176 
MB. H. L. C ALLEND A R ON THE PRACTICAL 
Formvlce 
The formulae applicable to this form of air-thermometer are, of course, very similar 
to those of the ordinary form. Let m be the mass of air confined. Let V 0 be the 
volume at 0° C. of the bulb, together with that portion of the capillary tube which is 
heated with it, and let v 0 be the volume of the capillary and gauge tubes from this 
point to the division x Q of the gauge tube. Let be the pressure at 0° C. when the 
temperature of the gauge tube is 6' and the acid stands at the division x Q of the 
scale. Let 9 0 be the absolute temperature corresponding to 0° C. Let v be the 
correction volume for the portion unheated at any other time when the temperature, 
pressure, and volume of the air in the bulb are 6 , p, V, respectively, and when 6" is 
the temperature of the gauge tube, and x the scale reading thereof. Then, by the law 
of a perfect gas, we have the equation 
= mk= P Q {J° + ~d}’ .w 
whence, to a first approximation, 
6 = ^ 
Po’ 
Let y be the mean cubical coefficient of expansion of the glass of the bulb 
between 6 0 and 6. 
Then 
v = v„{i +y(o-e 0 )}. 
Let u be the volume per centim. of the gauge tube. 
Then 
Let 
v = y 0 -f u(x— Xq). 
v 
V 
o- 
Making these substitutions in equation (1), and substituting for 0 the first approxi¬ 
mation in the small terms, we obtain at once 
If we write 
this becomes 
Po 
+A) = 2/ 0 and y0 o +P~ = y, 
* For be'ter method with aid of slide-rule, see Appendix, 
