498 OHM ON THE GALVANIC CIRCUIT. 



tive ; the sign of the function ip, therefore, changes when the 

 direction of the decomposition is transposed from the one con- 

 stituent to the other. The nature of the function <p is as Uttle 

 known to us as the size and form of the elements on which it is 

 dependent; nevertheless, we may, in our inquiries, regard its 

 absolute value as constant, since the size and form of the cor- 

 poreal particles, acting on each other, must be conceived to be 

 unchangeable so long as the two constituents remain the same, 

 and the supposition that the two constituents constantly main- 

 tain for every chemical equivalent the same volume, renders 

 attention to the mutual distance of the chemically different 

 particles unnecessary, as regard has already been paid, when de- 

 termining the electroscopic forces in the disc M, to the relative 

 distances of the elements of each constituent. 



35. To determine the magnitude of the reaction Y, which in 

 the disc M opposes the latent electricity of the neighbouring 

 discs to the decomposing force, we have nothing further to do 

 than to substitute in the expression for %, instead of u, the sum 

 of all the latent electroscopic forces in the disc M. Since now 

 the sum of these latent forces is m z + n (1 — z), we obtain for 

 the determination of the force Y, Avhich is called into existence 

 by the change in the chemical equivalent of the constituents, 

 and which opposes the decomposition, after due determination 

 of its sign, the following equation : 



Y = 4 X w -j— . I [n — m) . z {\ — z) 



dx ^ ' ^ ' ctz -\- ^ {\—z) 



If now we substitute forX % andX the values found in the 

 equation 



X + Y = Z, 



we obtain, after omitting the common factor 4z {\ — z), and 



multiplyino; the equation by —^, — ^^ r— , as the condition of 



^ '' " ^ -^ i{m ^ — noc) 



the permanent state ia the chemical equivalent of the two con- 

 stituents, the equation 



dx ■i[mp — nej) 

 which, M'hen we put 



