+------------+------+------+------+------+------+------+------+------+------+------+
| Step No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+------------+------+------+------+------+------+------+------+------+------+------+
| 1 | 0 | - 5 | +11 | +20 | +34 | +25 | + 7 | +26 | +23 | +32 |
| 2 | + 5 | 0 | +16 | +23 | +39 | +29 | +12 | +31 | +28 | +37 |
| 3 | -11 | -16 | 0 | + 8 | +24 | +13 | - 4 | +15 | +13 | +22 |
| 4 | -20 | -23 | - 8 | 0 | +15 | + 5 | -12 | + 7 | + 4 | +13 |
| 5 | -34 | -39 | -24 | -15 | 0 | - 9 | -26 | - 8 | -10 | - 2 |
| 6 | -25 | -29 | -13 | - 5 | + 9 | 0 | -17 | + 2 | - 1 | + 8 |
| 7 | - 7 | -12 | + 4 | +12 | +26 | +17 | 0 | +19 | +16 | +26 |
| 8 | -26 | -31 | -15 | - 7 | + 8 | - 2 | -19 | 0 | - 3 | + 6 |
| 9 | -23 | -28 | -13 | - 4 | +10 | + 1 | -16 | + 3 | 0 | + 9 |
| 10 | -32 | -37 | -22 | -13 | + 2 | - 8 | -26 | - 6 | - 9 | 0 |
+------------+------+------+------+------+------+------+------+------+------+------+
| Error of | | | | | | | | | | |
| step. | -17.3| -22.0| - 6.4| + 1.9| +16.7| + 7.1| -10.1| + 8.9| + 6.1| +15.1|
+------------+------+------+------+------+------+------+------+------+------+------+
|Corrections.| +17.3| +39.3| +45.7| +43.8| +27.1| +20.0| +30.1| +21.2| +15.1| 0|
+------------+------+------+------+------+------+------+------+------+------+------+
The advantages of this method are the simplicity and symmetry of the
work of reduction, and the accuracy of the result, which exceeds that
of the Gay Lussac method in consequence of the much larger number of
independent observations. It may be noticed, for instance, that the
correction at point 5 is 27.1 thousandths by the complete calibration,
which is 2 thousandths less than the value 29 obtained by the Gay
Lussac method, but agrees well with the value 27 thousandths obtained
by taking only the first and last observations with the thread of 5
deg. The disadvantage of the method lies in the great number of
observations required, and in the labour of adjusting so many
different threads to suitable lengths. It is probable that
sufficiently good results may be obtained with much less trouble by
using fewer threads, especially if more care is taken in the
micrometric determination of their errors.
The method adopted for dividing up the fundamental interval of any
thermometer into sections and steps for calibration may be widely
varied, and is necessarily modified in cases where auxiliary bulbs or
"ampoules" are employed. The Paris mercury-standards, which read
continuously from 0 deg. to 100 deg. C., without intermediate
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,