226 BELL SYSTEM TECHNICAL JOURNAL 



the core at the rate of approximately 1 per cent per month. In con- 

 trast, no change of resistivity was detected in an accelerated aging test 

 consisting of a bake at 100° C. for 150 hours. 



Discussion 



The ballistic data on both the present annealed 35 permalloy sheet 

 core and the previous compressed powdered iron core show that the 

 area of the hysteresis loop varies as B^^ in agreement with Rayleigh's 

 law. The magnitude of the loss is not given by the fractional slope X 

 of the yi,B line as required by Rayleigh's law because the loops are not 

 parabolic in shape. This discrepancy gives a measure of the skewness 

 of the hysteresis loop. The Bm^ portion of the a.-c. data agrees with the 

 loop areas obtained with the ballistic galvanometer. The threefold 

 agreement between the ballistic data, the harmonic measurements, 

 and the a.-c. resistance measurements indicates that the hysteresis loop 

 is substantially unchanged in shape over a frequency range extending 

 from to 10,000 cycles. 



Since the hysteresis loop has a size and shape independent of fre- 

 quency, and area strictly proportional to B,n^, it accounts for that part 

 of the effective resistance of a coil on a ferromagnetic core which is 

 proportional to the alternating magnetizing current. The remainder 

 consists of eddy current and residual losses. 



The ordinary graphical method of separating these losses is excluded 

 by the obviously non-linear relation between Rf/nofL/ and /. Using 

 an analytical method, the eddy current loss is found to be some 20 per 

 cent larger than computed by classical theory, indicating the presence 

 of low permeability surface layers on the sheet material. The residual 

 loss coefficient is found to increase with frequency up to about 500 cycles, 

 and to remain constant at higher frequencies (up to 10,000 cycles). 



The observed inductance diminishes with increasing frequency about 

 1 per cent below the value calculated for eddy current shielding, the 

 most noticeable decrease occurring below 1000 cycles where eddy current 

 shielding is practically absent. 



Various theories have been advanced to account for residual loss, as 

 noted in a previous paper.^ Goldschmidt ^ and Dannatt^" have at- 

 tributed the loss to non-homogeneous alloy structure, or preferred axes 

 in such directions as to give a flux component perpendicular to the 

 sheet surface, with accompanying eddy-currents unconstrained by the 

 sheet thickness. This theory fails to account for residual losses in com- 



9 R. Goldschmidt, Helv. Phvs. Act., 9, 33 (1936). 



10 C. Dannatt, I. E. E. J., 79, 667 (1936). 



