178 
MR. H. L. CALLENDAR ON THE PRACTICAL 
Then, finally, 
P — H+[M e — M L ] 0 +g r . 
For reasons previously given, p is correct only to the nearest tenth of a millimetre. 
Reduction of the Observations. 
This is a formidable piece of arithmetic, with the formulae as usually given for the 
ordinary air thermometer : it would he still more formidable with the sulphuric acid 
gauge. However, by the aid of graphic methods and a slide rule, it may be effected 
with great rapidity and accuracy. 
The value of y — 
r 0 4 u(x—x 0 ) 6 a 
Y 6 " 
is calculated for any two values of x and for 
temperatures 15° + 20 ° C. Two straight lines are ruled on logarithm paper joining 
these points, giving the value of y for any value of x at these two temperatures. A 
variation of one degree of temperature produces a variation of about 3 -^ in the value 
of y, so that the lines very nearly coincide. 
Similarly the value of q is calculated for two values of x, and the ruling of a straight 
line gives it for all other values; this line is ruled on the same piece of logarithmic 
paper, with the same abscissa scale. A correction diagram of this kind has to be con¬ 
structed from the calibration and other details once for all for each thermometer. The 
values of y and q, corresponding to the recorded value of x, are taken from the correc¬ 
tion diagram and copied into adjacent columns headed y and q ; p is evaluated by the 
simplest addition and subtraction; t he multiplication ypjp^ is performed in one operation 
on a slide-rule, and 8 is found by subtracting y 0 ; the product Sp is given at once by 
the slide-rule and added to p, giving P, which is proportioned to the absolute tempera¬ 
ture 9 : thus the whole of the calculation involved in finding P may be exhibited in 
a single line and worked out on the spot in the note-book used for recording the 
observations. This gives a great advantage in point of compactness, and the ease with 
which mistakes may be discovered and rectified. Where it is advisable, from the 
magnitude of the volume correction, to go to a third approximation, this may be 
taken as 
9 — ~p{ 1 fi-S+S 3 } by neglecting ySd 0 . 
ho 
8 3 is at once given by the slide-rule and added to 8 , so that this involves very little 
extra trouble. 
But the greatest advantage of this method of reduction is that it avoids the 
accumulation of superfluous and meaningless figures, and thereby escapes that fictitious 
accuracy which is so seductive and treacherous in all physical investigations. 
