THE VARIE TIES OF THE HUMAN SPECIES. 1 7 



cranium is hypsi-brachycephalic," is insufficient to define the 

 form. While cranial types so defined have equal indices, their 

 curves differ in degree, and therefore the skull may or not be 

 hypsi-brachycephalic. It is just as if we attempt to calculate the 

 size of an ellipsis by means of the relation of its two axes. Two 

 ellipses equal in this relation may be unequal in size, and this is 

 why these two relations cannot be compared. It is the same in 

 regard to the cephalic and vertical indices of the cranium. 



If it were true and there were no doubt respecting the value of 

 the celebrated cephalic index in determining cranial forms, it 

 would follow that all human crania of whatever type and volume 

 should be placed in the three categories of dolicho-, meso-, and 

 brachycephalic, or of hypsi-, ortho-, and chamaecephalic. Thus 

 all the populations of the earth, either of white, yellow, black or 

 red skin, would have crania belonging to the three categories. A 

 classification solely according to the cephalic index is therefore an 

 absurdity. It is incoherent and without meaning, as are those of 

 Retzius and KoUmann. 



This conclusion is so true that such anthropologists are obliged 

 to add descriptions to the forms of each part of the cranium, in 

 order to distinguish it, recognizing the insufficiency of cranial 

 data. Such descriptions can, to a certain degree only, supply the 

 defect of the method, but they always remain incomplete, and 

 leave the forms or types of the human cranium of various popu- 

 lations and regions indefinite. The French school has gone still 

 farther and has supplied the deficiency with an infinite number 

 of measurements, which only increase the obscurity, leaving the 

 conception of the form more uncertain, and fatiguing the most 

 patient student, who becomes convinced of never reaching any 

 satisfactory result from such a confused accumulation of numbers. 



In order to render classification more definite, or for the sake 

 of finding a second characteristic which might be associated with 

 the cephalic index, Retzius turned his attention to the prognath- 

 ism and the orthognathism of the molar teeth; Kollmann to the 

 facial index. Use could be made of the nasal index instead of the 

 facial, or the orbital index, or any isolated characteristic, and we 

 should have the same results. The combinations given by Ret- 

 zius and Kollmann are possible, but cannot indicate races or varie- 

 ties, from the fact that they are hybrid associations. 



