1054 THE THEORY OF TRANSFORMATIONS [ch. 



If into this new network we fill in, point for point, an outline 

 precisely corresponding to our original drawing of the middle toe, 

 we shall find that we have already represented the main features 

 of the adjacent lateral one. We shall, however, perceive that our 

 new diagram looks a httle too bulky on one side, the inner side, of 

 the lateral toe. If now we substitute for our equidistant ordinates, 



Fig. 509. 



ordinates which get gradually closer and closer together as we pass 

 towards the median side of the toe, then we shall obtain a diagram 

 which differs in no essential respect from an actual outline copy 

 of the lateral toe (c). In short, the difference between the outline 

 of the middle toe of the tapir and the next lateral toe may be almost 

 completely expressed by saying that if the one be represented by 

 rectangular equidistant coordinates, the other will be represented 

 by oblique coordinates, whose axes make an angle of 50°, and in 



i 



(After Albert Diirer.) 



which the abscissal interspaces decrease in a certain logarithmic 

 ratio. We treated our original complex curve or projection of the 

 tapir's toe as a function of the form F (x, y) = 0. The figure of 

 the tapir's lateral toe is a precisely identical function of the form 

 f (e*, ^i) = 0, where x^, 2/1 ^^® oblique coordinate axes inclined to 

 one another at an angle of 50°. 



