44° TRANS. ST. LOUIS ACAD. SCIENCE. 



When n = o the slope is therefore twice that of the line of 

 zero load. 



The value of « in (ii) is 



h-X-P^A-E , I I ; : 



« = - ^47 ± f+cj (^'+ A+^) (/'+/") . (13) 



Hence the vertex of this parabola is at the intersection of the line 

 of zero load (7) with the vacuum line. Its position is 



P' = — // 



^^„ _ _ h + P, + E 

 b-\-c 



This value of «'' is rather lai'ge and therefore the part of the para- 

 bola which corresponds to -a possible range of engine speed will 

 be very nearly a straight line. The axis of the parabola is of 

 course parallel to the pressure axis. It will be observed that all 

 lines of constant load represented by (8) intersect the vertical line 

 (parallel to the HP axis) which contains the vertex of the parabola 

 of maximum effort. In (8) the condition P' = — h at once gives 

 the condition 



" = V-\r^ 



and this entirely independent of iv. 



The observations made regarding the parabola of maximum 

 output justify the presentation of another formula which was de- 

 duced empirically from a large number of brake determinations. 

 The discovery of that formula was in fact the occasion for the 

 present investigation. 



The experiments were made by taking constant loads on a fixed 

 brake-arm varying the speed of the engine from 200 to 800 revo- 

 lutions, for each load, by means of a throttle. The pressure of 

 the supply steam was measured by means of a gauge between 

 the throttle and the steam-chest, the cut-off remaining fixed. 



The observations for constant load all satisfied, equations of the 



form 



P> = a-\-b'n . . . . (14) 



This equation is identical with (S). Computing from each 

 equation the value of n for a given pressure, these values of n 

 were plotted with their respective values of ty, and gave a line 



