On the Expenditure of Heat in the Hot-air Engine. 221 
or at constant volume, is the same for all densities between 1 and 
10; and for all temperatures between — 30° and + 225°, centi- 
grade ( —22° and + F.);* so that, for all the purposes of 
this inquiry, we may pce this element as invariable, even if it 
should not prove to be so under all possible circumstance 
Now, in the case presented in our paradox, the air, at ve end 
of the stroke, i is under a pressure easily determinable by the fol- 
lowing formula, 
p'=p(1+«4)o, 
which p’ represents the pressure — p the normal atmos~- 
haric pressure, 15 Ibs. per sq. inch, 6= the temperature above 
melting ice, in degrees F'ah., 9= the density of the atmospheric 
1 
Pl (the co-efficient of expansion per de- 
gree F., according to-Regnault, to be applied to the volume at 
: ) If, to simplify the matter, we m e o=1, then « 
will become at the assumed weather tem pote of 60°F. = 
1 
air at the time, and «= 
=) 
ae 
519 ico and @ must be reckoned from 60° upwards, in- 
stead of from 32°. Its value at the end of the stroke, according 
to our former ai atid is 422°. Hence p’=27°2 lbs. per sq. 
tip 1-813 atmosphere 
, as the air of the ie. at the temperature of 60°, when 
0=0, 5 es the same elastic force, its density must, by the same 
formula, be now =1:813. From this density to density 1, there- 
by Poisson, about 1- 30 If cies s air had been heated 
- Comptes goon, Apr. 18,1 
+ This is the mean, or about ap ean, of two values given by Poisson. But Pois 
son gives also 1421, ‘as a value determined by Dulong for air perfectly dry, and be 
also gives 14061, as a value determined by direct Tongue. on the velocity of 
oO 
e y Ma , for 
Jul scot received — the present article was tes apt rie at Ry 1 324, 
determined experimentally by Mr. Petrie. On the other hand, Mr. Rankine in the 
Lond. Phil. Mag., for * une, and supplement for the same sho ‘gives 1°40, a ‘41, 
as the cosa which contain the tru Pec and 1:4094 as the value determined by 
observati velocity of soun Z Poisson inclines to the largest of all the values, 
(1-421), on the gro that observations on sound, are liable i a f 
small, in ein Ss of a in the quantity of heat contained in the air un- 
dergoing compression and dilatation. 
With the increase a 7, bo cag the positive and the Piieth terms of pressure in 
the air engine are increased ; but the advantage is on the whole on thi sities ve side. 
Thus, if we se go pe ge infttead of 1 36, we lose above 7 per cent. of available ood 
es is, powe and nee Rs we adore F 14094, we shall gain n 
ly 11 per cent. of ‘available power, value first in duced into the text is fal 
ote to stand, though perhaps the Tpolate of sachs or of a higher 
num 
ing t Bg pores 
a_i Seeing obmet tion en that the ociaamsa equivalent of a unit of 
