MEASUREMENT OF TEMPERATURE. 
177 
Let 
Then, finally, 
V 
and write p(l+S) = P. 
Po 
e = p . -°. 
Po 
It is, in general, useless to proceed to a third approximation, because the uncertainty 
of the corrections is at least of the same order, as a rule. 
The value of P, which may be called the “ corrected ” pressure, is obtained directly 
from the observations by applying the small corrections in the manner detailed below. 
P is proportional to the absolute temperature. The ratio 0 o /p o is theoretically 
constant for each filling, though, as a matter of fact, it is variable with the “ zero- 
errors ” of the am thermometer. The value of 0 is calculated from P by the aid of 
logarithms, the logarithm of 6 0 /p 0 being tabulated once for all for each series of observa¬ 
tions. This is the only part of the reductions where logarithms are required. The 
correction terms being, from their very nature, uncertain, often to the extent of nearly 
1 per cent., it is quite sufficient to perform all the multiplications they involve by the 
aid of a small slide-rule giving results correct to 1 per 1000. This method saves 
trouble, paper, time, and mistakes. 
Reduction of the Pressure (p). 
The correction of the mercury columns for temperature is most easily applied by a 
graphic method : by ruling two series of straight lines, giving the correction to be 
applied to any length of mercury column less than 1 metre for each degree of 
temperature Centigrade, both for the glass millimetre scale and for the English 
standard barometer with the brass scale. The barometer lines need not extend 
through the whole range, since its reading never varies far from 7 6 centims. 
Let H be the height of the barometer, corrected for temperature, &c., as above 
described. Let M R , M L , be the readings of the right and left limbs of the mercury 
manometer ; and let M R —M L be corrected for temperature and added to H. Let x 
be the reading of the H 3 S0 4 gauge when the pressure is the same on the acid in both 
limbs. Let x be the recorded reading in centims. Let 
(x—x') density of H 2 S0 4 _ 
density of mercury ^ 
Then q is the pressure due to the acid, expressed in terms of mercury : q is usually so 
small that no temperature correction need be applied. Both x and the reduction 
factor are determined by previous experiment with the acid and gauge used. 
MDOCCLXXXVII.- A. 2 A 
