178 MR W. J. M. RANKINE ON THE 






Q 7 if 
and Or=—— OV 
V Peer 
iB a2a —1 
TT 
we obtain F 
Om kr 1 Vv 
x pee gee cr (43.) 
a 72 =i 
: : OV 
and denoting the coefficient of vy by -», 
dlog m _ _dlogS _ 
Diag Nala ad PAE eae 
_ dlogV _ 1 
and because alae = aaron 
7 t 7 
dlogm _ Bala 1 (44.) 
dlog P 2 ( aaa) 
ca. 7? 
dlog $ 1 
Tep= 7 @-» (I-=~_) =-« 
d log P ( ( 9 -) 
aay 
As the mean temperature of the liquid thus produced more or less exceeds 
that of the remaining vapour, a small fraction of it will be reconverted into 
vapour, if the expansion is carried on slowly enough; but its amount is so small, 
that to take it into account would needlessly complicate the calculation, without 
making it to any material extent more accurate. 
(23.) The extreme complexity of the exponent oc, considered as a function of 
the pressure P, would render a general formula for the expansive action / Pd S very 
cumbrous in its application. For practical purposes, it is sufficient to consider 
the exponent ¢ as constant during the expansion which takes place in any given 
engine, assigning it an average value suitable to the part of the scale of pressures 
in which the expansion takes place. For engines in which the steam is intro- 
duced at pressures not exceeding four atmospheres, I conceive that it will be suffi- 
ciently accurate to make 
6 
7 . 
while for engines in which the initial pressure lies between four and eight atmo- 
spheres, the suitable value is 
= 
The utmost error which can arise from using these exponents is about 74 of 
the whole power of the engine, and that only in extreme cases. 
Making, therefore, 
