CARNOT’S THEORY OF THE MOTIVE POWER OF HEAT. 555 
sulphurous acid, or carbonic acid under high pressure, which approaches the phy- 
sical condition of a vapour at saturation ; and therefore, in general, and especially 
in practical applications to real air-engines, it will be unnecessary to make any 
modification in the expressions. In cases where it may be necessary, there is no 
difficulty in making the modifications, when the requisite data are supplied by 
experiment. 
29.* Either the steam-engine or the air-engine, according to the arrangements 
described above, gives all the mechanical effect that can possibly be obtained from 
the thermal agency employed. For it is clear, that, in either case, the operations 
may be performed in the reverse order, with every thermal and mechanical effect 
reversed. Thus, in the steam-engine, we may commence by placing the cylinder 
on the impermeable stand, allow the piston to rise, performing work, to the posi- 
tion EK, F;; we may then place it on the body B, and allow it to rise, performing 
work, till it reaches E, F,; after that the cylinder may be placed again on the 
impermeable stand, and the piston may be pushed down to EH, F,; and, lastly, 
the cylinder being removed to the body A, the piston may be pushed down to its 
primitive position. In this inverse cycle of operations, a certain amount of work 
has been spent, precisely equal, as we readily see, to the amount of mechanical 
effect gained in the direct cycle described above; and heat has been abstracted 
from B, and deposited in the body A, at a higher temperature, to an amount pre- 
cisely equal to that which, in the direct cycle, was let down from A to B. Hence 
it is impossible to have an engine which will derive more mechanical effect from 
the same thermal agency, than is obtained by the arrangement described above ; 
since, if there could be such an engine, it might be employed to perform, as a 
part of its whole work, the inverse cycle of operations, upon an engine of the kind 
we have considered, and thus to continually restore the heat from B to A, which 
has descended from A to B for working itself; so that we should have a complex 
engine, giving a residual amount of mechanical effect without any thermal agency, 
or alteration of materials, which is an impossibility in nature. The same reason- 
ing is applicable to the air-engine; and we conclude, generally, that any two en- 
gines, constructed on the principles laid down above, whether steam-engines with 
different liquids, an air-engine and a steam-engine, or two air-engines with differ- 
ent gases, must derive the same amount of mechanical effect from the same ther- 
mal agency. 
30. Hence, by comparing the amounts of mechanical effect obtained by the 
steam-engine and the air-engine from the letting down of the H units of heat 
from A at the temperature (¢+7) to B at ¢, according to the expressions (2) and 
(3), we have 
* This paragraph is the demonstration referred to above, of the proposition stated in § 13; as it 
is readily seen that it is applicable to any conceivable kind of thermo-dynamic engine. 
