INDUCTANCE AND CAPACITY 385 



or uniting terms, 



x(R M + RN) - yR G - L G ^ - i B R N = 0. (10) 



Considering the mesh bed, the potential difference between 6 and 

 c is 



1 



+ y)dt, and similarly for V C d> 



XQ 



Hence 



- \(x + y)dt + ~ f(x + y)d* - 7^ f 'tad* + (x + y)R 

 ^x Jo ^pjo ^P Jo 



or uniting terms, 



dz dy 



" xRo Lo dt : 



^ I 



Up Jo 



yR G +L = 0. (11) 



(10) and (11) may be integrated from t = 0, when the key K is 

 closed, to the time t when the permanent state has been estab- 

 lished. Call Qx the quantity displaced by the current x in that 

 time, Q G the quantity displaced through the galvanometer by y, the 

 true galvanometer current, and Q B the quantity displaced by i B . 

 Integrating (10) and remembering that y is zero at the start and 

 zero at the finish, 



Q x (RM + RN} - QoRo - Q B R N = 0. (10a) 



Integrating (11) gives 



(Qx + QG) jr + (Qx + QG ~ QB) ^r = 0. (lid) 



From (10a) and (lla), 



.'.Qo 



7T - #"1 



L/p J 



(12) 



RM ~\~ RG ~\~ RN 

 If QG = 0, 



Cx R* 



25 



