OOU A century's i'Rogkp:ss of thk steam engine. 



our own time, unci sliohtly lesser gains, with a progressivelj'^ decreas- 

 ing" rate of gain, are likely to continue for the immediate future, pre- 

 cisely as the rates of increase of steam pi'(>ssure. of e\i)ansion ratios, 

 and of engme speeds may he expected to extend the curves, through 

 the next decade or more, ahmg the same directions as hitherto observa- 

 ble in the diagrams, provided no umwpected change, due to invention 

 or the approach of the curve to an as yet unknown critical point, 

 shall compel a change in the law of progress. No such change atf'ect- 

 ing our pro])hecy. we have a safe, a scientitic. and an instructive and 

 availably useful prediction. "Science here reads an oracle." 



The limit for the inunediate future would seem to be about lO 

 pounds of steam. 1 pound of fuel, and something inside 200,000,000 

 foot-pounds duty, beyi^nd which figure it would be rash to expect 

 further progress, except under conditions still l>eyond the view of the 

 engineer of this time. 



Individual engines have excelled in efficiency the recordj^ here itidi- 

 cated as the best general I'esults of the progressive improvement of 

 the century. It may prove interesting to gauge both the approxima- 

 tion of the averages already presented and of the individual machine 

 to the ideally perfect steam engine. Were it p!actical)le to produce 

 an absolutely perfect thermodynamic machine, whether steam engine 

 or any other form of heat engine, and whether operated with gas, 

 vapor, liquid, or even solid working substance, its maximum efficiency 

 would not be unity, but that fraction which is measured by the ratio 

 of the working range of temperature to the absolute temperature of 

 its maximum limit, the Carnot efficiency. This is therefore what 

 must be accejjted as the standard with which to compare any given 

 case. Numerically it is a variable quantity, obviously increasing with 

 the elevation of the steam pressure in the case of the steam engine. 

 It is known to be pro]joitional very closely to the logarithm of that 

 pressure where the back pressure is a practical minimum. Its value 

 is sufficiently accurately given for present purposes by the expression, 

 measuring costs in steam, heat, and fuel, 



in which for heat units per horsepower per hour a may be assumed 

 to l)e about 15,000; for sttMUu in pounds per horsepowei' per hf)ur, <( 

 may l)e taken at 15; and for fuel take a at 1.5. For the measure of 

 efficiency, unity as the standard, we will employ the expression," 



^=12.5 logy, 



which will serve within the customary range of steam pressures. 



Employing these several expressions, it is seen that the efficiency of 

 the Carnot engine, under the usual conditions of pressure range, may 

 be t;iken at 25 p(M- ccmt for 100 pounds steam pressure, and that the 



