124 Some Applications of Chance to Racial Differentiation. 



the proportions of 52*1 and 47*9 per cent. The slightly larger 

 element was a dolichocephalic race with an index of 73*554, 

 and the smaller element a brachycephalic race with an index 

 of 81*425. For the Long Barrow male skulls I have found 

 a mean cephalic index of 71*77 ((30 skulls) and a variability 

 of 3*89 ; for the Round Barrow male skulls a mean index 

 of 8092 (25 skulls) and a variability of 3*82. There can 

 be small doubt that one of our components coincides with the 

 Eound Barrow men or the " Celtic " element in Britain. 

 The other component is somewhat less dolichocephalic than 

 the Long Barrow skulls I have referred to above, but there is 

 little doubt that it represents the Iberian element. Thus the 

 mean index at Cro-Magnon was 73*34, and in the Caverne de 

 1' Homme Mort 73*22. The Brito-Celt differs indeed sensibly 

 from the Grermano-Celt* in his cephalic index (80*92 as com- 

 pared with 77*38), but this is a point which has been much 

 considered by anthropologists, and I need not reopen that 

 discussion here. 



It would seem therefore that if we had had no knowledge 

 of the nature of the burial-places of our skulls, we could still 

 have differentiated them into two groups — the Iberian and 

 Celtic ; and this, certainly, ought to give us confidence in the 

 usefulness of the method. 



(7) I have chosen in this paper, out of a wide range of 

 material, three cases dealing with one character only, because 

 that seemed to me to give most force to the illustrations. I 

 have no doubt that the method, in the hands of a competent 

 craniologist, would lead to most interesting anthropological 

 results. But in itself the method is perfectly general, and 

 applies to any material with which we may venture to deal on 

 the basis of the old-established mathematical theory of chance. 

 How far that theory has itself to be superseded is a question 

 I do not propose to enter on here, but I would urge by 

 means of these new illustrations of my method, which have 

 been worked out, by competent mathematicians it is true, 

 but still by comparative novices to statistical work, that the 

 process is not so laborious that it need be discarded for rough 

 methods of approximation based upon dropping the funda- 

 mental nonic and guessing suitable solutions to what then 

 become indeterminate equations. 



* Assuming with His and Rutyrneyer that the Sion type with an 

 index of 77*2 is really that of the "Celtic "' element in South Germany. 



