16 REPORT—1905. 
If the slightest departure inevitably increases as time goes on, the orbit 
is unstable ; if, on the other hand, it only leads toa slight waviness in the 
path described, it is stable. 
We thus arrive at another distinction : there are perpetual orbits, 
but some, and indeed most, are unstable, and these do not offer an 
immortal career for a meteoric stone ; and there are other perpetual 
orbits which are stable or persistent. The unstable ones are those which 
succumb in the struggle for life, and the stable ones are the species 
adapted to their environment. 
Tf, then, we are given a system of a sun and large planet, together 
with a swarm of small bodies moving in all sorts of ways, the sun and 
planet will grow by accretion, gradually sweeping up the dust and 
rubbish of the system, and there will survive a number of small planets 
and satellites moving in certain definite paths. The final outcome will be 
an orderly planetary system in which the various orbits are arranged 
according to some definite law. 
But the problem presented even by a system of such ideal simplicity 
is still far from having received a complete solution. No general plan for 
determining perpetual orbits has yet been discovered, and the task of dis- 
criminating the stable from the unstable is arduous. But a beginning 
has been made in the determination of some of the zones surrounding the 
sun and Jove in which stable orbits are possible, and others in which 
they are impossible. There is hardly room for doubt that if a complete 
solution for our solar system were attainable, we should find that 
the orbits of the existing planets and satellites are numbered amongst 
the stable perpetual orbits, and should thus obtain a rigorous mechanical 
explanation of Bode’s Jaw concerning the planetary distances. 
It is impossible not to be struck by the general similarity between the 
problem presented by the corpuscles moving in orbits in the atom, and 
that of the planets and satellites moving in a planetary system. It may 
not, perhaps, be fanciful to imagine that some general mathematical method 
devised for solving a problem of cosmical evolution may find another 
application to miniature atomic systems, and may thus lead onward to 
vast developments of industrial mechanics. Science, however diverse its 
aims, is a whole, and men of science do well to impress on the captains of 
industry that they should not look askance on those branches of investi- 
gation which may seem for the moment far beyond any possibility of 
practical utility. 
You will remember that I discussed the question as to whether the 
atomic communities of corpuscles could be regarded as absolutely eternal, 
and that I said that the analogy of other moving systems pointed to their 
ultimate mortality. Now the chief analogy which I had in my mind was 
that of a planetary system. 
The orbits of which I have spoken are only perpetual when the bodies 
are infinitesimal in mass, and meet with no resistance as they move. 
Now the infinitesimal body does not exist, and both Lord Kelvin and 
