GRAPHICAL ALGEBRA.* 
Francis EK. NrpHer. 
In the former paper it was shown that algebraic func- 
tions of a higher order than the second degree may be rep- 
resented in diagram upon a plane surface. 
In the present paper the same function will be repre- 
sented by widely different diagrams. 
The difference between the areas of two squares hav- 
ing sides the length of which are y’ and 2° is 
y—xv=y (y—a)+y’e (y—2) 
+ y'a? (y—a) + y’a* (y—2) 
+ y°at (y—a) + y’a* (y—2) 
+ yx’ (y—ax) + ya" (y—2) 
+ya*(y—a2)+2° (y—x) (5) 
This is Eq. (5) of the former paper. 
This equation may be written: 
yw y yt —ye ) tye 72) 
+ ytx (ya — ya?) + y’a* (y*a — y’2") 
+ y*a* (y*a* — y*a*) + y'a? (y*2* — y’@’) 
+ ea (y*a*— y x*) _ y x ( yas — y x") 
+yat(yat— o)+ a (yat— 2°) (7) 
=(y> +y'c) (yo —ya) 
+ (y‘x + y*a*) (ye — ya") 
+ (ya? + ya") (y*a’® — ya") 
+ (y?a* ne y a") (y'a* —y at) 
+(yat+ af) (yat— a) (7a) 
= ig aie yx’) os (yia? — y°a*) 
+ (ya — y*x*) + (y‘a® — y°a") 
Soe a (ya oes oe") 
*Continued from No. 6, Vol. XXIII. Presented by title before the 
Academy of Science of St. Louis, January 20, 1919. 
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