782 BELL SYSTEM TECHNICAL JOURNAL 



coefficients for specimens of grade "B" and grade "C" dust which 

 represent different dilutions of electrolytic iron. The coefficients 

 used were those tabulated in Part 1. In accordance with equations 

 (42) above we may write 



aio/( 1 +-y flio ) =26.2, Cio/ ( 1 +-y Gio ) =35.3, 



au/(l +yaio)' = 0.59, an /( 1 + y aio)' = 1.53, (51) 

 002/(1 +jaioy = 0.29, 000/(1+^010)'= 0.65. 



From these, we should have equality of the ratios 



0.59/1.53, 0.29/0.65, (26.2/35.3)\ 

 or 



0.37, 0.45, 0.41, 



which are evidently in fair agreement. It is clear then that the 

 properties of diluted materials may be calculated from the character- 

 istics of the original material, at least when the process of dilution 

 does not change the intrinsic properties of the magnetic material 

 involved. 



Applications to Transformers. The third harmonic flux component 

 may be obtained when the fundamental magnetizing force is given, 

 and the latter is easily obtained in toroidal core inductance coils from 

 the relation 



h = OAnild, (52) 



where both h and i refer to the fundamental frequency. In a trans- 

 former, however, the net magnetizing force is obtained as the sum of 

 two components, one due to the primary and the other produced by 

 the secondary, so that some further investigation is required before 

 the net magnetizing force in the core may be calculated in terms of the 

 transformer constants and the primary current. 



Net Magnetizing Force. To obtain the net magnetizing force which 

 determines uniquely the generated flux components we are required to 

 obtain the primary and secondary currents iiii-i), to multiply each 

 current by the number of times it encircles the core, to add the two 

 products, and fuially to multiply the sum by O.i/d: 



7/,„,t = 0.4(n,ii + W2«2)/^. (53) 



To evaluate (53) then we shall solve for the primary and secondary 

 fundamental currents in terms of the circuit constants and the applied 

 potential. 



