Nipher — The 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' ^ 

 1 Qi 



•••^^riTFiQ^^Q-; (9) 



is evidently the fraction of the spherical surface 



Q1-Q2 



Qi 



which the free charge Qi — Qa occupies. If the charge Qj 

 were alone in space, since the entire resistance around the 



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



^ 4 r ri 



ceeding from the free charge Qi — Q3 sufi'er the same resist- 

 ance when charge — Qg 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 pot appreciably disturb each 

 other. 



The charge on the larger sphere within the critical surface 

 is + Qj. From this charge 4 r Qj lines proceed to the other 

 sphere. The difference of potential between the two spheres 

 is 



Hence as before 



-<^-(| + |)i 



1 Qi . 1 



.'. It, — . f^ + 



4rriQ2^4:rr3 (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^S the recipro- 



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

 sphere which its bound charge occupies. 



