222 On the Expenditure of Heat in the Hot-air Engine. 
without enlargement of bulk, the same amount of — would 
have raised its. cama as much more than 422°, as 1°36 is 
greater than 1, that is, 573°°92. But as, at the end of ahs stroke 
its temperature is but 422° above that of the weather, it can give 
up only the 422° as it escapes. The difference =151°-92 has 
apparently been annihilated ; but it has actually been converted 
into expansive power, and is irrecoverable. 
In saying that it is irrecoverable, however, nothing more is 
meant than that it is utterly lost to any useful mechanical pur- 
elevate the ne i by an amount corresponding to the seem- 
ing loss. It is hardly necessary to say, that this amount of heat 
will be ie valoped, before the density shall have been reduced to 
that of the reservoir, 1°813, because the pressure in this reverse 
stroke is not constant, but rapidly rises, on account not only of 
the increase of density, but because of the developed heat itself. 
In this case there is a seeming as if we recovered the 151°-92 
degrees of heat which on our supposition had been imparted to 
the air by the regenerator, and had become insensible. But had 
the cylinder been filled with air from the atmosphere, and not 
from the reservoir, and had this air at density 1, been heated 422° 
as before, it would still yield to the same compression, precisely 
as large an increment of heat, as in the other case ; although, this 
time, it would have absorbed in truth only the 422° which it 
seemed to absorb. The fact is, that, in both cases, the rise of 
temperature is an effect of labor co onverted into heat; as in the 
first case, heat is converted into labor. . 
e can easily understand, now, why, if a charge of airbe sup- 
posed to pass through the re egenerator into the working cylinder, 
oT from the oa: supply cylinder, the whole amount of 
exer elastic Aide indent of the ratio between the two ici 
i P 
being taken ¢ amend and ¢ made = 1. th 1e value of 9’ will be gre r as 7 is less. 
rmula, 
_ b'=pi(l nnd 
may lead, through Poisson's formule, directly to the true value of 7; and ». 0. that 
a correct Be iedependent prabiiees 0 of 7, should furnish, through the same, the true 
equivalent of heat haat 
