in different forms of the Air-E'ngine. 167 
PIV 1 & Ve 
yal V,, 
But, according to Mariotte’s law, P’V’/=P”V”; and we have 
just seen that ain whence the area G C D H is equal to the 
/ Ww Sais 
area F K EB; or, in other words, the second expansion is exactly 
balanced by the second compression :—a conclusion which we 
might, indeed, have independently drawn, since the same amount 
of heat which disappears in the expansion, reappears in the com- 
pression, 
The area F GC B, according to the third general principle sta- 
ted above, is the measure of the total amount of heat which the 
air has received from the source, converted into mechanical ef- 
fect. To find its value we observe, first, that if p, » and ¢ repre- 
sent the simultaneous pressure, volume and temperature (reck- 
v Z Dp ‘i 
oned from the absolute zero) of any gas, the expression rE will 
be, for that gas, a constant quantity. And if we take p,, v, and 
t, to express the values of these variables under ascertained cir- 
cumstances, as for instance at Fahrenheit’s zero, and under a 

given barometric pressure, then p sos may be put =R, and in 
, 0 
Ri 
any other condition of the gas we have py=Ri, and p = —. 
_ Now the differential of F GCB is pdv; whence, representing 
it by M (mechanical effect), we have, 
: Ww 
M = [Ete — f= do = Re h, 1. Vv 
v v 
between the limits V/ and V”. 
In like manner, area K H D E (=M’) will be 
Vv, yu 
M’ = Rr, h. 1. T= Rr, h. |. yi 
Ww s 
And the differential area, F GH K, which we will represent by 
W, will be 
yi 
W=M—M=R(r—1) hl 
If H, then, be the total amount of heat received by the gas, 
and of which the entire mechanical effect is represented by M, 
the fraction converted into available work will be found thus: 
i y" _t'—T, 
M: We: Reb. ¥ RQ a hl. o7t? Hs ere 
It is geometrically evident that no larger a fraction of the heat 
absorbed by a gas fluctuating between the temperatures * and 1, 
“an be made available, than that here represented ; for the differ- 

T 
