MAGNETIC LOSSES AT LOW FLUX DENSITIES 219 



the Rayleigh loop. The hysteresis coefficient a and the permeability 

 coefficient, X are related by the equation a = SX/S/j. for a loop having 

 parabolic shape, in which case the interior angles are equal, and tan 

 4>-i-= iJ-oXBm. Since the latter equation applies for 0+ only, on the 

 observed skewed loop, it follows that the Rayleigh relation between a 

 and. X is more or less inaccurate. In fact, the ratio of 8X/3;u to a is a 

 measure of the skewness of the loop. For the present material, this 

 ratio is about 1.15. This result is in accord with our previous data, 

 but was evidently not noted by Rayleigh because the free poles in his 

 magnetic circuit tended to mask the asymmetry. The fact that these 

 hysteresis loops are slightly skewed shows that those processes which 

 produce the familiar ^-shaped loop at high flux densities are already 

 present at these low flux densities. 



Despite a skewed shape, the area of the observed loop approximates 

 closely the area of a parabola drawn through the remanence and the 

 tips. Hence, supplementary values of energy loss W were obtained 

 from remanence observations at several values of Hm, using the formula 

 W = 2BrH„J3ir. The slenderness factor of the loops may be measured 

 by the ratio Bm/Br, which varies from 211 to 890 for the different loops 

 studied. 



The a.-c. resistance introduced by the hysteresis loss of the core 

 material yields the ratio SttPF/^^^, as noted in Eq. (1). Values of this 

 quantity computed from the areas of the loops of Fig. 3. and from 

 remanence determinations are plotted in Fig. 4, They agree closely 

 with the aB,n term of Eq. (1) obtained by a.-c. measurements, as shown 

 by the solid line in Fig. 4. The sum of c + aBm is shown by the broken 

 line. It is evident that the ballistic galvanometer gives no indication of 

 residual loss. 



It is interesting to note that the hysteresis loop at low flux densities 

 can now be constructed in detail using the data obtained from a.-c. 

 measurements. The remanence is Br = j^a/jioBrJ and tan 4>+ = ixoXBm. 

 The angle included between the upper and lower branches of the loop 

 at the tips is {4>+ + (/>_) and is given by the equation tan [|(<^+ + 4>-)~\ 

 = s/i oaBm. 



A.-C. Results 



Values of R/ and Lf were measured as a function of the current at 

 fixed frequencies. The values of Rf/umfL/ are plotted in Fig. 5 as a 

 function of current with frequency as a parameter. In order to shorten 

 the vertical scale, the appropriate ordinates are indicated in connection 

 with each line. These form a family of straight lines parallel to one 

 another. This shows that the hysteresis coefficient is practically a 



