an endless series of cycles like a
circulating decimal. For the universe comprises everything; there could
therefore be no disturbance from without. Once a cycle, always a cycle.

Let us suppose the earth of given weight, moving with given momentum in a
given path, and under given conditions in every respect, to find itself
at any one time conditioned in all these respects as it was conditioned
at some past moment; then it must move exactly in the same path as the
one it took when at the beginning of the cycle it has just completed, and
must therefore in the course of time fulfil a second cycle, and therefore
a third, and so on for ever and ever, with no more chance of escape than
a circulating decimal has, if the circumstances have been reproduced with
perfect accuracy as to draw it into such a whirlpool.

We see something very like this actually happen in the yearly revolutions
of the planets round the sun. But the relations between, we will say,
the earth and the sun are not reproduced absolutely. These relations
deal only with a small part of the universe, and even in this small part
the relation of the parts _inter se_ has never yet been reproduced with
the perfection of accuracy necessary for our argument. They are liable,
moreover, to disturbance from events which may or may not actually occur
(as, for example, our being struck by a comet, or the sun's coming within
a certain distance of another sun), but of which, if they do occur, no
one can foresee the effects. Nevertheless the conditions have been so
nearly repeated that there is no appreciable difference in the relations
between the earth and sun on one New Year's Day and on another, nor is
there reason for expecting such change within any reasonable time.

If there is to be an eternal series of cycles involving the whole
universe, it is plain that not one single atom must be excluded. Exclude
a single molecule of hydrogen from the ring, or vary the relative
positions of two molecules only, and the charm is broken; an element of
disturbance has been introduced, of which the utmost that can be said is
that it may not prevent the ensuing of a long series of very nearly
perfect cycles before similarity in recurrence is destroyed, but which
must inevitably prevent absolute identity of repetition. The movement of
the series becomes no longer a cycle, but spiral, and convergent or
divergent at a greater or less rate according to circumstances.

We canno