232 KANSAS UNIVERSITY SCIENCE BULLETIN. 



to the boiling-point ; the area md'a'n represents the heat required to 

 heat the water to the point of vaporization ; na'h'o is the heat taken 

 in during evaporation; pc'd'm is the heat rejected during exhaust ; 

 a'b'c'd' is the heat equivalent of the work done. 



In actual engines, the expansion, instead of being carried to atmos- 

 pheric pressure, will stop at some point such as e (fig. 1), by the open- 

 ing of the exhaust, and there is a drop in pressure and temperature 

 approaching a constant- volume line, ef. In order to plot ef on the T</> 

 coordinates, we might find temperatures corresponding to slight drops 

 in pressure, and find the corresponding entropy values from the 

 formula : 



The curve may also be plotted graphically by making use of the 

 principle that corresponding points in each diagram divide the hori- 

 zontal lines through them in the same proportion. For example, to 

 transfer the point x from the pv diagram to the 7'^ diagram : Draw" 

 a horizontal gh through x, and draw also g^Ii^ at the temperature cor- 

 responding to the pressure at g. Divide g^h^ in a} in the same propor- 

 tion as gh is divided in x. Then we know that the percentage of 

 water evaporated, when x denotes its condition as to quality of dry- 

 ness, will be in the same ratio to gh, denoting complete evaporation, 

 as the heat required for partial evaporation will be to the heat re- 

 quired for complete evaporation; hence, -^ :=^ ~^- 



In order to apply this principle to transfer the constant-volume 

 line ef to the entropy diagram, we need simply take a number of 

 points on the line ef, pass horizontals through them, and draw the 

 corresponding horizontals on the entropy diagram, dividing the latter 

 set in the same proportion that the horizontals were divided in i\\Q pv 

 diagram by the line ef. 



It is evident that we may thus transfer any number of constant- 

 volume and constant-pressure lines to the entropy diagram, and that, 

 if a sufficient number are plotted, the diagram becomes a chart which 

 can be prepared in form for blue-printing or other method of duplica- 

 tion, and that any points, piVi, jhv-i, etc., may be exactly transferred 

 onto the chart by finding the intersection of the constant-volume and 

 constant-pressure lines corresijonding to piVi, p-iVi, etc., on the entropy 

 chart. 



As the chart represents the behavior of one pound of feed, it is 

 necessary, however, to transform an actual indicator diagram into a 

 diagram representing the behavior of one pound of steam before the 

 transfer to the entropy chart is made. This is done by measuring the 

 amount of cylinder feed by a water meter in the feed-water pipe, or 



