_Α_τ + (_E^2p_)/(μ(1 + _Et_)^2)τ.
But, since _B_ denotes the specific heat under constant pressure, the
quantity of heat requisite to bring the gas into this state, from its
primitive condition, is equal to _Β_τ, and hence we have
_B_ = _A_ + (_E^2p_)/(μ(1 + _Et_)^2). (12)
IV. _Comparison of the Relative Advantages of the Air-engine and
Steam-engine._
54. In the use of water-wheels for motive power, the economy of the
engine depends not only upon the excellence of its adaptation for
actually transmitting any given quantity of water through it, and
producing the equivalent of work, but upon turning to account the entire
available fall; so, as we are taught by Carnot, the object of a
thermodynamic engine is to economize in the best possible way the
transference of all the heat evolved, from bodies at the temperature of
the source, to bodies at the lowest temperature at which the heat can be
discharged. With reference, then, to any engine of the kind, there will
be two points to be considered:
(1) The extent of the _fall_ utilized.
(2) The economy of the engine, with the fall which it actually uses.
55. In the first respect, the air-engine, as Carnot himself points out,
has a vast advantage over the steam-engine; since the temperature of the
hot part of the machine may be made very much higher in the air-engine
than would be possible in the steam-engine, on account of the very high
pressure produced in the boiler, by elevating the temperature of the
water which it contains to any considerable extent above the atmospheric
boiling-point. On this account a “perfect air-engine” would be a much
more valuable instrument than a “perfect steam-engine.”[64]
Neither steam-engines nor air-engines, however, are nearly perfect; and
we do not know in which of the two kinds of machine the nearest approach
to perfection may be actually attained. The beautiful engine invented by
Mr. Stirling of Galston may be considered as an excellent beginning for
the air-engine;[65] and it is only necessary to compare this with
Newcomen’s steam-engine, and consider what Watt has effected, to give
rise to the most sanguine anticipations of improvement.