OF AN ELECTRIC DISCHARGE. 27 



ber of jars be denoted by n^ and n^^ all members which, in regard 

 to k, are of a higher order than the first being neglected, we 

 obtain the following series of expressions : — 



Q'=-Q V'=0 



■<2— ^ " 2" 



^(34) 



a^=-(i+/-)a Y^=-±a 



The potential of the whole compound battery is 



W=i(Q,V, + Q',V', + Q5V, + Q',Vg; . . (35) 

 and this gives 



W = -{l..[2«+(« + /3)g-*}(i-fi-)±Q- . (36) 



or, neglecting the member of the second order in respect 

 to k, 



W 



— {iyn)>' ^''^ 



As after the discharge the potential is equal to zero, — W is 

 the increase of the potential due to the discharge ; and if, as 

 before, we assume that, other things being the same, the heating 

 at any single place in the connecting wire is proportional to the 

 total action, we can write 



''<tm- <-) 



where C is the heat generated, and A is a constant. 



When we compare this formula with the results of the obser- 

 vations, we find in the first place the proportionality between 

 the generated heat and the square of the quantity of electri- 

 city corroborated. In regard, however, to the dependence of 

 the heat on the number of jars n and Wg? Dove gives for this a dif- 

 ferent formula. Let the entire superficial content of the coatings 



