182 MR W. J. M. RANKINE ON THE 
in fact, the resistance of the engine when unloaded. Now it is evident, that the 
maximum useful effect of the steam has been attained, as soon as it has expanded 
to a pressure which is in equilibrio with the pressure of the waste steam added 
to the resistance of the engine when unloaded; for any further expansion, though 
increasing the total effect, diminishes the useful effect. Therefore if we make 
R=R4+4 
R’ being the resistance arising from the useful work, and / the resistance of the 
engine when unloaded, both expressed in the form of pressure on the piston, the 
expansion corresponding to the maximum of useful effect will take place when 
| Ed hat | 
the corresponding ratio of expansion being . .. (3) 
fey (ST 
as (>; + ) 
The maximum useful effect with a given pressure on the safety-valve has 
been so fully discussed by M. pr Pamsour, that it is unnecessary to do more than 
to state that it takes place when the initial pressure in the cylinder is equal to 
that at the safety-valve: that is to say, when it and the useful resistance are the 
greatest that the safety-valve will permit. 
(30.) Annexed is a table of the values of some of the quantities which enter 
into the preceding equations in the notation of the Count DE Pampour’s works. 


Expression in the Notation Equivalent Expression in 
of this paper. M. DE PamBour’s Notation. 
BERRA. ee ao. (1+ 0) r+f 
Au > : - : av 
WV 3 : ; . Sx weight of one cubic 
foot of water. 
Pe : ; : : Pp 
l+e 
$ 
U+e 
c 
c a 
U+e 
(31.) As an illustration, I shall calculate the maximum useful effect of one 
pound, and of one cubic foot of water, in a Cornish double-acting engine, in the 
circumstances taken by M. p— Pampour as an example for that kind of engine : 
that is to say,— 
Clearance one-twentieth of the stroke, or c=a 
Resistance not depending on the useful load, f=  72\b. per square foot. 
Pressure of condensation, 3 P,= 576 |b. oie 
