XVII] THE COMPARISON OF RELATED FORMS 1051 



straight downwards, into a vertical instead of a transverse ellipse, 

 and is even narrowed to a point at the sternal border. 



We may now proceed to consider and illustrate a few permutations 

 or transformations of organic form, out of the vast multitude which 

 are equally open to this method of enquiry. 



We have already compared in a preliminary fashion the metacarpal 

 or cannon-bone of the ox, the sheep, and the giraffe (Fig, 493); 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 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 coordinate system, the 

 same ratios of x that served us 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 of y (Fig. 506). In such a case it may be 

 found possible to satisfy the varying values of y by some logarithmic 



* This significance is particularly remarkable in connection with the develop- 

 ment of speed, for the metacarpal region is the seat of very important leverage 

 in the propulsion of the body. In a certain Scottish Museum there stand side by 

 side the skeleton of an immense carthorse (celebrated for having drawn all the 

 stones of the Bell Rock Lighthouse to the shore), and a beautiful skeleton of 

 a racehorse, long supposed to be the actual skeleton of Eclipse. When I was 

 a boy my grandfather used to point out to me that the cannon-bone of the little 

 racer is not only relatively, but actually, longer than that of the great Clydesdale. 



