Nipher — TJie Electrical Capacity of Bodies. 113 



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

 ing Ohm's law we have 



Qi i 



4 , (Q.-Q,) = = ^ 



1 Qi 



•'■ El_ 4.r 1 Q 1 -Q; (9) 



-^j\ 2 is evidently the fraction of the spherical surface 



which the free charge Q : — Q 2 occupies. If the charge Q x 

 were alone in space, since the entire resistance around the 



sphere would be — — -> ^ follows from (9) that the lines pro- 

 1 4 it r x 



ceeding from the free charge Q x — Q 2 suffer the same resist- 

 ance when charge — Q 2 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 A so far apart that they do not appreciably disturb each 

 other. 



The charge on the larger sphere within the critical surface 

 is + Q 2 . From this charge 4 % Q 2 lines proceed to the other 

 sphere. The difference of potential between the two spheres 

 is 



V — V — — • + — 



v 1 — v 2 — r T 



Hence as before 



1 Qi 1 



•'• R2 -4V7; C£ + 4^r 2 (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-^ *, the recipro- 



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

 sphere which its bound charge occupies. 



