286 F. E. Nipher — Non-condensing Steam Eng%ne. 



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 



n , l= _ h+P + E 



b + c 

 This value of n" is rather large and therefore the part of the 

 parabola 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 ver- 

 tical 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 



b + c 

 and this entirely independent of w. 



The observations made regarding the parabola of maximum 

 output justify the presentation of another formula which was 

 deduced empirically from a large number of brake determina 

 tions. 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 revolutions, 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 (8). Computing from each 

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

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

 which could not be distinguished from a right line. Its equa- 

 tion was of the form 



w = k — Jen .... (15) 



This equation corresponds' to (9) with P' constant, which is 

 however the equation of an equilateral hyperbola, the asymp- 

 totes of which are 



., h + P a + E 



to= oo it n = — ^ 



b + c 



n= co if 10 = — — (b + P Q ) 

 r 



It is manifest therefore that the part of the parabola exam- 

 ined would differ so little from a right line that (15) would 

 satisfy any observations made upon an engine. 



