Whitehead and Hill — Measurement of Self -Inductance. 155 



using "generalized resistances," we obtain as the ratio of the 

 current in the battery arm to the current the bridge arm, 



C„ i(j) _ (r + ipl) (R, + R + R' + R" + »L) (R,+R*) (R, + R' + frL) 

 C, e ~ RR"-R /y R'- ipLK" 



Multiplying both sides of this expression by C/, rationalizing, 

 and equating the real parts we obtain, 



[R^-R.RT^R. + R. + R^ + RQ-^U + ^ + RJ^ +Rq 



^'° ' C0M>_ ' ~ [RR"-K // R'] 2 +/L 2 R" 2 



% P *LlR g (R, + R, + R' + R') -^LVR -^L 2 (R /y + R')R, 

 R^'-R^R'+^I/R" 2 



This expression must be equal to zero since we adjust the 

 bridge until 4> = 90°, therefore cos $ = 0. Equating to zero 

 and simplifying, 



T . lT ,i («' + B,)(B ,+B 1 



R"R / -R ;) R' j r(R, + R, + R' + R') + (R' + R,) (R' + R, 

 P'R. \ r + R" + R„ 



This formula is somewhat simplified if R /7 is chosen equal to 

 R/ However, for accurate work the equality must be exact. 

 Since the self -inductance of the hanging coil of the Rowland 

 electrodynamometer is so small, only '0007 henry, the correc- 

 tion of L due to it is very small, in the case of coil C amount- 

 ing to '0004: henry. 



In using the method the numerical work involved in the 

 calculation of L is rendered somewhat easier if we write the 

 formula, 



L + sLl = t 



when very approximately, since I is so small, 



L = * + §* 



where 



g = (R" + R „ )(R ; +R„) 



This method was found to be excellent. It is very sensitive 

 and very accurate provided certain precautions are taken. 

 Some little difficulty was experienced at first from the fact 

 that the values of the self-inductance of a coil measured on any 

 one day, although agreeing pretty well among themselves, 



