NIPHER — OUTPUT OP" THE NON-CONDENSING STEAM ENGINE. 44I 



which could not be chsthiguished ftom a right line. Its equation 

 was of the form 



ZV =: k /''// . . . . . (15) 



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

 however the equation of an equilateral hyperbola, the asymptotes 

 of which are 



if « = 



b-\-c 



/?2 / 



« = CO if ^y = ^ - {k-\-P,) 



It is manifest therefore that the part of the parabola examined 

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

 observations made upon an engine. 



Multiplying (15) through by ^~^" ^ve have 



33000 



S^^ ^2.rkn _2r:rkn^ (16) 



33000 33000 



This is the equation of a parabola and corresponds to (10), 

 which is likewise a parabola when P' is constant. 



Differentiating (16), the condition of maximum output is found 

 to be 



n' = ^ \, (17) 



or the speed must be one-half that which the engine should have 

 at the same boiler pressure if rv = 0. 



The condition for maximum, according to this, would be 



P- = a^ + 2b'^n (iS) 



It will be observed that this is a right-line, tangent to the para- 

 bola (11) where n = o. According to (11), these values of n 

 represented by (17) would be somewhat too large. 



2 TT ^ TV 



Solving (15) for n and multiplying by 



33000 



The condition for maximum obtained from this equation is 



iv' = \ k (20) 



where ~v' is one-half the load which will bring the engine to rest 

 -at that pressure. 



