or both of these two sources, yet
found themselves unable to assign how the demand was distributed
between the two conceivable sources of supply.

We are indebted to Professor Purser of Belfast for having indicated
the true dynamical principle on which the problem depends. It involves
reasoning based simply on the laws of motion and on elementary
mathematics, but not in the least involving questions of astronomical
observation. It would be impossible for me in a lecture like this to
give any explanation of the mathematical principles referred to. I
shall, however, endeavour by some illustrations to set before you what
this profound principle really is. Were I to give it the old name I
should call it the law of the conservation of areas; the more modern
writers, however, speak of it as the conservation of moment of
momentum, an expression which exhibits the nature of the principle in
a more definite manner.

I do not see how to give any very accurate illustration of what this
law means, but I must make the attempt, and if you think the
illustration beneath the dignity of the subject, I can only plead the
difficulty of mathematics as an excuse. Let us suppose that a
ball-room is fairly filled with dancers, or those willing to dance,
and that a merry waltz is being played; the couples have formed, and
the floor is occupied with pairs who are whirling round and round in
that delightful amusement. Some couples drop out for a while and
others strike in; the fewer couples there are the wider is the range
around which they can waltz, the more numerous the couples the less
individual range will they possess. I want you to realize that in the
progress of the dance there is a certain total quantity of spin at any
moment in progress; this spin is partly made up of the rotation by
which each dancer revolves round his partner, and partly of the
circular orbit about the room which each couple endeavours to
describe. If there are too many couples on the floor for the general
enjoyment of the dance, then both the orbit and the angular velocity
of each couple will be restricted by the interference with their
neighbours. We may, however, assert that so long as the dance is in
full swing the total quantity of spin, partly rotational and partly
orbital, will remain constant. When there are but few couples the
unimpeded rotation and the large orbits will produce as much spin as
when there is a much larger number of couples, for in the lat