irst place, only through quantitative determinations
be sure we have made accurate observations, observations
uncolored by personal idiosyncrasies. Both errors of
observation and errors of judgment are checked up and
averted by exact quantitative measurements. The relations
of phenomena, moreover, are so complex that specific causes
and effects can only be understood when they are given precise
quantitative determination. In investigating the solubility
of salts, for example, we find variability depending on
differences in temperature, pressure, the presence of other salts
already dissolved, and the like. The solubility of salt in
water differs again from its solubility in alcohol, ether, carbon,
bisulphide. Generalization about the solubility of salt,
therefore, depends on the exact measurement of the phenomenon
under all these conditions.[1]

[Footnote 1: See Jevons, p, 279 ff.]

The importance of exact measurement in scientific discovery
and generalization may be illustrated briefly from one
instance in the history of chemistry. The discovery of the
chemical element _argon_ came about through some exact measurements
by Lord Rayleigh and Sir William Ramsay of the
nitrogen and the oxygen in a glass flask. It was found that
the nitrogen derived from air was not altogether pure; that
is, there were very minute differences in the weighings of
nitrogen made from certain of its compounds and the weight
obtained by removing oxygen, water, traces of carbonic acid,
and other impurities from the atmospheric air. It was found
that the very slightly heavier weight in one case was caused
by the presence of argon (about one and one third times as
heavy as nitrogen) and some other elementary gases. The
discovery was here clearly due to the accurate measurement
which made possible the discovery of this minute discrepancy.

It must be noted in general that accuracy in measurement
is immediately dependent on the instruments of precision
available. It has frequently been pointed out that the Greeks,
although incomparably fresh, fertile, and direct in their thinking,
yet made such a comparatively slender contribution to
scientific knowledge precisely because they had no instruments
for exact measurement. The thermometer made possible the
science of heat. The use of the balance has been in large part
responsible for advances in chemistry.

The degree to which sciences have attained quantitative
accuracy varies among the physical