774 BELL SYSTEM TECHNICAL JOURNAL 



These relations provide us with an expression for the ratio fln/aoo 

 which may be obtained from impedance measurements. It will be 

 recalled that Rayleigh's relation would give this ratio the value two, 

 and a.c. bridge measurements may be used to check this relation. 

 The change of resistance with current is given by (27), and the change 

 of reactance with current may be calculated from (25) and (26), since 

 we have _ 



A A" = aiii/2^w^io-8/7V2 

 = \A2-\Q-^n^Aflanld\ 



Hence if we denote Rh by AR, we may write 



^ = 0.85^^ 



The results obtained on some dust cores of different composition and 

 two solid materials may be tabulated as follows: 



Material Number of Specimens aii/ao2 



Grade ' B ' Iron Dust 10 2.65 



Grade ' C ' Iron Dust 1 2.63 



Permalloy Dust ^ 'A' 3 2.10 



'B' 3 1.81 



Iron Dust No. 1 1 2.80 



Iron Dust No. 2 2 2.55 



Perminvar lo 1 3.0 



Alloy 'D' 2 1.84 



The method of analysis and the results obtained above may be 

 summarized as follows. Starting with the general development of 

 the hysteresis branches in a double power series and making use of 

 only the most fundamental experimental observations, equations have 

 been derived for the normal magnetization curve, the remanence 

 characteristic, and the hysteresis loss characteristic in terms of the 

 original hysteresis branch coefficients by combining the equations 

 for the two branches in a trigonometric series. The series for the 

 normal magnetization curve is found to start with the first power of 

 the magnetizing force, the remanence starts with the second power, and 

 the hysteresis loss starts with the third power, the curv-es var\^ing in 

 accordance with their respective first terms when // is small. These 

 results seem to be in general agreement with experience. For large 

 values of // the shapes of the different cur\es depend of cotuse upon 

 the size and sign of the coefficients invohed, about which nothing 

 can be said imtil the coefficients have been evaluated from experimental 

 data. 



^ Shackelton and Barber, "Compressed Powdered Permalloy," A. I. E. E. Con- 

 vention, February 1928. 



^^ Elmen, "Magnetic Properties of Perminvar," J. F. I., September 1928. 



