Notions of exact equality and of measure having been reached, there came to be definite ideas of relative magnitudes as being multiples one of another; whence the practice of measurement by direct apposition of a measure.  The determination of linear extensions by this process can scarcely be called science, though it is a step towards it; but the determination of lengths of time by an analogous process may be considered as one of the earliest samples of quantitative prevision.  For when it is first ascertained that the moon completes the cycle of her changes in about thirty days—­a fact known to most uncivilised tribes that can count beyond the number of their fingers—­it is manifest that it becomes possible to say in what number of days any specified phase of the moon will recur; and it is also manifest that this prevision is effected by an opposition of two times, after the same manner that linear space is measured by the opposition of two lines.  For to express the moon’s period in days, is to say how many of these units of measure are contained in the period to be measured—­is to ascertain the distance between two points in time by means of a scale of days, just as we ascertain the distance between two points in space by a scale of feet or inches:  and in each case the scale coincides with the thing measured—­mentally in the one; visibly in the other.  So that in this simplest, and perhaps earliest case of quantitative prevision, the phenomena are not only thrust daily upon men’s notice, but Nature is, as it were, perpetually repeating that process of measurement by observing which the prevision is effected.  And thus there may be significance in the remark which some have made, that alike in Hebrew, Greek, and Latin, there is an affinity between the word meaning moon, and that meaning measure.

This fact, that in very early stages of social progress it is known that the moon goes through her changes in about thirty days, and that in about twelve moons the seasons return—­this fact that chronological astronomy assumes a certain scientific character even before geometry does; while it is partly due to the circumstance that the astronomical divisions, day, month, and year, are ready made for us, is partly due to the further circumstances that agricultural and other operations were at first regulated astronomically, and that from the supposed divine nature of the heavenly bodies their motions determined the periodical religious festivals.  As instances of the one we have the observation of the Egyptians, that the rising of the Nile corresponded with the heliacal rising of Sirius; the directions given by Hesiod for reaping and ploughing, according to the positions of the Pleiades; and his maxim that “fifty days after the turning of the sun is a seasonable time for beginning a voyage.”  As instances of the other, we have the naming of the days after the sun, moon, and planets; the early attempts among Eastern nations to regulate the calendar so that the gods might not be offended by the displacement of their sacrifices; and the fixing of the great annual festival of the Peruvians by the position of the sun.  In all which facts we see that, at first, science was simply an appliance of religion and industry.