prevision.

And this is the unexpressed difference which leads us to consider
certain orders of knowledge as especially scientific when contrasted
with knowledge in general. Are the phenomena _measurable_? is the test
which we unconsciously employ. Space is measurable: hence Geometry.
Force and space are measureable: hence Statics. Time, force, and space
are measureable: hence Dynamics. The invention of the barometer enabled
men to extend the principles of mechanics to the atmosphere; and
Aerostatics existed. When a thermometer was devised there arose a
science of heat, which was before impossible. Such of our sensations as
we have not yet found modes of measuring do not originate sciences. We
have no science of smells; nor have we one of tastes. We have a science
of the relations of sounds differing in pitch, because we have
discovered a way to measure them; but we have no science of sounds in
respect to their loudness or their _timbre_, because we have got no
measures of loudness and _timbre_.

Obviously it is this reduction of the sensible phenomena it represents,
to relations of magnitude, which gives to any division of knowledge its
especially scientific character. Originally men's knowledge of weights
and forces was in the same condition as their knowledge of smells and
tastes is now--a knowledge not extending beyond that given by the
unaided sensations; and it remained so until weighing instruments and
dynamometers were invented. Before there were hour-glasses and
clepsydras, most phenomena could be estimated as to their durations and
intervals, with no greater precision than degrees of hardness can be
estimated by the fingers. Until a thermometric scale was contrived,
men's judgments respecting relative amounts of heat stood on the same
footing with their present judgments respecting relative amounts of
sound. And as in these initial stages, with no aids to observation, only
the roughest comparisons of cases could be made, and only the most
marked differences perceived; it is obvious that only the most simple
laws of dependence could be ascertained--only those laws which, being
uncomplicated with others, and not disturbed in their manifestations,
required no niceties of observation to disentangle them. Whence it
appears not only that in proportion as knowledge becomes quantitative do
its previsions become complete as well as certain, but that until its
assumption of a quantitative character it is necessarily