NIPHER OUTPUT OF THE NON CONDENSING STEAM ENGINE. 435 



or P=P,^'^^^ .... (I) 



2~R-ln 



Multiplying this equation by 



33000 



/IIP = ^^-^^^'i^ 1 ^^^""^ (2) 



33000 33000 



The indicated horse-power is equal to the brake horse-power 

 plus the power required to drive the engine alone. 



In the equation leading to (i) the second member should 

 strictly contain a term =f{F', F") the exact form of which 

 would depend upon how the belt is applied. It is so small that 

 it cannot usually be measured on an indicator card, and is here 

 omitted. It may be inserted, however, without changing the 

 form of any of the succeeding equations. 



The equation for brake horse-power is 



^ilP = 



2 - r n zv 

 330'30 



^"' = iP-Po) (4) 



33000 ^ "' vt/ 



-^T R^ In P 

 /IIP = " "^ ^^ ^ . . . . (5) 



33000 



Taking /HP, as a function of ft and /', and (5) is the equation 

 of an hyperbolic paraboloid, the constant for which is entirely 

 independent of the condition of the engine or the steam with 

 which it is supplied. It depends solely on the geometry of the 

 engine (the unit of power being fixed). It involves only the 

 volume swept through by the piston-face during one stroke. The 

 performance of all engines in which this volume is the same 

 would always be represented by points on a common surface. 

 These points may be made to move about in any arbitrary man- 

 ner by variations in boiler pressure and load. 



If the boiler pressure is held constant, then h becomes some 

 definite function of if, and the point representing the 'perform- 



