358 
PROFESSOR W. THOMSON AND MR. J. P. JOULE ON THE 
pressure in pounds on the square foot into the volume in cubic feet of a pound of the 
gas at 0° Cent. ; P is the ratio of the pressure on the high pressure side to that 
on the other side of the plug ; ^ is the observed cooling eflFect ; t the temperature 
Cent, of the bath, and K the thermal capacity of a pound of the gas under constant 
pressure equal to that on the low pressure side of the gas. To establish this equa- 
tion it is only necessary to remark that is the heat that would have to be added 
to each pound of the exit stream of air, to bring it to the temperature of the bath, 
and is the same (according to the general principle of mechanmal energy) as would 
have to be added to it in passing through the plug, to make it leave the plug with 
its temperature unaltered. We have therefore K^=-H, in terms of the notation 
used in the passage referred to. 
On the above hypothesis (that the gas fulfils the laws of compression and expansion 
ordinarily assumed) would be the same for all values of P ; but Regnault has 
shown that the hypothesis is not rigorously true for atmospheric air, and our experi- 
ments show that ^ increases with P. Hence, in reducing the experiments, a 
correction must be first applied to take into account the deviations, as far as they 
are known, of the fluid used, from the gaseous laws, and then the value of ^ may 
be determined. The formula by which this is to be done is the following (Dynamical 
Theory of Heat, equation (/), § 74, or equation (17), § 95, and (8), § 89)— 
1 j{ w — —pu)} + KS 
ju. dw ’ 
dt 
where w=^jydv, 
u and u' denoting the volumes of a pound of the gas at the high pressure and low 
pressure respectively, and at the same temperature (that of the bath), and v the 
volume of a pound of it at that temperature, when at any intermediate pressure p. 
An expression for w for any temperature may be derived from an empirical formula 
for the compressibility of air at that temperature, and between the limits of pressure 
in the experiment. 
The apparatus, which we have been enabled to provide by the assistance of a grant 
from the Royal Society, consists mainly of a pump, by which air may be forced 
into a series of tubes acting at once as a receiver of the elastic fluid, and as a means 
of communicating to it any required temperature ; nozles, and plugs of porout 
material being employed to discharge the air against the bulb of a thermometer. 
The pump a, fig. 1, consists of a cast-iron cylinder of 6 inches internal diameter, 
in which a piston, fig. 2, fitted with spiral metallic packing (of antifriction metal), 
works by the direct action of the beam of a steam-engine through a stroke of 
22 inches. The pump is single-acting, the air entering at the base of the cylinder 
during the up-stroke, and being expelled thence into the receiving tubes by the 
down-stroke. The governor of the steam-engine limits the number of complete 
