8 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



titles of work be united in an algebraic sum with the increase of 

 the potential, the said sum forms the right-hand side of the 

 equation (2), that is, of the equation 



2 2 •>^ 'o 



while the member to the left expresses the increase of the vis 

 viva of the entire system due to the discharge. This last can 

 also be of a twofold nature. In the first place, under favourable 

 circumstances, actual visible motions may be produced in the 

 system by the electric attractions and repulsions ; secondly, and 

 more especially, heat will be excited by the current in the con- 

 ductors. 



Let us suppose all the above-mentioned quantities of negative 

 work to be positive and brought over to the left-hand side of the 

 last equation, so that only the increase of the potential remains 

 to the right ; the proposition contained in the equation can be 

 expressed in a very complete manner as follows : — 



The Sum of all the effects produced by an electric discharge is 

 equal to the increase of the potential of the entire electricity 

 upon itself, 

 in which place under electric discharge is meant every alteration 

 in the arrangement of the electricity, by which the electric states 

 of the various portions of a system of conducting bodies, in 

 which the earth itself may be included, entirely or partially 

 neutralize each other. 



We will now apply this general proposition, which for the 

 sake of brevity will be hereafter called the principal proposition, 

 to the special case of a Leyden jar, or to a battery composed of 

 a number of such jars; this case is of peculiar interest on 

 account of its frequent occurrence, and presents the best oppor- 

 tunity of comparing the results of theory with those of ex- 

 perience. With regard to the latter, the investigations of Riess, 

 which are carried out with the greatest care and ability, furnish 

 us with a fund of materials in which the greatest confidence may 

 be placed; the comparison of the same with our principal pro- 

 position is rendered the more easy by the circumstance that 

 Riess himself has deduced from the facts which he has observed 

 determinate laws, which he has expressed in strict mathematical 

 formulas. 



