( 4 ) 
M'-- 
16 
fflr 
(r= radius of the disc). 
The ratio -— of this couple for an angle of 45° to the fundamental 
M 
couple is 
M'_3 \by'), r . 
16 ( N,—N t )I 
If then we suppose that the relative change of the field in the 
space occupied by the ellipsoid is of the order of 1 in 1000, the 
formula given above shews us that although the disturbing couple is 
a little smaller than the chief couple, the two are of the same order 
of magnitude. Hence we see the great influence that this source of 
error can have in the investigation of weakly magnetic substances. 
(With ferro-magnetic bodies it is quite negligible: see the previous paper). 
We have accordingly devoted the greatest attention to this source 
of error. The conical pole-pieces were made slightly concave, during 
which process we every time determined the in homogeneity of the field 
by means of a ballistic galvanometer and a small coil that was slightly 
displaced. We ascertained that the change in the field in a space of 
about 1 c.c. was certainly less than 1 in 2000. We have not had 
time to pursue this investigation farther, and, besides, we should 
have to obtain a much more sensitive ballistic galvanometer. But it 
will be seen that the homogeneity of the field was sufficient for the 
comparative measurements we proposed to make. We may further 
remark that all these precautions refer exclusively to the conical 
pole-pieces; the experiments with the cylindrical pble-pieees were 
nearly free from these sources of error. 
We allow for these disturbing couples in the following way: 
Assuming that the expression for the couple due to 
inhomogeneity given above becomes (tf — 45°): 
which we shall represent by 
pKH* . 
If a is the angle of torsion of the holder and C the constant 
of the spring, then 
