22 MATHEMATICS 



The main thing to be remembered is that when a formula is 

 given in which the same letters occur several times, all like letters 

 having the same primes or subs, represent the same quantities, 

 while those which differ in any respect represent different 

 quantities. Thus, in the formula 



R, A/A+/2 + /3 + /4 



R= \ A 



R represents the radius of gyration of a section composed of 

 four parts ; /i , 1 2, Is, and /4 represent the moment of inertia 

 of the respective parts about the same axis around which R is 

 taken; and A represents the total area of the section. 



It is very easy to apply the above formula when the 

 values of the quantities represented by the different letters 

 are known. All that is required is to substitute the numerical 

 values of the letters, and then perform the indicated oper- 

 ations. Thus, suppose that the values of I\, 1 2, fs, and 1 4 

 are 4.2, 3.6, 7.5, and 9.8, respectively, and that A is equal 

 to 8 sq. in. Then, the value of R may be found by substi- 

 tuting in the above formula; thus, 



j. ^-3375-1.77 in. 



Attention is called to one or two other facts relating to 

 formulas. 



Expressions similar to r^rr sometimes occur, the heavy line 



indicating that 160 is to be divided by the quotient obtained 

 by dividing 660 by 25. If both lines were light, it would be 



impossible to tell whether 160 was to be divided by -^- or 



o 



whether ^^ was to be divided by 25. If this latter result 



OOU 



160 



rififl 



were desired, the expression would be written -^r-. In every 



300 



case the heavy line indicates that all above it is to be divided 

 by all below it. 



In an expression like - g^, the heavy line is not neces- 

 7+ ~25 



