360 
MR. J. P. JOULE AND PROFESSOR THOMSON ON THE 
Air-Engine, since confirmed by Regnault’s observations ; we have three simple 
equations for determining the three unknown quantities, a, (3, y ; and then a single 
simple equation (34) for determining By solving these, we find 
a=-00128ir 
(3=1-3918 
y=353-20 
3 ^ = 26247-9 
Using these and (33) in (17), we have 
(38) 
pv—Wy— ^*001281 1 
an empirical formula which represents the pressure of air, in terms of its temperature 
on the absolute thermo-dynamic scale and its density, consistently with Regnault’s 
observations on the increase of pressure from 0° to 100° Cent, and on the compres- 
sibility at 4 0- 75 Cent., and consistently with our own on the thermal effects of air at 
the temperature 17° Cent., forced with various pressures through a porous body. 
It also agrees perfectly with Regnault’s observations on the expansion of air under 
constant pressure. 
The only other observations on the variations of pressure and density available for 
testing the formula, are Regnault’s comparisons of different air-thermometers. The 
Table at the end of Section IV., which has been calculated from our empirical 
formula (39), shows, in its second and third columns, the indications to be expected 
of constant-volume and of constant-pressure air-thermometers in terms of tempe- 
rature on the absolute thermo-dynamic scale; and the differences between the 
numbers show the discrepancies to be expected between different air-thermometers 
themselves. These discrepancies, although considerably greater than have been 
observed by Regnault on thermometers with air at different densities or pressures 
of from half to double those of the standard, appear to be within, or scarcely to exceed, 
the limits of errors of observation. If further examination of this subject proves that 
there is in reality a closer agreement between air-thermometers than shown in the 
Table, it will be necessary to introduce another equation of condition to reconcile 
them, and to determine another constant in the general empirical formula for p. At 
present however we do not think it necessary to take up this question, as we hope 
soon to have much more extensive experimental data on the cooling effects, with 
more varied pressures and at different temperatures ; which should both show whether 
any other functions of the density than that of simple proportionality will be required, 
and enable us to determine other terms of the series in descending powers of t, and 
will so give us probably a much more exact empirical formula for air than all the 
data at present available enable us to obtain. 
We have also calculated formulae for the specific heats of air under constant pres- 
sure and constant volume, by which the variations of these elements with the tempe- 
1-3918 353-2 \<h 
t ' t* ) V 
(39) 
