16 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



sition from the equation (21), which might at first sight be 

 taken for a complete corroboration of our conclusion. Accord- 

 ing to this proposition, the total heat which is excited in the 

 entire circuit by an electric discharge is independent of the nature 

 of the circuit^. This proposition is indeed brought forward by 

 Helmholtz as coincident with the theory f; I do not think, how- 

 ever, that it is quite applicable, inasmuch as it contains many 

 inaccuracies. 



In the first place, Vorsselman de Heer limited the considera- 

 tion expressly to " the wire which unites both the coatings of 

 the battery J." The development of heat extends however to 

 the other bodies of the system, a portion of it indeed is excited 

 within the battery itself; and another portion, in case the battery 

 and connecting wire are not insulated but are connected with the 

 earth, within the conducting wire and the earth. The latter 

 portion will in general be trifling, as the excess alone of the one 

 or the other electricity escapes to the earth, and this, in com- 

 parison with the total quantity of electricity, is very small ; the 

 same may perhaps be assumed with regard to the former portion, 

 under the condition that the connecting wire possesses a con- 

 siderable reduced length. With very short connecting wires, on 

 the contrary, such an assumption would be unwarrantable, and 

 this portion must, at all events for the present, be regarded as 

 unknown. 



Further, he treats the connecting wire so as if it were one 

 continuous piece. In this respect Riess § has already drawn at- 

 tention to the fact that his connexion was established by several 

 pieces of wire attached together ; and as his experiments refer 

 only to the continuous wires, and not to the heat developed at 

 the points of junction, so his proposition, so far as it is a conclu- 

 sion from his experiments, was refuted. From a theoretic point 

 of view, indeed, those places of junction where actual metallic 

 contact takes place, and where the electricity in its passage gives 

 rise to no mechanical alterations, would be embraced in the 

 general proposition, without its being necessary to know the 

 quantity of heat developed in each singly. It is otherwise, how- 

 ever, with the places where an interruption occurs, where a 



* Pogg. Ann. vol. xlviii. p. 298. % Pogg- -^^^^^ vol. xlviii. p. 297. 



f His memoir, p. 44. § l*ogg. Ann, vol. xlviii. p. 320. 



