374 T. Russell—Calibration of Thermometers. 
column and the principal points 7, and &, be neglected, the fol- 
lowing relation holds: 
Sun (h, ) + 4-4; 
If the column is moved and placed with the ends near other 
principal points, other similar equations will be obtained, in 
which the left side will be the same, but on the right side in 
place of ¢ and &, there will be in succession 7+1 and &+1, 7+2 
and k+2, ete. If each of these equations is subtracted from 
the equation following it, a new set of equations will result of 
the form 
6;-6,= (k+1,i+ 1) - (4, 4) 
The further development of the method can best be shown in 
Thermometer, Green, 4470, is divided to fifths of a degree, 
Fahrenheit. The apparent lengths of columns given below are 
from estimated readings of the ends to the nearest tenth of a di- 
vision, or 0°02, As it is not intended to use this thermometer at 
temperatures above 122°, no special effort was made to get the 
corrections above that point. On account of this the calibration 
falls into two parts, which illustrate both branches of the 
method; the one where all requisite columns are used, and the 
other where some of the columns are wanting. Part first con- 
sists in the derivation of the corrections at 77°, 122° and 167°, 
with columns of 45°, 90° and 185°. Part second consists in 
the derivation of the corrections for every tenth degree up to 
122°, by the use of columns which are in length multiples of 
ten degrees. 
Table I contains the measured lengths of columns for the 
first part of the work. 
TABLE I. 
Apparent lengths of columns. 
45° column. 90° column. 185° column. 
3217 44°68 32°122 90°07 $2°167 134°61 
0: +0 +0°07 
RELI: sei TT167 90°09 77-212 134°68 
+0° : 
122°167 44°72 122°212 90°11 
0°02 
167-212 44°75 
Table II is formed by placing vertically the first horizontal 
line of differences of table I, and parallel to it the other lines 
of differences, beginning one line lower each time. This being 
done the numbers in the vertical lines are copied horizontally, 
with the signs changed. These two parts of the table are sep- 
arated by a diagonal line of double zeros. 
