SCIENCE AND PRACTICE. 293 



we obtain the value of the intensity, y, in the side c, con- 

 taining the strange element, in terms of both the electro- 

 motive forces E' and E. 



=".-*- E' 

 - C _AD 



*y ~ 



B 

 E 



A (D + K) + B (A + K) 



And from these, the relation between the two electro-motive 

 forces 



h JT = BC AD 



~ E A (D -f E) + B (A + R) 



which supplies a method of comparing the electro-motive 

 forces of two batteries. The value of the resistance C, when 



TSf 

 the relation -f- is known, is found by the formula 



AJD _j_ E^ A (D + R) + B ( A + E) 

 = ~B~~ " E B 



or, when the resistances A, B, C, and D are very great in pro- 

 portion to R (the battery resistance), the latter may be neg- 

 lected, and C becomes 



C:rz AD_ E; A (D + B) 



Lastly, if we suppose E' ^= 0, or that there is no electro- 

 motive force in the side C, the member 



JS' A (D + R) + B (A + R) 



Ei. 

 4ft 



of the above falls away, and we get the common expression 

 of relations of Wheatstone's balance 



B 



Four corollaries from the two laws developed by Kirchhoif 

 have been published by Bosscha, which in many calculations 



