66 
MR. J. P. JOULE ON THE AIR-ENGINE. 
pressure through mn. The moment the piston has passed the point n the valve will 
open, admitting the air into the receiver C ; and as this receiver may be conceived 
to be of indefinite magnitude, the alteration of pressure in it, consequent upon the 
introduction of fresh air, may be neglected. Heat is then communicated to the air 
in the receiver, in order to restore its temperature to the intensity which existed 
before the admission of air at a lower temperature. The air is then allowed to escape 
from the receivei’ into the base of the cylinder B, evolving work until, on the arrival 
of the piston at w', the same quantity has been removed from the receiver as was 
forced into it by the pump. The further supply of air from the receiver is then cut 
off, and that which has entered the cylinder expands, evolving work until, on the 
arrival of the piston at m!, its pressure is reduced to that of the atmosphere. By 
opening valves at the bases of A and B, the pistons are then brought to their first 
positions. 
The problem which must be solved in order to estimate the power and consump- 
tion of fuel in an engine similar to that just described, is as follows : — To determine 
the pressure and temperature for any point of the stroke of a piston which com- 
presses a given volume of air, and the quantity of work absorbed in forcing the 
piston to that point. For the temperature and pressure Poisson has furnished the 
following formulae, — 
T_ / V y-' 
T— (^V7 ’ 
and 
P'_ / V\* 
P“VV7 ’ 
where T, P, and V are the temperature from absolute zero (estimated at 491° Fahr. 
below the freezing-point of water), pressure, and volume of the air before com- 
pression ; T', P', and V' the temperature from absolute zero, pressure, and volume of 
air after compression ; and ^ is the ratio of the speeific heat of air at constant pressure 
to that at constant volume. Professor VV. Thomson has deduced, as a consequence 
of the above, the following formula for the work absorbed. 
From the foregoing formulae I have calculated the work absorbed by compressing 
air in a cylinder 1 foot long, and. of the capacity of 12 cubic inches, the absolute 
temperature of the air, and its pressure at each tenth of an inch of the piston’s pro- 
gress. The following data were employed in the computation : — Weight of 100 
cubic inches of atmospheric air of 15 lbs. pressure on the square inch, and 491° 
* The above formula was kindly communicated to the author by Professor Thomson, in a letter dated 
January 15, 1851, from which the following is an extract: — “It is required to find the work necessary to 
compress a given mass of air to a given fraction of its volume, when no heat is permitted to leave the air. Let 
P, V, T be the primitive pressure, volume, and temperature, respectively ; let p, v, and t be the pressure, 
volume, and temperature at any instant during the compression ; and let P', V', and T' be what they become 
