PROBLEM OF WHEATSTONE'S BRIDGE. 345 



eliminate the resistance b' by the equation of the equilibrium of 

 the bridge, 



i=b 



a -E a , + e)-a(E b -E b ,-e) 



M 



.*' P. Q 



M 



(23) 



./>r fl + a'N (0 + OM M 



aP Q gE- 



' ' 



P 



M 



Q a(E b -E b ,-e) 



a + a'N (a + a')M M 



It will be seen that the intensities I and t are respectively 

 independent of the electromotive forces and of the resistances of 

 the conjugate sides, as should be the case (945). 



950. When the electromotive force E is the only permanent 

 one, and the coefficients of mutual induction of the various wires 

 may be neglected, the other electromotive forces only depend on 

 the effects of self-induction due to variations of the currents. If 

 L a , L a / ..... are the respective coefficients of self-induction of the 

 branches the resistances of which are a, a' .... , we have (518) 



These values, substituted in the preceding equations (23), will 

 give the intensities at each instant. 



For the branch r in particular, which contains the galvanometer, 

 we have 



/ dp d& , di\ ( d* da' . di\ 



a ( L 6 - L,/ -- L r ) - b ( L n -- L ' + L r ) 



. V dt b dt r dt) \ a dt a dt r dt) 



. . . 



If the total variation takes place during a time which is very 

 short compared with the time of oscillation of a needle, this 



