12 Preston—Radiating Phenomena in a Strong Magnetic Field. 
not resolved clear of each other, but until this resolution is effected it remains 
possible that b, C may be a triplet. These lines are all in the ultra-violet part 
of the spectrum, and are weak, so that a prolonged exposure is necessary to bring 
out all the details. When the double-image prism is not employed they 
photograph as triplets, or rather as bands possessing three dense ribs; but this 
arises from the components of A overlapping the outer edges of B and C, while 
B and C@ overlap each other a little, and thus form the middle rib of the triplet. 
It appears, therefore, that if we can explain the production of the ordinary 
quartet form (fig. 2) we are on the high road to the explanation of all the other 
types of modification which the spectral lines suffer in the magnetic field. For 
this purpose, therefore, let us consider briefly the investigation set forth in 
Dr. Larmor’s paper, already cited. In this investigation he considers the case 
of a single ion describing an elliptic orbit under a central force directly 
proportional to the distance. The influence of the magnetie field upon this 
moving ion (supposed otherwise quite free from restraints) is such that its 
elliptic orbit is forced into precession round a line drawn through its centre in 
the direction of the lines of magnetic force. For the equations of motion of the 
ion moving round the centre of force in the magnetic field are, as a first 
approximation, the same as those which hold for a particle describing an elliptic 
orbit under a central force when the orbit is forced to precess or revolve round a 
line drawn through its centre in the direction of the lines of force. Thus the 
equations which determine the motions of the ion are— 
&=-— OPa + k (ny -— m3) 
y=- Oy+hk (& — ne) 
8 =— O's + k (me- ly) } 
(1), 
where / is a quantity depending on the strength of the field, and the ratio of the 
ionic charge to the inertia associated with it. While the equations of motion of 
a particle describing an elliptic orbit under a central force while the orbit is forced 
to precess with angular velocity » round a line whose direction cosines are /, m, n 
are easily found by taking as axes of reference a system of moving axes which 
revolve round /, m,n with angular velocity w, and are— 
@ = — Oa + 2w (ny — m8) + wa — w'l (le + my + 3) 
Yj =-— Oy + 2w (lB = n&) + wy — wm (le + my + nz) ee oe e((o)) 
8 =— O73 + 2w (me — ly) + ws — wn (le + my + nz) 
> is small enough to be neglected, and 
and these agree with equations (1), when 
if 2 be taken equal to /. 
If WV be the frequency of revolution of the ion in its orbit, and if be the 
frequency of the precessional revolution, then the combined movement is 
