184 
ME. MACQrOEN EA^fKIKE OX THE THEEMO-DTXAAHC THEOET 
of the expansion, but for the partial liquefaction ; and the proportion of the steam 
liquefied is 
ID (11.) 
AD ^2 
The expenditure of heat per pound of steam (supposing the feed-water to be supplied 
to the boiler at the temperature of exhaustion, t^) is represented by the mdefinitely-pro- 
longed area EFBCM, and consists of two parts, — 
The sensible heat KFBL= J(^,-4), where J is the specific heat of nquid-water,| ^ 
772 lb. per degree of Fahrenheit, and the latent heat LBCM=H (see eq. 7.)J 
If the feed-water is supplied to the boder, not at the temperature of exhaustion, f,. 
but at some lower temperature, the latter temperature must be substituted for the 
former in the formul®. 
The application of these principles to steam-engines without jackets has been fidl) 
explained and exemplified in the paper already referred to in the Philosophical Trans- 
actions for 1864. 
Calculations respecting such engines in ordinary cases are facilitated by approximate 
formulge, founded on the fact that within the usual limits of pressm-e, inz. with 
from one to twelve atmospheres, the coordinates of the curve C^I are related by the 
equation 
p OC s- V nearly * ( 
The expenditure of heat can be roughly computed to within about of the truth. b> 
the formula i \ 
^;,(13ii?,-f4000)*, (1^-) 
being in cubic feet and in pounds on the square foot *. 
Theory of the Work, Heat, and Efficiencij of Dry Saturated Steam. 
In the following investigation it is assumed that the steam while expanding receives 
just enough of heat to prevent any part of it from condensing, without super-heating it. 
This assumption is founded on the fact, that dry steam is a bad conductor of heat as 
compared with liquid water, or with cloudy steam, and that after cloudy steam has 
received enough of heat to make it dry or nearly dry, it will probably receive little more. 
The assumption is justified by the fact, that its results are confirmed by expermient. 
The symbol r is used to denote the volume of one pound of steam in cuhc feet, and 
the symbol p to denote pressure m pounds on the square foot ■, so that pressure in pounds 
P 
on the square inch is denoted by 
In fig. 2, as before, let CDG be the curve whose coordinates represent the volumes 
and pressures of dry saturated steam. 
* Manual of Applied Mechanics, Art. 056. 
