886 
MR. G-. H. DARWIN ON THE SECULAR CHANGES IN 
Herschel gives the following eccentricities of orbit:— 
Tethys ‘04 (?), Dione '02 (?), Rhea ’02 (?), Titan ‘029314, Hyperion “rather large;” 
and he says nothing of the eccentricities of the orbits of the remaining three satellites. 
If the dubious eccentricities for the first three of the above are of any value, we seem 
to have some indication of the early maximum of eccentricity to which the analysis 
points ; but perhaps this is pushing the argument too far. The satellite Iapetus 
appears always to present the same face to the planet.* 
Concerning Uranus and Neptune there is not much to be said, as their systems are 
very little known ; but their masses are much larger than that of the earth, and their 
satellites revolve with a short neriodic time. The retroo-ade motion and high inch- 
nation of the satellites of Uranus are, if thoroughly established, very remarkable. 
The above theory of the inclination of the orbit has been based on an assumed small¬ 
ness of inclination, and it is not very easy to see to what results investigation might 
lead, if the inclination were large. It must be admitted however that the Uranian 
system points to the possibility of the existence of a primitive planet, with either 
retrograde rotation, or at least with a very large obliquity of equator. 
It appears from this review that the other members of the solar system present 
some phenomena which are strikingly favourable to the tidal theory of evolution, 
and none which are absolutely condemnatory. Perhaps by further investigations 
some light may be thrown on points which remain obscure. 
Appendix. 
(Added July, 1880.) 
A graphical illustration of the effects of tidal friction when the orbit of the 
satellite is eccentric. 
In a previous paper (Proc. Roy. Soc., No. 197, 1879+) a graphical illustration of the 
effects of tidal friction was given for the case of a circular orbit. As this method 
makes the subject more easily intelligible than the purely analytical method of the 
present paper, I propose to add an illustration for the case of the eccentric orbit. 
Consider the case of a single satellite, treated as a particle, moving in an elliptic 
orbit, which is co-planar with the equator of the planet. 
Let C h be the resultant moment of momentum of the system. Then with the 
notation of the present paper, by § 27 the equation of conservation of moment of 
momentum is 
n +f ( l —v) = h 
* Herschel’s ‘ Astron.’ 9tli ed., § 547. 
t The last sentence of this paper contains an erroneous statement; the line of zero eccentricity on the 
energy surface is not a ridge as there stated. See the figure on p. 890. 
