XVII] THE COMPARISON OF RELATED FORMS 739 



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 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. 362). In such a case it may be found possible to satisfy 

 the varying values of y by some logarithmic or other formula; 

 but, even if that be possible, it will probably be somewhat difficult 

 of discovery or verification in such a case as the present, owing 

 to the fact that we have too few well-marked points of corre- 

 spondence between the one object and the other, and that especially 

 along the shaft of such long bones as the cannon-bone of the ox, 

 the deer, the llama, or the giraffe there is a complete lack of easily 

 recognisable corresponding points. In such a case a brief tabular 

 statement of apparently corresponding values of y, or of those 

 obviously corresponding values which coincide with the boundaries 

 of the several bones of the foot, will, as in the following example, 

 enable us to dispense with a fresh equation. 



This summary of values of y' , coupled with the equations for the 



* 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 the Museum of the Royal College of Surgeons 

 in Edinburgh, 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, which (though the fact is disputed) 

 there is good reason to beUeve is the actual skeleton of EcUpse. When 1 was a 

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

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



47—2 



