We have made the foregoing examination because, when we began our work, the general idea was that, according to the nebular hypothesis, the material for the formation of each planet was abandoned by the ideal nebula in a distinct and separate mass from any other--we are not at all sure, however, that this was Laplace's idea. This, we found out, could not be the case when we attempted to give some sort of separate or distinct form to the matter out of which Neptune was supposed to have been formed; and when we became convinced that all the matter abandoned by the nebula, from first to last, must have been thrown off in one continuous and, most probably, uninterrupted sheet. This, of course, makes us think of how the division of the sheet into separate rings was brought about, for there must have been absolute separation between them, otherwise separate planets could not have been made out of the sheet; and the only explanation that can be given is, that it must have depended on the quantity of matter that was abandoned, in nearly equal times, at different periods of the operation; for the areolar law precludes the idea of there having been very rapid changes in the rate of rotation of the nebula, and certainly of its decrease at any period as long as condensation and contraction went on. Whereas, although the sheet thrown off may have been continuous, we have no reason to suppose that it was of constant volume or density from beginning to end of the operation; in fact, we have already seen that its density was constantly increasing, and have suggested, in the reversal of Bode's law, that the differences in dimensions and densities of the planets have arisen, from irregularity in the quantities of matter abandoned from time to time. This irregularity could only arise from the mode of construction of the nebula, and from the forms it assumed during condensation, as we shall attempt to show in due time. Meanwhile we can conclude that the region of greatest density in any of our nebulæ had no influence whatever on the position of the orbit of the planet that was formed out of it.
We have shown, very clearly we believe, at page 109, from quotations--at second hand--from his own exposition of his hypothesis, that Laplace considered that condensation could only take place at the surface, or in the atmosphere as he called it, of his nebula, on account of its being possible only after radiation into space of part of its excessive heat; and that consequently there could be no acceleration of rotation in the nebula, due to the areolar law, except where there was condensation. On the other hand, in our cold hollow-sphere nebula, condensation could only take place at the region of greatest density, or greatest mass, which must be always very much nearer to the surface than to the centre; so that in both cases, equally, the abandoning of matter under the influence of centrifugal force would be virtually the same, and no further remarks are called for, on our part, on that head.