ter case
the diminished freedom will lessen the quantity of spin produced by
each individual pair. It will sometimes happen too that collision will
take place, but the slight diversions thus arising only increase the
general merriment, so that the total quantity of spin may be
sustained, even though one or two couples are placed temporarily _hors
de combat_. I have invoked a ball-room for the purpose of bringing out
what we may call the law of the conservation of spin. No matter how
much the individual performers may change, or no matter what
vicissitudes arise from their collision and other mutual actions, yet
the total quantity of spin remains unchanged.

Let us look at the earth-moon system. The law of the conservation of
moment of momentum may, with sufficient accuracy for our present
purpose, be interpreted to mean that the total quantity of spin in the
system remains unaltered. In our system the spin is threefold; there
is first the rotation of the earth on its axis, there is the rotation
of the moon on its axis, and then there is the orbital revolution of
the moon around the earth. The law to which we refer asserts that the
total quantity of these three spins, each estimated in the proper way,
will remain constant. It matters not that tides may ebb and flow, or
that the distribution of the spin shall vary, but its total amount
remains inflexibly constant. One constituent of the total amount--that
is, the rotation of the moon on its axis--is so insignificant, that
for our present purposes it may be entirely disregarded. We may
therefore assert that the amount of spin in the earth, due to its
rotation round its axis, added to the amount of spin in the moon due
to its revolution round the earth, remains unalterable. If one of
these quantities change by increase or by decrease, the other must
correspondingly change by decrease or by increase. If, therefore, from
any cause, the earth began to spin a little more quickly round its
axis, the moon must do a little less spin; and consequently, it must
shorten its distance from the earth. Or suppose that the earth's
velocity of rotation is abated, then its contribution to the total
amount of spin is lessened; the deficiency must therefore be made up
by the moon, but this can only be done by an enlargement of the moon's
orbit. I should add, as a caution, that these results are true only on
the supposition that the earth-moon system is isolated from all
external interference