"Such, then, is the present state of the question. Thirty-six elements of nine planets (four being hypothetical) appear to harmonize with Kirkwood's analogy in all the four fundamental equations of condition for each planet.
"To suppose that so many independent variable quantities should harmonize together by accident, is a more strained construction of the premises than the frank admission that they follow a law of nature.
"If, in the course of time, the hypotheses of Laplace and Kirkwood should be found to be the laws of nature, they will throw new light on the internal organization of the planets in their present, and in any more primitive, state through which they may have passed.
"For instance, we may compute the distance from the centre at which any planet must have received its projectile force, in order to produce, at the same time, its double movement of translation and rotation.
"If the planet, in a more primitive state, existed in the form of a ring revolving round the Sun, having its present orbit for that of the centre of gravity of the ring, the momentum of rotation must, by virtue of the principle of conservation of movement, have existed in some form in the ring. It is easy to perceive that this momentum is precisely the amount which must be distributed among the particles of the ring, in order to preserve to all the condition of dynamical equilibrium, while those of each generating surface of the ring were wheeling round with the same angular velocity.
"If the planets have really passed from the shape of a revolving ring to their present state, the prevalence of Kirkwood's analogy shews a nice adaptation of parts in every stage of the transition.
"If the primitive quantity of coloric (free and latent) had undergone a very great change beyond that now indicated in the cooling of their crusts; if the primitive quantity of movement of rotation had been different from its actual value for any planet; if the law of elasticity of particles for a given temperature and distance from each other varied from one planet to another in the primitive or present state; in either of these cases, the analogy of Kirkwood might have failed. As it is, no such failure is noticed; we are authorised, therefore, to conclude, that the primitive quantity of coloric, the law of elasticity, the quantity of movement of rotation, the past and present radii of percussion, the primitive diameter of the generating surface of the rings, and the present dimensions and density of the planets, have been regulated by a general law, which has fulfilled for all of them the four fundamental conditions of Kirkwood's hypothesis[N26].
“We may extend the nebular hypothesis and Kirkwood's analogy to the secondary system. If they are laws of nature, they must apply to both. In the secondary systems, the day and month are the same. This fact has remained hitherto unexplained. Lagrange shewed that if these values were once nearly equal, a libration sets in round a state of perfect equality; but he offered no conjecture as to the cause of the primitive equality. On the nebular and Kirkwood's hypothesis, it would only be necessary that, upon the breaking up of the ring, the primitive diameter of the generating figure and law of relative density of layers should be preserved.”
Professor Peirce, whose opinions will probably be regarded as of more value on such a subject than that of any other man in this country,—especially since his successful discussion with Leverrier,—remarked, that Kirkwood's analogy was the only discovery of the kind since Kepler's time that approached near to the character of his three physical laws. Bode's law, so called, was at best only an imperfect analogy. Kirkwood's analogy was more comprehensive, and more in harmony with the known elements of the system. The diameter of the sphere of attraction, a fundamental element in this analogy, now for the first time gave an appearance of reality to Laplace's nebular hypothesis which it never had before. The positive testimony in its favour would now outweigh the former negative evidence in the case, however strong it may have been. It follows at least from Kirkwood's analogy, that the planets were dependent upon each other, and therefore connected in their origin, whatever may have been the form of the connection, whether that of the nebular hypothesis, or some other not yet imagined.
At a later period of the meeting, M. B. A. Gould junior, stated that he had gone through the necessary calculations, using different quantities, and had come to the same conclusions as Mr Walker. He expressed his opinion, that at some future day the world will “speak of Kepler and Kirkwood as the discoverers of great planetary laws.”