GENERAL MEETING. 31 
powers of the temperatures in changing the capacity of the tube 
from 0° to 100° are neglected. The capacity of the tube is only 4 
part of that of the bulb. 
f,, 2 2, are the coefficients of expansion for glass for the first, 
second, and third powers of the temperature. 7,, 7,, 7; are the 
same for mercury. 
To make an adjustment of the differences between the mercurial 
and air-thermometers equation (4) can be put in the form 
(100¢ — #) x + (10000¢ — #) y + 0.000026?— 0.0026¢+4=0 (5) 
i Ps ier 8 
a 
proximate than (4) but still sufficiently rigorous for the purpose 
intended. 
Forming observation-equations on this model with the observed 
differences A, as the absolute terms, and solving by the method of 
least squares, the values of x and y are found to be 
2 = — 0.0001391 
y = + 0.000000863 
Substituting these in (5) it becomes 
— 0.00788¢ + 0.000165 — 0.000000863# + a = 0. (6) 
: Ba ‘ he Me 
Differentiating (6) with respect to ¢ and A, and putting 7, = 0, 
in which « = anda = T—t. This is less ap- 
the following quadratic-equation is found 
0.0000025897 — 0.000330¢ + 0.00788 = 0, (7) 
the solution of which gives for the temperatures at which the differ- 
ences between the mercurial and air-thermometer are greatest t = 
31.8 and t= 95.8. To find the temperatures at which the mercurial 
and air-thermometer agree, put A = 0 in (6); the values of ¢ that 
then satisfy the equation are t = 0, t= 100, and ¢ = 91. 
At 32° the mercurial thermometer reads higher than the air- 
thermometer, at 96°, it reads lower. A curve representing the 
differences has the following form: 
25° 73" z00° 
Fig. 1.—T 4207 minus Air-thermometer. Abscissas = Temperatures. 
Centigrade. Ordinates = Differences. 
50° 
