MORPHOLOGY AND MATHEMATICS. 



871 



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 correspondence 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 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 dis- 

 pense with a fresh equation. 



y(Ox) . . . 







18 



27 



42 



100 



y (Sheep) . 







10 



19 



36 



100 



y" (Giraffe) . 







5 



10 



24 



100 



This summary of values of y , coupled with the equations for the value of x, will 

 enable us, from any drawing of the ox's foot, to construct a figure of that of the 

 sheep or of the giraffe with remarkable accuracy. 



Fin. 12. 



That underlying the varying amounts of extension to which the parts or segments 

 of the limb have been subject there is a law, or principle of continuity, may be dis- 

 cerned from such a diagram as the above (fig. 12), where the values of y in the 

 case of the ox are plotted as a straight line, and the corresponding values for the 

 sheep (extracted from the above table) are seen to form a more or less regular and 

 even curve. This simple graphic result implies the existence of a comparatively 

 simple equation between y and y. 



An elementary application of the principle of co-ordinates to the study of propor- 

 tion, as we have here used it to illustrate the varying proportions of a bone, was in 



