1052 THE THEORY OF TRANSFORMATIONS [ch. 



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 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. 



y (Ox) 



y' (Sheep) 

 y" (Giraffe) 



b 



27 

 19 

 10 



42 

 36 

 24 



100 

 100 

 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 con- 

 struct a figure of that of the sheep or of the giraffe with remarkable 

 accuracy. 



^n 



i 



100 



Sheep Giraffe 



100 



Fig. 506. 



Fig. 507. 



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 discerned from such a diagram 

 as the above (Fig. 507), where the values of y in the case of the ox 

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



