t that existing uncivilised races have made them--we come to the
first known astronomical records, which are those of eclipses. The
Chaldeans were able to predict these. "This they did, probably," says
Dr. Whewell in his useful history, from which most of the materials we
are about to use will be drawn, "by means of their cycle of 223 months,
or about eighteen years; for at the end of this time, the eclipses of
the moon begin to return, at the same intervals and in the same order as
at the beginning." Now this method of calculating eclipses by means of a
recurring cycle,--the _Saros_ as they called it--is a more complex case
of prevision by means of coincidence of measures. For by what
observations must the Chaldeans have discovered this cycle? Obviously,
as Delambre infers, by inspecting their registers; by comparing the
successive intervals; by finding that some of the intervals were alike;
by seeing that these equal intervals were eighteen years apart; by
discovering that _all_ the intervals that were eighteen years apart were
equal; by ascertaining that the intervals formed a series which repeated
itself, so that if one of the cycles of intervals were superposed on
another the divisions would fit. This once perceived, and it manifestly
became possible to use the cycle as a scale of time by which to measure
out future periods. Seeing thus that the process of so predicting
eclipses is in essence the same as that of predicting the moon's monthly
changes, by observing the number of days after which they repeat--seeing
that the two differ only in the extent and irregularity of the
intervals, it is not difficult to understand how such an amount of
knowledge should so early have been reached. And we shall be less
surprised, on remembering that the only things involved in these
previsions were _time_ and _number_; and that the time was in a manner
self-numbered.

Still, the ability to predict events recurring only after so long a
period as eighteen years, implies a considerable advance in
civilisation--a considerable development of general knowledge; and we
have now to inquire what progress in other sciences accompanied, and was
necessary to, these astronomical previsions. In the first place, there
must clearly have been a tolerably efficient system of calculation. Mere
finger-counting, mere head-reckoning, even with the aid of a regular
decimal notation, could not have sufficed for numbering the days in a
year; much less t