BAKU8.1 PORCELAIN AIR THERMOMETRY. 189 
gas and fi the coefficient of cubical expansion of bulb, stem, etc. The 
equation assumes that the gas is perfect and that the bulb expands pro- 
portionally to its temperature. The equation is sufficient for the calcu- 
lation of any one of the variables involved, supposing all the others to 
be known. In the method of constant volume, A=0. 
In high-temperature measurement there are at least three parts of 
the air thermometer to be considered. The first of these is the hot re- 
gion, and includes the bulb and the part of the stem at the same tem- 
perature; the second is the part of the stem in which temperature varies 
from the high value to that of the atmosphere; the third is the part in 
which the temperature is practically that of the atmosphere, and it in- 
cludes the cold part of the porcelain stem, the capillary tubes, and the 
space of cold air above the meniscus of mercury. The whole of this 
may be appropriately called the cold part of the stem. It is obvious 
that the corrections to be applied are specially important when the tem- 
peratures of the bulb are high and the air is employed originally under 
small pressure. It is therefore expedient to derive the rigorous expres- 
sion for temperature in terms of all the variables involved, and from 
this to derive a safe practical form by simplification. 
The full expression in question introduces variables which may be 
symmetrically put as follows : 
h 
H 
V 
a 
t 
T 
V 
fi 
V 
T 
v" 
t" 
r£;i 
where h is the tension of the gas at the lower tehiperature, t of the 
bulb, and V and t" of the variable aud cold parts of the stem ; where H 
is the tension of the gas at the high temperature, T, of the bulb, and T' 
and T'- of the variable and cold parts of the stem ; where v is the vol- 
ume of the bulb and hot stem, v' the volume of the variable stem, and 
v' the volume of the cold stem, all at zeio degrees; where or, finally, is 
the coefficient of expansion of the gas, and /i the coefficient of expan- 
sion of porcelain. The relation between these variables may then be 
rigorously expressed by the formula 
,'-'%g+T!KO}fg;-',':£ fr*" „, 
11 TJ-^t ~2j L » \ T+ZF " h l + ZPjj 
Jriiere the symbol 2 denotes that similar expressions occur additively 
or each — , — , — . . . , to be considered, two of which, however, have 
xmmi deemed sufficient. 
(843) 
