520 M. E. Jochmaim on the Electric Currents induced 



where p a denotes the distance of any external point from the 

 centre of the sphere ; and for an internal point, that 



Hence, since 



we have 



C n*TR/ll 5 2 \ 



Such is the density of the electricity on the surface of the 

 sphere, the interior being at the same time filled with free elec- 

 tricity having the constant density 



wifcT 



7T 



The constant C is determined from the arbitrary total quantity 

 of free electricity which exists on the sphere. In fact the quan- 

 tity within the sphere is 



-fnifcTR 8 , 

 o 



and the quantity spread over the surface is 



CR + 2nkTW. 



Consequently were the sum of all the quantities of electricity to 

 vanish, we should have 



C=-|tt&TR 2 , 

 o 



and hence 



nkTJifo .., \ 



"When a solid of revolution of any form rotates around its axis 

 under the influence of a magnetic pole /j., situated thereon at the 

 distance c from the origin of coordinates, we have 



P = 



v/r s +(c-*)*' 



2nkfA{c — z) 

 V i= / a V, x 2 + const * 



If y denote the angle made with the axis of rotation by the con- 

 nector of the magnetic pole and the point of the conductor under 

 consideration, the last equation may be written thus : 



V»= — 2nk/ju eosy-\- const. 



