870 



D'ARCY WENTWORTH THOMPSON ON 



the glassblower lets one side of his bubble get cold, and such as is actually present 

 in the stomach itself in the form of a muscular band. 



We may now proceed to consider and illustrate a few permutations or transforma- 

 tions of organic form, out of the vast multitude which are equally open to this method 

 of inquiry. 



We have already compared in a preliminary fashion the metacarpal or cannon- 

 bone of the ox, the sheep, and the giraffe (fig. 3) ; and we have seen that the essential 

 difference in form between these three bones is a matter of relative length and 

 breadth, such that, if we reduce the figures to an identical standard of length (or 

 identical values of y), the breadth (or value of x) will be approximately two-thirds 



I 



3 



TV. 



Ox Sheep 



Fig. 11. 



Giraffe 



that of the ox in the case of the sheep and one-third that of the ox in the case of the 

 giraffe. We may easily, for the sake of closer comparison, determine these ratios 

 more accurately, for instance, if it be our purpose to compare the different racial 

 varieties within the limits of a single species. And in such cases, by the way, as 

 when we compare with one another various breeds or races of cattle or of horses, the 

 ratios of length and breadth in this particular bone are extremely significant. 



If, instead of limiting ourselves to the cannon-bone, we inscribe the entire foot 

 of our several Ungulates in a co-ordinate system, the same ratios of x that served ns 

 for the cannon-bones still give us a first approximation to the required comparison ; 

 but even in the case of such closely allied forms as the ox and the sheep there is 

 evidently something wanting in the comparison. The reason is that the relative 

 elongation of the several parts, or individual bones, has not proceeded equally or 

 proportionately in all cases; in other words, that the equations for x will not suffice 

 without some simultaneous modification of the values oiy (fig. tl). In such a case it 



