R. Crewdson Benington 
321 
differentiation is wholly real, indeed I think it may often be traced under the chaos 
produced by personal equation in measurement. A not uninteresting example 
of this is the Zygomatic Upper Face Index, or the ratio of the distance of the 
nasion from the alveolar point to the maximum zygomatic breadth (100 G'HJJ) — 
this measurement has been much approved by some craniologists. But its range 
is very small throughout the races of man, and personal equation both in the 
matter of the alveolar point, and in placing the callipers on the zygomatic 
arches brings chaos into the racial table. When the racial range is small even 
moderate personal equation produces serious effects. The following table will 
illustrate the point : 
Zygomatic Upper Face Index, 100 G'H/J ( found from means of absolute values). 
6 
? 
6 
? 
Congo ... 
50-1 
48-5 
Northern Negroes ... 
52-5 
_ 
Gaboon, 1880 
50-8 
51-9 
English, Moorfields ... 
52-8 
52-6 
Aino ... 
50-8 
50-5 
Sweden, Stone Age ... 
53-0 
Gaboon, 1864 
51-5 
52-1 
Theban Mummies 
53-6 
54-4 
Kaffirs 
51-5 
Wurtemberger 
53-6 
52-9 
Reihengraber ... 
52-0 
Naqada 
53-8 
56-3 
Zulus ... 
52-2 
English, Whitechapel 
53-8 
54-8 
Long Barrow 
52-2 
Scottish 
54-4 
55-1 
French 
52-3 
Copts ... 
54-6 
52-6 
Bavarian 
52-4 
52-9 
The difference between the two English series alone would suffice to carry 
the North African Negroes to a place fourth or fifth on the list right among 
their racial fellows. The fact that, only roughly, the female, order is the same as 
the male shows that nothing is final in the list, but generally the appearance of the 
Negroes at one end of the scale and the Europeans at the other, with the prehistoric 
races towards the centre, indicates that with longer series and more careful 
standardisation the zygomatic upper face index might be of value. At present the 
racial range, under five points for males, is too small to indicate profitable results in 
the face of small series and large personal equation in measurement. 
(5) On the Variability of the Negro Skull. It is of interest to consider 
whether there is less variation in the Negro than in the European skull. *The 
first of the accompanying tables gives the coefficients of variation for the absolute 
measurements of the Congo and Gaboon 1864 series compared with Naqada, Aino, 
Theban mummy, English, Bavarian and other European data. The following 
table gives the standard deviations of the indices. When one examines the gaps 
in these tables one notices the vast amount of laborious arithmetic still waiting to 
be done on actually measured series ! Such work is too often shirked by the 
craniologist, but yet it is absolutely needful if we are to determine the relative 
variability of the various races of man. Without a knowledge of such variability 
how can we determine the range within which selection can act or has acted ? 
Taking first the table of coefficients of variation for the absolute measurements, we 
Biometrika via 41 
