SCIENCE AND PRACTICE. 



291 



which Kirchhoff's laws provide expressions. I, i i9 3 , i& 4 , and 

 i 5 are the currents, &, r lt 



r 5 the resist- 

 ances in the several cir- 

 cuits, and E the electro- 

 motive force of the bat- 

 tery. 



For the currents ap- 

 proaching and receding 

 from the points a and b, 



and 



1) - *. * 8 'i = 







2) , * 4 ''. 

 for the circuit r 3 , r 4 , and r 5 , 



3) '*. v* + V5- 



and, lastly, for the two parallel circuits, 



The principle of Wheatstone's balance is based upon the 

 relation which must exist between the resistance r lt r 2 , r s , 

 and r 4 , when the position of the points a and b is so arranged 

 that their electrical tensions are the same, or that no cur- 

 rent passes between them when they are joined by a con- 

 ductor. Supposing this to be the case, the value of fl' 5 in the 

 above equation becomes = 0, and from 1, 2, and 3 we obtain 

 the values of the intensities in three of the sides, in terms of 

 the remaining one, 



'2 '4 



These values we set in 4, and have 



^,,+,,^3-^-^=0, 



and, dividing each side by ?' 4 and clearing away the fractions, 

 obtain the expression, 



