h that the total
moment of momentum must remain constant, therefore what is lost by the
rotation must be made up in the revolution; the orbit of Jupiter
around the sun must accordingly be swelling. So far the reasoning
appears similar to that which led to such startling consequences in
regard to the moon.

[Illustration: Fig. 5.--Comparative sizes of Planets.]

But now for the fundamental difference between the two cases. The
moon, it will be remembered, always revolves with the same face
towards the earth. The tides have ceased to operate there, and
consequently the moon is not able to contribute any moment of
momentum, to be applied to the enlargement of its distance from the
earth; all the moment of momentum necessary for this purpose is of
course drawn from the single supply in the rotation of the earth on
its axis. But in the case of the system consisting of the sun and
Jupiter the circumstances are quite different--Jupiter does not always
bend the same face to the sun; so far, indeed, is this from being
true, that Jupiter is eminently remarkable for the rapidity of his
rotation, and for the incessantly varying aspect in which he would be
seen from the sun. Jupiter has therefore a store of available moment
of momentum, as has also of course the sun. Thus in the sun and planet
system we have in the rotations two available stores of moment of
momentum on which the tides can make draughts for application to the
enlargement of the revolution. The proportions in which these two
available sources can be drawn upon for contributions is not left
arbitrary. The laws of dynamics provide the shares in which each of
the bodies is to contribute for the joint purpose of driving them
further apart.

Let us see if we cannot form an estimate by elementary considerations
as to the division of the labour. The tides raised on Jupiter by the
sun will be practically proportional to the sun's mass and to the
radius of Jupiter. Owing to the enormous size of the sun, the
efficiency of these tides and the moment of the friction-brake they
produce will be far greater on the planet than will the converse
operation of the planet be on the sun. Hence it follows that the
efficiency of the tides in depriving Jupiter of moment of momentum
will be greatly superior to the efficiency of the tides in depriving
the sun of moment of momentum. Without following the matter into any
close numerical calculation, we may assert that for every one part the