to Reversals of Magnetization in Soft Iron. 213 



through both, can be expressed very approximately when 

 time is sensibly small by 



whence we see that the temperature-curve bends toward or 

 away from the time-axis according as QH is greater or less 

 than f3c 2 . Now Q depends upon the rate of reversals of magne- 

 tization as well as on the magnitude of the magnetic hysteresis. 

 Hence we see that the temperature-curve is turned upward 

 when «§, the magnetizing field, is large compared with the 

 hysteresis, and vice versa. By referring to the figs. 1 to 20, 

 one sees now why some of them are curved upward while 

 others are curved downward. The downward curvature 

 only occurs when the hysteresis is large compared with the 

 field 1q, that is in the steepest part of the curve of magnetization. 



In order to find Q from the observed data an empirical 

 equation v = At + Bt 2 was assumed, and A was taken to be 

 equal to Q — o?c for each curve, instead of determining the 

 tangent to the curve from H h q f c. The equation will be 

 true if the heat generated were immediately communicated 

 to the thermo-junction. But on account of the cotton 

 covering, which lies between the iron and the junction, there 

 will be a slight time-lag for the temperature-bore to reach 

 the junction. To take this into account another constant is 

 added to the equation thus 



v = A£ + B£ 2 +C. 

 This C will give the temperature which the ring would have 

 had at the beginning if there were no time-lag ; or it might 

 otherwise be looked upon as a constant error in zero of the 

 galvanometer. 



The constant A was found for each curve from the observed 

 data by the usual method of least squares. It was found, how- 

 ever, in the course of calculation that when the number of obser- 

 vations was only 3 or 4, the three constants gave too much 

 freedom to the curve ; that is, the law of least squares is not 

 nearly fulfilled by so few points. In other words, errors of 

 observation rather tended to modify the form of the curve 

 instead of compromising amongst themselves as would be the 

 case when there are many. From this it was thought expe- 

 dient to take the equation with only two constants, A, B, when 

 there were less than 6 points (double the number of constants) 

 in the curve, and three constants A, B, 0, when there were more. 



The tangent A thus found is now to be corrected for the 

 differential Joule's effect, which was denoted by ac 2 . Fig. 22 

 shows the curves of temperature growth when a continuous cur- 

 rent of given strength was sent through both the rings, and 



Phil. Mag. S. 5. Vol. 28. No. 172. Sept. 1889. R 



