254 Prof. J. J. Thomson on the 
p for a series of values of nm are given in the following 
table :— 
m.. 0 6 4 8 9 1002202 tee 
PaO L 1 1) 2 Bg 359 ae eee 
For large values of n the values of p are proportional to. 
n’. When p is greater than one, the internal corpuscles 
necessary to produce equilibrium cannot all be at the centre: 
of the sphere, they will separate until their repulsions are 
balanced by the attraction of the positive electricity in the 
sphere. Thus when there are two internal corpuscles, as. 
when n=9, these two will separate and will form a pair with 
the line joining them parallel to the plane of the ring. If we 
assume, as is approximately the case, that the pair of equal 
corpuscles exerts at external points the same force as a double 
charge placed at a point midway between them, the preceding 
theory will apply, and the system consisting of the ring of 9 
and the pair of corpuscles will be in stable equilibrium. 
When n= 10, the internal corpuscles must be three in number ; 
these three will arrange themselves at the corners of an 
equilateral triangle, and the system of 13 corpuscles will 
consist of a ring of 10 and a triangle of 3, the planes of 
the ring and triangle being parallel but not coincident ; the 
corpuscles are all supposed to be in rapid rotation round the 
diameter of the sphere drawn at right angles to the planes of 
the rmg. For a ring of 12 corpuscles we require 7 inside, 
but 7 corpuscles, as we have seen, cannot form a single ring, 
but will arrange themselves as a ring of 6 with one at the 
centre. Thus the system of 19 corpuscles will consist of an 
outer ring of 12, an inner ring of 6 in a plane parallel to the 
outer ring, and one corpuscle along the axis of rotation. 
In this way we see that when we have a large number of 
corpuscles in rapid rotation they will arrange themselves as 
follows :—The corpuscles form a series of rings, the corpuscles 
in one ring being approximately in a plane at right angles. 
to the axis of rotation, the number of particles in the rings 
diminishing as the radius of the ring diminishes. If the 
corpuscles can move at right angles to the plane of their 
orbit, the rings will be in different planes adjusting themselves 
so that the repulsion between the rings is balanced by the 
attraction exerted by the positive electrification of the sphere 
in which they are placed. We have thus in the first place a 
sphere of uniform positive electrification, and inside this 
sphere a number of corpuscles arranged in a series of parallel 
rings, the number of corpuscles in a ring varying from ring 
to ring: each corpuscle is travelling at a high speed round 
