time, distance, or weight.
Forces hardly suspected to exist by one generation are clearly
recognized by the next, and precisely measured by the third generation.[1]

[Footnote 1: Jevons: _Principles of Science_, p. 270.]

The history of science exhibits a constant progress from
rude guesses to precise measurement of quantities. In the
earliest history of astronomy there were attempts at quantitative
determinations, very crude, of course, in comparison
with the exactness of present-day scientific methods.

Every branch of knowledge commences with quantitative notions
of a very rude character. After we have far progressed, it is often
amusing to look back into the infancy of the science, and contrast
present with past methods. At Greenwich Observatory in the present
day, the hundredth part of a second is not thought an inconsiderable
portion of time. The ancient Chaldreans recorded an eclipse to
the nearest hour, and the early Alexandrian astronomers thought it
superfluous to distinguish between the edge and center of the sun.
By the introduction of the astrolabe, Ptolemy, and the later
Alexandrian astronomers could determine the places of the heavenly
bodies within about ten minutes of arc. Little progress then ensued
for thirteen centuries, until Tycho Brahe made the first great step
toward accuracy, not only by employing better instruments, but
even more by ceasing to regard an instrument as correct.... He
also took notice of the effects of atmospheric refraction, and
succeeded in attaining an accuracy often sixty times as great as that of
Ptolemy. Yet Tycho and Hevelius often erred several minutes in
the determination of a star's place, and it was a great achievement of
Roemer and Flamsteed to reduce this error to seconds. Bradley, the
modern Hipparchus, carried on the improvement, his errors in right
ascension, according to Bessel, being under one second of time, and
those of declination under four seconds of arc. In the present day
the average error of a single observation is probably reduced to the
half or the quarter of what it was in Bradley's time; and further
extreme accuracy is attained by the multiplication of observations,
and their skillful combination according to the theory of error. Some
of the more important constants... have been determined within
a tenth part of a second of space.[2]

[Footnote 2: _Ibid._, pp. 271-72.]

The precise measurement of quantities is important because
we can, in the f