GRAPHICAL ALGEBRA. 



75 



Table I. Graphical multiplication. 

 One factor tabulated as function of the product and the other factor. 



10 35 



6-/ 



These two equations lead to the same 

 table , table I , in which we are equally right <p - ^J* 

 in interpreting a as argument and /3 as 

 tabulated quantity or /3 as argument and 

 a as tabulated quantity. 



Fig. 68 exemplifies the use of the 

 table . In drawing , for instance , the curve 

 for the constant value <p = 30 of the pro- 

 duct, we use the line in the table which 

 has the argument <p = 30. When we con- 

 sider a as argument and (8 as the tabu- 

 lated quantity, this line of the table tells 

 us that the curve <p = 30 is to be drawn 

 through that point of the curve = 3 

 where /3 = 10, through that point of the 

 curve a = 4 where /3 = 7.5, through that 

 point of the curve a = 5 where 13 = 6, and FlG ' ^.-Graphical multiplication 



3. 4. and = 11, 10, 9, . 



so on. If we consider /3 as the argument tors, the thick lines <p =50, 45, 4c 



and a as the tabulated quantity, we see 



that the curve ip = 30 is to be drawn through that point of the curve /3 = 1 2 where 



a = 2.5, through that point of the curve /3 = 1 1 where = 2.7, an d so on. 



The fine lines = 2, 

 . represent the fac- 

 . . their product. 



