224 On the Expenditure of Heat in the Hot-air Engine. 
But the temperature of the regenerator can never be lower than 
that of the blast which cools it, that is to say, of the air of the 
reservoir. And hence it follows, as a necessity of the case, that 
the heat of compression must be unavailable ; and that the fur- 
nace must furnish the power ae to compress the air, as 
Well as to do the work of the engine. The amount of heat thus 
unprofitably spent, depends on ne degree of compression which 
the air has undergone, which last is determinable by the follow- 
ing formula of Poisson: 
g\7 
(p’=p (£) (1) 
In which p’, p, ¢ and 7 are used as before; and ¢ is the density 
ue to the compression. In the present case, & is found to be 
=1-5489= 1-55 nearly. 
The temperature of the compressed air is determined by the 
following, in which it is represented by ”, © being the number of 
degrees required to double the es at 32° original temperature. 
= (046) Sie _6 (2) 
Putting 9=491, according to ss ee we shall have 6 = 1169-54 
= 88°:54 above the original temperature. 'T'o this extent, there- 
os the regenerator must fail, even if suipposed perfect, to absorb 
sensible heat which the air contains at the end of the 
stoke The difference, 333°-46, is the limit of possible economy 
o be secured by the use of this contrivance. Now expression 
(1) with the substitution of the value of 6 here Sbeuineal gives 
us, as the total amount of heat converted into power, 
0 
of non is balanced by the waste heat developed by unavailable 
88:54 MK, 
la 
reducing the mechanical power actually developed to an available 
amount of 31:5 MK,,. 
on as this waste is unavoidable, we are obliged, in instituting 
a comparison between the power necessarily expended, and the 
effect produced, to regard the engine as debtor to the entire 
amount of 120 MK,, while we pans it with the available power 
as computed by the formule laid down in another article in this 
Journal. 
Now 120-0456 MK, =88-2688 MK,, 
in which K, is the mechanical : equivalent of the specific heat of 
air at constant pressure. And, as ‘2376 is (according to Regnault’s 
most recent determination) the specific heat of air at constant 
pressure, that of water being taken as unity, 
88-2688 x -2376= 20-97 MK,, 
expresses the positive power developed by the engine in mechatl- 
ical equivalents of the specific eet Sega other words, 
