August 31, 1905] 



NATURE 



441 



does really exactly confirm the hypothesis of Laplace, for 

 1 imagine that what we see indicates a spiral rather than 

 ^ ring-like division of nebulae.' 



This is not the time to pursue these considerations 

 further, but enough has been said to show that the nebular 

 hypothesis cannot be considered as a connected intelligible 

 whole, however much of truth it may contain. 



In the first theory which I sketched as to the origin 

 of the sun and planets, we supposed them to grow by the 

 accretions of meteoric wanderers in space, and this hypo- 

 thesis is apparently in fundamental disagreement with 

 .the conception of Laplace, who considered the transform- 

 ations of a continuous gaseous nebula. Some years ago 

 a method occurred to me by which these two discordant 

 schemes oF origin might perhaps be reconciled. A gas is 

 not really continuous, but it consists of a vast number of 

 molecules moving in all directions with great speed and 

 frequently coming into collision with one another. Now 

 I have ventured to suggest that a swarm of meteorites 

 would, by frequent collisions, form a medium endowed 

 •with so much of the mechanical properties of a gas as 

 would satisfy Laplace's conditions. If this is so, a nebula 

 may be regarded as a quasi-gas, the molecules of which 

 are meteorites. The gaseous luminosity which undoubtedly 

 is sent out by nebulze would then be due only to incan- 

 descent gas generated by the clash of meteorites, while 

 the dark bodies themselves would remain invisible. Sir 

 Norman Lockyer finds spectroscopic evidence which led 

 him long ago to some such view as this, and it is certainly 

 ■of interest to find in his views a possible means of re- 

 conciling two apparently totally discordant theories." How- 

 ever, I do not desire to lay much stress on my suggestion, 

 for without doubt a swarm of meteors could only maintain 

 the mechanical properties of a gas for a limited time, and, 

 as pointed out by Prof. Chamberlin, it is difficult to under- 

 stand how a swarm of meteorites moving indiscriminately 

 in every direction could ever have come into existence. 

 But my paper may have served to some extent to suggest 

 to Chamberlin his recent modification of the nebular hypo- 

 thesis, in which he seeks to reconcile Laplace's view with 

 a meteoritic origin of the planetary system." 



We have seen that, in order to explain the genesis of 

 planets according to Laplace's theory, the rings must be 

 ill-balanced or even broken. If the ring were so far from 

 being complete as only to cover a small segment of the 

 whole circumference, the true features of the occurrences 

 in the births of planets and satellites might be better re- 

 presented by conceiving the detached portion of matter 

 to have been more or less globular from the first, rather 

 than ring-shaped. Now this idea introduces us to a group 

 of researches whereby mathematicians have sought to 

 explain the birth of planets and satellites in a way which 

 might appear, at first sight, to be fundamentally different 

 from that of Laplace. 



The solution of the problem of evolution involves the 

 search for those persistent or stable forms which biologists 

 would call species. The species of which I am now going 

 to speak may be grouped in a family, which comprises all 

 those various forms which a mass of rotating liquid is 

 capable of assuming under the conjoint influences of gravi- 

 tation and rotation. If the earth were formed throughout 

 of a liquid of the same density, it would be one of the 

 species of this family ; and indeed these researches date 

 back to the time of Newton, who was the first to explain 

 the figures of planets. 



The ideal liquid planets we are to consider must be re- 

 garded as working models of actuality, and inasmuch as 

 the liquid is supposed to be incompressible, the conditions 

 depart somewhat widely from those of reality. Hence, 

 when the problem has been solved, much uncertainty 

 remains as to the extent to which our conclusions will be 

 applicable to actual celestial bodies. 



We begin, then, with a rotating liquid planet like the 

 earth, which is the first stable species of our family. We 

 next impart in imagination more rotation to this planet, 



1 Prof. Ch.imberlin, of ChicagOj has recently proposed a modified form 

 of the nebular hypothesis, in which he contends that the spiral form is 

 po'mal. See " Year Book," No. 3, for 1904, of the Carnegie Institution of 

 Washington, pp. 195-258. 



- Newcomb considers the objections to Lockyer's theory insuperable. 

 See p. 190 of " The Stars." (London : John Murray, 1904.) 



•* See preceding reference to Chamberlin's paper. 



NO. 1870, VOL. 72] 



and find by mathematical calculation that its power of 

 resistance to any sort of disturbance is less than it was. 

 In other words, its stability declines with increased rota- 

 tion, and at length we reach a stage at which the stability 

 just vanishes. At this point the shape is a transitional 

 one, for it is the beginning of a new species with different 

 characteristics from the first, and with a very feeble degree 

 of stability or power of persistence. As a still further 

 amount of rotation is imparted, the stability of the new 

 species increases to a maximum and then declines until a 

 new transitional shape is reached and a new species comes 

 into existence. In this way we pass from species to species 

 with an ever-increasing amount of rotation. 



The first or planetary species has a circular equator like 

 the earth ; the second species has an oval equator, so that 

 it is something like an egg spinning on its side on a table ; 

 in the third species we find that one of the two ends of 

 the egg begins to swell, and that the swelling gradually 

 becomes a well-marked protrusion or filament. Finally 

 the filamentous protrusion becomes bulbous at its end, and 

 is only joined to the main mass of liquid by a gradually 

 thinning neck. The neck at length breaks, and we are 

 left with two separated masses which may be called planet 

 and satellite. It is fair to state that the actual rupture 

 into two bodies is to some extent speculative, since mathe- 

 maticians have hitherto failed to follow the whole process 

 to the end. 



In this ideal problem the successive transmutations of 

 species are brought about by gradual additions to the 

 amount of rotation with which the mass of liquid is 

 endowed. It might seem as if this continuous addition 

 to the amount of rotation were purely arbitrary and could 

 have no counterpart in nature. But real bodies cool and 

 contract in cooling, and, since the scale of magnitude on 

 which our planet is built is immaterial, contraction will 

 produce exactly the same effect on shape as augmented 

 rotation. I must ask you, then, to believe that the effects 

 of an apparently arbitrary increase of rotation may be 

 produced by cooling. 



The figures which I succeeded in drawing, by means of 

 rigorous calculation, of the later stages of this course of 

 evolution, are so curious as to remind one of some such 

 phenoinenon as the protrusion of a filament of protoplasm 

 from a mass of living matter, and I suggest that we may 

 see in this almost life-like process the counterpart of at 

 least one form of the birth of double stars, planets, and 

 satellites. 



As I have already said, Newton determined the first of 

 these figures ; Jacobi found the second, and Poincar^ in- 

 dicated the existence of the third, in a paper which is 

 universally regarded as one of the masterpieces of applied 

 mathematics ; finally I myself succeeded in determining 

 the exact form of Poincare's figure, and in proving that it 

 is a true stable shape. 



My Cambridge colleague Jeans has also made an 

 interesting contribution to the subject by discussing a 

 closely analogous problem, and he has besides attacked the 

 far more difficult case where the rotating fluid is a com- 

 pressible gas. In this case also he finds a family of 

 types, but the conception of coinpressibility introduced a 

 new set of considerations in the transitions from species to 

 species. The problem is, however, of such difficulty that 

 he had to rest content with results which were rather 

 qualitative than strictly quantitative. 



This group of investigations brings before us the process 

 of the birth of satellites in a more convincing form than 

 was possible by means of the general considerations 

 adduced by Laplace. It cannot be doubted that the sup- 

 posed Laplacian sequence of events possesses a consider- 

 able element of truth, yet these latter schemes of trans- 

 formation can be followed in closer detail. It seems, then, 

 probable that both processes furnish us with crude models 

 of reality, and that in some cases the first and in others 

 the second is the better representative. 



The moon's mass is one-eightieth of that of the earth, 

 whereas the mass of Titan, the largest satellite in the 

 solar system, is 1/4600 of that of Saturn. On the ground 

 of this great difference between the relative magnitudes 

 of all other satellites and of the moon, it is not unreason- 

 able to suppose that the mode of separation of the moon 

 froiTi the earth mav also have been widely different. The 



