OHM ON THE GALVANIC CIRCUIT. 505 



and determine in accordance with this statement the constant c, 

 our last equation acquires the following form : — 



^ ^ , ib —a) 2— a n, , 



S + flz = S + ^-r _ ,a6.r.-,„) ^^-^-> 

 a + (6 — a) s o + (6 — a) ^ * 



where e denotes the base of the natural logarithms. The fol- 

 lowing consideration leads to the determination of the value y^. 

 Since, namely, ^ represents the space which the constituent A 

 occupies in each individual disc of the changeable portion pre- 

 vious to the commencement of the chemical decomposition, if 

 we denote by / the actual length of this portion, / ^ expresses 

 the sum of all the spaces which the constituent A occupies on 

 the entire expanse of the changeable portion ; but this sum 

 must constantly remain the same, since, according to our suppo- 

 sition, no part of either of the constituents is removed from this 

 portion, and both maintain, under all circumstances, the same 

 volume, even after chemical decomposition has taken place ; we 

 obtain, therefore, 



l^ = f z dx, 



where for z is to be substituted its value resulting from the pre- 

 vious equation, and the abscissae corresponding to the com- 

 mencement and end of the changeable portion are to be taken 

 as limits of the integral. 



These two last equations, in combination with that found at 

 the end of the previous paragraph, answer all questions that 

 can be brought fonvard respecting the permanent state of the 

 chemical alteration, and the change in the electric current thus 

 produced, and so form the complete base to a theory of these 

 phaenomena, the completing of the structure merely awaiting a 

 new supply of materials from experiment. 



40. At the conclusion of these investigations we will bring 

 prominently forward a particular case, which leads to expres- 

 sions that, on account of their simplicity, allow us to see more 

 conveniently the nature of the changes of the current produced 

 by the chemical alteration of the circuit. If, for instance, 

 we admit a = b, and a = /3, the differential equation obtained in 

 the preceding paragraph changes into the following : 



0=2 dx — aia {a — m) d z, 



whence we obtain by integration 



