The nebula then quickened its pace until a stage was reached at which centrifugal speed could no longer be controlled by gravity; separation became inevitable, and an equatorial ring was abandoned, which thenceforward revolved on its own account in the period conformed to by the undivided mass at the epoch of its secession. This was the first of many subsequent crises of instability, each eventuating in the detachment of a nebulous ring. These rings, however, were regarded as merely transitional forms. They survived, just for illustrative purposes, in the Saturnian system; elsewhere they broke up into fragments, which ultimately coalesced into globes, and the globes were embryo planets. There was, indeed, a hitch in the line of argument which did not escape the acumen of the French geometer. The direction of the axial movement imparted to the members of the solar family depended essentially upon the relative velocities of the portions of matter brought together for their construction. If the inner sections of the self-shaping mass moved faster than the outer, the resulting rotation should have been retrograde; if slower, direct rotation would have ensued. Now, in a ring like that of Saturn, composed of discrete particles, linear speed decreases continuously outward, each of its minutest constituents obeying independently Kepler's law of periods and distances. Such a formation, since it would necessarily have yielded backward-spinning planets, would have been unfit for the purpose in view, and Laplace accordingly substituted an annulus endowed with a considerable amount of cohesion, and capable of rotating, like a solid, in a single period. It is true that such unanimity of movement was incompatible with the other postulated conditions; but the anomaly escaped notice for above half a century. Professor Darwin has moreover pointed out[10] that a ring of matter distributed with any approach to uniformity must concentrate, if at all, round its own centre of gravity. It should accordingly collapse upon, and become re-absorbed by, the parent-body. If markedly unsymmetrical and ill-balanced, its materials might certainly collect at an interior point more or less remote from the centre; but in no case could the focus of condensation be situated in any part of the annular circumference, where it was located by Laplace.