250 M. Werner Siemens on the 
tioned :—If an iron cylinder of radius 7, regarded as of infinite 
length, is, anywhere sufficiently far from the ends, encircled by 
a coil of wire, and if we denote by y the magnetic moment 
which a current flowing through this coil gives to the unit 
section at any desired distance « from the centre of the coil, then 
the magnetic moment of this section is 7°my. This magnetic 
moment must become smaller as w increases, and, if our theory 
is correct, by so much as is connected with the moment of the 
layer of air in contact with it, or the increment dz. Hence 
the differential equation 
—rndy=2rrdzy, 
Bila 
Oo ® 
lid yy? e 
log y Te Nees 
holds good if ¢ denote the interval for which integration is to 
be performed, or 
Uae 
log ag C, 
and for equal displacement, with rods of different diameters 
2r and 2p, 
loo” : loo =p: r. 
OSG oS Te 
These equations show, first, that for the same iron cylinder 
the ratio of the magnetic moments of two sections equally 
distant from each other is constant upon the whole halt- 
cylinder ; that therefore also equal displacements of a test coil 
must always result in equal percentage decrease in magnetic 
moment. They show, further, that with rods of different thick- 
ness, and for equal displacement of the test-coil, the logarithms 
of the ratio of moments vary inversely as the diameter of the 
rods. In writing the differential equation, however, the as- 
sumption is made that the moment of the layer of air in con- 
tact with the surface of the rod depends only on the moment 
of the unit section of the rod at the point in question. ‘This 
would mean that the resistance to magnetic disturbance of all 
external magnetic circuits was the same. But in fact the 
disturbing action takes place between each element of the 
surface of one half of the rod and all the oppositely magnetic 
points of the other half. It is therefore also dependent on the 
distance from the centre of the rod. This source of error will 
become so much the more important the less the distance from 
