222 CARNEGIE INSTITUTION OF WASHINGTON. 



ring of Saturn revolve about that planet in a little more than one-half 

 the time of the planet's rotation.* These are exceedingly trouble- 

 some facts from the viewpoint of the Laplacian hypothesis, for 

 under it the contraction of these planets, after they had shed their ' 

 secondaries, should have greatly accelerated their rotations, and these 

 should have become much shorter than the revolutions of the sec- 

 ondaries. Before Moulton's citation of the second case an attempt 

 was made to explain the case of Phobos by a supposed tidal retarda- 

 tion of the planet's rotation, but the Saturnian case appears to render 

 this explanation incompetent. f 



Under the hypothesis of growth from a nucleus by the addition of 

 planetesimals, the rotations of the planets were dependent largely on 

 the special phases of the impacts of the infalling planetesimals, and 

 no necessary relations between the rotation of a planet and the revo- 

 lution of its satellite are assignable. But if this be neglected, and 

 the rotation-period of the planetary nucleus be assumed to have been 

 originally the same as the revolution-period of the satellite's nucleus, 

 the growth of the mass of the planet must have drawn the satellite 

 nearer to itself and shortened the time of its revolution. If the 

 whole of the periodic difference between Mars and Phobos be due to 

 this cause, the growth of the nucleus of Mars is deducible from it. 

 Under this view the matter of the rings of Saturn may have been 

 satellite nuclei at the outset, and have been drawn within the Roche 

 limit by the growth of Saturn, and then disintegrated by tidal action 

 and distributed into the ring form. All other satellites should, 

 under this view, have been drawn toward their primaries during 

 the growth of the latter, and this may be a not unimportant factor 

 in their evolutionary history. 



The concurrent bearings of these two considerations are quite in 

 harmony with what might be gathered independently from a com- 

 parison of the apparent amounts of matter in the nebular knots with 

 the amounts in the nebular haze in existing nebulae. It was there- 

 fore assumed in my further study that the nuclei con.stituted only a 

 small portion of the mass of the grown planets. The fraction was 

 probably larger proportionally for the small planets than for the 

 large planets, for the power of growth probably rose with increased 

 mass in geometrical ratio. In the case of the asteroids and satellites 

 the growth may not have been large. 



* For a discussion of these phenomena, see "An Attempt to Test the Nebular 

 Hypothesis by an Appeal to the Laws of Mechanics," F. R. Moulton, Astrophys. 

 Jour., 1900, p. 109. 



t See Moulton's discussion, loc. cit., pp 109-110. 



