740 



THE THEORY OF TRANSFORMATIONS 



[CH. 



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. 



That underlying the varying amounts of extension to which 



the parts or segments of the 



TOO ^ . . 



limb have been subject there is 

 a law, or principle of continuity, 

 may be discerned from such a 

 diagram as the above (Fig. 363), 

 where the values of y in the 

 case of the ox are plotted as a 

 straight line, and the corre- 

 sponding 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 proportion, as we have here used it to illustrate the 

 varying proportions of a bone, was in common use in the sixteenth 

 and seventeenth centuries by artists in their study of the human 

 form. The method is probably much more ancient, and may 



Fig. 363. 



Fig. 304. (After Albert Diirer.) 



even be classical * ; it is fully described and put in practice by 

 Albert Diirer in his Geometry, and especially in his Treatise on 

 Proportion f . In this latter work, the manner in which the 



* Cf. Vitruvius, in, 1. 



■f Le<i quntres livres (V Albert Diirer de la projwriion des parties et pourtraicts 

 des corps humains, Arnheim, 1613, folio (and earlier editions). Cf. also Lavater, 

 Essays on Physiognomy, iii, p. 271, 1799. 



