MATHEMATICS 31 



To find these quantities, the, order of the terms in the fore- 

 going formula must be altered, bringing the values to be 

 found to the left of the equality sign and the remainder to 

 the right. This operation is called a transformation of a 

 formula. The horsepower formula, transformed so as to give 

 the values of the piston area and the mean effective pressure 

 necessary to produce a desired horsepower, are 



33,0007? 

 = PLN 

 and 



33.00Qg 



LAN 



EXAMPLE. Find the diameter of the piston of a steam engine 

 that is designed to produce 40 H. P., if the stroke is 30 in., 

 the mean effective pressure is 28 Ib. per sq. in., and the speed 

 is 75 R. P. M. 



SOLUTION. The length of stroke in feet is L = 30-=-12 

 = 2.5 ft.; the mean effective pressure is P 2S Ib. per sq. in.; 

 as there are two working strokes to each revolution, 2V = 2X75 

 = 150; and // = 40. Substituting these values in the formula 

 for the area of the piston, 



33,000X40 



The diameter of a circle having an area of 125.7 sq. in, is 

 about 12f in. The required diameter of the piston, or of the 

 cylinder, therefore, is 12| in. 



If a segment of a circle is not greater than a semicircle, its 

 area may be found by the formula 



irr z E c 



A= --- (r-h), 

 360 2 



in which A = area of segment ; 

 7r = 3.1416; 

 r = radius of circle; 



E = angle, in degrees, obtained by drawing lines from 

 the center to the extremities of arc of segment; 

 c = chord of segment; 

 h = height of segment. 



