SPALDING AND SHAW. — COEFFICIENT OF SELF-INDUCTION. 247 



X. 



A HEAT METHOD FOR MEASURING THE COEFFI- 

 CIENT OF SELF-INDUCTION. 



By p. G. Spalding and H. B. Shaw. 



Presented by Professor John Trowbridge, May 9, 1894. 



The coefficient of self-induction of a coil having an iron core and 

 traversed by an alternating current depends upon the permeability of 

 the iron, and therefore upon the current strength, in a manner which 

 can be seen by examining the hysteresis curves of Ewing and others. 



If the coil has no iron core, its coefficient of self-induction is con- 

 stant for all current strengths, and may be measured by some method 

 where the current used is small, " Rayleigh's bridge method," for 

 instance. 



If we try to calculate the coefficient of self-induction when a coil 

 with an iron core is subjected to an alternating current, we have a 

 practically impossible problem ; but if we regard the effects as a 

 whole, we can measure the effective coefficient of self-induction for 

 any given impressed electromotive force. 



The effective coefficient of self-induction of a coil having an iron 

 core may be defined as the equal of the constant coefficient of that 

 coil which would give the same integral current flow as the former 

 under the given conditions. 



Let us first examine the case theoretically. Given a simple 

 branched circuit and an impressed electromotive force which varies 

 as the ordinate of a sine curve, we obtain the following for the values 

 of the currents in the two branches : — 



(1) «i = sin (jo < -f ^i) ; 



(2) ^2 = , sin {p t -{■ B^)', 



