R Crewdson Benington 
293 
the means obtained by both Dr Benington and Dr Shrubsall are based is that they 
are far too few to base at present any very dogmatic statements of racial 
differentiation upon them. Dr Shrubsall most courteously placed at our disposal 
a number of unpublished measurements of negro crania, but the frequency of each 
racial group seemed too small to render them of much service from the standpoint of 
statistical investigation. Not till at least 50, better 100 crania of each sex and 
local race are available will it be possible to draw valid conclusions biometrically 
as to the finer racial differences among the African negroid races. Meanwhile a 
comparison of the statistical constants* recorded in this paper may be of value 
as suggesting possible but not proven differences. 
No one appreciates better than the present writer the real difficulty of getting 
long series of crania, and further how often such long series run the risk of being 
heterogeneous. But the deduction of local or racial differences by craniometric 
argument from series of 10 to 20 crania is a perfectly idle task. It cannot be too 
often asserted that the publication of measurements on small series of crania is of 
value only because, if they have been made on a standardised system, they can 
later be pooled with other material. That is the immense advantage that would 
arise from an international standardised catalogue. The anatomist may from 
inspection and by appreciation be able to draw conclusions as to racial peculiarities 
from small cranial series — the biometrician does not feel called upon either to 
dispute the fact, or to accept such conclusions. He is working by other methods ; 
but he does feel justified in asserting that such conclusions do not receive adequate 
confirmation by appeal to the slight craniometric differences discoverable in small 
series of allied human races. Too often we find craniometric distinctions made 
between two small series, where no evidence is given that two random samples of 
the same local race might not have exhibited as large differences. Furthermore 
even, when probable errors are provided, we often find in small, apparently 
random, samples of the same race, differences quite beyond those of random 
sampling. The probable explanation of this is that we are meeting in such cases 
of small numbers with a marked influence of heredity in clan or even with family 
peculiarities. A cranial series ought to be sufficiently large to insure that the 
members of a single family or blood group will not markedly influence the results; 
this is wholly impossible with any cranial series under 50, and the minimum dealt 
with ought to be 100 adult crania of one sex. The craniologist may often have 
to content himself with fifty or fewer, but if he does, it will be only wise, as long 
as he is arguing from craniometry and not from anatomical appreciation, to replace 
dogmatic statement by cautious suggestion. 
(2) Material used. The following series have been dealt with, the first three 
being measured and reduced, the second three reduced only. The seventh series 
is one which was reduced by Cicely D. Fawcett and published in Biometrika, 
Vol. I, p. 426. 
* The statistical constants of Dr Shrubsall's published material have all been independently re- 
calculated in the Laboratory. 
