In this connection it must, however, be pointed out, in the first
instance, that the eclipses which occur in any particular year are in
no way associated with those which occurred in the previous year. In
other words, the mere fact that an eclipse takes place upon a certain
day this year will not bring about a repetition of it at the same time
next year. However, the nicely balanced behaviour of the solar system,
an equilibrium resulting from aeons of orbital ebb and flow, naturally
tends to make the members which compose that family repeat their ancient
combinations again and again; so that after definite lapses of time the
same order of things will _almost exactly_ recur. Thus, as a consequence
of their beautifully poised motions, the sun, the moon, and the earth
tend, after a period of 18 years and 10-1/3 days,[5] to occupy very
nearly the same positions with regard to each other. The result of this
is that, during each recurring period, the eclipses comprised within it
will be repeated in their order.

To give examples:--

The total solar eclipse of August 30, 1905, was a repetition of that of
August 19, 1887.

The partial solar eclipse of February 23, 1906, corresponded to that
which took place on February 11, 1888.

The annular eclipse of July 10, 1907, was a recurrence of that of June
28, 1889.

In this way we can go on until the eighteen year cycle has run out, and
we come upon a total solar eclipse predicted for September 10, 1923,
which will repeat the above-mentioned ones of 1905 and 1887; and so on
too with the others.

From mere observation alone, extending no doubt over many ages, those
time-honoured watchers of the sky, the early Chaldeans, had arrived at
this remarkable generalisation; and they used it for the rough
prediction of eclipses. To the period of recurrence they give the name
of "Saros."

And here we find ourselves led into one of the most interesting and
fascinating by-paths in astronomy, to which writers, as a rule, pay all
too little heed.

In order not to complicate matters unduly, the recurrence of solar
eclipses alone will first be dealt with. This limitation will, however,
not affect the arguments in the slightest, and it will be all the more
easy in consequence to show their application to the case of eclipses of
the moon.

The reader will perhaps have noticed that, with regard to the repetition
of an eclipse, it has been stated that the conditions which bring it on
at e