of energy upon air and getting almost exactly one horse power in return.
Such would be the case provided we used the compressed air power
_immediately and at the point where the compression takes place_. This
is never done, but the heat which has been boxed up[1] in the air is
lost by radiation, and we have lost power. Let us see to what extent
this takes place.

[Footnote 1: I use material terms because they add to simplicity of
expression and notwithstanding the fact that heat is vibration.]

Thirteen cubic feet of free air at normal temperature and barometric
pressure weigh about one pound. We have seen that 116 degrees of heat
have been liberated at half stroke. The gauge pressure at this point
reaches 24 pounds. According to Mariotte's law, "The temperature
remaining constant, the volume varies inversely as the pressure," we
should have 15 pounds gauge pressure. The difference, 9 pounds,
represents the effect of the heat of compression in increasing the
relative volume of the air.

[Illustration: FIG. 1.: CURVES OF COMPRESSION ILLUSTRATEDIN VOLUMES,
PRESSURES, AND TEMPERATURES.]

The specific heat of air under constant pressure being 0.238, we have
0.238 × 116 = 27.6 heat units produced by compressing one pound or
thirteen cubic feet of free air into one-half its volume. 27.6 × 772
(Joule's equivalent) = 21,307 foot pounds. We know that 33,000 foot
pounds is one horse power, and we see how easily about two-thirds of a
horse power in heat units may be produced and lost in compressing one
pound of air. I would mention here that exactly this same loss is
suffered when compressed air does work in an engine and is expanded down