ampoules, were calibrated by Chappuis in five sections of 20 deg.
each, to determine the corrections at the points 20 deg., 40 deg., 60
deg., 80 deg., which may be called the "principal points" of the
calibration, in terms of the fundamental interval. Each section of 20
deg. was subsequently calibrated in steps of 2 deg., the corrections
being at first referred, as in the example already given, to the mean
degree of the section itself, and being afterwards expressed, by a
simple transformation, in terms of the fundamental interval, by means
of the corrections already found for the ends of the section.
Supposing, for instance, that the corrections at the points 0 deg. and
10 deg. of Table III. are not zero, but C deg. and C' respectively,
the correction C_n at any intermediate point n will evidently be given
by the formula,

C_n = C deg. + c_n + (C' - C deg.)n/10 (3)

where c_n is the correction already given in the table.

If the corrections are required to the thousandth of a degree, it is
necessary to tabulate the results of the calibration at much more
frequent intervals than 2 deg., since the correction, even of a good
thermometer, may change by as much as 20 or 30 thousandths in 2 deg.
To save the labour and difficulty of calibrating with shorter threads,
the corrections at intermediate points are usually calculated by a
formula of interpolation. This leaves much to be desired, as the
section of a tube often changes very suddenly and capriciously. It is
probable that the graphic method gives equally good results with less
labour.

_Slide-Wire._--The calibration of an electrical slide-wire into parts
of equal resistance is precisely analogous to that of a capillary tube
into parts of equal volume. The Carey Foster method, employing short
steps of equal resistance, effected by transferring a suitable small
resistance from one side of the slide-wire to the other, is exactly
analogous to the Gay Lussac method, and suffers from the same defect
of the accumulation of small errors unless steps of several different
lengths are used. The calibration of a slide-wire, however, is much
less troublesome than that of a thermometer tube for several reasons.
It is easy to obtain a wire uniform to one part in 500 or even less,
and the section is not liable to capricious variations. In all work of
precision the slide-wire is supplemented