But, in fact, the temperature is lowered, because expansion has taken place, and the indicator curve which would then be described is called an “adiabatic curve,” which is more inclined to the horizontal line when the volumes are represented by horizontal and the pressures by vertical co-ordinates.  In this case it is supposed that there is no conduction or transmission (diabasis) of heat through the sides of the containing vessel.  If, however, an additional quantity of heat be communicated to the air, so as to maintain the temperature at 1,000 deg. absolute, the piston will rise until it is 121/2 feet above its original position, and the indicator will describe an isothermal curve.  Now mark the difference.  When the piston was fixed, only a heating effect resulted; but when the piston moved up 121/2 feet, not only a heating but a mechanical, in fact, a thermodynamic, effect was produced, for the weight of the atmosphere (2,116 lb.) was lifted 121/2 feet = 26,450 foot-pounds.

The specific heat of air at constant pressure has been proved by the experiments of Regnault to be 0.2378, or something less than one-fourth of that of water—­a result arrived at by Rankine from totally different data.  In the case we have taken, there have been expended 500 x 0.2378, or (say) 118.9[theta] to produce 26,450 f.p.  Each unit has therefore produced (26,450 / 118.0) = 222.5 f.p., instead of 772 f.p., which would have been rendered if every unit had been converted into power.  We therefore conclude that (222.5 / 772) = 29 per cent. of the total heat has been converted.  The residue, or 71 per cent., remains unchanged as heat, and may be partly saved by a regenerator, or applied to other purposes for which a moderate heat is required.

The quantity of heat necessary to raise the heat of air at a constant volume is only 71 per cent. of that required to raise to the same temperature the same weight of air under constant pressure.  This is exactly the result which Laplace arrived at from observations on the velocity of sound, and may be stated thus—­

Specific        Foot-   Per
heat.        pounds. cent.

Kp = 1 lb. of air at constant pressure 0.2378 x 772 = 183.5 = 100
Kv = 1 lb. of air at constant volume 0.1688 x 772 = 130.3 = 71
                                             ------ --- ----- ---
Difference, being heat converted into power 0.0690 x 772 = 53.2 = 29

Or, in a hot-air engine without regeneration, the maximum effect of 1 lb. of air heated 1 deg.  Fahr. would be 53.2 f.p.  The quantity of heat Ky necessary to heat air under constant volume is to Kv, or that necessary to heat it under constant pressure, as 71:100, or as 1:1.408, or very nearly as 1:SQRT(2)—­a result which was arrived at by Masson from theoretical considerations.  The 71 per cent. escaping as heat may be utilized in place of other fuel; and with the first hot-air engine I ever saw, it was employed for drying blocks of wood.  In the same way, the unconverted heat of the exhaust steam from a high-pressure engine, or the heated gases and water passing away from a gas-engine, may be employed.