific inductive capacity of the sphere. 



In addition to this particular solution we have an oscillatory 

 •part represented by the complementary integral of the 

 conditions. This is obtained by trying solutions of the con- 

 ditions with w = of the form 



/ ct-r+a \ 



f(ct-r) = Ae K a \ 



^(c't-fl^Be K a ; , 



cj) 2 (c ! t + r) = —Be 



4?) 



