MATHEMATICS 21 



that are to be multiplied together, and this is frequently done 

 in works on mathematics when it is desired to economize 

 space. In such cases it is customary to put the dot higher 

 than the position occupied by the decimal point. Thus, 2-3 

 means the same as 2X3; 542-749-1,006 indicates that the 

 numbers 542, 749, and 1,006 are to be multiplied together. 



It is also customary to omit the sign of multiplication in 

 expressions similar to the following: aX ^Ib + c, 3X(bi-c), 

 (b + c)Xa, etc., writing them a^lb + c, 3(b + c), (b + c)a, etc. 

 The sign is not omitted when several quantities are included 

 by a vinculum, and it is desired to indicate that the quantities 



so included are to be multiplied by another quantity. 



For example, 3Xb+c, b + cXa, ^b + cXa, etc., are always 

 written as here printed. 



Before proceeding further, it may be well to explain one 

 other device used by formula makers, and which is apt to 

 puzzle one who encounters it for the first time. It is the 

 use of what mathematicians call primes and subs., and what 

 printers call superior and inferior characters. As a rule, 

 formula makers designate quantities by the initial letters of 

 the names of the quantities. For example, they represent 

 moment by M, stress by s, length by /, etc. This practice 

 is to be commended, as the letter itself serves in many cases 

 to identify the quantity that it represents. Some authors 

 carry the practice a little further and represent all quantities 

 of the same nature by the same letter throughout the book, 

 always having the same letter represent the same thing. 

 Now, this practice necessitates the use of the primes and 

 subs, above mentioned when two quantities have the same 

 name, but represent different things. Thus, consider the 

 word moment as applied to beams. The safe moment equals 

 the ultimate moment divided by the factor of safety. If it 

 is decided to designate all moments by M, it will be necessary 

 to make a distinction between the M that refers to safe 

 moment and the M that refers to ultimate moment. This 

 may be effected by designating the safe moment as Ms, and 

 the ultimate moment as M. The formula may then be 



written Ms = ~r , in which F equals the factor of safety. 



