( 65 & ) 
M = (N.—NJTv mi (fj cos (p 
where and JV, are the coefficients of demagnetization of the 
ellipsoid, f, the intensity of magnetization of the substance, v the 
volume, and <f the angle between / and the major axis of the 
ellipsoid. The maximum value of this couple is 
for 7 . === 45°. Hence to measure I it is not necessary to know either 
the strength or azimuth of the field which yields the maximum 
couple. To make use of these methods the ellipsoid is suspended 
from a torsion-spring whose displacement is determined by a mirror- 
method, and an electromagnet turning round a vertical axis is used. 
The method has already been described 1 ). Its advantages consist of 
the small range over which strong fields are necessary and the extreme 
simplicity of the relative measurements. 2 ) We shall now discuss two 
sources of error which affect it and which, although they may be 
made as small as one wishes in theory, render it Jess suitable for 
the search after the law of approach to saturation, although they 
do not take away from its value as a method of comparing in the 
same field two successive and slightly differing states of the same 
substance. 
Influence of inhomogeneity of the field. 
The ellipsoid is placed in the centre of a magnetic field possessing 
the symmetry of a body of revolution. The strength of the field at 
this centre is a maximum for a displacement in the plane of the 
equator, y, and a minimum for a displacement in the direction of 
the x axis. It it given by the series 
. 
which, remembering the equation AF=0 for the magnetic potential 
V, and converting to polar coordinates r and 6, transforms into 
J ) P. Weiss, Joum. de Phys. 4 ser. t. VI, p. 655, 1907. 
®) For comparing the intensities of magnetization I and I 7 at two temperatures 
we have to take into account that v — m/d, m being the mass of eflipsoid and 
, . I |/M i/d a |/M l/cP 
d .ts density, so j, = p^,. and ^ ^. The dilatation at the low 
temperatures and therefore the proportion of d and d' being unknown, we have 
omitted the correction for the difference of this proportion and unity, the value of 
which may be estimated at 0,004. [Added in Translation]. 
Royal Acad. Amsterdam. Vol. XII. 
T4 
