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BELL SYSTEM TECHNICAL JOURNAL 



circuit impedance to the third harmonic which includes that of the coil. 

 We have now to determine the coil impedance to a complex magnet- 

 izing force constituted by the fundamental and the third harmonic. 

 It is evident at the outset that if we restrict consideration to a very 

 small third harmonic, the impedance to the fundamental cannot be 

 very materially altered. 



In general the fundamental and third harmonic may exist in any 

 phase but for our present purpose we shall take the magnetizing force 

 to be 



H = //i cos pt + Hz cos Spt, (29) 



in which the phase angle is assumed zero. This seems to be an 

 arbitrary assumption, but it may be shown that the results are not 

 materially different for other phase displacements, and there is some 

 gain toward simplicity of treatment by taking the phase angle zero. 

 The equations of Part 1 may then be carried over without change, and 

 details of the analysis are given in Appendix 4. 



The ratio of the resistances to the third harmonic and to the funda- 

 mental is 0.77, from the relations deduced in the appendix. Some 

 experimental work has been done to test the validity of the expres- 

 sions derived above for the reactance and resistance components of 

 the third harmonic, the results of which are given in Fig. 4. It is seen 

 that the check for the inductance to the third harmonic is very good 

 but that the resistance component appears to be substantially that of 

 the fundamental rather than 77 per cent of it, as the analysis indicates. 



Ir MILS 



Fig. AA 



