176 Mr. G. A. Schott on the 
temperature, since its velocity is exceedingly small in com- 
parison with c, the velocity of light. Hence w may be taken 
to mean the velocity of the centre of the ring relative to its 
position in the undisturbed atom. 
§ 7. Let the axis of the undisturbed ring be Oz ; the 
azimuth of the ith electron may be written in the form 
2iri 
cot + §-\- - — -, where h is an arbitrary angle ; its coordinates 
(#, y, z) , referred to axes fixed in the plane of the ring, are 
/ 2.TTl\ . / 2777 \ 
#=pcosi cot + 8 + - — I, y — p sinl cot + 8 + — ), z = Q. (4) 
When the ring is disturbed these coordinates are increased 
by terms of the form 
&V-— — f sin I cot + 8 + - — I — V cos ( cot + 8 -f- - — J 
By = f cos I cot + 8 + ^- J —7] sin I cot + $ + - — | 
^= f '.. ■ ' 
where f, ?;, ^ are the components of the displacement, sup- 
posed small and measured from the j:)osition that the electron 
would have occupied at the same time, if it had not been 
disturbed from steady motion. They may be expressed as 
the sums of functions of the type 
b • (S) 
Ae- Kt cos (qt - h — - + *\ 
where h is an integer between + ^, such that the number of 
nodes, and also of loops, in the disturbed ring is 2k. q is the 
frequency relative to the rotating ring, q + Leo that relative to 
an outside observer. 
§ 8. The particular type of disturbance we have to consider 
is that due to a constant external magnetic force h, which 
we shall suppose makes an angle 6 with the axis of the 
undisturbed ring, the axis being drawn to correspond to a 
right-handed rotation. We shall choose the arbitrary angle a. 
so that h lies in the plane of xz ; then the components of h 
are (A sin 6, 0, h cos 0). Assuming the usual expression for 
the mechanical force on a moving charge as given by the 
Maxwell-Lorentz theory, we find for the components of the 
force on the ith electron in the directions of the tangent, 
