or STEAM-EIS'GINES WITH DET SATUEATED STEAM. 
187 
some standard temperature, such as that of melting ice (i^9=32°+461°‘2=493®'2 Fahr.); 
and let 
U=f 'U(?» = ahyp. log”--J(^— ^o) (22.) 
jpo ^0 
be the area contained between HG and another parallel ordinate of the curve CDG, 
corresponding to the absolute temperature t. 
Then by the aid of tables of the function U, the equations 18 and 19 can be put into 
the following form : — 
W=:U,-U,+i;,(^2-i?3); ] .23) 
=U, — U 2 + J (4 — ^4 )-\-a—U^ J 
Tables of the values of jp, v, and U, for every ninth degree of Fahrenheit’s scale 
from 32° to 428° above the ordinary zero, have been calculated, and are now being 
printed*. As an example of the results contained in them, the following extract is given 
for every thirty-sixth degree from 104° to 392° Fahrenheit. 
Extract from Table. 
T. 
t. 
P- 
V. 
u. 
104 
565-2 
152-6 
312-8 
112290 
140 
601-2 
414-3 
122-0 
161340 
176 
637-2 
987-6 
53-92 
206410 
212 
673-2 
2116-4 
26-36 
247950 
248 
709-2 
4152 
14-00 
286290 
284 
745-2 
7563 
7-973 
321780 
320 
781-2 
12940 
4-816 
354670 
356 
817-2 
20990 
3-057 
385200 
392 
853-2 
32520 
2-025 
413580 
For the purpose of interpolating intermediate numbers in such tables, the logarithms 
ofp and V are more convenient than those numbers themselves, as their successive diifer- 
ences are more nearly uniform. 
Approximate Formulce. 
As the formulas of the preceding section require in their use a considerable amount 
of calculation, and in some cases the solution of transcendental equations by trial and 
error (unless special tables are at hand), it is desirable to have, for the purpose of 
solving ordinary practical problems, approximate formulae of a more simple kind. 
Those which will now be explained were arrived at by a process of trial, based upon 
a table of the results of the exact formulae ; and their agreement with the exact for- 
mulae, and with experiment, has been tested for initial pressures ranging from 30 to 
120 lbs. on the square inch, and for ratios of expansion ranging from four to sixteen. 
* In a work “ On the Steam-Engine and other Prime Movers.” 
2 c 2 
