282 F. E. JVipher — Non-condensing Steam Engine. 



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 



_ Inmw . . 



Php = .... (3) 



33000 v ' 



j? H p = ^i^(P_P o ) ... (4) 

 33000 v 0/ v ; 



InRHnP 



aiKl JHP = ^3000- • * • {5) 



Taking 7hp, as a function of n and P, 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 sur- 

 face. These points may be made to move about in any arbi- 

 trary manner by variations in boiler pressure and load. 



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

 definite function of w, and the point representing the perform- 

 ance of any engine would traverse some definite line upon the 

 surface. 



Equation (4) which represents brake horse-power, is also the 

 equation of an hyperbolic paraboloid, having the same constant 

 as the one represented by (5). The two surfaces have a com- 

 mon pressure axis, and the coordinate planes of HP, n for the 

 two surfaces are separated by the distance P a . On each of 

 these surfaces, a condition of constant load, w y would be repre- 

 sented by some definite line, and (3) which is the ordinary 

 formula for ^hp is a projection of that line upon the coordi- 

 nate plane of HP, n. 



For any definite values of n and _P, a vertical ordinate drawn 

 through the surfaces of _5hp and 7hp would determine simul- 

 taneous values of brake and indicated horse- power. The dis- 

 tance between the surfaces measured on this ordinate would 

 represent the power consumed in the engine itself. Passing a 

 plane through these surfaces at right-angles to the speed axis, 

 the intersections with the two surfaces would be parallel lines. 

 The distance between these lines measured parallel to the HP 

 axis is constant, and represents as stated the power consumed 

 in the friction. It is constant for all loads, as experiment 

 shows it to be, and increases uniformly with the speed at con- 

 stant pressure, or by (4) and (5), 



