MAGNETIC MEASUREMENTS AT LOW FLUX DENSITIES 49 



obtained be plotted against Bm, they generally fall upon a fairly 

 straight line whose slope is a, and whose intercept on the line Bn = 

 is c. The value of a so obtained agrees fairly well in most cases with 

 the value calculated from the permeability variation coefficient X, 

 which is the justification cited above for the Rayleigh equation. The 

 presence of residual loss necessitates rewriting the loss equation with 

 an additional term — 



^^ aBm + c + ef. (42) 



f^mfL 



The value of the intercept c, however, has no counterpart in the 

 Rayleigh equation. It indicates the presence of a power loss propor- 

 tional to the frequency, and thus similar to hysteresis, but contrarily 

 proportional to the square of the magnetizing force, instead of to the 

 cube. It is found not to contribute to harmonics or modulation 

 generated by a core material, and might thus be represented by an 

 elliptical increment to the Rayleigh loop.^^ 



Residual loss has been ascribed to viscosity or "after-effect" in the 

 core material. ^^ The chief obstacle to this explanation is the observed 

 constancy of c over a wide range of frequencies, in contrast to the 

 variation to be expected from ordinary viscosity losses. Residual loss 

 has been ascribed to inhomogeneities in the magnetic material ^^ 

 which lead to higher a-c. power losses than expected from the area of 

 the hysteresis loop. This explanation seems promising, but the work 

 to date has been chiefly qualitative, and it has not been shown to 

 yield the required additional loss proportional to H^. The parallel 

 between this loss and eddy current loss, which is also proportional 

 to H^, is alluring, but the dependence of eddy current loss upon p has 

 remained a stumbling block. The mechanical dissipation of power 

 through magnetostrictional motions seems also a possible explanation. ^^ 



Somewhat analogous to the residual loss is the excess eddy current 

 loss generally observed. When the observed value of e is used to 

 calculate the resistivity of a magnetic material, it generally gives 

 a value somewhat smaller than the true resistivity, which indicates 

 that the observed eddy current losses are correspondingly too large. 

 The apparent resistivity so obtained approaches the true resistivity 

 quite closely for well insulated laminations of pure, well annealed 

 materials. It is interesting to note that the residual loss for such well 



13 H. Jordan, Ann. d. Physik [5] 21, 405 (1934). 



'' H. Jordan, E. N. T. 1, 7 (1924); F. Preisach, Zeit.f. Phys. 94, 277 (1935). 



15 L. VV. McKeehan and R. M. Bozorth, Phys. Rev. [2] 46, 527 (1934). 



1* For a more thorough discussion sec W. B. Ellwood, Physics 6, 215 (1935). 



