to the Anthropology of the Sudan. 147

units. Now the probable error of the Shilluk index is + 0*G0 while that of the Tagalawi is + 0*42. Hence the probable error of the difference of the means1 is

+ 0*73, which is far less than a quarter of the difference of the two means (7'36). Again, the difference between the means of the Shilluk and the Nubawi cephalic indices is 4*48, while the probable error of the difference of the two means is

+ 0*85, which again is far less than a quarter of the difference of the means. Thirdly, the mean cephalic index for the Shilluks differs from that of the Bertawi by 4*16, while the probable error of the difference of these means is + 0*96 which is again less than a fourth of the found difference. These three differences, therefore, are with high probability not due to accident.2

On the other hand, the difference between the mean cephalic index for the Shilluks and the Dinkas is only 1*01, while the probable error of the difference is

+ 0*48; and the difference between the mean cephalic index of the Nubawi and Furawi is 1'79, while the probable error of the difference is + 0*78. In each of these two cases the probable error of the difference is more than a quarter of the difference of the means. These differences cannot therefore be regarded as

necessarily significant.

Comparing the mean cephalic indices of the Tagalawi and the Nubawi, of which the former are said to be a branch, we find that the difference of the two means is 2*88 while the probable error is + 0*77. The significance of this difference must hence be regarded as doubtful, an attitude which is justified when we come to consider the relations between the two tribes and the scanty figures from which the conclusion is drawn. The mean cephalic indices of the Bertawi and the Nubawi differ by 0*32 while the probable error of the difference is

± 0-96.

From these figures we may legitimately conclude that the Shilluks and Dinkas are appreciably more dolichocephalic than any of the other Sudanese tribes for which we have adequate data; and that the differences between the Furawi and the Nubawi, together with those between the Bertawi and the Nubawi, are probably not significant. The number of subjects measured in other tribes (Table II) is too small to enable us to calculate differences, but we may note that the tribes in Dar Fertit (Fertitawi 78*76, Digawi 77*00) as well as those in the south-west Ghazal district (Bandawi 77*53, Bongawi 76*14) are likewise far more round-headed than the Nilotic Sudanese, while the Nuer and Jur, whose cephalic indices measure 72*34 and 72*64 respectively, agree very closely with their neighbours, the Dinkas and Shilluks.

Nasal Index.—The most divergent values for the mean nasal index in Table I are those for the Shilluks (93*32) and the Tagalawi (103*21). The difference is -enormous and cannot be accidental in spite of the few observations made,

1 The probable error of the difference of two means is the square root of the sum of the squares of the p.e. of the means.

2 It is generally admitted that a difference acquires significance when it is more than four .times its probable error.

b 2