168 Kirkwood's Analogy in the Periods of 



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 par- 

 ticles of the ring, in order to preserve to all the condition of dynami- 

 cal 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 under- 

 gone 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, there- 

 fore, 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 hypothethis. 



" "We may extend the nebular hypothesis and Kirkwood's analogy 

 to the secondary system. If they are laws of nature, they nmst 

 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 Kirk- 

 wood's hypothesis, it would only be necessary that, upon the break- 

 ing 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 moi'e in harmony with the known elements of the system. The 



