On the Expenditure of Heat in the Hot-air Engine. 35) 
Arr, XXXVI.— Theoretic Determination of the Expenditure of 
Heat in the Hot-air Engine: Supplementary Article; by 
Freverick A. P. Barnarp, Professor of Chemistry aA Natural 
History, in the University of Alabama. 
A wearand direct expression may be obtained, for the total con- 
sumption of heat in the air engine, in terms of the numerical ratio 
between the cylinders, se rede part of the stroke of the pis- 
ton before cut-off, and constants. We must include in this, how- 
ever, a loss from a source ie considered in the article published 
in the last number of this Journal; viz., that which is occasioned 
the expansion of the air at the moment of final escape. It is 
evident that if, at the close of the stroke, the air in the working tyil 
inder has a higher elasticity than that of the atmosphere, it will 
expand as it emerges, until an oe is established, and a 
portion of its heat will disappear.* This is provided for in the 
following. We will employ, as Ee lore, 
a? 4 represent en working temperature. 
at of the weather. 
: sy “ it of the air tome compression 
a “that of the same at the moment of esc 
@ « “¢ the reciprocal of the coéfficient of scrap 
(i.e. 4919 F, 
The other Sambal employed in the former article, will-be sim- 
ee employed her 
t has been shoot that, of the heat received from the furnace, 
there is apes converted into expansive power an amount equal 
to (T—) (y—1). There is also lost by expansion, in the act of 
escaping, the additional amount of (T—6”). And there is a com- 
pensation, in consequence of cooling under the constant atmos- 
pheric pressure, i to (0”—&) (y—1). These expressions 
united, are reducible 
O) 75 
which is a general ee for ihe ‘total expenditure. 
But 6” is not a constant. While T and 4 remain the same, it 
will be a function of J and m, the Leiethe of the stroke betel vai 
off, and the ratio*of the cylinders to each other in cross section. 
By Poisson’s first equation, 
y=)" 
* To the truth, in ming particular, of the paradox introduced by way of rooted 
tion, in — commencement of the former article, it is evidentl J 
which is a escape after being heated without previous compression, should 
rr igay Nad Se le , for instance, by being returned direct- 
ly to the : wenighy eplnder. Pr owever, it would be impossible for the re- 
a to abstract fro: as air all th the heat it had received; but if it could, the 
would be as there an. 
