20 MATHEMATICS 



This expression could be shortened by representing each 

 quantity by a single letter. Thus, representing the safe load 

 by W, the area of the cross-section of the post in square 

 inches by A, the length of the post in inches by L, the least 

 dimension of its cross-section in inches by D, and substi- 

 tuting these letters for the quantities that they represent, 

 the preceding expression would reduce to 



a much simpler and shorter expression. This last expression 

 is called a formula. 



As a further example, consider the rule as explained on 

 page 300 for finding the safe resisting moment of a rein- 

 forced-concrete beam, which is as follows: 



Multiply the area of the steel reinforcement in square inches 

 by the distance from the center of the steel to the top of the beam. 

 Multiply the product by 13,760. The result is the safe resisting 

 moment of the beam in inch-pounds. 



In this case, let M represent the safe resisting moment 

 in inch-pounds; a, the area of the steel, in square inches; 

 and d, the distance, in inches, from the center of the rein- 

 forcement to the top of the beam. Then, the preceding 

 rule may be expressed by the following formula: 

 M=13,760XdXa 



The formula just given shows, as was stated in the begin- 

 ning, that a formula is really a shorthand method of express- 

 ing a rule. It is customary, however, to omit the sign of 

 multiplication between two or more quantities when they 

 are to be multiplied together, or between a number and a 

 letter representing a quantity, it being always understood 

 that when two letters are adjacent with no sign between 

 them, the quantities represented by these letters are to be 

 multiplied. Bearing this fact in mind, the formula just 

 given can be further simplified to 



M=13,760<fa 



The sign of multiplication, evidently, cannot be omitted 

 between two or more numbers, as it would then be impossible 

 to distinguish the numbers. A near approach to this, how- 

 ever, may be attained by placing a dot between the numbers 



