45$ MEASUREMENT OF CAPACITY. DIELECTRICS. 



and the electroscope shows that the potential of the cylinder B is 

 zero. Excepting for the unequal influence of the edges, the same 

 would take place if the rings A and A', while always of the 

 same radius, were of different lengths, their capacities being pro- 

 portional to their lengths. It must be assumed, however, that these 

 rings are so far from each other, that their reciprocal inductive action 

 may be neglected in comparison with that which they exert on the 

 internal cylinder. 



In order to compare any two capacities C and C', they may be 

 connected separately with the two rings A and A' of the platymeter. 

 If the experiment, repeated in the same conditions, shows that the 

 potential of the cylinder BB' is zero after the two rings have been 

 connected, it follows that the total capacity of the two systems are 

 in the ratio of the capacities of the rings, which gives 



a C + a C 



a' C' + a' C 



We may then verify the equality between a and a'. It is suf- 

 ficient to permute the capacities C and C' in respect of the rings. 

 If equilibrium still exists, we have 



C _a 



c~*" 



and therefore a = a'. 



When this condition is not realised, and equilibrium has first 

 been established with the capacities C and C', and then in a second 

 experiment with the capacities C" and C, equations 



C_a_ C^_a 



C'~a" C~a" 



give 



The experiment is analogous to that which consists in deter- 

 mining the weight of a body, the arms of which are unequally long. 



1048. BALANCE OF CAPACITIES. This name may be given to 

 several experimental arrangements which suggest those of Wheat- 

 stone's bridge. 



