act, we are at once reminded that
in early history, events are commonly recorded as occurring in certain
reigns, and in certain years of certain reigns: a proceeding which
practically made a king's reign a measure of duration.

And, as further illustrating the tendency to divide time by natural
phenomena and natural events, it may be noticed that even by our own
peasantry the definite divisions of months and years are but little
used; and that they habitually refer to occurrences as "before
sheep-shearing," or "after harvest," or "about the time when the squire
died." It is manifest, therefore, that the more or less equal periods
perceived in Nature gave the first units of measure for time; as did
Nature's more or less equal lengths and weights give the first units of
measure for space and force.

It remains only to observe, as further illustrating the evolution of
quantitative ideas after this manner, that measures of value were
similarly derived. Barter, in one form or other, is found among all but
the very lowest human races. It is obviously based upon the notion of
_equality of worth_. And as it gradually merges into trade by the
introduction of some kind of currency, we find that the _measures of
worth_, constituting this currency, are organic bodies; in some cases
_cowries_, in others _cocoa-nuts_, in others _cattle_, in others _pigs_;
among the American Indians peltry or _skins_, and in Iceland _dried
fish_.

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 ma