Nipher — TJte Electrical Capacity of Bodies. 113 



Calling Ri the resistance to flow within this tube and apply- 

 ing Ohm's law we have 



4.(Q,-Q,) = |i 



p _i Qi 



Qi — Q2 



— Pj is evidently the fraction of the spherical surface 



which the free charge Q^ — Q., occupies. If the charge Q^ 

 were alone in space, since the entire resistance around the 



sphere would be » it follows from (9) that the lines pro- 



* 4 TT r^ 



ceeding from the free charge Q^ — Qo suffer the same resist- 

 ance when charge — Q2 is present as when it is absent and the 

 lines are all radial. 



This is due to the fact that we have assumed that the bodies 

 are^so far apart that they do not appreciably disturb each 

 other. 



The charge on the larger sphere within the critical surface 

 is + Q2. From this charge 4 rr Q2 lines proceed to the other 

 sphere. The difference of potential between the two spheres 

 is 



V — V — -5i _L ^ 



Hence as before 



^-Q^=U + 7;JR2 



1 Q, 1 



4 7: ri Q2 ' 4 TTTj (10) 



This is the resistance of the internal tube terminating on 

 the two bodies. The charges on the ends of this tube may 

 be called bound charges. 



Q 



The first term of eq. (10) contains a factor-T^^, the recipro- 



cal of which is the fraction of the surface of the larger 

 sphere which its bound charge occupies. 



