274 The Origin and Evolution of the Solar System [OH. xn 



To make the matter definite, let us suppose the mean radius r of the 

 original nebula to have been equal to the radius of Neptune's orbit, about 

 4'5xl0 14 cms. The total mass of the nebula being 2 x 10 33 grammes, the 

 mean density p must have been 5'5 x 10~~ 12 . From the table just given, p et 

 the density in the outer regions of the nebula must have been less than 

 O'OOlT times this, say less than 9 x 10~ 15 , whereas the density of the ejected 

 matter when condensation began must have been greater than 0'36/5 and so 

 greater than 2 x 10~ 12 . The ejected matter must have had a density more 

 than 200 times as great as the density in the outer regions of the nebula. 



If the ejected matter remained gaseous such an increase of density would 

 be unthinkable. It will, however, be remembered that we have already ( 211) 

 found reasons why the ring of matter imagined by Laplace could not be 

 gaseous. For Laplace's hypothesis to be saved, it seems to be necessary to 

 suppose that the ejected matter liquefied shortly after ejection so that the 

 planets were born in a liquid, or possibly even in a solid state*. 



This supposition is not objectionable in itself, but it leads into difficulties 

 when we proceed to the consideration of the further stages of evolution. 

 According to the Nebular Hypothesis, the planets shrunk further after their 

 birth, until the rotation had increased to such an extent that a further 

 break-up took place, resulting in the formation of satellites. Now if the 

 planets were born in the fluid state, it is impossible to imagine a further 

 shrinkage of anything like sufficient amount to effect a second break-up. 

 Using the relation o) 2 /27rjp = 0'36, and assigning to p the value already 

 assumed, namely 5'5 x 10~ 12 , it is found that the period of rotation of the 

 original nebula must have been about 35 years, and this must also have been 

 approximately the period of rotation of the planets when first born. It is 

 inconceivable that the planets, already fluid, should shrink until this period 

 was reduced to a few hours, which is the period necessary for rotational 

 break-up to occur in a fluid mass. Moreover, even if the inconceivable were 

 to happen, if this shrinkage took place and the planets broke up further, the 

 break-up of the fluid planets would necessarily be by fission into masses of 

 comparable size, and the final formation of the planets would be that of a 

 system of binaries of the well-known type. 



290. For the foregoing reasons, it seems probable, although by no means 

 certain, that we must abandon the Nebular Hypothesis of Laplace. Before 

 abandoning the rotational theory altogether, we ought perhaps to consider 

 the possibility, not contemplated by Laplace at all, of the ejected matter 

 being localised in one or two streams, as we imagined it to be in the forma- 

 tion of the spiral nebulae. 



* A modified form of the foregoing argument has been presented by Jeffreys (Monthly 

 Notices R.A.S. 78 (1918), p. 424), who arrives at the same conclusion as that stated here. 



