50 
MESSRS. G. F C. SEARLE AND T. G. BEDFORD 
The secondary current is given by 
Sc = Kncl^jclt + (G — A) .(28). 
Substituting for C from (27) we find 
TttN'S I Ccdt = An I (H + h) dB + (G - A) u j (H + h) dH. 
Hemenibering that = 0 for a cycle or a semi-cycle, we have, on using (7), 
= Sf Codt = {[HrfB + \h.m + Aj j. . . (2.), 
. Hence the throw of the dynamometer is larger than that corresjKjnding to J HdB, 
and thus if we calculate W from the throw of the dynamometer Ave must subtract a 
correction depending upon the integrals | /n7B and J AdH. The correction can be 
found only when h is known both as a function of B and also as a function of H. 
§ 18. Lord Bayleigh"'" Avas the first to shoAV hoAv to correct an I—H cui’Am for the 
demagnetising force. He supposes that the specimen is an ellipsoid, and that the 
applied magnetic force is constant throughout its volume; tlie magnetic quantities 
H, B, I, and A are, in this case, constant throughout the specimen, and thus Ave can 
Avrite A = pi, Avhere p is a constant factor (usually denoted by N). This relation 
between H and I alloAvs the I—H curve for an infinitely long ellipsoid to be deduced 
from the curve for a short elliiASoid ])y “ shearing ” through a distance eAmryAvhere 
proportional to I. 
Some investigators, supposing that the demagnetising force. A, at the centre of a long 
cylinder is the same as that for the ellipsoid inscril)able in the cylinder, liaAm applied 
Lord PtAYLEiGH’s construction to the case of long cylinders. Others, such as Dr. H. 
DU BoiSjt thougli avoiding this error, have assumed that A can be expressed in tlie 
form A = pil, Avhere p is a function of the ratio of the lengtli to the diameter, but is 
independent of I, the intensity of magnetisation at the centre of the cylinder. But 
it is easy to see that, quite apart from the influence of hysteresis, cannot be 
constant, since the permeability of iron is not independent of the magnetic force- 
For, on account of the demagnetising action of the ends of the rod, the magnetic 
force near the ends differs from tliat near the centre of the rod, and thus the rod has, 
in effect, different values of p in different i)arts. If p Avere constant for each part, 
p AA’ould still he constant, but in the actual case, AATien the applied magnetic force is 
* “On the Energy of Magnetised Iron,” ‘Phil. Mag.,’ 1886, a'oI. 22, p. 175, or ‘ Scientific Papers,’ a'oI. 2, 
art. 139. 
t ‘ The Magnetic Circuit in Theory and Practice,’ p. 41. Dr. DU Bois, howec'er, describes (p. 123) the 
e.xperiments of Lehmann upon the magnetisation of a toroid A\-ith a radial slit, and points out that 
Leiijiann’s results show that the demagnetising factor increases, Imt oidy gradually, as I increases up to 
about half its maximum A'alue; beyond this point the increase is more rapid. The experiments Avere not 
ar 
ranged so as to show the ctleets of hysteresis. 
