August 25, 1910] 



NATURE 



'■6:> 



is perhaps more astonishing still, there is no descrip- 

 tion or statement of any kind about the septibranch 

 Pelecypoda. The statement that there are nephro- 

 stomes in Amphioxus needs correction, and the reten- 

 tion of the Ctenophora as a class of Coelenterata 

 justification. 



Several new figures have been introduced into the 

 ninth edition, and these are all of considerable value, 

 but it is a pitv that the only illustrations of the large 

 and important order of the Alcyonaria are copied from 

 the old, and in some respects incorrect, figures by de 

 I.acaze Duthiers of Coralliuni nibrum. It is very 

 desirable that a figure of a Pcnnatulid and some draw- 

 ings of Alcyonarian spicules should be added. A 

 better figure of Millepora should be found than that 

 which appears on p. 217. But with all these faults, 

 which are many when the book is critically examined, 

 there can be no question that in general scope and 

 breadth of treatment Hertwig's " Lehrbuch der 

 Zoologie " is one of the most notable of the text- 

 books of our times. 



COSMOGOW AND GEOPHYSICS. 

 Scientific Fapirs. By Sir George Howard Darwin, 

 K.C.B., F.R.S. ^'ol. iii., Figures of Equilibrium 

 of Rotating Liquid and Geophysical Investigations. 

 Pp. xvi + 527. (Cambridge: University Press, 1910.) 

 Price 15s. net. 



THIS volume opens with the well-l-cnown paper, 

 "On the Influence of Geological Changes on the 

 Earth's .'Vxis of Rotation " (1S77), 'i which Sir George 

 Darwin investigated whether it was possible for 

 known causes to produce a motion of the earth's axis 

 comparable with that required by geologists to account 

 for the supposed "Glacial period" in the earth's 

 history. The result is definitely established that any 

 change in the obliquity of the ecliptic which can have 

 been produced by gradual deformation of the earth's 

 shape is necessarily very small, about 1/2200 of a 

 second of arc at most. The possibilities of wanderings 

 of the pole are shown to be greater — from 1° to 3° in 

 each geological period is possible. Cumulative motions 

 of this type might account for the change since the 

 supposed Glacial period, but any such explanation 

 would be incompatible with the belief of geologists 

 that where the continents now stand thev have always 

 stood. 



This important paper is followed bv six shorter 

 ones, and the remaining eight papers, all of them 

 of extreme complexity, deal with figures of equilibrium 

 of rotating liquid. 



A mass of fluid left to itself will, of course, form 

 into a sphere under the gravitational action of its 

 parts. If set into rotation this sphere will flatten at 

 the poles, and Maclaurin showed that the flattened 

 bodies corresponding to all deforces of rotation may be 

 a series of spheriods so far as conditions of equili- 

 brium are concerned, although obviously the very flat 

 figures would be unstable. It has been known for 

 some time that these spheroids are not the only figures 

 of equilibrium. Jacobi found that certain ellipsoids 

 with three unequal axes were possible figures, while 

 NO. 2130, VOL. 84] 



Thomson and Tait pointed out that figures consisting 

 of one, two, or more rings may be figures of equili- 

 brium, although probably fev.' of these will be stable. 



The subject, of course, derives its great interest from 

 its bearing on the origin of stellar systems and on 

 Laplace's nebular hypothesis in particular; conse- 

 quently the question of stability or instabilitv is one of 

 e.\trem3 importance. As an actual nebula in space 

 loses its heat it will shrink in size, while keeping 

 its angular momentum constant. For abstract dis- 

 cussion it is easier to deal with a fictitious mass of 

 fluid of constant size, the anjjular momentum of 

 which continually increases. Unless some cataclysmic 

 breakdown occurs, this rotating mass must find for 

 itself a continuous path through series of configura- 

 tions of equilibrium all of which are stable. The 

 problem of fundamental importance for cosmogony is 

 that of discovering^- the far end of this path. Do we 

 see it represented, as Kant and Laplace may have 

 thought, in Saturn and his rings, or do we see it, as 

 Sir George Darwin and others now think probable, in 

 the earth-moon type of system ? Or does the path 

 lead only for a certain way through stable continuous 

 configurations, and then end in a cataclysm ? 



This is the problem on which Sir George Darwin 

 has for some years been leading the attack. Obviously 

 there are the two methods of trying to trace out the 

 path from the beginning to the end, and of trying to 

 guess at the end and construct the path back to the 

 beginning. Papers ix. and xv. of the present volume 

 are devoted to the latter method. If increased rota- 

 tion is going to lead to an earth-moon system, it ought 

 to be possible to trace back the earth-moon system 

 through diminishing rotation and through continuous 

 stable configurations to the initial spherical form. In 

 this connection. Sir George Darwin has directed atten- 

 tion to some almost overlooked, although highly im- 

 portant, work of Roche, who showed that a system 

 consisting of a planet with an infinitesimal satellite 

 in contact cannot be stable. He has accordingly 

 attempted to examine above what limit the ratio of 

 the masses of satellite to primary must lie for stability 

 to be ensured. No perfectly definite conclusion is 

 reached, but it seems as if the limit must be greater 

 than the ratios observed in the solnr system. This 

 somewhat nugatory result is disappointing, and sug- 

 gests that a better way of attacking the problem may 

 be the direct one of examining all possible series of 

 configurations, starting from the initial sphere. 



The only road which the fluid can take on leaving 

 the spherical form consists of the series of Maclaurin 's 

 spheroids, but this road is intersected by an infinite 

 number of cross-roads at different points ("points of 

 bifurcation "). At the first point of bifurcation, the 

 series of Maclaurin's spheroids loses its stability, and 

 the configurations represented on the cross-road 

 through this point are found to be stable. Moreover, 

 it appears that this particular cross-road represents 

 the well-known series of Jacobian ellipsoids. Poincar6 

 has shown that this road also is intersected by an 

 infinite number of cross-roads, and that the first of 

 these cross-roads represents a series of pear-shaped, 

 figures which look as though they might end by 



