up on the decimal system is 5, 2, 1, 1, or 5, 2, 2, 1. These
do not admit of the independent calibration of each group by
substitution. The arrangement 5, 2, 1, 1, 1, or 5, 2, 2, 1, 1, permits
independent calibration, but involves a larger number of weights and
observations than the 1, 2, 3, 4, grouping. The arrangement of ten
equal weights in each group, which is adopted in "dial"
resistance-boxes, and in some forms of chemical balances where the
weights are mechanically applied by turning a handle, presents great
advantages in point of quickness of manipulation and ease of
numeration, but the complete calibration of such an arrangement is
tedious, and in the case of a resistance-box it is difficult to make
the necessary connexions. In all cases where the same total can be
made up in a variety of ways, it is necessary in accurate work to make
sure that the same weights are always used for a given combination, or
else to record the actual weights used on each occasion. In many
investigations where time enters as one of the factors, this is a
serious drawback, and it is better to avoid the more complicated
arrangements. The accurate adjustment of a set of weights is so simple
a matter that it is often possible to neglect the errors of a
well-made set, and no calibration is of any value without the most
scrupulous attention to details of manipulation, and particularly to
the correction for the air displaced in comparing weights of different
materials. Electrical resistances are much more difficult to adjust
owing to the change of resistance with temperature, and the
calibration of a resistance-box can seldom be neglected on account of
the changes of resistance which are liable to occur after adjustment
from imperfect annealing. It is also necessary to remember that the
order of accuracy required, and the actual values of the smaller
resistances, depend to some extent on the method of connexion, and
that the box must be calibrated with due regard to the conditions
under which it is to be used. Otherwise the method of procedure is
much the same as in the case of a box of weights, but it is necessary
to pay more attention to the constancy and uniformity of the
temperature conditions of the observing-room.

_Method of Equal Steps_.--In calibrating a continuous scale divided
into a number of divisions of equal length, such as a metre scale
divided in milli