On the Expenditure of Heat in the Hot-air Engine. 227 
to give the best velocity to the piston. For it will be obvious 
that, though the theoretical consumption of heat is less when m 
=1, than when it is less, as 3, yet the volume of air which must 
be heated and cooled at every stroke is fifty per cent. greater in 
the former case than in the latter. Moreover, since the theoretic, 
cylinder is larger. If there were no waste at all from this cause, 
then condensing cylinders of large dimensions, with supply cylin- 
ders to throw the air into the reservoir after condensation, as de- 
scribed in the following article already referred to more than once, 
and with 7<1, would furnish engines much more powerful than 
those of Ericsson, both absolutely and with relation to the con- 
sumption of heat. 
It is no part of the present purpose to investigate the question, 
what would be the best theoretical proportions of the cylinders to 
each other, and of the cut-off to the stroke; or the numerical ra- 
tio of 7: m, which would render the largest amount of heat avail- 
able. The results of such an enquiry must always be subordinate 
ences which theory cannot anticipate. Leakage, moreover, may 
possibly be dependent, in some measure, upon the relative propor- 
tions of the cylinders. But losses from radiation, conduction, 
and by escape through the smoke-pipes, will not be materially 
different, so long as the working cylinder remains invariable in 
size, whatever be the magnitude of the supply cylinder. 
Upon the whole, it cannot be denied that the results of theory 
are, in one important point of view, favorable to the hot air en- 
gine. The available power developed in this machine ought to 
bear a much larger ratio to the mechanical equivalent of the heat 
expended, than is true of the steam-engine, even when steam is 
worked with large expansion. But, in another point of view, the 
air engine is yet, even in theory, far behind the steam-engine ; 
since, though it lays out the heat to advantage, it requires a very. 
ulky and ponderous apparatus to lay out the amount of heat he- 
cessary for the creation of great power. Whether there is any 
escape from this difficulty is more than doubtful; but whether 
the evil may not be so far reduced as to render the engine an eli- 
gible motor on the ocean, for commercial purposes, if not for high 
speed, is a question which we are not yet justified in answering 
in the negative. 
University of Alabama, July 7, 1853. 
