or STEAM-ENOINES AVITH DET SATUEATED STEAM. 
185 
Let OB=^„ and BC^'Ui, represent the pressure and volume of admission, and the 
corresponding absolute temperature 
Let 0A=^2? AD=W2, represent the pressure and volume at the end of the expan- 
sion, and #2 the corresponding absolute temperature ; then 
is the ratio of expansion^ and 
the effective cut-off. 
Let AF=j93 be the pressure of exhaustion, and 4 the corresponding absolute tempe- 
rature ; 
Let ^4 be the absolute temperature of the feed-water ; and 
Let 0Q=P4 be the corresponding pressure. 
The work of one pound of steam is represented by the area of the diagram ABCDEFA, 
consisting of 
the area ABCDA=\ vdp, and 
Jp. V (15.) 
the area ADEF =vj^p.;,—p^ ; J 
while the expenditure of heat per pound of steam is represented by the area contained 
between the line QFABCD, and the two indefinitely extended adiabatic curves, QS, DN, 
and may be distinguished into the following parts : — 
the sensible heat SQBL =^{ti — ^4)) 
the latent heat of evaporation, LBCM=Hi ; > (1^-) 
the latent heat of expansion =MCDN.j 
Thus it appears that the work of one pound of dry saturated steam exceeds that of 
one pound of steam which expands from the same initial pressure to the same final 
pressure without receiving heat, by an amount represented by the area JICDEJ, while 
the expenditure of heat is greater by the quantity represented by the area MCDN. 
To find the area ABCDA, which represents part of the work, the value of v corre- 
sponding to any value of^ is to be taken from equation 6, and that of H, the correspond- 
ing latent heat of evaporation, from equation 7, giving 
v= 
a — bt 
dp ’ 
dt 
WO 
which being multiphed by dt, and integrated between and fke initial and final 
temperatures of the expanding steam, we obtain for the area ABCDA, 
J" vdp=^^ 0 — ^^(^^=ahyp. logy— J(^i— 4); 
(17.) 
MDCCCLIX. 
2 c 
