Kirkwood. ] 1 66 [Oct. 6, 
The preceding table of the primary system seems to indicate the de- 
pendence of the periods of Mars and the earth on the powerful mass of 
Jupiter. The relations expressed between the periods of the earth, Venus, 
and Mercury are sufficiently obvious. It is worthy of remark that the 
original distances of the exterior planets have been, in all probability, 
sensibly diminished. While the solar nebula was undergoing the process 
of condensation all cometary and meteoric matter attracted towards its 
centre, would, if the perihelion distance were considerably less than the 
radius of the nebula, become incorporated with the central body. This 
growth of the solar mass would produce a shortening of the periodic times 
of all planets previously formed. 
The approximations to commensurability in the secondary systems are 
still more striking, and must produce the impression in every inquiring 
mind that they are not without their physical significance. 
The rings of Saturn formerly supposed to be solid and continuous, are 
now regarded as consisting of an indefinite number of extremely small 
satellites. They are, in short, a compact cluster of secondary asteroids, 
analogous to the primary zone between Mars and Jupiter. In the latter, 
it is true, a large proportion of the primitive matter has collected in dis- 
tinct, planetary masses ; while a similar result has been prevented in the 
Saturnian rings by their proximity to the central body. In one respect» 
however, we observe a striking correspondence. It has been shown that 
several positions occur in the asteroid zone where planetary periods would 
have simple relations of commensurability with the period of Jupiter, 
and that portions of the original ring occupying these positions would be 
liable to great disturbance. Now, the ring of Saturn is evidently subject 
to like perturbation by the nearest satellites. Hence gaps or chasms, 
analogous to those in the zone of asteroids, ought also to be found in the 
secondary ring. It has accordingly been noticed that Cassini’s, or rather 
Ball’s division occurs precisely where the periods of satellites would be 
commensurable with those of the four members of the system immediately 
exterior.* 
But astronomers have sometimes seen the ring of Saturn apparently 
separated by several black lines into concentric annuli. At other times, 
however, no such divisions could be detected. The fact, therefore, of the 
permanence of these gaps is extremely doubtful, except in the case of a 
division of the exterior bright ring. This has been frequently seen by ° 
eminent astronomers ; and it is probable, though not absolutely certain, 
that it is never entirely closed. Most observers agree in placing it out- 
side of the middle of the exterior ring. Let us now inquire whether any 
simple relation of commensurability obtains between the periods of satel- 
lites revolving at the distance of this outermost gap, and those of Mimas, 
Enceladus, Tethys, and Dione. 
4 of the period of Mimas — 12" 56 
2 . Tethys = 12 57 
* Meteoric Astronomy, Chap. XII, 
