14 Preston—Radiating Phenomena in a Strong Magnetic Field. 
pairs of lines, like the great D pair of sodium, and Dr. Stoney’s object was te 
explain these pairs of lines. In the first place, he showed that if the disturbing 
forces exist which cause the orbit to revolve in its own plane, that is produce an 
apsidal motion, then each spectral line will become a pair of lines, and if WV be 
the frequency of the original line, that is the frequency of revolution of the ion in 
its orbit, and » the frequency of the apsidal revolution, then the frequencies of the 
new pairs will be V+n2 and N—n. ‘This is very easily deduced by Dr. Stoney 
from the expressions for the coordinates of the moving ion at any time 7. 
Thus, if a particle describes an elliptic orbit under a central force (law of 
direct distance) directed towards its centre, its coordinates at any instant may 
be written in the form 
=a cos Qt, y = 6 sin Qt, 
in which © is equal to 27N where WV is the frequency of revolution. But if, in 
addition, the orbit be forced to revolve round its own centre in its own plane 
with angular velocity w, then it is easily seen by projection that the coordinates 
at any time are— 
x =a cos Qt cos wt — b sin Qé sin wt, 
y =a cos Qt sin wt + 6 sin QE cos of; 
and these are equivalent to 
w= % (a+ b) cos (Q+ w) t+ 3 (a— 5) cos (Q—- w)t, 
ab 
( 
y=4(a+ b) sin (Q + w) t- 3 (a —- 6) sin (Q- wo) FZ, 
while these in turn are equivalent to the two opposite circular vibrations 
a, =4(a+b) cos (Q+w)t &, = 4 (a — b) cos (Q—w) ¢ 
i 
y= 3 (a+ 6)sin (Q + w) t Y2 = — 4 (a — 5) sin (Q-w) ¢ 
The resultant motion is consequently equivalent to two circular motions described 
in opposite senses, and of frequencies V + n and NV — n respectively. These 
circular motions will be polarised when the perturbating forces remain fixed in 
direction, and for this reason the doublets, &c., produced by the magnetic field 
are polarised. On the other hand, the doublets, &c., existing in natural spectra 
are not polarised, and this is what we should expect when we consider the effects 
of collisions. 
This is an analysis of the motion without any regard to the dynamical origin 
of it. It is merely postulated that certain perturbations exist, and their effects 
on the pure radiation frequencies are examined. If, however, we treat the 
question from a dynamical point of view, the equations of motion will exhibit the 
forces which are necessary to bring about the supposed motion. Thus, if a 
