558 



NATURE 



[June 30, 192 1 



to take as our starting point the most famous 

 theory of cosmogony ever propounded — the 

 nebular hypothesis of Laplace — and we shall ex- 

 amine to what extent it remains tenable in the 

 light of modern observational and theoretical 

 research. 



Laplace's hypothesis referred primarily to the 

 genesis of the solar system, which he believed to 

 have originated out of a hot nebulous mass that 

 shrank as it cooled. The nebula was supposed 

 to be in rotation, so that the principle of con- 

 servation of angular momentum required that as 

 the mass cooled its speed of rotation should in- 

 crease. It is well known that a mass either of 

 gas or of liquid in rotation cannot rest in equi- 

 librium in the spherical shape which would be 

 assumed in the absence of rotation. If the rota- 

 tion is very slow the equilibrium shape will be 

 an oblate spheroid of small eccentricity. As the 

 rotation increases, the ellipticity will increase, but 

 it is found that the spheroidal shape is soon de- 

 parted from. Laplace believed, as a matter of con- 

 jecture rather than of reasoned proof, that with 

 continually increasing rotation a mass of gas 

 would in time reach a stage at which it coujd 

 no longer exist as a single continuous mass. 

 When this stage was reached he believed that a 

 ring of particles would be discharged from the 

 equator through the centrifugal force of rotation 

 outweighing the centripetal force of gravitation. 

 The mathematical researches of Roche (1873) pro- 

 vided some support for this general conjecture, 

 and more recent investigations put its general 

 accuracy beyond doubt. 



It is found that the changes of shape which 

 accompany increase of rotation are, in their 

 general features, the same for all masses, 

 whether gaseous or fluid, provided only that there 

 is sufficient central condensation of mass. When 

 the rotation becomes so great that the spheroidal 

 figure is departed from, the equator of the mass 

 is found to pull out into a pronounced edge which 

 ultimately becomes perfectly sharp (see Fig. i). 

 The mass has now assumed a lenticular shape, 

 and any further increase of rotation results in 

 matter being discharged from this sharp edge. 

 The lenticular shape is retained from now on, the 

 sharp edge acting like a safety valve and emit- 

 ting just so much matter as is necessary to carry 

 off the excess of angular momentum beyond the 

 maximum which can be carried by the central 

 mass.. Fig. i shows the configurations of the 

 lenticular figures for masses of gas in adiabatic 

 equilibrium, in which y (ratio of specific heats) 

 has the extreme values 12 and 22 respectively. 

 Other calculated lenticular figures show generally 

 similar shapes. With a further increase of rota- 

 tion beyond that for which these curves are 

 drawn, the figures would remain unaltered save 

 for the addition of a distribution of matter in the 

 equatorial plane — the matter already thrown off 

 from the sharp edge of the lens. 



If gaseous stars assume these forms our tele- 

 scopes refuse to reveal them. Even in the most 

 powerful telescopes the stars remain infinitesimal 

 NO. 2696, VOL. 107] 



points of light; the only bodies which show any 

 observable shape are the nebulae. It is highly 

 significant that a number of these exhibit pre- 

 cisely the lenticular shape just described. This 

 is in most cases accompanied by a distribution 

 of matter in the plane through the sharp edge 

 of the lens. A number of such nebulae have been 

 found by direct spectroscopic observation to be 

 in rotation about an axis perpendicular to this 

 plane. Thus there is very strong justification for 

 supposing that these nebulae are masses of gas or 

 other matter with high central condensation be- 

 having precisely as imagined by Laplace — rotating 

 and throwing off their excess of angular 

 momentum as they cool by the ejection of matter 

 in their equatorial planes. 



There is, however, almost incontrovertible evi- 

 dence that the nebulae which have just been de- 

 scribed are nothing but ordinary spiral nebulae 

 seen edgewise, for observation discloses a con- 

 tinuous sequence of nebulae the shapes of which 

 bridge completely the gap between the lenticular 

 nebulae, in which we are looking at right angles 

 to the axis of rotation, and the familiar spiral 

 nebula in which we look approximately along this 

 axis. The characteristic nebula shows a nucleus 

 which we can now identify with the lenticular 



Fig. I.— Figures of equilibrium for rotating masses of gas. 



figure demanded by theory, having two arms 

 emerging symmetrically from opposite points of 

 the nucleus. If our identification is correct these 

 arms must be formed out of the matter already 

 discharged from the nucleus. It has in point of 

 fact been found by van Maanen and Kostinsky 

 that the matter in the arms appears to be in 

 motion approximately along the arms and in the 

 outward direction. 



Any external gravitational field, whether of the 

 universe as a whole or of neighbouring stars or 

 nebulae, would produce a tidal field similar to 

 that produced by the sun and moon on the surface 

 of our earth, a field specified mathematically by 

 a second harmonic. This field, no matter how 

 small in amount, would suffice to destroy the exact 

 circular shape of the " equator " of the nucleus 

 and so would concentrate the emission of matter 

 at two opposite points on this equator. Thus it 

 is easy to understand why the nebulae, as a rule, 

 exhibit two symmetrical arms emerging from 

 antipodal points. It is very much less easy to 

 understand why these arms should be of the uni- 

 versal spiral form — the absence of any explana- 

 tion of this form must be regarded as a serious 

 drawback to our interpretation of the spiral 

 nebulae. It is readily proved that the ejected 

 filaments of matter, whatever the shape they 

 assume, could not remain of uniform line-density. 



