in different forms of the Air-E‘ngine. 169 
We have now four temperatures. That which we have called 
v must be raised in the same ratio as the volume is increased dur- 
ing the expansion at constant pressure. Put 7” for the tempera- 
ture at volume V”, and also +, and +,, for those corresponding to 
, and V,,. 
_The mechanical equivalent of the total amount of heat in the 
ait at volume V’ and pressure P’, may be found thus. In expand- 
ing from V’ to any other volume, v, the pressure (p) becomes 
¥eVs 
-»() 
P v 
And the work done, during an infinite expansion, will be 
& oo / Vs 
[oin=ft(C)t0=P®, 
yv' v' Pw 
If, then, 7 represent the ratio of the specific heat of air at 
constant pressure to that at constant volume, the mechanical - 
equivalent of the heat absorbed, while the temperature is rising 
om t’ to t” and the pressure is constant, will be 

vP'V! [a — 1 
(ee) 
And, in the value of W- above, Me ee si and (; Ls - 
Which, substituted, give us W = a =] (1 an 5 
Whence aA => 2H; 
In an air engine which discharges the air from the working 
cylinder at a pressure above that at which it is received into the 
economical ratio. In this case, if the valves are adequate to afford 
lustant relief to the excess of pressure, 
the air, without being set free, were sud 
the supply before compression. : 
In this case, F BC G may represent, as 5 
Ore, the work, done at the constant F s 
Pressure P’, and GC DH, that during the 
second expansion. DEK L will be the L 
tepresentative of the effect of the first 
. 
compression; and F BEK that of the 
Second, 
Seconp Series, Vol. XVIII, No. 53.—Sept., 1854. 
