yd by: Nae Prof. J. J. Thomson on the 
amount of positive electrification within a sphere of radius 6: 
At 
3 
thus ve/b? is equal to —, p, where p is the density of the 
positive electrification in the sphere: thus, if the density of 
the electrification be kept constant, the radius of the ring will 
be independent of the size of the sphere. Now let us take a 
Jarge sphere and place within it a ring of such a size that 
the ring would be in stable equilibrium if its centre were 
at the centre. of the sphere. To fix our ideas, let us take the 
case of three corpuscles at the corners of an equilateral 
triangle, and place this triangle so that its centre O’ is no 
longer at the centre of the sphere: we can easily see that the 
corpuscles will remain at the corners of an equilateral triangle 
of the same size, and that the triangle will move like a rigid 
body acted upon by a force proportional to the distance of 
its centre from O the centre of the sphere. To prove this 
we notice that the repulsion between the corpuscies is the 
same as when the centre of the triangle isat O. The attraction 
of the sphere on a corpuscle P is proportional to OP, and so 
may be resolved into two forces, one proportional to O'P 
along PO’ (O’ is the centre of the triangle) and the other 
proportional to OO’ acting along O’O. Now the corpuscles 
are by hypothesis in equilibrium under their mutual re- 
pulsions, and the attraction to the centre proportional to O’P: 
thus the relative position of the corpuscles will remain 
unaltered, and the system of three corpuscles will move as 
a rigid body under a central force acting on its centre of 
gravity proportional to the distance of that point from the 
centre of the sphere. 
The three corpuscles will, at a point whose distance from 
their centre is large compared with a side of the triangle, 
produce the same effect as if the charges on the three 
corpuscles were condensed at the centre of the triangle; they 
will thus at such points act like a unit, and the results we 
have previously obtained for single corpuscles may be ex- 
tended to the case when the single corpuscles are replaced 
by rings of corpuscles which would by themselves be in 
equilibrium. It should be noted that the atom in which 
these systems are placed must be large enough to allow these 
rings of corpuscles—sub-atoms we may call them, to be 
separated by distances considerably greater than the distance 
between the corpuscles in one of the rings. 
If we regard the atoms of the heavier elements as produced 
by the coalescence of lighter atoms, it is reasonable to suppose 
that the corpuscles in the heavier atoms may be arranged in 
secondary groups or sub-atoms, each of these groups acting 
