Polytechnic Association. 



833 



P' O B, and CBY'H^CBGE + BGY'; for all which areas 

 may be found simple numerical expressions. 



To make the case more 

 general, let the cut-off be 

 taken nearer to O or P, as 

 in figure 6. Then we need 

 to draw P' Y' so as to 

 mak©PP'.BC , D = d , B 

 Y'H'; orPOBO'D- 

 P'OB = C'BGH' + 

 BGY\ 



Putting, as before, P O 

 and OB = r, the foregoing equation 



P'r 



= P; P'0 = P 



becomes : 



K 1+hl l)-^ p *( 1+h ^ )- p *( 1+h HEf+x 



OrPV=2P/t(l-fhl-£-)- Vic (l + hl^) 



=P^(2+hlg)-P^(l + hl 2 T :) ; 



And PV=PJfc(l-Hi 1^-) 



If now we put r=l, and &=-|=J, as before, we shall find, 



F=£P fl+hl2l =±*p- 

 Now, as P, in this case, viz., k= 



-0.423P, nearly. 



:-§-, must be 2.6 times p (the mean 

 pressure, or that which would do the same work without cut-off), hence, 

 P '=0.423 x 2.6p=-1.0998p=1.1p, nearly. 



Inasmuch as the great advantage to be secured from the heavy- 

 piston high-speed engine is uniformity of distribution of work over 

 the stroke, it is evident that the proportion of the total steam pres- 

 sure which can be most beneficially employed in generating living 

 force during the first quarter revolution, in order that it may be trans- 

 ferred to the crank during the second, is, for every given value of the 

 cut-off, fixed and definite. The weight, therefore, which should be 

 given to the reciprocating parts of the engine, in order to secure the 

 most beneficial effect, is also equally fixed, when the steam pressure, 

 the area of piston surface, the length of stroke, and the angular 

 velocity of revolution, are given, along with the cut-off. 



Thus, if a is the piston area in square inches, and P' the pressure 

 per square inch, corresponding to P'O in Fig. 5, above (a pressure 

 ascertained by the formula foregoing, from the given values of P = 

 [Inst."1 53 



