SECT, v.] NONCONDENSING ENGINES. 179 



Oliver Evans made a rude attempt to investigate the advantage of cutting off 

 the steam in high pressure engines, claiming the principle as his own ; but the 

 engine he describes is not arranged for that purpose ; he uses valves for the steam 

 passages: 1 the objection to valves above a certain size is the difficulty of opening 

 them. 



376. The proportions of the parts for expansion engines may be ascertained 

 by the same rules as for full pressure, (art. 366.) excepting that the velocity 

 should be found by the rule, art. 336. 



377. To determine the power of a noncondensing engine working expansively, 

 it will be most useful first to ascertain the mean effective pressure on the piston, 

 and from thence the power. 



To find the mean pressure, let the steam have to be cut off at the part of 



the stroke. Add 1 to 2*3 times the logarithm of n ; divide the sum by n and 

 subtract 0'4 from the result ; then the remainder multiplied by the whole force 

 of the steam in the boiler in Ibs. per circular inch, and 11 '55 subtracted from 

 the product, for the pressure of the atmosphere, the result is the mean effective 

 force of the steam on the piston in Ibs. per circular inch. 2 



To find the power, multiply the mean effective pressure by the square of the 

 diameter of the piston in inches, and by the velocity in feet per minute ; the 

 product is the Ibs. raised 1 foot per minute. 



To find its equivalent in horse power, divide by 33,000. 



378. Example. If an engine work expansively, the steam being cut off at 



1 Steam Engineers' Guide, p. 30 and 67. Philadelphia, no date. 



2 Making b + x = I, and b = , we have, (see art. 306) 



n 



pb(l+ hyp. log. *il ) = Jd. (1 + hyp. log. ) ; 



and therefore the power of a cylinder a inches in diameter, working at a velocity of v feet per 

 minute, is 



(1 + hyp. log. n) friction and resistance of the atmosphere. 

 The latter is -4 pa- v + 11-55 a 2 v ; hence 



a* v | p( l + h yP- lo g- " _ -4\ _ 11-55 j = the Ibs. raised 1 foot per minute. 



The hyperbolic logarithm of n is equal 2-30285 times the common logarithm of ; whence 

 the rule. 



When n is fixed by the rule, art. 372. viz. n = ?- , the formula reduces to the 



4tp + 11-55 



more simple form of, 



a v P (hyp. log. n) = the power in Ibs. raised 1 foot high per minute. 



