1882. 113 Trans. N. Y. Ac. Sez. 
expansion, and a better notion of the relation of these several curves 
gained, than by the study of the tabled quantities. 
The writer next describes the curves of efficiency, of work and of 
mean pressures, to be obtained where steam is expanded in a non-con- 
ducting cylinder. They are easily deduced and easily constructed, and, 
by reference to Zeuner’s formula, the engineer can determine them with 
a satisfactory degree of accuracy for all cases likely to arise in his prac- 
tice. 
Next, studying the behavior of steam in a metallic cylinder, he finds 
vitally different conditions and results; but given the law of variation 
of composition of the mixture with change of point of cut-off, or of 
ratio of expansion, it is, nevertheless, not only practicable but easy to 
determine curves of efficiency and to deduce values of the best ratio of 
expansion for any given case. 
Where direct experience can be resorted to, to determine the cylinder 
condensation, it is easy, as shown later, to obtain exact results when 
seeking the ratio of expansion at maximum efficiency of fluid, of engine, 
or of capital, or in the solution of a rarer case which requires that the 
point of cut-off which gives most work for a given expenditure on the 
whole plant be determined. 
The author describes and illustrates the construction and application 
of curves of efficiency for real engines, in the solution of important 
problems, and concludes by summarizing his work and leading the 
reader to the final deductions : 
“The curve of variation of efficiency above traced, of which the ab- 
scissas measure varying quantities of steam used in a given steam-cyl- 
inder, while the ordinates are proportional to the quantities of work 
done by those amounts of steam, is a curve of entirely different charac- 
ter and form, and often widely different in location, from the curve of 
adiabatic mean pressures or other curve of mean pressures exhibiting 
the work done by various quantities of steam expanding under given 
fixed conditions in a non-conducting vessel. 
‘That no predetermination of the efficiency of any proposed engine, 
whether of fluid, of machine, or of capital, can be made unless the true 
curve of efficiency can be obtained for the assumed case. 
“That the most certain and the most satisfactory solution of any 
problem of efficiency will be that obtained by first securing the elements 
of the curve of efficiency from actual engines operated in the manner 
proposed for the case taken. 
“That having obtained by experiment upon any engine, the ‘curve 
of efficiency,’ as defined by the writer, the efficiency of fluid, of engine, 
and of capital expended to do a given amount of work, and the quan- 
tity of work to be obtained most cheaply from a given engine, may all 
