420 



Mr. J. Buchanan. 



[May 27, 



dV\ dK J dK> } 



Performing the differentiations and making use of (2) we have — 



If (4) be differentiated with respect to Y and (2) be again applied, 

 we find — 



dV^dK' ' ' ' ' (5 ° 



Hence, finally, the theorem can be expressed in either of the 

 forms — 



^ 



Since as a rale tt will probably increase with Y, ^ will usually 



ct V 



have the same sign as tt. 



The form (6'), amongst other uses, enables us to get at once an 

 important result, viz., the circumstances under which h is zero. We 

 have h = when — 



dir y d?7T ~ 



Integrating twice we get successively — 



dir Tr 



where a is an arbitrary constant ; and 



I 



— 2 



aY2 (7.) 



The constant of the second integration will in general be zero. 



Equation (7), taken in connexion with (5), gives by differentiation, 



dC . 



= const. = —a. 



dK 



It appears therefore that in order to have no electrification of the 

 dielectric when the specific inductive capacity is altered, the change 

 of capacity of the system must be proportional to the change of 

 specific inductive capacity. 



