196 PROCEEDINGS OF THE AMERICAN ACADEMY. 







Hence, 





The current in the Z,th cell may be positive, zero, or negative accord- 

 ing to circumstances. If the electromotive forces and the internal 

 resistances of all the cells are given, C^ will be positive if r be made 



less than -^ p — . 



*^/i, ft ^k -^ n. ft 



The currents in all the cells will be positive if r be made sufficiently 

 small. If the electromotive forces of the cells are unequal, and if r is 

 very large, the currents in the weakest cell or cells will be negative. 

 If the outside conductor be removed so that the poles of the battery 

 are not connected externally, the current in the i'th cell will be positive 

 if gj is greater than S^ ^ -i- P„ ^. Thus, if the battery consists of three 

 unlike cells numbered in order of descending electromotive force, 

 Cj^ must be positive and C^ negative, but 0^ will be positive or not 



• • , ^1 ^1 H~ ^3 ^1 



according as e., is or is not greater than -^,- — . 



The case of a number of cells of the same internal resistance but of 

 different electromotive forces joined up in multiple arc is of some in- 

 terest when one has to use a number of unequally charged storage 

 cells to send a very heavy current through an outside circuit of 

 extremely low resistance. When the b's are all equal, 



b (b + n r) b 



^ — \- r 



n 



so that the equivalent cell has an electromotive force equal to the 

 average of the electromotive forces of the given cells, and an internal 

 resistance equal to ~th of that of each cell. This case also throws 

 some light on the properties of a thermal junction of large area formed 

 of two plates of metal soldered together flatwise when, as is sometimes 

 the case in practice, it is impossible to keep the whole junction at 

 exactly the same temperature. 



Equations (1) and (5) give the equation 



