14 CLAUSIUS ON THE MECHANICAL EQUIVALENT 



discharge take place only partially, and the potential of the re- 

 sidue be denoted by Wp then the work produced will be 



=W,-W, (19) 



which, as W and W, are always negative, and Wj has an abso- 

 lutely smaller value than W, is a positive quantity. If, on the 

 contrary, a complete discharge takes place, we must set Wi = 0, 

 and in this case the work produced is 



= -W (20) 



We will now consider the effects which are due to the dis- 

 charge. 



Let us suppose the discharge to be occasioned by connecting 

 one coating wath the other by conducting bodies, whose ends 

 are brought either so near that a spark springs from one to the 

 other, or else brought into actual contact. In this case, during 

 the act of approximation, an electric action takes place, inasmuch 

 as the approximated ends of the connecting arc attract each 

 other, and thus render their approximation easier. In our case, 

 however, where the greatest portion of the electricity is bound 

 to the coatings, and hence cannot contribute to this attraction, 

 the latter must be so trifling that it may be neglected altogether. 



Further, to simplify the matter, we will for the present not 

 take into account the excitation of induced currents, nor any 

 permanent changes which are due to magnetical or chemical 

 action ; we w ill assume that the work expended at the places where 

 the connexion is interrvpted, and where a spark must spring across, 

 together with the heat generated in the system, are the only ac- 

 tions w hich present themselves. Then, in accordance with our 

 principal proposition, the sum of these both must be equal to the 

 increase of the potential. 



Let it be next assumed that in a series of experiments the 

 strength of the discharge, that is, the increase of the potential, re- 

 mains the same, but that the connexion is altered, in this case 

 the sum of the actions must be constant. 



With regard to the development of heat, we possess, in refer- 

 ence to its dependence on the nature of the connexion, the fol- 

 lowing two important laws established by Riess*: — 

 * Pogg. Ann. vol. xliii. and xlv. 



