5. M. Comte, of Paris, has proved, according to principles 

 by which periods of rotation maintain a relation to the mass 

 of the given rotating body, that the sidereal year of each planet 

 actually corresponds to the period in which the sun must have 

 rotated on his axis, supposing his mass to have extended to 

 the orbits of such planets ; and he also ascertained that the 

 periods of rotation of the primary planets with their mass, in 

 a state of vapor, extending to the orbits of their satellites, 

 must, in like manner, have corresponded with the present or- 

 bitual periods of those satellites. 



6. A new planetary law has recently been discovered by 

 Mr. Kirkwood, which seems to have an important bearing on 

 the question at issue. This law, as I understand it, is, that 

 the square of the number of rotations of any given planet in its 

 year, is to the square of the number of rotations of any other 

 planet in its year, as the cube of the diameter of the sphere 

 of attraction of the first planet, is to the cube of the diameter 

 of the sphere of attraction of the second planet.* Thus, for 

 instance, the number of rotations of the earth in its year, bears 

 a definite relation to the quantity of matter (or the amount of 

 attractive force) in the Earth, in Mars, and in Venus. 



Here, then, is an indication of another relation existing be- 

 tween the forces and movements of the different planets, so 

 definite as to preclude every reasonable supposition that it 

 came by chance, and a relation which, in common with facts 

 before noticed, seems to refer all the planets to a common 

 parentage, and common law of production, which is accounted 

 for only by the nebular theory. Certainly so many remark- 



* The sphere of attraction of a planet, is a circle whose radius is determined by the 

 point between two contiguous planets in conjunction, where an object would be at- 

 tracted to neither of them, but would be exactly poised between the two contending 

 forces. For an account of Kirkwood's discovery, see Silliman's American Journal of 

 Science, Vol. ix., Second Series, p. 395. 



