SECT, iv.] AND PROPORTIONS OF ENGINES. 165 



logarithm of n; then 120 times the square root of the product is the velocity in 

 feet per minute. 1 



Example. Let the steam be cut off at one-fourth of the stroke, then n = 4 ; 

 and let the length of the stroke be 8 feet. The logarithm of n is O60206 ; 

 therefore, 0-60206 x 2-3 + -7 is 2-0847, which multiplied by one-fourth of the 

 length, or 2, is 4'169. The square root of 4-169 is 2'04 ; consequently, 2-04 x 120 

 = 245 feet per minute, the velocity for an 8 feet stroke when the steam is cut off' 

 at one-fourth of the stroke. 



337. In the usual construction of engines not intended to act expansively, put 

 n = | ; and then take 103 times the square root of the length of the stroke. 



For steam engines working expansively at the ordinary pressure of about 8 

 Ibs. on a circular inch of the safety valve of the boiler, the best proportion 

 for cutting off the steam is about one-half the stroke, and then the rule becomes 

 100 times the square root of the length of the stroke in feet, for the best velocity in 

 feet per minute. 



Other rules may be easily derived from the investigation in the note. 



338. In single acting engines, regulated by a fly, the same relation would 

 obtain between the length of the stroke and the velocity of the piston ; but such 

 engines cannot be used with advantage for producing a continuous motion. 



OF THE MAXIMUM OF USEFUL EFFECT IN ENGINES FOR RAISING WATER. 



339. In single engines for raising water we have two strokes to consider, of 

 different species ; the piston being caused to ascend by a counter weight, which 

 should be capable of raising the piston in a short time without adding materially 



1 It has been shown (art. 306) that the expanding power of steam is p b hyp. log. ^ + J , 



b 



which added to the uniform portion, and the resistance r from friction and uncondensed vapour 

 being subtracted, it is 



p b ( 1 + hyp. log. - - r j = the power ; 



but b + x = I, the length of the stroke, and b = ; hence, 



n 



S- (1 + hyp. log. n r) = the power. 

 n 



In ordinary circumstances r = -3, consequently, 



120 V (-7 + hyp. log. n) = the velocity in feet per minute. 



