MORPHOLOGY AND MATHEMATICS. 



881 



rest, we shall find a long series of genera in which we can refer not only the changing 

 contours of the skull, but even the shape and size of the many constituent bones and 

 their intervening spaces or " vacuities," to one and the same simple system of trans- 

 formed co-ordinates. The manner in which the skulls of various Crocodilians differ 

 from one another may be sufficiently illustrated by three or four examples. 



Let us take one of the typical modern crocodiles as our standard of form, e.g., 

 C. porosus, and inscribe it, as in fig. 39, in the usual Cartesian co-ordinates. By 

 deforming the rectangular network into a triangular system, with the apex of the 

 triangle a little way in front of the snout, as in fig. 40, we pass to such a form as 

 C. americanus. By an exaggeration of the same process we at once get an approxima- 



Fig. 37.— Diodon. 



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Fig. 38. — Orthagoriscus. 



tion to the form of one of the sharp-snouted, or longirostrine, crocodiles, such as the 

 genus Tomistoma ; and, in the species figured, the oblique position of the orbits, the 

 arched contour of the occipital border, and certain other characters suggest a certain 

 amount of curvature, such as I have represented in the diagram (fig. 40), on the part 

 of the horizontal co-ordinates. In the still more elongated skull of such a form as 

 the Indian Gavial, the whole skull has undergone a great longitudinal extension, or, 

 in other words, the ratio of xjy is greatly diminished ; and this extension is not 

 uniform, but is at a maximum in the region of the nasal and maxillary bones. This 

 especially elongated region is at the same time narrowed in an exceptional degree, 

 and its excessive narrowing is represented by a curvature, convex towards the median 

 axis, on the part of the vertical ordinates. Let us take as a last illustration one of 

 the Mesozoic crocodiles, the little Notosuchus, from the Cretaceous formation. This 

 little crocodile is very different from our type in the proportions of its skull. The 

 region of the snout, in front of and including the frontal bones, is greatly shortened ; 

 TRANS. ROY. SOC. EDIK, VOL. L, PART IV (NO. 27). 126 



