THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
885 
the inclinations of the orbits to the proper planes appear to be very interesting from a 
theoretical point of view. They are as follows :— 
Satellite. 
First 
Second 
• Third 
F ourth 
Inclination of orbit 
to proper plane. 
o / // 
0 0 0 
0 27 50 
0 12 20 
0 14 58 
Now we have shown above that the orbit of a satellite is at first coincident with its 
proper plane, that the inclination afterwards rises to a maximum, and finally declines. 
If then we may assume, as seems reasonable, that the satellites are in stages of 
evolution corresponding to their distances from the planet, these inclinations accord 
well with the theory. 
The eccentricities of the orbits of the two inner satellites are insensible, those of the 
outer two small. This does not tell strongly either for or against the theory, because 
the history of the eccentricity depends considerably on the degree of viscosity of the 
planet; yet it on the whole agrees with the theory that the eccentricity should be 
greater in the more remote satellites. It appears that the satellites of Jupiter always 
present the same face to the planet, just as does our moon.t This was to be expected. 
The ca.se of Saturn is not altogether so favourable to the theory. The extremely 
rapid rotation, the ring, and the short periodic time of the inner satellites point to an 
early stage of development ; whilst the longer periodic time of the three outer satel¬ 
lites, and the high obliquity of the equator indicate a later stage. Perhaps both views 
may be more or less correct, for successive shedding of satellites would impart a 
modern appearance to the system. It may be hoped that the investigation of the 
effects of tidal friction in a planet surrounded by a number of satehites may throw 
some light on the subject. This I have not yet undertaken, and it appears to have 
peculiar difficulties. It has probably been previously remarked, that the Saturnian 
system bears a strong analogy with the solar system, Titan being analgous to Jupiter, 
Hyperion and Iapetus to Uranus and Neptune, and the inner satellites being analo¬ 
gous to the inner planets. Thus anything which aids us in forming a theory of the 
one system will throw light on the other.| 
The details of the Saturnian system seem more or less favourable to the theory. 
The proper planes of the orbits (except that of Iapetus) are nearly in the plane of the 
ring, and the inclinations of all the orbits to their proper planes appear not to be large. 
* Hbrschel’s ‘ Astron.’ Synoptic Tables in appendix. 
t Herschel’s ‘ Astron.’ 9th ed., § 546. 
t An investigation, now (September, 1880) almost completed, seems to show pretty conclusively that 
tidal friction cannot be in all cases the most important feature in the evolution of such systems as that 
of Saturn and his satellites, and the solar system itself. I am not however led to reject the views 
maintained in this paper. 
MDCCCLXXX. 5 X 
