MORPHOLOGY AND MATHEMATICS. 



863 



x and y we have substituted :i\ and cyi, and the equation to our original circle, 

 .r 2 +2/ 2 =« 2 , becomes that of the ellipse, ■r 1 2 -rc 2 yi' =« 2 . 



If 1 draw the cannon-bone of an ox (fig. 3, A), for instance, within a system of 

 rectangular co-ordinates, and then transfer the same drawing, point for point, to a 



Fig. 1. 



Fig. 2. 



ffl 



CM 







Fio. 4. 



A B 



Fig. 3.— A. Ox ; B. Sheep ; 0. Giraffe. 



system in which for the x of the original diagram we substitute x = 2/3 x, we 

 obtain a drawing (fig. 3, B) which is a very close approximation to the cannon-bone 

 of the sheep. In other words, the main (and perhaps the only) difference between 

 the two bones is simply that that of the sheep is elongated, along the vertical axis, 

 as compared with that of the ox in the relation of 3/2. And similarly, the long 

 slender cannon-bone of the giraffe (fig. 3, C) is referable to the same identical type, 

 subject to a reduction of breadth, or increase of length, corresponding to x" =x/B. 



