44 
MESSRS. G. F. C. SEARLE AXD T. G. BEDFORD 
is negligible or else be able to determine it. In most of our experiments the specimens 
have been fine wires, and X has been insignificant in comparison with W, but with 
rings of solid metal, such as those used by Mr. E,. L. Wills,* with a sectional 
area of over 1 scp centim., X becomes of real importance. Now from the behaviour of 
the eddy currents in a rod of circular section, we may assert that when the “ time 
constant” (inductance/resistance) of the primary circuit is large compared with Trga-'cr, 
where a is the radius of the largest circle inscribable in the section, and fi and cr 
are the permeability and specific resistance of the material, then the eddy current at 
any point may be calculated on the assumption that the magnetic induction has at 
any instant the same value at all points of the section (Apjiendix I.). In this case 
the eddy current at any given point is proportional to cZB/hi, and hence, as the 
method of “ Dimensions ” shows, the space-average of the rate at which heat is 
generated per unit volume may be written 
hX/f/^ = QA {clB/dtfla- = 1677''NWQ/o- . (cZB/hH)3. (c/C/ch)~ . . • (13), 
where Q is a constant depending upon the form of the section. On reference to the 
meaning of X it will be seen that the total rate of heat production by eddy currents 
per unit length of the specimen is QA^(hB/h^)'Yo'- For a circular section Q = fi Stt = 
•03979, and for a scpiare section Q = '03512. (Appendix I.) 
We can now write (12) as follows :—• 
W = 
NC'P 
(^1 + 0 ,) 
Ancj) 
N 
\dKj SAw. 
47r?i-A rZB 
1. m 
+ l) I ItthAN '(I + M 
/ \ tt-H- 
(IQ 
(U 
clC 
= U~X-Y (§13) 
(14). 
If the specimen be built uji of p similar wires so that the total cross-section is A, 
then X is Ijp times the value for a single wire of section A. The p wires must he 
insulated from each other so that there are no eddy currents from wire to wire. 
The quantity f/B/WH, which occurs in the correcting integral, is for a given specimen 
a nearly definite (double valued) function of H and therefore of C, for given limits 
i Cq, provided that the “ time constant ” of the primary circuit is large compared 
* Mr. R. L. tViLLS, of St. John’s College, 1851 Exhibition Scholar, began in 1900, at the CaA'enclish 
Laboratory, a series of experiments on the effect of temperature upon the energy dissipated through 
hysteresis in iron and alloys of iron, in continuation of his work on the “ Effects of Temperature 
on the Magnetic Properties of Iron and Allo 3 's of Iron ” (‘Phil. Mag.,’ July, 1900). At the suggestion of 
Professor J. J. THOMSON he employed the method described in the present paper, while u’e gladfv 
furnished him with some of the apparatus emj^lojmd by us in our own researches. It was plain that in 
the specimens used by Mr. MTj.ls the energy dissipated by eddy currents was comparatively much greater 
than in our own specimens, and so might be far from negligible. 5Ye were thus led to extend the theory 
so as to take acconnt of the eddj" current loss, and to devise a method of determining that loss. 
