MORPHOLOGY AND MATHEMATICS. 



893 



of the eye, like the modification in form and number of the teeth, is a separate 

 phenomenon, which supplements but in no way contradicts our general comparison of 

 the skulls taken in their entirety. 



Let us now inscribe in our Cartesian co-ordinates the outline of a human skull 

 (fig. 62), for the purpose of comparing it with the skulls of some of the higher apes. 

 We know beforehand that the main differences between the human and the simian 

 types depend upon the enlargement or expansion of the brain and braincase in man, 

 and the relative diminution or enfeeblement of his jaws. Together with these 













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Fig. 62. — Human skull. 



Fig. 63.— Co-ordinates of chimpanzee's skull, as a projection of the Cartesian co-ordinates of fig. 62. 



changes, the "facial angle" increases from an oblique angle to nearly a right angle 

 in man, and the configuration of every constituent bone of the face and skull under- 

 goes an alteration. We do not know to begin with, and we are not shown by the 

 ordinary methods of comparison, how far these various changes form part of one 

 harmonious and congruent transformation, or whether we are to look, for instance, 

 upon the changes undergone by the frontal, the occipital, the maxillary, and the 

 mandibular regions as a congeries of separate modifications or independent variants. 

 But as soon as we have marked out a number of points in the gorilla's or chimpanzee's 

 skull, corresponding with those which our co-ordinate network intersected in the human 

 skull, we find that these corresponding points may be at once linked up by smoothly 



