ed from them, the weights will remain at _equal_
altitudes. And we may further notice how, in this first step of rational
mechanics, we see illustrated that truth awhile since referred to, that
as magnitudes of linear extension are the only ones of which the
equality is exactly ascertainable, the equalities of other magnitudes
have at the outset to be determined by means of them. For the equality
of the weights which balance each other in scales, wholly depends upon
the equality of the arms: we can know that the weights are equal only by
proving that the arms are equal. And when by this means we have obtained
a system of weights,--a set of equal units of force, then does a science
of mechanics become possible. Whence, indeed, it follows, that rational
mechanics could not possibly have any other starting-point than the
scales.

Let us further remember, that during this same period there was a
limited knowledge of chemistry. The many arts which we know to have been
carried on must have been impossible without a generalised experience of
the modes in which certain bodies affect each other under special
conditions. In metallurgy, which was extensively practised, this is
abundantly illustrated. And we even have evidence that in some cases the
knowledge possessed was, in a sense, quantitative. For, as we find by
analysis that the hard alloy of which the Egyptians made their cutting
tools, was composed of copper and tin in fixed proportions, there must
have been an established prevision that such an alloy was to be obtained
only by mixing them in these proportions. It is true, this was but a
simple empirical generalisation; but so was the generalisation
respecting the recurrence of eclipses; so are the first generalisations
of every science.

Respecting the simultaneous advance of the sciences during this early
epoch, it only remains to remark that even the most complex of them
must have made some progress--perhaps even a greater relative progress
than any of the rest. For under what conditions only were the foregoing
developments possible? There first required an established and organised
social system. A long continued registry of eclipses; the building of
palaces; the use of scales; the practice of metallurgy--alike imply a
fixed and populous nation. The existence of such a nation not only
presupposes laws, and some administration of justice, which we know
existed, but it presupposes successful laws--laws conforming in som