1884.] Ill [Klrkwood. 



The process would be similar when one period of Jupiter was equal to two 

 rotation periods of the central nebula. 



■ VIII. The Rotations of the Planets. — It is well known that the analogy 

 between the periods of rotation of the primary planets, as published by 

 the present writer several years since, assigned a much longer period of 

 rotation to Uranus than to Jupiter or Saturn. But as that of Uranus had 

 not been measured, and the observations of the polar compression were 

 by no means accordant, the fact was not then thought incompatible with 

 the proposed law of rotation. Recent measurements, however, leave no 

 room to doubt that the ellipticity is even greater than that of Jupiter, and 

 consequently that the planet moves rapidly on its axis. The law con- 

 necting the rotation periods must accordingly require an important modi- 

 fication. 



In a planet having a constant mass, with a variable volume, the time of 

 rotation varies as the square of the radius. It is easy to show, however, 

 that this law could not have obtained from the origin of the solar system. 

 For instance, in tracing backward the history of the earth, we find that 

 when the radius was 8000 miles, its rotation period, according to this law, 

 was 96 hours; when the former was 12,000 miles, the latter was 216 

 hours ; and, finally, if the earth ever extended to the moon's orbit, the 

 time of rotation, by the same law, instead of having been equal to the 

 moon's orbital period, was nearly ten years. So likewise when Mars 

 filled the orbit of Phobos, his rotation period was 7 days and 16 hours, or 

 24 times the orbital period of the satellite. We conclude, therefore, that 

 during the earlier stages of its condensation all parts of the mass did not 

 rotate in the same time. It is easy to see, in fact, that tidal retardation 

 must have been much more eftective at the surface than in the interior ot 

 a large planet in the gaseous state. 



In so fiir as we know, the rotation period of the smaller planets. Mer- 

 cury, Venus, the Earth and Mars, are nearly two and a half times those 

 of the larger and more remote. What cause can be assigned for this re- 

 markable difFerence ? In other words, why did the process of condensa- 

 tion continue longer in the large and less dense planets exterior to the 

 asteroids than in the small bodies nearer the sun ? It may be answered in 

 a general way that in small and dense planets solidification would occur 

 at a comparatively early epoch in their history, and hence the acceleration 

 of their rotary velocity would be, in a large measure, arrested. It seems 

 probable, therefore, that, while the same law of rotation may obtain be- 

 tween the members of each separate group, it cannot apply where one of 

 the planets is in the inner and the other in the outer cluster. 



As regards their axial movements, the solar system appears to contain 

 at least three distinct classes of planetary bodies ; the obvious characteris- 

 tics of each being traceable to their relative primitive densities. These 

 are as follows, the primitive density of Neptune being taken as unity : 



