of the Electrical Current, 385 



consumption of zinc of a single element with the resistance X 



would be . — -• Hence 

 l-j- X 



e '< e v < , 

 = ^-— ^ according as m = n. 



m 



If the consumption of zinc and the vis viva of mn elements 

 joined as a battery are to be greater than those of mn isolated 

 elements, each of which has the resistance X, m must be greater 

 than n. The vis viva and consumption of zinc of a battery 

 attains a maximum if ?z=l, but a minimum if m = l. It fol- 

 lows by no means from this that the actions to be produced by 

 a battery attain simultaneously their maximum or their minimum. 

 This depends upon the distribution of vis viva between motor 

 and conductor. 



While L has a constant value in the case of a battery closed 



Tie 

 without an interpolar, P= -r is variable, and hence the action 



on the conductor must also be variable. The impact of a moving 

 body exhibits a similar difference in action if the vis viva is con- 

 stant but the velocity variable; and therefore, on investigating 

 this problem, results are to be expected which agree in form 

 with the electrodynamic laws. As a series of analogies frequently 

 serves to indicate the correct path in further investigations, I 

 did not think it superfluous to discuss this problem more mi- 

 nutely. The supposed agreement has been fully confirmed, as 

 will be seen from the following examples. 



lot. An inelastic body a, with a velocity v, strikes centrally 

 against an inelastic body b at rest. What is the loss A of vis viva ? 



We have 



2g 2/" + } \a + b) ~2g"a' a + b 



E 



I 0. In a battery ^7 closed by one or more interpolars, the re- 

 sistance X is interposed. What is the decrease A o/vis viva, or of 

 the consumption of zinc* ? 



We have 



W_ E 9 X /JM 



r :a+\ _ iivri+\/' 



* In dissimilar batteries eZ and RP 2 are proportional; in similar ones Z 

 and RP 2 . 



