Before considering certain grave errors in the theory of Laplace, it may be remarked that Sir Isaac Newton had given much thought to the motions of the planets and satellites, espec daily remarking on the beautiful, orderly and symmetrical arrangement of the solar system; but he was unable to explain the orderly move ments of these bodies, except by supposing that they had been set revolving in their orbits by the immediate hand of the Deity. Laplace's theory had the great advantage, from a scien tific point of view, that for a teleological it substituted a mechanical explanation of the motions of the planets, in harmony with Her schel's observations of the nebula:. Notwith standing the fundamental error involved in the theory of detachment, the nebular hypothesis as a whole has guided our thought pretty much up to the present time. the difficulties en countered by the theory of Laplace have steadily increased, and of late years became so overwhelming that the old conceptions of rings detached by rotation have had to be entirely abandoned.
As the solar system was held to have re sulted from the condensation of a globular or planetary nebula, the subject of the nebular hypothesis is closely connected historically with the gravitational theory of the sun's heat. For a long time it was assumed by investigators that the sun was originally expanded into a nebula filling the planetary orbits, and rotating in equilibrium under the hydrostatic pressure and attraction of its parts. In order to keep this figure of equilibrium the temperature would have had to be enormous, and such a temperature really could not be maintained, owing to the extreme tenuity of the hypothetical nebula. For when the nebula extended to Neptune's orbit the average density would be 260,000,000 times less than that of atmospheric air at sea-level; and such a tenuous medium could exert no hydrostatic pressure from the centre outwards, for detaching the planets by increase of centrifugal force under accelerating rotation, as imagined by Laplace. This criticism against Laplace's theory was urged by Kirk wood and Peirce over 40 years ago, and such an objection is valid and convincing; but as there was no other suggested way in which the planetary bodies could be started revolving in their nearly circular orbits, it was not doubted that such detachment had occurred.
In 1861 the French physicist, Babinet, pointed out a fatal weakness of Laplace's theory which is now usually known as s criterion.D It is based on the mechanical prin ciple of the conservation of areas, so much ap plied by Laplace and other investigators since Newton's proof of the constancy of the areas described by any system of particles contract ing and accelerating its rotation under central forces. It readily follows from this principle
that whatever changes may take place in the system, its whole quantity of rotation must re main constant ; by this is meant that if the mass of each particle of the system is multiplied by the square of its distance from the central axis of rotation and also by its angular velocity, and if all the products thus obtained for the par ticles are added together, the sum will remain forever constant. Now it is possible to obtain a quite approximate value for this sum de rived from the actual system as we see it to day, for the masses of its various parts, their distances from the central axis, and their ob served angular velocities of motion are all known. Having found this quantity, we may proceed to test the Laplacian hypothesis in a great variety of ways, many of which lead to necessary assumptions which are not only quite incredible, but in some cases impossible.
For example, we may readily determine the period of rotation of the solar nebula when it extended outward to each of the planets suc cessively; by so doing we obtain the results given in the following table: Table showing the application of Babinees cri terion to the planets and satellites, when the Sun and planets are expanded to fill the orbits of the bodies revolving around them It will at once be noticed how greatly the num bers of the third column exceed those of the second. Should we suppose that Neptune, for example, could have been formed in this way it would be necessary to assume that the period of its ring was diminished from nearly 3,000,000 to but 165 years, notwithstanding that we can recognize no imaginable cause which could produce this diminution.
Babinet's criterion furnishes us with several other tests, some of them even more conclusive than this, of the impossibility of the material from which the planets are formed having been abandoned by the original nebula in the.,form of rings. If, overlooking these, we admit that a ring were abandoned, it can be shown that so far from the material of the ring ultimately being gathered into a single mass, the tidal ac tion of the central portion of the cloud would separate and scatter it, so that a ring would not even start to gather into a planet. But further than this, it can be shown that even if the greater part of the ring could be gathered into a single planet, it would be quite impossible for this mass to gather to itself the remaining parts of the ring.