MR. J. P. JOULE ON THE AIR-ENGINE. 
67 
Fahr. from the absolute zero, 33’2237 grs. ; specific heat of air at constant volume, 
0-19/42. Ratio of the specific heat of air at constant pressure to that at constant 
volume, as determined from the experiments of Delaroche and Berard, and the 
mechanical equivalent of heat, 1-3519325*. The results are shown in Table I. 
I now proceed to give some estimates of the performance of an air-engine similar 
in principle to that already described, worked at various pressures and temperatures, 
those of the atmospheric air being- 15 lbs. on the square inch, and 32° Fahr. or 491° 
Fahr. from the absolute zero. In order to render the results easily available in 
calculating the duty of engines of greater size, I shall assume that the condensing 
pump is 12 inches long, and has a sectional area equal to 1 square inch, and that 
the cylinder, also of 1 inch section, has a length which may be made to vary accord- 
ing to the pressure and temperature employed. 
I take as the first example, a case in which the receiver C contains air of the 
atmospheric density, and of which the absolute temperature is 849°-464 Fahr. or 
390°-464 of the scale of Fahrenheit’s thermometer. The pressure in the receiver 
will then be 25-95104 lbs. on the square inch, as given in the third column of 
Table II. The air in the pump A will be brought to the same pressure, and 
to the absolute temperature 566°-3094 after the piston has traversed 4 inches. The 
work absorbed by the air will be 6-53/154 foot-pounds, from which, by subtracting 
5 foot-pounds, the work communicated by the pressure of the atmosphere following 
the piston, we obtain 1-537154 foot-pounds as the work of the engine absorbed by 
the first part of the stroke. Tliis result is consigned to column 6. Immediately after 
the piston has passed the fourth inch of the pump, the valve will be opened admitting 
the compressed air into the receiver C. Tlie work of the engine absorbed by the re- 
when the compression is concluded. Then if k denote the ratio of the specific heat of air at constant pressure 
to the specific heat of air kept in a space of constant volume, and if, as appears to be nearly, if not rigorously 
true, k be constant for varying temperatures and pressures, we shall have by the investigation in Miller’s 
‘Hydrostatics’ (Edit. 1835, p. 22) — • 
1 + E^ /V ' 
1 + ET ~ V u y 
But" 
pv i+E/ 
pv~h-et’ 
therefore 
;,„=PV(X) 
Now the work done in compressing the mass from volume v to volume v—dv will he pdv, or by what precedes, 
PV . V*“'— • 
Hence by the integral calculus we readily find, for the work, W, necessary to compress from V to V', 
* The experiments of Desormes and Clement give 1-354; those of Gat-Lussac and Welter 1’375; and 
those described under the article ‘ Hygrometry ’ (Enc. Brit.), 1-333. See Art. ‘ Sound,’ Enc, Brit., 7th Edit. 
K 2 
