ON THE MEASUREMENT OF MAC4NETIC HYSTERESIS. 
89 
2'g cycles. In each case the last cycle is indicated by isolated points ; when the 
positive load is increasing a + is used, and when the positive load is decreasing a X 
is used. 
In their general forms the curves due to the last cycle for 20 and 50 turns of 
permanent set resemble those obtained after several comparatively rapid cycles of 
torsion for 25 and 50 turns of permanent set in § 62. Any close comparison is 
impossible on account of the fact that the curves of § 62 do not form closed figures. 
In the case of 6 turns of permanent set, the curves for the last cycle differ widely 
from those for 5 turns of permanent set in the experiments of § 62. ' The part of the 
curve which corresponds to a decreasing positive couple now lies always above that 
part which corresponds to an increasing positive couple instead of crossing it. The 
two parts of the curve show, however, a tendency to approach each other with 
repetition of the cycles of torsion. 
In this case there is a very great recovery of magnetic quality in the first 
1^ cycles of torsion. When the load was reduced to zero for the first time Bq was 
5190, at the second zero load we found Bq = 6310, and at the third zero load Bq = 
8050. Since Hq = 5, the permeability rose from 1038 to 1610. 
Relation connecting W with Bq and Hq. 
§ 64. A cursory examination of the curves recording the effect of strain upon the 
hysteresis and the induction, for given values of the magnetic force, is sufficient to 
make it evident that the changes in Bq, due to strain, are very closely followed by 
the consequent changes in W. This correspondence is so close that it invites the 
attempt to express it mathematically. We have here the means of analysing W and 
determining it as a function of Hq and Bq ; this is impossil:)le with the W — Bq 
curve for zero stress, since we cannot, without straining the specimen, change Bq 
without changing Hq. Our plan has been to j^lot curves showing W in terms of Bq 
for definite values of Hq, the variations of Bq and W being due to strain. 
§ 65. The first example is taken from the expeiiments on the effect of torsion iqjon 
a soft iron wire, the corresponding values of Bq and Wg for definite values of Hq being 
recorded in § 58. Five curves connecting W and Bq were plotted for five values of 
Hq upon fig. 10, where the W — Bg curve for zero stress is also shown. The 
points corresponding to increasing torsion lie so closely on the same curves as 
those corresponding to diminishing torsion, that we have marked both sets in the 
same manner. For the larger values of Hg each curve consists of a straight 
line with a small hook at one end—the end corresponding to zero strain. The 
straight parts of the curves all pass, on prolongation, through the point —600 on the 
axis of W, and hence over the greater part of the variation of Bg, caused by torsion 
under a constant maximum magnetic force Hq, the value of W is given by 
W = mBQ — 600, 
VOL. cxcvni,— A, 
N 
