384 Dr. Gerlach on the Mechanical Theory 



or 



1 e e l 

 hence 



ez\ e^z^rp* irtff. 



Combining this equation with equation (1), we obtain by an 

 easy calculation the proportion 



eZ:e l Z l = 'KP*:'EL 1 V 1 * (2) 



Now, according to Joule and Lenz'slaw, the expression RP 2 de- 

 notes the relative quantity of heat which a battery disengages ; 

 hence, if c denotes the compensation, we have 



cZ:c 1 Z 1 = RP 8 :R 1 P 1 2 = W:W 1 = C:C 1 . . . . (3) 



As in the following we shall only be concerned with ratios of 

 the quantities of heat, it is unnecessary to add constants to the 

 expressions eZ and HP 2 . Hence let eZ denote in each case 

 the compensation, RP 2 the heat disengaged, and also let the 

 consumption of zinc be indicated by the expression to which it 

 is proportional. 



If a phenomenon of motion be considered to exist in the cur- 

 rent, KP( = E), as regards its form, is analogous to the quantity 

 of motion, RP 2 analogous to the vis viva of a moving body. I 

 shall use the latter name for 11P 2 = L, though it be nothing 

 more than a similar designation for similar analytical expressions. 



For a battery, 



\n J\m j / ml-\-n\ 



— 1-\- A- 

 n 



If both poles be directly connected without any interpolar, \=0, 



and therefore L = —j- • Here mn is constant, and therefore 



also L. 



A number of elements joined in any manner to form a battery, 

 or a given surface of zinc, represents, in the absence of an inter- 

 polar, a constant quantity of vis viva, which is first modified, by 

 the interposition of a resistance. In every individual element 



e 

 the quantity y of zinc is thereby used, just the same quantity as 



in an isolated element closed without any interpolar. On intro- 



7n ne 



ducing a conductor (X), the total consumption of zinc is — , ' 



° v ■ r ml-\-n\ 



while is the consumption of an individual element. The 



1+ -X 

 m 



