MORPHOLOGY AND MATHEMATICS. 



887 



from the North American Cretaceous formations — a bird showing some resemblance 

 to the modern Terns. The pelvis of Arch&opteryx is taken as our type, and referred 

 accordingly to Cartesian co-ordinates (fig. 48) ; while the corresponding co-ordinates 

 of the very different pelvis of Apatomis are represented in fig. 49. In fig. 50 the 

 outlines of these two co-ordinate systems are superposed upon one another, and those 



3 * 3 * * 6 7 ~g~ 



Fig. 52. — The second intermediate co-ordinate network, with its corresponding inscribed pelvis. 



Fig. 53. —The third intermediate coordinate network, with its corresponding inscribed pelvis. 



of three intermediate and equidistant co-ordinate systems are interpolated between 

 them. From each of these latter systems, so determined by direct interpolation, a 

 complete co-ordinate diagram is drawn, and the corresponding outline of a pelvis is 

 found from each of these systems of co-ordinates, as in figs. 51 to 53. Finally, in 

 fig. 54 the complete series is represented, beginning with the known pelvis of 

 Archaeopteryx, and leading up by our three intermediate hypothetical types to the 

 known pelvis of Apatomis. 



Among Mammalian skulls I will take two illustrations only, one drawn from a 

 comparison of the human skull with that of the higher apes, and another from the 



