OHM OX THE GALVANIC CIRCUIT. 501 



pai't of the circuit, in which no chemical change occurs, are 

 unalterable and given, it is, in accordance with the general 

 equation given in § 18, which likewise holds for our present 

 case, only requisite for the perfect knowledge of the function u, 

 that we are able to determine the tensions and reduced lengths 

 for each place within the extent in which the chemical change 

 takes place. 



But evidently the reduced length of the disc M is 



dx ^ 

 X CO ' 



or if we substitute for x its value just found, 



we accordingly obtain the reduced length of any part of that 

 extent, if we integrate the above expression, and take the limits 

 of the integral corresponding to the commencement and end of 

 the part. If now we bear in mind that the integral 



''a -\- {b — a) z 



r- 



, d X 



aoM 



may also be -v^Titten thus : 



I b — a 



+ 



b CO ab 



—,/ z CO dx, 



when I represents the length of the part, over which the in- 

 tegral is to be extended, and z (ad x expresses merely the 

 space w hich the constituent A in the disc M occupies ; con- 

 sequently f z ui dx, the sum of all the spaces which the con- 

 stituent A fills in the part whose reduced length has to be 

 found, it is obvious that the reduced length of the entire 

 portion, in the act of decomposition, remains unchangeable 

 during the chemical change, since, as we have supposed, each 

 constituent maintains, under all circumstances, constantly the 

 same volume. The same result may also be directly deduced 

 from what was advanced in the preceding paragraph ; however, 

 this unchangeability only relates to the reduced length of the 

 entire portion ; the reduced length of a part of it does not in 

 general depend merely on the actual length of this part, but 

 likewise on the contemporaneous chemical distribution of the 

 constituents in the extent, and must therefore, in each separate 

 case, be first ascertained in the manner indicated. 



VOL. II. I'AItT VIII. 2 L 



