214 MEASUREMENT OF HIGH TEMPERATURES. [bull. 54.) 
The variations of v here observed I was first inclined to attribute to 
the difficulty of defining the volume of a bulb, the interior of which is, 
not glazed; but they are due to thermal disturbances. In order that 
the present method maybe made to yield the best results the tempera., 
ture of the bulb and of the manometer tube B G (Fig. 40) must either' 
be rigorously the same, or the respective temperatures must be known. 
For, if 2v be the volume of the bulb and capillary stems at the tern- j 
perature t, and if V 1 and V 2 be the two volumes read off on the manom- 
eter tube B G at the temperature 2\, and if Hi aud H 2 be the pressures < 
or gas tensions which correspond, respectively, to V\ and V 2 , then 
fm H 1 V 1 -R 2 Y 2 __ 
-fit) R 2 -H x - 2 ^' 
an expression in which if T x and t differ by as little as a few tenths of 
a degree the factor f(T±)/ f(t) can no longer be considered negligible.] 
It will be seen below that 2 (v) must be measured with a degree ofl 
precision scarcely exceeding 0.02 per cent., i. e., to about 0.1 cc for the! 
given capacity of bulb, if the absolute value of Tis to be correct to one! 
pro mille. But after many measurements, the further citation of which] 
is here superfluous, I convinced myself that when due regard is paid to] 
the temperature factor the accuracy in question is attainable. /( T A ) -r-f(t)\ 
is approximately l+a (t— Ti), in which form it may be easily applied. 
Errors of the approximations. — It is necessary to discuss the corrective! 
member of the equation (5). 
T- _ M 
- L - aM-6 
S 
M ' 8 
viz? -^r — 7,1 or as it may be written with sufficient accuracy, -^ 
aM—j3 J * aM* 
For practice it is best to write for this the equivalent form v — i-j 
a ' 
and then to calculate a table from which, for each value of T, the value 
of this corrective function may be taken at once. It is usually suffiJ 
cient to proceed as follows : The full form of the corrective function isj 
(i±^p{y ( T)- m] \. 
For those parts of the capillary stem whose temperatures are con- 
stant, f(T") and f(t") are practically identical. Hence the part of the- 
stem along which temperature varies from the high value to that os 
the atmosphere alone enters into the consideration. It follows that the 
last expression may be written 
(1+aTY ?' [f{T')—f(t')]. 
(MS) 
