Use of Mutual Inductometers. 505 



Then we have 



and therefore 



I 3 2 (R 2 + LW)=FWI 1 2 . . . . (22) 



Also 



(m — M)ai 1 = — Qii — Gaz 3 , 



FGw 2 ^ 



Hence 

 and 



_ n . FG&r^ FGLft) 2 ^ 

 - ^i+ R2 + L2fi)2 R2 + L2ft)2 ' 



FGLa) 2 



m 



-M = 



Q= 



R 2 + LV 

 F 2 Ra> 2 



R 2 + L 2 a) 2 ~~ 6(R 2 + LV) ' 6Ii 2 ' 



otal iron loss RI 3 2 



= QI 1 2 6=QI 1 2 .N 1 /N 2 (23) 



Also 



m-M=-QL/R (24) 



I have assumed that the conditions are not sensibly 

 affected by the small harmonic currents of higher frequency 

 which pass through the galvanometer without any consider- 

 able effect on its deflexion. The object of the inductance 

 coil J is to check these, and this could be done even more 

 effectively by adding also a condenser of suitable capacity. 



Since the magnetizing current i x is of sine wave form, the 

 flux density 38 and the total flux <I> will in general not be 

 sinoidal. It is usually necessary to reduce the results of 

 iron tests to a standard value of 38^1 with induced secondary 

 voltage of sine wave form. When this is required the <^ mas 

 and the form factor of the secondary voltage are observed 

 simultaneously with the above measurement of power. This 

 is done in the usual way by the help of a synchronous com- 

 mutator *. By making tests at two different frequencies the 

 hysteresis and eddy current losses may be separated. 



It should be noticed that the work done in the iron by 

 the current %i is got by integrating i x d$ ; if i x has no 

 harmonics, the harmonics in ^disappear in the integration. 



* See Lloyd, < Bulletin Bureau of Standards,' p. 467, vol. iv. 1908 ; 

 also the Author, Proc. Inst. El. Engs. p. 553, vol. xliii. 1909. 



