e value of the
unit to which the measurements are referred by comparison with a
standard unit of the same kind. This is often described as the
_Standardization_ of the instrument, or the determination of the
_Reduction factor_. (2) The verification of the accuracy of the
subdivision of the scale of the instrument. This may be termed
calibration of the scale, and does not necessarily involve the
comparison of the instrument with any independent standard, but merely
the verification of the accuracy of the relative values of its
indications. In many cases the process of calibration adopted consists
in the comparison of the instrument to be tested with a standard over
the whole range of its indications, the relative values of the
subdivisions of the standard itself having been previously tested. In
this case the distinction of two parts in the process is unnecessary,
and the term calibration is for this reason frequently employed to
include both. In some cases it is employed to denote the first part
only, but for greater clearness and convenience of description we shall
restrict the term as far as possible to the second meaning.

The methods of standardization or calibration employed have much in
common even in the cases that appear most diverse. They are all
founded on the axiom that "things which are equal to the same thing
are equal to one another." Whether it is a question of comparing a
scale with a standard, or of testing the equality of two parts of the
same scale, the process is essentially one of interchanging or
substituting one for the other, the two things to be compared. In
addition to the things to be tested there is usually required some
form of balance, or comparator, or gauge, by which the equality may be
tested. The simplest of such comparators is the instrument known as
the _callipers_, from the same root as calibre, which is in constant
use in the workshop for testing equality of linear dimensions, or
uniformity of diameter of tubes or rods. The more complicated forms of
optical comparators or measuring machines with scales and screw
adjustments are essentially similar in principle, being finely
adjustable gauges to which the things to be compared can be
successively fitted. A still simpler and more accurate comparison is
that of volume or capacity, using a given mass of liquid as the gauge
or test of equality, which is the basis of many of the most accurate
and m