T80 JOURNAI, OF FOKKSTKY 



A series of uniform graduations is all that is needed on BA and CD, 

 but the graduating of CB must be calculated from the last of the above 

 equations. 



In any given chart CB is an easily obtainable constant. Suppose, for 

 example, that CB = lo units, then we have 



CF 



lo — CF 



lO V 



which reduces to CF = 



I -|- y 



It follows that if y ^ i CF = 5 



= 2 = 6 . 67 — 



= 3 =7-5 

 = 4 =8. etc. 



In practice it is often simpler to graduate this diagonal axis by inter- 

 secting it with a series of straight lines connecting values on the 

 initial axes to correspond with the successive values of 3'. For example, 

 the line connecting 2 on the AB scale and 2 on the CD scale must inter- 

 sect CB at I ; 2 on the AB scale and 4 on the CD scale must intersect 

 CB at 2 ; 2 on the AB scale and 6 on the CD scale at 3, etc. This 

 method also eliminates the slight confusion which results from using 

 different scales on AB and CD, as is often desirable. 



DIVISION OF VARIABLES 



The method of performing division is deduced from multiplication, 

 just as subtraction from addition. In this case also there are two 

 alternatives: (o) a multiplication chart can be used in a reverse direc- 

 tion, since r = — can be written .r = v^; or (b) we mav substitute for 



division by a number, multiplication by its reciprocal, since ::^— may 



y 



be written .c = a' (— ). Each of these alternatives is applicable to 

 either form of multiplication chart. 



VARIABLE EXPONENTS 



Such an equation as s = x^' may be written log. r = v log. x. In its 

 latter form it can be readily charted as a multiplication. If the 5:-chart 

 method is used, one vertical axis may be regularly graduated to express 

 values of 3',- the other,, or final, vertical to correspond with the log- 

 arithms of values of .c, and the diagonal most simply by intersections. 



