504 OHM ON THE GALVANIC CIRCUIT. 



reduced length of the entire circuit, which, as we have seen, re- 

 mains under all circumstances the same, it results 



o, _A — <P {n—m) [z" — z) 



A 



or, if we write for ^ its equivalent S, 



s' = s — ^(^"-'^ ) (^"— ~0 



^ itt ~ wxl \Z ^ \ 



so that, therefore, — ^ —^ —'- designates the decrease 



produced in the magnitude of the current by the chemical al- 

 teration. 



39. After all these intermediate considerations, we now pro- 

 ceed to the final determination of the chemical alteration in 

 the changeable portion, and the change of the current in the 

 whole circuit produced by this chemical alteration, where, how- 

 ever, we have constantly to keep in view only the permanent 

 state of the altered portion. If we substitute in the equa- 

 tion ( J ) given in § 35, for x w -7— its value S', which, as we 



have just found, is solely dependent on the fixed and unalter- 

 able values of z, and therefore has to be treated in the calculation 



as a constant magnitude ; further, for x its value j-, r — , 



^ ' ' a + (6 — c) 2i 



given ia § 3fi, this equation changes into 



or if we place S' + 4/ w /3 = 2, and vj/ w (« — /3) = O, into 



^ _ a b CO (n — m) d z 

 a-ir (b — a) z dx 



from which, by integration, we deduce the following : 



(6-a)2-an , S + fl;: 



C — -—J 7 r- X + log 77 r— , 



a oi yn — m) ^ a-\- [b — a)z 



where c represents a constant remaining to be determined. If 

 we designate by p^ the abscissa of that place of the chemically 

 changed portion for which s has still the same value, which,! 

 previous to the commencement of the chemical decomposition,! 

 belonged to each place of this portion, for which therefore s = ?,| 



