Structure of the Atom. 269 
as a unit. When the corpuscles are done up in bundles in 
this way, it is possible to have stability when these bundles 
are arranged in a ring with a smaller number of corpuscles 
inside than when the corpuscles in the bundles are arranged 
at equal intervals round the circumference of the ring. 
Thus, take the case of a ring of 30 corpuscles; if these 
were arranged at equal intervals, 101 corpuscles would .be 
required inside the ring to make it stable. If, however, the 
30 corpuscles were grouped in ten sets of three each, oualy 
3x38=9 corpuscles in the interior would be required to 
make the arrangement stable. 
Constitutzon of the Atom of a Radioactive Element. 
Our study of the stability of systems of corpuscles has 
made us acquainted with systems which are stable when the 
corpuscles are rotating with an angular velocity greater than 
a certain value, but which become unstable when the velocity 
falls below this value. Thus, to take an instance, we saw 
(p. 249) that four corpuscles can be stable in one plane at 
the corners of a square, if they are rotating with an angular 
velocity greater than °325ve*/mb*, but become unstable if the 
velocity falls below this velocity, the corpuscles in this case 
tending to place themselves at the corners of a tetrahedron. 
Consider now the properties of an atom containing a system 
of corpuscles of this kind, suppose the corpuscles were 
originally moving with velocities far exceeding the critical 
velocity ; in consequence of the radiation from the moving 
corpuscles, their velocities will slowly—very slowly—diminish; 
when, after a long interval, the velocity reaches the critical 
velocity, there will be what is equivalent to an explosion of 
the corpuscles, the corpuscles will move far away from their 
original positions, their potential energy will decrease, while 
their kinetic energy will increase. The kinetic energy 
gained in this way might be sufficient to carry the system 
out of the atom, and we should have, as in the case of radium, 
a part of the atom shot off. In consequence of the very slow 
dissipation of energy by radiation the life of the atom would 
be very long. We have taken the case of the four corpuscles 
as the type of a system which, like a top, requires for its 
stability a certain amount of rotation. Any system possessing 
this property would, in consequence of the gradual dissi- 
pation of energy by radiation, give to the atom containing 
it radioactive properties similar to those conferred by the four 
corpuscles. 
