FERROMAGNETIC DISTORTION OF A WAVE 325 



to consist approximately of two parabolic branches, the exact shape 

 of each dependent upon its point of origin. For fields confined 

 somewhat below maximum permeability, the situation customarily 

 obtaining in communication circuits, this representation has proved 

 to be sufficiently exact to warrant the neglect of higher order terms in 

 analyses. In conformity, terms of higher than second order will not 

 be retained in equations used here; the development so presented can 

 be extended to include them without other change in procedure. The 

 induction at any point on a simple loop centered on the origin is 

 expressed as a function of the instantaneous magnetizing force h by 

 means of a formula developed by Peterson, 



B = (aio + auTDh ± a.^iW - ¥). (1) 



The upper sign of the double sign is used for the descending (upper) 

 branch of the loop, and the lower sign for the ascending (lower) branch. 

 H is the maximum magnetizing force and the coefficients are constants 

 of the ferromagnetic material, determinable by single-frequency meas- 

 urements. They have the following significance: aio is the initial 

 permeability, an the rate of change of permeability with magnetizing 

 force, and ao2 a factor of proportionality between the hysteresis loss 

 and the cube of the maximum magnetizing force. The concepts in 

 terms of which these parameters are defined acquire extended meanings 

 for complex loops. 



In the absence of an adequate theory of ferromagnetism the question 

 of whether branches of complex loops and of simple loops have similar 

 forms must be answered by experiment. The steady state of retracing 

 alternately the two branches of a simple loop may eventuate in a dif- 

 ferent relation of B versus h than results from the first cycle; such a 

 condition would mean that transient branches compose the complex 

 loop, inasmuch as it is not retraced. It is also possible that the biasing 

 effect of one sinusoidal component of the magnetizing force upon the 

 other might cause the branches of the two types of loops to be dis- 

 similar. The coefficients which specify the branches of the simple 

 loop are evaluated with it centered at the origin of the B-h plane, using 

 single-frequency methods, and cannot be assumed a priori to apply to 

 to other situations, or to an unrepeated branch. 



According to experiments by R. Goldschmidt * the superposed field 

 necessary to cause much change of either the shapes or axial slopes of 

 loops exceeds the weak fields to which this development is limited. 

 Likewise, Lord Rayleigh ^ in his original investigation found small super- 



' Zeits.f. Techn. Physik, Vol. 11, pp. 8-12, 1930. 

 "• Phil. Mag., Vol. 23, 1887. 



