262 THE ELECTRIC TELEGRAPH. 



of the elements, E p E 2 , E 3 . . . E n , are different, and resist- 

 ances, r 19 r 2 , r 3 ... r n , also, the intensity of the current is 



P + r, + r 2 + r 3 + . . . r n 

 the elements being connected together in series, and, 



TT-+ + ~+ + :r 



I - r i r * ^ r n . . (XII. 



' / 1 1 1 1\ 



hp V~+77+7T '7-J 



when they are connected together parallel. 



Lastly, in addition to these methods, it is sometimes neces- 

 sary to determine the best combination and number of 

 elements for a battery, under given circumstances, in order 

 to produce a given effect. For this, some of the elements 

 may be connected parallel, and then these combinations con- 

 nected together in series. This problem of finding the most 

 advantageous combinations is solved nearly as follows by 

 Eisenlohr : 



If we call the ^surface of the exciting plates = 1, and 

 connect the same in equal elements, the surface of each 



element will be - of the whole surface ; and if the resistance 



X 



of the whole parallel = 1, that of each of the elements sepa- 

 rately = x, and that of all the elements, in series, = x 2 ; 

 then, n being the external resistance, 



1-1 T71 



(XIII. 



The denominator x + - of this fraction evidently attains its 



minimum, the value of x being variable, when p = a? 2 ; but 

 when the denominator of a fraction is minimum, the fraction 

 itself has its maximum value ; therefore, the strength of the 

 current of a battery of given surface of plates is at its maximum 



