HARMONIC PRODUCTION IN MAGNETIC MATERIALS 767 



that the different branches of a family have the same form, so that by 

 suitable change of plate or of grid potential the plate current-grid 

 voltage curves may be superposed. A relation of precisely the same 

 form in the case of magnetic hysteresis loops was stated by Lord Ray- 

 leigh ^ upon examination of data obtained by a magnetometric study 

 of the behavior of a single low permeability specimen. Examination 

 of his data enabled Rayleigh to conclude that the branches corre- 

 sponding to different loops of a family could be superposed when re- 

 ferred to a common loop tip, the branches all having the same parabolic 

 form within the limits of accuracy of the measurements, over the 

 range of magnetizing forces involved. 



It is of course evident that even if this relation held at low fields in 

 all materials it would break down at sufficiently high fields. Further, 

 there is no a priori reason to expect this relation to hold for magnetic 

 materials other than the one Lord Rayleigh investigated unless we 

 restrict consideration to a very small range of magnetizing force. 

 With these ideas in mind it seems the safer procedure to assume no 

 such simple relation between the different loops of a family, however 

 convenient it might be, and to treat the problem in more general terms; 

 if any such simplifying relations exist they will be made apparent 

 after application to definite materials. We may anticipate matters a 

 bit to state at this point that certain materials seem to obey the 

 relation while certain others seem to violate it within the range of 

 forces involved in communication work, and further light is shed on 

 the significant processes involved in harmonic production by treating 

 the problem in this way.^ 



General Equations for Hysteresis Branches. The equations of both 

 the upper branch family and the lower branch family have the form of 

 equation (1) — we may designate the upper branches by Bi and the 

 lower branches by B^ — but the coefficients of the two series differ in 

 general. 



In order to put the equations in shape so that they may be of 

 practical utility it is now necessary to determine the coefficients of 

 the expressions for Bi and B2 so that they apply to a definite loop 

 family, and this is accomplished by reference to some of the more 

 general properties of the loops and of the normal magnetization curve. 

 These properties are as follows : 



^ "Notes on Electricity and Magnetism, III," Phil. Mag., 1887, V. 23. 



® Unpublished work based on assumptions which include Rayleigh's relation was 

 independently carried out by W. P. Mason of these Laboratories in 1922 and 1923. 

 An account of some applications of Rayleigh's relation is to be found in an interesting 

 paper by Jordan published in the Elektrische Nachrichten Technik, B. 1, H. 1, July 

 1924. 



49 



