436 TRANS. SI . LOUIS ACAD. SCIENCE. 



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 common 

 pressure axis, and the coordinate planes of HI*, n for the two surfaces 

 are separated by the distance Pq. On each of these surfaces, 

 a condition of constant load, tv, would be represented by some 

 definite line, and (3) which is the ordinary formula for ^111' is a 

 projection of that line upon the coordinate plane of HI', n. 



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

 through the surfaces of ^ HP and /HP would determine simulta- 

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

 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 be- 

 tween 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 constant pressure, or by (4) and (5), 



r^(/HP)1 zTtR^lP 



I ^'' ) p ^ 33000 



r ^(^l lP)l 2 7:R-^l{P-Po') _ 2-^'^^' 



[ ^« J ^ ^ 33000 ^ ■" 33000 



In Fig. I, oP' and oA" are the axes of pressure, and HP. ^.4 " 

 is the line of atmospheric pressure, and VV is the vacuum line. 

 The lines of and P^ p' are rectilinear elements in the surfaces of 

 /HP and ^HP at constant speed, the ordinates Pp" and Pp' rep- 

 resenting simultaneous values. If the mean effective pressure 

 were reduced to zero, the engine being driven at the same 

 speed by means of the belt, the power required is represented by 



