After the discoveries that a lunation occupies nearly thirty days, and that some twelve lunations occupy a year—­discoveries of which there is no historical account, but which may be inferred as the earliest, from the fact 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 the years, months, and days between eclipses.  Consequently there must have been a mode of registering numbers; probably even a system of numerals.  The earliest numerical records, if we may judge by the practices of the less civilised races now existing, were probably kept by notches cut on sticks, or strokes