440 



NA TURE 



[August 31, 1905 



us either practically or theoretically, for the solar system 

 contains in itself other seeds of decay which will probably 

 bear fruit long before the occurrence of any serious dis- 

 turbance of the kind of which I speak. 



Before passing on to a new topic I wish to pay a tribute 

 to the men to whom we owe the recent great advances 

 in theoretical dynamical astronomy. As treated by the 

 master-hands of Lagrange and Laplace and their 

 successors, this branch of science hardly seemed to afford 

 scope for any great new departure. But that there is 

 always room for discovery, even in the most frequented 

 paths of knowledge, was illustrated when, nearly thirty 

 years ago. Hill of Washington proposed a new method of 

 treating the theory of the moon's motion in a series of 

 papers which have become classical. I have not time to 

 speak of the enormous labour and great skill involved in 

 the completion of Hill's Lunar Theory, by Ernest Brown, 

 whom I am glad to number amongst my pupils and 

 friends ; for I must confine myself to other aspects of 

 Hill's work. 



The title of Hill's most fundamental paper, namely, 

 " On Part of the Motion of the Lunar Perigee," is almost 

 comic in its modesty, for who would suspect that it con- 

 tains the essential points involved in the determination of 

 perpetual orbits and their stability? Probably Hill him- 

 self did not fully realise at the time the full importance 

 of what he had done. Fortunately he was followed by 

 Poincar^, who not only saw its full meaning but devoted 

 his incomparable mathematical powers to the full theo- 

 retical development of the point of view I have been laying 

 before you. 



Other mathematicians have also made contributions to 

 this line of investigation, amongst whom I may number 

 ray friend Mr. Hough, chief assistant at the Royal Observ- 

 atory of Cape Town, and myself. But without the work 

 of our two great forerunners we should still be in utter 

 darkness, and it would have been impossible to give even 

 this slight sketch of a great subject. 



The theory which I have now explained points to the 

 origin of the sun and planets from gradual accretions of 

 meteoric stones, and it makes no claim to carry the story 

 back behind the time when there was already a central 

 condensation or sun about which there circled another 

 condensation or planet. But more than a century ago 

 an attempt had already been made to re-construct the 

 history back to a yet remoter past, and, as we shall see, 

 this attempt was based upon quite a different supposition 

 as to the constitution of the primitive solar system. I 

 myself believe that the theory I have just explained, as 

 well as that to which I am coming, contains essential 

 elements of truth, and that the apparent discordances will 

 some day be reconciled. The theory of which I speak 

 is the celebrated nebular hypothesis, first suggested by 

 the German philosopher Kant, and later re-stated in- 

 dependently and in better form by the French mathe- 

 matician Laplace. 



Laplace traced the origin of the solar system to a nebula 

 or cloud of rarefied gas congregated round a central con- 

 densation which was ultimately to form the sun. The 

 whole was slowly rotating about an axis through its 

 centre, and, under the combined influences of rotation 

 and of the mutual attraction of the gas, it assumed a 

 globular form, slightly flattened at the poles. The justifi- 

 ability of this supposition is confirmed by the observations 

 of astronomers, for they find in the heavens many nebul;E, 

 while the spectroscope proves that their light at any rate 

 is derived from gas. The primeval globular nebula is un- 

 doubtedly a stable or persistent figure, and thus Laplace's 

 hypothesis conforms to the general laws which I have 

 attempted to lay down. 



The nebula must have gradually cooled by radiation 

 into space, and as it did so the gas must necessarily have 

 lost some of its spring or elasticity. This loss of power 

 of resistance then permitted the gas to crowd more closely 

 towards the central condensation, so that the nebula con- 

 tracted. The contraction led to two results, both inevit- 

 able according to the laws of mechanics : first, the central 

 condensation became hotter; and, secondly, the speed of 

 its rotation became faster. The accelerated rotation led 

 to an increase in the amount of polar flattening, and the 

 nebula at length assumed the form of a lens, or of a 

 NO. 1870, VOL. 72] 



disc thicker in the middle than at the edges. Assuming 

 the existence of the primitive nebula, the hypothesis may 

 be accepted thus far as practically certain. 



From this point, however, doubt and difliculty enter 

 into the argument. It is supposed that the nebula became 

 so much flattened that it could not subsist as a continuous 

 aggregation of gas, and a ring of matter detached itself 

 from the equatorial regions. The central portions of the 

 nebula, when relieved of the excrescence, resumed the 

 more rounded shape formerly possessed by the whole. As 

 the cooling continued the central portion in its turn became 

 excessively flattened through the influence of its increased 

 rotation ; another equatorial ring then detached itself, and 

 the whole process was repeated as before. In this way the 

 whole nebula was fissured into a number of rings surround- 

 ing the central condensation, the temperature of which 

 must by then have reached incandescence. 



Each ring then aggregated itself round some nucleus 

 which happened to exist in its circumference, and so formed 

 a subordinate nebula. Passing through a series of trans- 

 formations, like its parent, this nebula was finally replaced 

 by a planet with attendant satellites. 



The whole process forms a majestic picture of the history 

 of our system. But the mechanical conditions of a rotating 

 nebula are too complex to admit, as yet, of complete 

 mathematical treatment ; and thus, in discussing this theory, 

 the physicist is compelled in great measure to adopt the 

 qualitative methods of the biologist, rather than the 

 quantitative ones which he would prefer. 



The telescope seems to confirm the general correctness 

 of Laplace's hypothesis. Thus, for example, the great 

 nebula in Andromeda presents a grand illustration of what 

 we may take to be a planetary system in course of form- 

 ation. In it we see the central condensation surrounded 

 by a more or less ring-like nebulosity, and in one of the 

 rings there appears to be a subordinate condensation. 



Nevertheless it is hardly too much to say that every 

 stage in the supposed process presents to us some difficulty 

 or impossibility. Thus we ask whether a mass of gas of 

 almost inconceivable tenuity can really rotate all in one 

 piece, and whether it is not more probable that there would 

 be a central whirlpool surrounded by more slowly-moving 

 parts. Again, is there any sufficient reason to suppose 

 that a series of intermittent efforts would lead to the 

 detachment of distinct rings, and is not a continuous out- 

 flow of gas from the equator more probable? 



The ring of Saturn seems to have suggested the theory 

 to Laplace ; but to take it as a model leads us straight 

 to a quite fundamental difficulty. If a ring of matter ever 

 concentrates under the influence of its mutual attraction, 

 it can only do so round the centre of gravity of the whole 

 ring. Therefore the matter forming an approximately 

 uniform ring, if it concentrates at all, can only fall in on 

 the parent planet and be re-absorbed. Some external force 

 other than the mutual attraction of the matter forming 

 the ring, and therefore not provided by the theory, seems 

 necessary to effect the supposed concentration. The only 

 way of avoiding this difliculty is to suppose the ring to 

 be ill-balanced or lop-sided ; in this case, provided the want 

 of balance is pronounced enough, concentration will take 

 place round a point inside the ring but outside the planet. 

 Many writers assume that the present distances of the 

 planets preserve the dimensions of the primitive rings ; but 

 the argument that a ring can only aggregate about its 

 centre of gravity, which I do not recollect to have seen 

 before, shows that such cannot be the case. 



The concentration of an ill-balanced or broken ring on 

 an interior point would necessarily generate a planet with 

 direct rotation — that is to say, rotating in the same direc- 

 tion as the earth. But several writers, and notably Faye, 

 endeavour to show — erroneously as I think — that a retro- 

 grade rotation should be normal, and they are therefore 

 driven to make various complicated suppositions to explain 

 the observed facts. But I do not claim to have removed 

 the difliculty, only to have shifted it; for the satellites of 

 Neptune, and presumably the planet itself, have retrograde 

 rotations ; and, lastly, the astonishing discovery has just 

 been made by William Pickering of a ninth retrograde 

 satellite of Saturn, while the rotations of the eight other 

 satellites, of the ring and of the planet itself, are direct. 

 Finally, I express a doubt as to whether the telescope 



