of the Electrical Current, 383 



agree in many respects. The present research has the object of 

 calling attention to such an agreement. I will endeavour at the 

 outset, for the sake of the connexion, once more to solve a pro- 

 blem, though in a different manner, which, from the researches 

 of Messrs. Thomson, Clausius, Holtzmann, Quintus Icilius and 

 others, has long been considered settled. 



When a hydro-electrical current has become constant, there 

 must be a constant compensation in the motor in order to keep 

 it up ; and if the current performs neither external nor perma- 

 nent internal work, but only developes heat, this heat is the 

 equivalent of the compensation. In homogeneous batteries 

 (such, that is to say, as are only distinguished by the number 

 and magnitude of the elements united), in the solution of each 

 atom of zinc (or when each atom of the electropositive body 

 changes its condition) the same process is repeated. Hence the 

 compensation, like the development of heat, is in all cases pro- 

 portional to the consumption of zinc, and 



In heterogeneous batteries dissimilar processes take place in the 

 solution of each atom of zinc; and for this we have 



where x and x x are constants to be independently determined. 



The magnitude of the consumption of zinc may be easily de- 

 termined. Let e be the electromotive force of an element, r = I -f A. 



e 

 its total resistance, p— -. — — the intensity of the current, z the 



/ + A. 



consumption of zinc; while these magnitudes are denoted, in the 

 case of batteries, either by the corresponding large letters or by 

 functions of the small ones. Let a battery consist in each case 

 of mn elements, consisting of m cells each containing n pairs of 

 plates, and let it be constant. 



First of all we have in homogeneous batteries 



e:E = l : m. 



The consumption of zinc is proportional to the intensity of the 

 current i?; hence Z is proportional to mT. Therefore 



"• Z 



-=l:m = e:E = r/;:RP, 



further, 



P 

 ^:Z = rp 2 :llP 2 ; 



ZiZ^RP^RJY 2 (1) 



For unequal batteries we have 

 Z:Z =p:p lf 



