246 Mr. J. M. Baldwin on the Behaviour of 



Substituting these values in the equations 



/j, = fju r sec 0, k = — tan #, 



CO ..... 



the values obtained for /i are 



155-3 153-2 150-7 140*3, 

 and for h 



•00165 -00217 -00206 -00179; 



which must be considered a fairly satisfactory agreement. 



It appears then that the experiments agree fairly well with 

 the assumptions that at very low inductions the permeability 

 tends to a definite limiting value, and that the lag in the 

 phase of the induction at any point behind that of the 

 magnetic intensity at that point is zero. 



As regards the third harmonics, b 3 appears to have an 

 approximately constant value for each series, its value 

 decreasing as the frequency is increased, while -^ 3 increases 

 as the induction decreases, tending to a value of about 60° 

 in all cases for very low inductions. 



In fig. 3 (lower curves) is shown the relation between the 

 total iron loss and the induction, and the curves here show 

 the marked effect of the eddy currents in increasing the loss 

 of energy in such a rod as that at present being discussed. 

 It will be noticed in Table V. that the calculated eddy- 

 current loss is greater than the total iron loss. This 

 eddy-current loss w T as calculated from a formula (§ 4) obtained 



7TT 



on the assumptions that /x was constant and that -j~ w r as 



constant over the section. It appears then that for a thick 

 rod such as the present one these assumptions depart con- 

 siderably from the truth, and the question arises how far the 

 results calculated on these assumptions for any particular 

 specimen are in error. Owing to the uncertainty of the eddy- 

 current loss, no attempt has been made to recognize kinetic 

 hysteresis in the rod. 



In fig. 5, Steinmetz's coefficient a is plotted against B maI . 

 a is seen to decrease rapidly as the induction is diminished, 

 and for very low inductions takes a very low value not very 

 different from zero. 



In fig. 6 the hysteresis loops are shown for four of the 

 experiments, the upper ones being the 1st and 7th of 

 Table II. and the lower ones the 1st and 7th of Table VI., 

 the frequency for all four being very nearly 28,. Each pair 



