(661 ) 
horizontal asymptote will be found. This was shown clearly in some 
of the foregoing experiments. If the field is constant the disturbing 
couple increases with I. Therefore, if in the measurements with the 
greatest values of 1 for which the experiments are carried out, made 
with a certain apparatus the disturbing couple does not make its 
presence felt, then a fortiori is it negligible for the smaller values 
of 1. The last equation shows that the relative value of the couple 
for non-uniformity of the field increases as the intensity diminishes. 
Hence it is to be feared particularly when one works with small 
magnetizations, and when, to increase the sensitivity of the apparatus, 
the torsion spring is replaced by a weaker one. 
For the purposes of our measurements it is sufficient to get an 
idea of the order of magnitude of the error. For this purpose the 
non-uniformity of the field was measured for three different values 
of y; it was found to be proportional to y* with t? = 0.0087 as factor. 
With a = 0.15 it follows that — = 0.00023 -—- . For the 
M (A T j — iV,) I 
ellipsoids used iV, =1.90 and AT =5.59, and {N\ — JSF t ) I is almost 
6600 gauss for iron and 1800 gauss for nickel. Hence, for iron the 
correction is scarcely 1 in 1000, while for nickel it increases to 
some thousandths. 
Reaction of the ellipsoid on the pole-pieces. 
When the ends of the ellipsoid come into the immediate neigh¬ 
bourhood of the end surfaces of the poles, they exert a noticeable 
influence upon the distribution of magnetism 'in the pole-pieces, and 
the couple becomes increased thereby. This fact was established by 
previous experiments with a larger electromagnet with flat pole-pieces 
of 15 cm. diameter. In these experiments was measured the couple 
exerted upon an ellipsoid with various distances between the poles 
by a field of the constant value of 9770 gauss regulated each time 
by passing the required current. In this way the following values 
were obtained for an iron ellipsoid 9 mm. long and 4 mm. thick. 
Distance between poles Maximum couple 
335.6 
320.45 
319.32 
319.18 
319.08 
