MORPHOLOGY AND MATHEMATICS. 



873 



the lateral toe (fig. 14, 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 co-ordinates, the 

 other will be represented by oblique co-ordinates whose axes make an angle of 50°, 

 and in 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 x , yi}=0, where x 1} y± are oblique co-ordinate axes inclined 

 to one another at an angle of 50°. 



Fig. 15. (After Albert Durer.) 



Durer was acquainted with this type of co-ordinates also, and I have copied two 

 illustrative figures (fig. 15) from his book. 



In fig. 16 1 have sketched the common Copepod Oithona nana, and have inscribed 

 it in a rectangular net, with abscissse three-fifths the length of the ordinates. Side 

























% 



X 























1 











V 











Fig. 16. — Oithona nana. 



Fig. 17. — Sapphirina. 



by side (fig. 17) is drawn a very different Copepod, of the genus Sapphirina; and 

 about it is drawn a network such that each co-ordinate passes (as nearly as possible) 

 through points corresponding to those of the former figure. It will be seen that 

 two differences are apparent, (l) The values of y in fig. 17 are large in the upper 

 part of the figure, and diminish rapidly towards its base. (2) The values of x 

 TRANS. ROY. SOG. ED1N., VOL. L, PART IV (NO. 27). 125 



