68 
MR. J. P. JOULE ON THE AIR-ENGINE. 
g 
maining 8 inches of the piston’s stroke will be (25‘95104— 15) = 7*300693 foot- 
pounds, as given in the seventh column. The air thus forced into the receiver at 
the absolute temperature 566°'3094 Fahr. must then be raised to 849°'464 Fahr., 
the constant absolute temperature of the receiver. The heat necessary for this 
purpose, being that due to the capacity for heat of air at constant pressure, will be 
that which is able to raise the temperature of 1 lb. of water 0°'04304312 Fahr., as 
given in column 15. On leaving the receiver, the air enters the cylinder of expan- 
sion B, and having propelled the piston through 12 inches, the same quantity of air 
will have passed out of the receiver as was pumped into it by A. The further supply 
of air is then cut off, and the air after expanding through the remaining 6 inches of 
the cylinder (which in this case must be 18 inches long), will be reduced to the 
3 
pressure of 15 lbs. on the square inch, and the absolute temperature^ (491°)=736°'5. 
The work evolved by the piston will also be to that absorbed in the condensing 
pump, as the volume of the cylinder B is to that of the pump A; from which we find 
I (7‘300693) = 10-95104 foot-pounds, and | (l-537154) = 2-305731 foot-pounds, the 
work evolved by the first and second parts of the piston’s stroke, as given in columns 
II and 12. The work evolved by the engine on the whole, being the difference 
between the work evolved by B, and the work absorbed by A, will be equal to one- 
third of the former, or one-half of the latter, or 4-418924 foot-pounds, as given in 
column 14. Dividing this by 0°-04304312, we obtain 102-66276 foot-pounds as the 
work evolved by the engine out of each 1° Fahr. per lb. of water communicated to 
the receiver. This result, which is consigned to the sixteenth column, informs us of 
the economical value of the engine, which is of course great in proportion to its 
approach to 772 foot-pounds, the theoretical maximum. The seventeenth column 
contains the theoretical duty according to Professor Thomson’s law, viz. that the 
range of temperature divided by the maximum absolute temperature is equal to the 
fraction of heat converted into force by any perfect engine*. 
It will be observed that the numbers in column 16, representing the work evolved 
out of each unit of heat, increase with the temperature and pressure of the air in the 
receiver. In every example given, with the exception of the first, the economical 
value of the air-engine in question is greater than that of the steam-engine calculated 
by Mr. Rankine in his paper on the Mechanical Action of Pleat -f. In considering 
the relative merits of the engines, we must not, however, lose sight of a most im- 
portant fact discovered by Rankine and Clausius, viz. that a portion of the heat 
* See Professor Thomson’s " Investigation of the Duty of a perfect Thermo-Dynamic Engine,” at the end 
of this paper. 
t Transactions of the Royal Society of Edinburgh, vol. xx. part 1. Professor Thomson, in a paper “On 
the Dynamical Theory of Heat,” recently read before the Royal Society, Edinburgh, gives 209 foot-pounds as 
the duty of an absolutely perfect steam-engine, with a range of temperature between 30° and 140° Centigrade. 
