142 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



electricity by E, the radius of the sphere by R=lj for this 

 sphere we have the constant 



that is, the constant C is equal to the free tension. 



In accordance with this, the tensions of two conductors which 

 contain equal quantities Q of positive and negative electricity 

 are 



As C^ is negative, the algebraic diiference Ca—Cf^ is equal to the 

 absolute sum of both. If the capacity of discharge of B be very 

 great, and consequently C^ nearly =0, the quantity of the elec- 

 tric tensions is -77-^="" ^ — -; if the distance between the 



two conductors be also very great, the above becomes — ^W^. 



We have found that the vis viva generated by the motion 

 of two electric masses is equal to the decrease of the sum 



— ° " — ^— ^. This vis viva is gained as mechanical force, if 



the velocity of the electricity in the bodies be a vanishing quantity 

 when compared with the velocity of propagation of the electric 

 motion ; we must obtain it as heat when this is not the case. 

 The heat % developed by the discharge of equal quantities Q 

 of the opposed electricities is therefore 



where a is the mechanical equivalent of the unit of heat, or 

 when Cj = 0, as is the case with batteries whose external coating 

 is not insulated, and whose capacity of discharge is S, so that 

 CS = Q, 



Riess* has proved by experiment that, with different charges 

 and different numbers of similarly constructed jars, the quantity 

 of heat developed in every single portion of the same connecting 



* l*<>gg« Ann, vol. xliii. p. 47. 



