92 
MESSES. G. F. C. SEARLE AND T. G. BEDFORD 
§ 68. So far the strains have been practically within the elastic limit. We now 
examine some cases in which this limit was much exceeded. 
In the W—-Bj curve, plotted from the experiments described in § 60, the points 
appear to be irregularly placed till the torsion wheel has made about eight revolutions. 
For greater strains the points lie well on the straight line, W = '610 
Since Hq = 5 this may he written 
W = •273HioBo + 450 . 
In the experiments of § 61 the points corresponding to both the curves (2a) and 
(26) cluster round a single curve, which when Bq exceeds 2500 is represented by 
W = •352moBo - 850 (H = 5). 
§ 69. We are not j^repared to oiler any physical explanation of the formula 
W = aHioBo — But as it has a rational ajjpearance it seemed worth while to 
test it on some results obtained under zero stress. We plotted W against H-qBq for 
several of the tables given by Professor J. A. Ewing and Miss Klaassen,! as well 
as for the results for cobalt obtained by Professor J. A. Fleming, j In every case 
the resulting curve was straight over a considerable range of B^. For small values 
of B(j the value of W given by W = oH-qBq — 6 is too small, while for large values 
of Bq it is too large. The value of oH-Bq — 6 begins to be too large when with 
increasing B^ the permeability p. begins to fall rapidly below its maximum value'. 
When, with decreasing Bq, p falls much below its maximum value, gH-Bq — 6 
becomes too small. It also appears that when B,-, is less than B'q, the value corre¬ 
sponding to tlie maximum of p, p may, without causing serious error, differ much 
more from its maximum value than when Bg exceeds B'q. The following examples 
from the experiments of Professor Ewing and Miss Klaassen will serve as illustra¬ 
tions. 
* [November 4, 1901. ]Mr. Wills lias obtained from his experiments a series of curves showing how 
W, for constant values of Hq, depends upon Bq, when Bo is varied by vaiying the temperature. These 
curves exhibit in a striking manner the characteristic features of our own curves. Thus the ciu’ve for a 
given value of Hq consists of a straight line and a hook, while the straight lines, corresponding to different 
values of Ho, all radiate from a point on the axis of W. Mr. Wills, however, finds that the index of Ho 
is J instead of A The relation deduced from his experiments is thus W = aH^Bo - h] 
t “ On the Magnetic Qualities of Iron,” ‘Phil. Trans.,’ A, vol. 184, p. 985. 
I “ The Magnetic Hysteresis of Cobalt,” ‘ Proc. Physical Soc.,’ vol. 16, p. 519. 
