)54 



Economical Expansion in Steam Engines. 



For : when the steam-pressure (p^) becomes infinite, the 

 ratio (r^^) becomes zero, and the tangents to the curve of 

 efficiency are drawn from the origin {0, Fig. 1). 



/Q O JO £0 30 40 SO CO 70 SO 



Fig. 1, Curves of Efficiency. 



The point of tangency, which, for the ideal case, ABO 

 is found at the origin 0, where r=a: , is for the real case, C D H 

 found at H, a point corresponding to some finite value of r. 

 This point thus constitutes a limit to economical expansion such 

 as is here considered, and which is now, so far as the writer is 

 aware, first discovered. 



It was shown, in a paper read before the Society of Mechanical 

 Engineers, April, 1882,* that, by making the distance 0' , 

 measured toward the left from the origin, proportional to tbe 

 costs of engine, apart from the costs of supplying steam, and 

 drawing tangents from 0' , ratios of expansion at maximum 

 commercial efficiency could be determined. It is now seen that 

 such a limit as is above described is found not only for the real 

 but also for the ideal engine, when commercial efficiency is 

 studied, their limit being determined by the points of tangency 

 B or H, given by the lines 0' B, 0' K'. 



* Trans. Am, Soc. Mech. Engrs., 1882; Jour. Franklin Inst., May, June and September, 1882. 



