30 MA THEM A TICS 



and brackets are used in formulas to indicate that the quan- 

 tities enclosed by them are to be subjected to the same opera- 

 tion. The sign before an expression in parentheses or 

 brackets affects the entire expression, and if the parentheses or 

 brackets are removed, the signs + and within them must 

 be interchanged; but if the sign + precedes the brackets, 

 they may be removed without changing any signs. For 

 example, the expression 212 (36+75 49) becomes, when 

 the parentheses are removed, 212-36-75+49; but the 

 removal of the brackets from the expression 65 + [20 +9 14] 

 gives 65+20+9 14. The multiplication sign is ordinarily 

 omitted before and after parentheses or brackets, and before 

 the radical sign; thus, the expressions 36 X( 18 +22) ,[760 315J 

 X1.07, and .21 X VT40 27 would ordinarily be written 

 36(18+22), [760-315]1.07, and .21A/140-27. The following 

 examples will serve to illustrate the use of formulas. 



EXAMPLE. What is the volume of a block of cast iron 28 in. 

 long, 15 in. wide, and 12 in. high? 



SOLUTION. Applying the formula previously given, and 

 substituting 28 for /, 15 for w, and 12 for h, the volume is 

 r = 28X15X12 = 5,040cu. in. 



One of the most familiar formulas, to the operating engineer, 

 is that used for finding the indicated horsepower of an engine. 

 This formula, as usually stated, is 



PLAN 



33,000 



in which H = indicated horsepower; 



P = mean effective pressure on piston, in pounds per 

 square inch; 



L = length of stroke, in feet; 



A =area of piston, in square inches; 



N = number of working strokes per minute. 

 The formula as stated may be used to find the horsepower 

 of any engine, provided the values of the quantities denoted 

 by P, L, A, and N are known. But sometimes it is desired 

 to find some other quantity, as for example, the diameter of 

 cylinder required to produce a certain horsepower, or the mean 

 effective pressure necessary to produce the desired power. 



