ost important methods of calibration. The common balance for
testing equality of mass or weight is so delicate and so easily tested
that the process of calibration may frequently with advantage be
reduced to a series of weighings, as for instance in the calibration
of a burette or measure-glass by weighing the quantities of mercury
required to fill it to different marks. The balance may, however, be
regarded more broadly as the type of a general method capable of the
widest application in accurate testing. It is possible, for instance,
to balance two electromotive forces or two electrical resistances
against each other, or to measure the refractivity of a gas by
balancing it against a column of air adjusted to produce the same
retardation in a beam of light. These "equilibrium," or "null," or
"balance" methods of comparison afford the most accurate measurements,
and are generally selected if possible as the basis of any process of
calibration. In spite of the great diversity in the nature of things
to be compared, the fundamental principles of the methods employed are
so essentially similar that it is possible, for instance, to describe
the testing of a set of weights, or the calibration of an electrical
resistance-box, in almost the same terms, and to represent the
calibration correction of a mercury thermometer or of an ammeter by
precisely similar curves.

_Method of Substitution._--In comparing two units of the same kind and
of nearly equal magnitude, some variety of the general method of
substitution is invariably adopted. The same method in a more
elaborate form is employed in the calibration of a series of multiples
or submultiples of any unit. The details of the method depend on the
system of subdivision adopted, which is to some extent a matter of
taste. The simplest method of subdivision is that on the binary scale,
proceeding by multiples of 2. With a pair of submultiples of the
smallest denomination and one of each of the rest, thus 1, 1, 2, 4, 8,
16, &c., each weight or multiple is equal to the sum of all the
smaller weights, which may be substituted for it, and the small
difference, if any, observed. If we call the weights A, B, C, &c.,
where each is approximately double the following weight, and if we
write a for observed excess of A over the rest of the weights, b for
that of B over C + D + &c., and so on, the observations by the method