/ 



SCIENCE AND PRACTICE. 361 



and 



which, divided by each other, give 



rr" 



I ~ e R' + r' 



(5 and (6 combined 



m e W(r + 





m, e (E' + r 1 ) r" 



The cable is now inserted in its place, as in Fig. 164 ; E, is 

 adjusted to obtain a balance between the active magnetic 

 effects of the currents. I and I' being the currents, 





. . .(9 



And their relation to each other is 



L-5--K 



I ~~ m~ 



therefore 



E (E + /) 

 and 



The resistance of the cable, according to this, is equal to 



the product of the resistance of the circuit R + r, the relation 



p 



of the electro-motive forces ^, and the constant K of the 



Sit' 



initial magnetic forces of the coils of the galvanometer. 



Fig. 166 represents a plan of a convenient method of 

 arranging a board by which not only this, but also the 

 foregoing systems may be introduced, by simply changing 

 the positions of a few contact plugs. 



* In this equation, as in some of those which precede it, the resistance x 

 is regarded as the whole resistance of the circuit. The galvanometer resist- 

 ance is neglected, as the value of x is very great in comparison with it. 



