206 



Trans. Acad. Sci. of St. Louis. 



This equation is represented in diagram in Fig. 1. The 

 ten terms of Eq. (7) are represented by the areas of the 

 rectangles marked with numerals 1 to 10. 



f* 



*v 



»v 



«y* 



1 



/o 



g 



Diagram of y 10 — x 10 . 

 Fig. 1. 



Any values may be assigned to x and y and this dia- 

 gram may be drawn to scale if the assigned values are 

 not too large, or do not differ too much from unity. 



The computed values are of interest in some cases even 

 if they cannot be laid off to scale. For example assume 

 the values of y and # to be 5 and ^4, the unit of length be- 

 ing the inch. The squares y 2 and x 2 would then have sides 

 the length of which would be 5 inches and % inch. 



Multiplying these sides by y* and x 4 the sides of the 

 resulting squares would have lengths y 5 = 3125 inches 



