August 31, 1905] 



NA rURE 



439 



undergone the dynamic action of an artificial whirlpool 

 in all points comparable with the dynamic action of a 

 torrential current of water, present all the characteristics 

 of the ancient river-gravels ; it is easy to find among 

 them, after a few minutes' search, all the most charac- 

 teristic forms of eoliths, such as are given as typical. 

 My colleagues and I have been able to make a collection 

 of flints admirably retouches, identical with the forms 

 called by M. Rutot hammer-stones, planes, notched flints. 

 Sic. We have also collected flints showing the cone of 

 percussion, which is generally regarded as an infallible 

 mark of intentional fashioning. 



T//E BRITISH ASSOCIATION. 



Inaugural Address by Prof. G. H. Darwin, M.A., 



LL.D., Ph.D., F.R.S., President of the Association. 



Part II.' 



Thus far we have been concerned with the almost in- 

 conceivably minute, and I now propose to show that 

 similar conditions prevail on a larger scale. 



Many geological problems might well be discussed from 

 my present point of view, yet I shall pass them by, and 

 shall proceed at once to Astronomy, beginning with the 

 smallest cosmical scale of magnitude, and considering after- 

 wards the larger celestial phenomena. 



The problems of cosmical evolution are so complicated 

 that it is well to conduct the attack in various ways at 

 the same time. Although the several theories may seem 

 to some e.vtent discordant with one another, yet, as I have 

 already said, we ought not to scruple to carry each to its 

 logical conclusion. We may be confident that in time the 

 false will be eliminated from each theory, and when the 

 true alone remains the reconciliation of apparent disagree- 

 ments will have become obvious. 



The German astronomer Bode long ago propounded a 

 simple empirical law concerning the distances at which 

 the several planets move about the sun. It is true that 

 the planet Neptune, discovered subsequently, was found to 

 be considerably out of the place which would be assigned 

 to it by Bode's law, yet his formula embraces so large 

 a number of cases with accuracy that we are compelled to 

 believe that it arises in some manner from the primitive 

 conditions of the planetary system. 



The explanation of the causes which have led to this 

 simple law as to the planetary distances presents an 

 interesting problem, and, although it is still unsolved, we 

 may obtain some insight into its meaning by considering 

 what I have called a working model of ideal simplicity. 



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. The conditions imposed 

 may seem simple, yet the problem has so far overtaxed 

 the powers of the mathematician that nothing approach- 

 ing 3 general answer to our question has yet been given. 

 We know, however, that under the combined attractions 

 of the sun and Jove the meteoric stone will in general 

 describe an orbit of extraordinary 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 individual 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 initially 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. 



1 Delivered at Johannesburg on August 30. The first part of the Address, 

 delivered at Cape Town on August 15, appeared in Nature of August 17. 



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 making the delay indefinitely long we reach the 

 conception of a meteoric stone which moves so as never 

 to come into collision with either body. 



There are, therefore, certain perpetual orbits in which 

 a meteoric stone or minor planet may move for ever with- 

 out collision. But when such an immortal career has been 

 discovered for our minor planet, it still remains to discover 

 whether the slightest possible departure from the pre- 

 scribed orbit will become greater and greater and ulti- 

 mately lead to a collision with the sun or Jove, or whether 

 the body will travel so as to cross and re-cross 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 per- 

 petual 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. 



If, 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 ot such 

 ideal simplicitv is still far from having received a complete 

 solution. No 'general plan for determining perpetual orbits 

 has yet been discovered, and the task of discriminating 

 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 law 

 concerning the planetary distances. . 



It is impossible not to be struck by the general similarity 

 between the problem presented bv 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 thev should not look askance on those 

 branches of investigation which may seem for the moment 

 far beyond any possibility of practical utility. 



You' will remember that I discussed the question ais to 

 whether the atomic communities of corpuscles could be 

 regarded as absolutelv 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 PoincariJ concur 

 in holding that disturbance will ultimately creep in_ to 

 any system of bodies moving even in so-called stable orbits ; 

 and this is so even apart from the resistance offered to 

 the moving bodies by any residual gas there may be 

 scattered through space, the stability is therefore only 

 relative, and a planetary system contains the seeds of its 

 own destruction. But this ultimate fate need not disturb 



NO. 1870, VOL. 72] 



