ON THE HEASUEEMENT OF MAGNETIC HYSTERESIS. 
fi7 
for specimens of high permeability, is enormously greater during the 
second than during the first stage. Thus, for a given value of C, the product 
. dCjdt during the first stage is small compared with its value during the 
second stage. Hence by far the greater part of the eddy current loss occurs during 
the rise of the current. In fact, if the choking coil have a core of the same iron as 
the specimen and be similarly wound, and if the current be reversed in the manner 
described in § 15, the eddy current losses during the fall and subsequent rise of the 
current are proportional to R X area adh and (R + T) X area ach'e respectively, the 
areas being shown in fig. 1. Thus the main part of the eddy current loss occurs 
during the rise of the current; this part is very nearly proportional to E. The eddy 
current loss during the fall of the current is indeed only roughly j)roportional to E, 
but it is small in comparison with the loss during the rise of the current. Hence the 
total eddy current loss during a semi-cycle is nearly proportional to E, and thus can 
be determined approximately by the formula X = (U' — U) E/{E' — E), as explained 
in § 15, since Y is now negligible, and X is thus sensildy equal to Z. 
As illustrations we now give two examples kindly furnished us by Mr. R. L. Wills. 
In the first example the specimen was a portion, 2'49 centims. in length, of a circular 
tube of radii 3’810 and 3MS5 centims. A plane through the axis forms a rectangular 
section of the ring, the sides of the rectangle being a = 2'49, h = '625 centim. 
Thus A = 1'56 sq centims., ajh = 4, while the mean circumference is ^ = 22 centims. 
Hence, treating the ring as a straight rod, we find by Apjiendix I., Q = '0176. Now 
the resistance, S, of the secondary circuit varied from 23 to 523 ohms, while n, the 
number of turns, was 50, so that X/Y [= varied from 356 to 8300. Hence 
Y was negligible in comparison with X, and X was thus sensibly equal to Z. 
For each value of Hq three determinations of U were made with batteries of 8, 16, 
and 24 volts. The value of W was deduced from the three values of U by the formulae 
W = 2U — U', W = 3U' — 2U", which follow from § 1 5. In the last column we 
give the value of X, the space-average of the eddy current loss corresponding to 
E = 8 volts, X as well as W l)eing expressed in ergs per cub. centim. per cycle. 
IB. 
Bo. 
S. 
ohms. 
u. 
E = 8. 
1 
U'. 
E' = 16. 
U". 
E" = 24. 
2U - 
3U' - 2U''. 
W. 
(mean). 
X. 
E = 8. 
•31 
194 
23 
5-9 
7-3 
8-8 
4-5 
4-3 
4-4 
1-5 
•68 
.540 
23 
32-3 
38-2 
44-1 
26-4 
26-4 
26-4 
5-9 
1-02 
1205 
23 
154 
169 
185 
139 
137 
138 
16 
1-36 
2657 
73 
585 
655 • 4 
721 
514-6 
524-2 
519-4 
65-6 
1-70 
4629 
123 
1528 
1640 
1736 
1416 
1448 
1432 
96 
2-04 
6107 
223 
2471 
2702 
2919 
2240 
2268 
2254 
217 
2-38 
7139 
223 
3396 
3714 
4017 
3078 
3108 
3093 
303 
2-72 
8077 
523 
4242 
4683 
5124 
3801 
3801 
3801 
441 
3-06 
8749 
523 
5159 
5702 
6211 
4616 
4684 
4650 
509 
3-40 
9332 
523 
5940 
6551 
7161 
5329 
5331 
5330 
610 
1 4-02 
i 
10150 
! 523 
1 
7297 
8146 
8960 
6448 
6518 
6483 
814 
K 2 
