us.] PORCELAIN AIR THERMOMETRY. 211 
experiments accomplish a similar purpose by making H=h ; for the 
value of A is easily found as 
where Y x is the excess of the volume of the gas at the high-temperature 
measurement Tover that at the low-temperature measurement t, and 
where Ti is the temperature of V l . The older method therefore eliminates 
the volume factor 5 the present method eliminates the pressure factor. 
If we expand equation (1) for the present case we find the following 
correlative variables : 
v t T 
v' V T' 
v' t" T" 
V, - T v 
where v is the volume of the bulb, v' the volume of the part of the 
stem along which temperature varies from T to t, v" . . . the volumes 
of the remaining capillary stem and capillary tubes of nearly constant 
temperature, Vi, finally, the excess of volume of gas at the high-temper- 
ature measurement typified by J, over that of low-temperature measure- 
ment typified by t Temperatures referring to the same volume are 
similarly accentuated. If for abbreviation 
and 
2=HS=2^Hf(T<)-hf(t')~j, 
then equation (1) leads to the following value of T: 
T _ <^/(^))-V(^ (2) 
This equation is rigorously true ; but it is unwieldy, and to be made 
practical must be simplified. 
The equation simplified. — Equation (2) may be easily put into the form 
H-hf{t)+H^f(T x ) + (l + aT)2 
T=~ y-y —-> . • . • (3) 
which for E=h 1 the condition underlying the present method, and for 
M=f(t)- Y yf{T x ) (4) 
(865) 
