250 
that 4 =0, C must be greater than A. Then the body can perform 
a vibration consisting in periodical changes of the angle 9, and for 
infinitely small amplitudes we find the frequency : 
Pilly. C—A a 
Wiid Wd tia (5) 
If there are circulating electrons we shall have to introduce new 
parameters in addition to the angles y and 9. For these parameters 
we choose the angles wp, measured from a fixed point in the path 
of each electron towards its momentary position. 
The kinetic energy will now contain a part corresponding to (1) 
which depends on # and g and which we shall call 7. But besides 
it will contain two parts 7, and 7, to which we shall soon refer. 
As to 7, it is the question, whether when there are moving 
electrons, the moments of inertia A, B, C will perhaps depend on 
w, so that they are no longer constants. 
For the sake of simplicity we suppose the iron core to be mag- 
netized to saturation, so that all the molecular axes are directed 
along the axis of the coil, while the circular currents are perpendi- 
cular to this line. We neglect the heat motion which would prevent 
this perfect orientation. 
To caleulate the moment of inertia with respect to one of the 
axes OX, OY, OZ for an electron, moving in a circle with the 
center J/, we draw through Ma line parallel to the axis considered. 
‘The moment of inertia with respect to this line can easily be cal- 
culated and from it we deduce the required moment of inertia by 
a well known rule. It is evident, that the part contributed to A 
by the circulating electrons will not depend on the positions in 
their paths, but will have a constant value. 
On the contrary, the part contributed by one circulating electron 
to B and C (i.e. to the moments of inertia with respect to the 
axes in the plane of the cirele) will change continually. But as 
soon as there are in each circle more than two electrons, at fixed 
distances from each other (so that one angle y determines the 
positions of them all) the terms in B and C due to them will have 
constant value. This is easily seen. Let » electrons circulate in the 
path. Their moment of inertia with respect to a diameter of the 
circle is proportional to 
; : 2m ; An 
sin® Fn | w + — |H sn {[yt——]....= 
. n n 
an 4a 
= |x — em 20 —cos2| w + — |— cos2| wp + — ae 
n n 
