442 TRANS. ST. I.OUIS ACAD. SCIENCE. 



This value of w is somewhat too small to satisfy (ii), although 

 as stated the error is probably always too small to have any im- 

 portance. Substituting these two values of «' and iv' in (3) and 

 we undoubtedly have a very close approximation to the maximum 

 output at any pressure P., 



^HP 



k 



33000 '^' 



where -— is the speed at that pressure when w ^ <? as com- 

 puted from (7) 'Vnd kr = the turning moment which for that 

 pressure must be applied to the shaft in order to bring the en- 

 gine to rest. This can be computed from (9). It is wr when 

 n = 0. 



In a similar manner we may represent indicated horse-power 

 as a function of boiler pressure. Solving (6) for P and substi- 

 tuting, as before. 



It may be remarked in passing that, for a constant value of/", 

 this is an hyperbola which represents the relation between mean 

 effective pressure and speed, with varying load. The asymptotes 

 of the curve are the vacuum line and the axis of the parabola of 

 maximum output, where 



b-\rc 



The only part of this curve which has any practical significance 

 is that included between the pressure axis and the line where P=^ 

 Pq. This part of the curve is marked P on Fig. 2, P' being the 

 line representing the corresponding fixed boiler pressure. Dur- 

 ing the operation here considered, the point representing the 

 performance of the engine would travel through a definite path 

 on the surface represented by (4). The hyperbola marked P on 

 Fig. 2 would be a projection of that path on the plane /*, «, while 

 the parabola (10) with P' constant would be a projection of that 

 path on the plane HP, n. 



The engine might indeed be driven by a belt at a greater speed 

 than that given it by the steam when w = o, and the mean eftec- 



