ON THE xMEASUREMENT OF MAGNETIC HYSTERESIS. 
35 
The work spent per unit volume during any finite change is thus 
= . 
tlie expression found by Hopkinson. 
When the change is cyclic, so that B and H have the same values at the end as at 
the beginning of the cycle, we can throw the expression into a different form. For 
since B = H + 47 rl we have c/B = r/H + 47 r(/I. But when H goes ( 1 ) through the 
cycle + Hg, — Hg, + Hg or (2) goes from -f- Hg to — Hg, then | H(/H — 0, and tlius 
we recover Warbupg’s expression j Hc/I. 
In the present paper we are only concerned with the work spent in causing a 
complete cycle of magnetic changes. We shall always use W to denote the energy 
dissipated by hysteresis per cub. centim. per cycle of magnetic changes, and we 
shall express W in ergs per cub. centim. per cycle. We liavc thus 
W = 7 I hk/B.( 2 ). 
Air J 
To obtain the value of W by means of this expression, it has l)een usual to 
construct a cyclic B-IT curve, best by the method described by Ewing, and to find 
its area. This process is easy enougli, but since it involves the observations necessary 
to find at least ten or twelve points on tbe B—H curve, and the subsequent estimation 
of the ai'ea of the curve after it lias been plotted, quite an hour is required for each 
determination of W. 
§ 2. We have given the sketch contained in § 1 for the purpose of contrasting the 
physical ideas involved in the two mathematical methods by which the formulae 
W — — J WH and W = l / 47 r. | Hr/B have been obtained, and of showing the manner 
in which the subject presented itself to one of us in 1895. 
The remarks of § 1 refer only to mathematical processes and not to the experi¬ 
mental methods of studying the effects of hyst( resis as exhibited in the relation of 
I or B to H. To the experimental knowledge of the subject the first contributions 
were made by the independent and nearly simultaneous papers of Warburg and 
Ewing. In addition to the theory noticed in § 1 , Warburg gave magnetometric 
observations of cyclic I—H curves, but his observations were few. Ewing made a 
much more systematic attack on the subject, using the ballistic as well as the mag¬ 
netometric method, and determining the values of — j IdH for a graded series of 
I—H curves for the same specimen of iron. An account of the subsequent develop¬ 
ment of the subject, in which Ewing has liad a great share, will be found in his book 
on ‘ Magnetic Induction in Iron and other Metals.’ We owe much to Professor Ewing, 
It was his hysteresis tester which formed the initial incentive to the research described 
* Ewing, ‘ Magnetic Induction in Iron .and other Metals,’ 3rd ed., revised, § 192, 
F 2 
