Mechanical Theory of Heat to the Steam Engine. 43 
since the negative work done by these must be equal to the pos- 
itive work done by the former, since otherwise, an acceleration 
or retardation of the motion would occur, which contradicts the 
supposition made, according to which the motion is to be uni- 
form. The surface of the piston describes the space (1—s) V, 
while a unit of weight of steam passes into the cylinder, and we 
therefore obtain for the work W the expression 
W = (1—«) V[(1+9).R+/}. . 
The useful portion of this work, on the other hand, which, to dis- 
tinguish it from the whole work, may be denoted by (W), may 
be represented by the expression 
= (1-—«)V. BR. 
If we eliminate the quantity R from this equation by means of 
the previous one, we hav 
W—(i—e) V.f 
(58) (W)= C3 2 
With the help of this equation, we may deduce the useful work 
from the whole wor as soon as the quantities f and 3 
termines these last, since the determination still rests upon too 
uncertain foundations, and the friction in general, is foreign to 
the particular object of this memoir. 
TABLE CONTAINING THE VALUES OF THK PRESSURE p WHICH HOLD GOOD 
d. 
FOR STEAM, OF ITS DIFFERENTIAL CO-EFFICIENT = g AND OF THE 
PropucT 7’.g EXPRESSED IN MILLIMETERS OF MERCURY. 
oe 
Centigrade, P A g A T’.g 4 
40° 54.906 “003 “935 0139 91 46 
4 57°909 ~3-145 t Sed 0144 365 Ps 
42 61-054 3291 -218 per 1014 
43 64-345 44h 3: o15, I po 
44 67-789 -60r 3522 o-16r 1116 
45 713 766 | 3-683 o167 | 117% 57 
46 35156 +935 o-173 1228 
47 Pe ee 4112 4023 o' 180 1287 64 
48 83-203 43 4:203 o185 ots 6 
49 87:4 a3 | 4388 ae a 
5o gr’ 4-679 4581 o 199 69 
St | 96-65 862 | 4780 | © 7 
52 101-541 “on 4987 o-2I 1621 74 
53 106-633 Seas 5-200. 0-221 1 78 
54 111-942 a 5-421 0-228 80 
55 117-475 5-766 0°237 1853 83 
56 123-241 6:006 5 0-244 87 
57 129°247 6°254 6-130 0-252 2023 3 
38 135-501 6-510 6-382 o 2112 
59 142°01L ¢ 775 6 o 2205 6 ‘ 
60 | 148-786 | 4048 | 6g o 2301 100 
61 155834 | 330 189 0286 24ot 103 
