# The New Student's Reference Work/Measurement

**Measurement** consists essentially in the
comparison of one quantity with another.
Thus the measurement of a length, which is
one of the simplest of all measurements,
consists in determining how many times greater
or less the given length is than some other
given length which we agree to take as a unit.
In like manner an interval of time is measured
by comparing it with the interval
which we employ as a unit, namely, the mean
solar day. Evidently, therefore, it is possible
to measure a quantity without
understanding much about that quantity. No
intelligent measurement, however, can be
made unless one understands just what
quantities are necessary to define the quantity
about to be measured. The position of a
point in space is intelligently measured only
when we know that three definite and
independent co-ordinates are required to locate
the point and have determined the numerical
values of these three co-ordinates. To measure
the kinetic energy of a body in translation
we must know how many units of mass
there are in the body and with how many
units of speed it is moving. Thus also we
may accurately and definitely measure the
acceleration of gravity at various points on
the earth's surface, and yet not know the
explanation of gravitation.

Practically all the quantities involved in
physical science and engineering can be
measured in terms of three quantities: a
*length*, a *time* and a *mass*. The units of these
three quantities are therefore called the
*fundamental* units.

The standard of length, except in English
and American commerce, is the *meter*; the
standard of time the *mean solar day*; and the
standard of mass the *kilogram*. (See Earth,
Kilogram and Meter.) Units are founded
upon standards, but they often differ in size
from standards and may be chosen of a size
which, for any particular purpose, is most
convenient. Thus, in physics the centimeter
or hundredth of a meter is most frequently
employed; and in astronomy the second
(186,400 of a day) is frequently a very convenient
unit of time, though often the year (or
365 days roughly speaking) is more
convenient.

No physical measurements can be carried
out with absolute accuracy. Every
comparison is affected with error to some extent.
Even the standard meter at Paris, which is
correct by definition, may be changing its
length owing to crystallization. The rate of
rotation of the earth is probably diminishing
(and hence the length of the mean solar day
increasing) owing to tidal friction. Even if
comparisons could be made with perfect
accuracy, the final measurement would be
affected with error. On the other hand, the
precision of modern measurement almost
surpasses belief. Michelson, for instance,
has succeeded in making a comparison of the
standard meter with a wave-length of
cadmium light in which the error does not
exceed about one part in 2,000,000. Two
masses may be compared with even greater
accuracy. See Everett's *Units and Physical*
*Constants*.