September 1, 1905.] 



SCIENCE. 



259 



Imagine, then, a sun round, which there 

 moves in a circle a single large planet. I 

 will call this planet Jove, because it may 

 be taken as a representative of our largest 

 planet, Jupiter. Suppose next that a 

 meteoric stone or small planet is projected 

 in any perfectly arbitrary manner in the 

 same plane in which Jove is moving; then 

 we ask how this third body will move. It 

 appears that under the combined attrac- 

 tions of the sun and Jove the meteoric stone 

 will in general describe an orbit of extra- 

 ordinary complexity, at one time moving 

 slowly at a great distance from both the 

 sun and Jove, at other times rushing close 

 past one or other of them. As it grazes 

 past Jove or the sun it may often but just 

 escape a catastrophe, but a time will come 

 at length when it runs its chances too fine 

 and comes into actual collision. The indi- 

 vidual career of the stone is then ended by 

 absorption, and of course by far the greater 

 chance is that it will find its Nirvana by 

 absorption in the sun. 



Next let us suppose that instead of one 

 wandering meteoric stone or minor planet 

 there are hundreds of them, moving in- 

 itially in all conceivable directions. Since 

 they are all supposed to be very small, their 

 mutual attractions will be insignificant, and 

 they will each move almost as though they 

 were influenced only by the sun and Jove. 

 Most of these stones will be absorbed by 

 the sun, and the minority will collide with 

 Jove. 



When we inquire how long the career of 

 a stone may be, we find that it depends on 

 the direction and speed with which it is 

 started, and that by proper adjustment 

 the delay of the final catastrophe may be 

 made as long as we please. Thus by ma- 

 king the delay indefinitely long we reach 

 the conception of a meteoric stone which 

 moves so as never to come into collision 

 Math either body. 



There are, therefore, certain perpetual 



orbits in which a meteoric stone or minor 

 planet may move forever without collision. 

 But when such an immortal career has. 

 been discovered for our minor planet, it 

 still remains to discover whether the slight- 

 est possible departure from the prescribed 

 orbit will become greater and greater and 

 ultimately lead to a collision with the sun, 

 or Jove, or whether the body will travel sO' 

 as to cross and recross the exact perpetual, 

 orbit, always remaining close to it. If the 

 slightest departure inevitably increases as 

 time goes on, the orbit is unstable ; if, on 

 the other hand, it only leads to a 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 un- 

 stable ones are those which succumb in the 

 struggle for life, and the stable ones are 

 the species adapted to their environment. 



If, then, w^e 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 rub- 

 bish 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 sys- 

 tem in which the various orbits are ar- 

 ranged according to some definite law. 



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 or- 

 bits, and should thus obtain a rigorous me- 

 chanical explanation of Bode's law con- 

 cerning the planetary distances. 



In the fi.rst portion of my address I de- 

 scribed the orbits in which the corpuscles, 

 move in the atoms of matter, and drew 



