THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
883 
The preceding history might vary a little in detail, according to the degree of 
viscosity which we attribute to the earth’s mass, and according as oceanic tidal friction 
is or is not, now and in the more recent past, a more powerful cause of change 
than bodily tidal friction. 
The argument reposes on the imperfect rigidity of solids, and on the internal friction 
of semi-solids and fluids ; these are verce causes. Thus changes of the kind here dis¬ 
cussed must be going on, and must have gone on in the past. And for this history of 
the earth and moon to be true throughout, it is only necessary to postulate a sufficient 
lapse of time, and that there is not enough matter diffused through space to materially 
resist the motions of the moon and earth in perhaps several hundred million years. 
It hardly seems too much to say that granting these two postulates, and the 
existence of a primeval planet, such as that above described, then a system would 
necessarily be developed which would bear a strong resemblance to our own. 
A theory, reposing on verce causes, which brings into quantitative correlation the 
lengths of the present day and month, the obliquity of the ecliptic, and the inclination 
and eccentricity of the lunar orbit, must, I think, have strong claims to acceptance. 
But if this has been the evolution of the earth and moon, then a similar process 
must have been going on elsewhere. The present investigation has only dealt with a 
single satellite and the sun, but the theory may of course be extended, with some 
modification, to planets attended by several satellites. I will now therefore consider 
some of the other members of the solar system. 
A large planet has much more energy of rotation to be destroyed, and moment of 
momentum to be redistributed than a small one, and therefore a large planet ought 
to proceed in its evolution more slowly than a small one. Therefore we ought to find 
the larger planets less advanced than the smaller ones. 
The masses of such of the planets as have satellites are, in terms of the earth’s 
mass, as follows: Mars =i 1 u -; Jupiter =301; Saturn =90; Uranus =14; Neptune =16. 
Mars should therefore be furthest advanced in its evolution, and it is here alone in 
the whole system that we find a satellite moving orbitally faster than the planet 
rotates. This will also be the ultimate fate of our moon, because, after the moon’s 
orbital motion has been reduced to identity with that of the earth’s rotation, solar 
tidal friction will further reduce the earth’s angular velocity, the tidal reaction on the 
moon will be reversed, and the moon’s orbital velocity will increase, and her distance 
from the earth will diminish. But since the moon’s mass is very large, the moon must 
recede to an enormous distance from the earth, before this reversal will take place. 
Now the satellites of Mars are very small, and therefore they need only to recede a 
short distance from the planet before the reversal of tidal reaction.* 
* In tLe graphical method of treating the subject, “ tbe line of momentum ” 
“the curve of rigidity.” See Proc. Roy. Soc., No. 197, 1879. 
will only just intersect 
