160 Prof. Barnard on the Elastic Force of Heated Air. 
' pes i eae | 
And, in the present case, ™” being =1220°-7, and m=:75, l 
will Have" the value ‘37309 instead of -25; and the dependent va- 
riables will be, 
1’ =815° (356° F 
P=10-823 Is. to the square theh. 
0-92 
Comparing this arrangement with ihe first in regard to econo- 
my, we find it to be inferior, in the ratio of ‘8264 to 1; but it 
has the advantage of requiring only about two-thirds as much ab- 
solute pressure in the cylinder 
hrough the formulas above given, we find by a tentative pro- 
cess, that the absolute maximum of power under this tempera- 
ture occurs, when the value of m is about 1-094, and that of l, 
‘4363. We have, ap these conditions, 
7’ = 869° a 
P=12-069 bs. to ae square ach 
= 88-52 
p 
And this arrangement compares with the first, in point of econ- 
omy, as *7285 to 1. Thus the increase of :power is accompanied 
by a more than oe increase of ome eee although the 
absolute pressure is still comparatively modera 
The relative economy of these several sides geioints as com- 
pared with steam expanding from five or three atmospheres to 
one, is exhibited at one view in the following. The temperature 
of steam at 5 atmospheres i is, according to the French academi- 
cians, 308°-8; and Prof. Thompson’s formula for the per-centage 
of heat converted into useful labor gives,* 
* The formula of Prof. Thompson is the follo owing. Let H be the mechanical 
equivalent of the total amount of caloric entering any thermo-dynamic machine; let 
7'’ be the tem ig ie ure 0 i e pad by fe auiering the machine, and 1, the same 
at leaving it; nf? s the fe ssion of temperature in working; 
and, putting Wi ib: ere the total w ref effect, it will generally be true that 
Wadi 
The formula of Prof. Thompson is apa however, only when the conditions. 
conform to the definition of a perfect thermo-dynamic = Dgin e, as laid down by Car- 
and adopted ompson and Clansius :—that is to say, an engine which, by 
e same amoun 
following. ori to ust be true, viz 
2% OF 
The formula which, in the at keneral. ‘Tosiiner, expresses the amount of heat 
utilized, rang H aang ae pnt amount drawn. from the source, is the follow 
ing ; 
a mi r kia Ie oh : 
