Resistance of Compound Conductors, 493 



number of turns per unit length in the magnetizing helix and 

 C the current (proportional to e ipt ), we have 



I^*=4wm0; (14) 



and for the electromotive force (E) due to the change of mag- 

 netic induction in the core, reckoned per unit length, 



E = m—<27rj crdr 1 



= 4m 2 7r 2 aV^>C. <///(£ (15) 



In order to interpret this, we must separate the real and 

 imaginary parts of <// / <£. If we write 



9 



then the part of E which is in the same phase as dC / dt is 

 4m 2 7r 2 a 2 fM .ipC . P; and the part which is in the same phase 

 as C is 4m W//, .pC . Q. The first manifests itself as an 

 increase of self-induction, and the second as an increase of 

 resistance. If p = oo , P = 1, Q = 0. 



What we require to know for our present purpose is the 

 effect of introducing the core; and to obtain this we must 

 subtract any part of E which remains when we put p = oo , 

 fi=l. Calling this E , we have 



E =4mW.fC, 

 and 



E-E =4mV 2 a 2 ^>C(>P--l) +/*pC . Q}. 



Thus if &L, SB be the apparent augmentations of self- 

 induction and resistance in the helix due to the introduction 

 of the core, reckoned per unit length, 



8L = 4mVa»(A*P-l)n a(n 



8E=4mV , aV/>Q. J ' ' ' > } 



From the calculation already made for the purposes of the 

 other problem, we have 



£S) =(1,M6tixM) "' 



= -31047 -ix -26044 ; 



so that for the stout iron wire of 3*3 millim. diameter and 

 /u=99-5, 



P = -31047, Q = -26044, 



