SCIENCE AND PRACTICE. 289 



for which expressions, if we can consider B, = 0, we obtain 

 the same values for the intensities in the three branches, which 

 would be due were only one branch inserted at a time, or, 



, 



and 



E 



' a = ~, 



Therefore, we can accept as a law that when the resistance 

 (E) of the battery is inappreciably small in comparison with 

 that of the lines, or other circuits, the current in each of the 

 latter is of the same intensity as it would be were the battery 

 in circuit with that line alone, and that when the resistances 

 of the lines are equal, the currents circulating in them will be 

 equal also. 



It more seldom happens, however, that the resistances of 

 several lines are equal than that the currents traversing them 

 from a common battery are required to be so. In the latter case 

 it is necessary to distribute the 

 battery in such a way as to make 

 the intensity in each branch as 

 nearly the samo as possible. To 

 find how this distribution is to 

 be made, let us suppose the 

 three lines t\, r 2 , and r 3 , (Fig. 

 136), in which we have to put Fi &* 136> 



three parts, E 1? E 2 , and E 3 , of the whole battery ; E x being 

 common to all the lines, E 2 common to r 2 and r& and E 3 serving 

 r 3 only. Retaining the same designations, we have the fol- 

 lowing equations for the three lines : _ 



I, E, + t, r, = E' 



T 1 E 1 + I 2 B 2 + ; 2 r 2 = E 8 + E r 



I, E, + I, E 2 + 7 3 (R 8 + r s ) = E 3 + E 2 + E, 



in which, when the resistances of the lines are considerable 



