0. D. Fawcett 
425 
few crania and the measurements as stated in Maciver's tables, not sufficiently 
definite to give the indices accurately*. 
(b) Ancient Theban Mummies. The means were found by Professor Pearson 
and Dr Alice Lee from Dr E. Schmidt's measurements published in the Leipzig 
portion of the German Anthropological Catalogue. Their date is approximately 
1500 B.C. 
(c) Modern Egyptian skulls collected chiefly by Mook from a cemetery near 
Cairo, extracted from the German Anthropological Catalogue, and reduced by 
Dr Alice Lee. They are almost certainly Copts. 
(d) Modern Negroes from the North of Africa. These have been extracted 
from the German Anthropological Catalogue, and were reduced by Mr N. Blanchard. 
Another table (see Table VI.) for modern Negroes but for a few characters only 
is given later. These were chiefly from Algiers, the Soudan and the West Coast 
* We must express our entire disagreement with the method of exhibiting measurements adopted in 
D. Randall Maciver's Tlie Earliest Inhabita7its of Abydos, Oxford, 1901. His series are somewhat 
smaller than ours, running in each case from about 20 to 60 measurements. He says that they 
belong to two, and perhaps, to three periods. Now it is perfectly certain that no graphical method will 
enable us to distinguish in the case of small frequency distributions like this whether a divergence is due 
to random sampling or to difference of race. We can only proceed as we have attempted to do in 
Art. 0 by calculating the means and their probable errors, and then ascertaining the degree of 
significance of the diiferences. Mr Maciver has not given us a single mean, a single variability, or a 
single probable error. Until he does tliis no statistically trained craniologist would venture to draw any 
conclusions whatever from his results. To those who know the large errors of random samples when 
the sample consists of not more than 20 to 60 individuals, especially in the case of low correlation, it 
will be an obvious truth that no conclusions at all can be drawn from the graphical display of these 
results. For variation the rough observations must be replaced as we have endeavoured to do by the 
smooth curves. For correlation, the only profitable proceeding is to calculate by Bravais' formula the 
coefficient of correlation. Hundreds of correlation tables have been formed and published by the 
workers at University College during the last few years, but although our numbers are often twice to 
thrice Mr Maciver's, we refrain from publishing a single correlation table on the present occasion. We 
feel quite convinced that a correlation table with even 100 entries is in 9 cases out of 10 only misleading 
to the eye. What we want is the correlation coefficient and its probable error. For example in 
Table 14 Mr Maciver gives the correlation table of breadth and height of orbit for male skulls, only 27 
in number ! We see no conclusion whatever which can be safelj' drawn from a mere table of this kind. 
Although when we state for this race that the correlation between breadth and height of orbit is 
■43 ± '06, we can at once make a comparison with other races, and present our material in an 
intelligible form to the trained statistician. On p. 2 of his memoir Mr Maciver states : " The methods 
commonly employed for recording anthropometrical data are unsatisfactory in the extreme Those 
who realize the importance of full publication yet usually content themselves with flinging together 
simple lists. Even for a small series of examples such a list is cumbrous and when the series is a long 
one it becomes most tedious and distracting. The entire labour of tabulation is left to be done by the 
reader who must be possessed of exceptional patience to undertake it at all." We can only criticise this 
by saying that Mr Maciver leaves the entire labour of calculation to be done by the reader, and that we 
should have been grateful had he flung a simple list together. Throughout his measurements never 
once apparently has a skull stood midway between two units ! It is impossible to read the indices 
accurately, and to determine such an important correlation as that between the orbital and nasal 
indices would take hours of work and " a reader possessed of exceptional patience," if indeed it could be 
properly done at all. For some purposes Mr Maciver's tables might possibly be of use as a supplement 
to a " simple list," but we trust sincerely they may not again replace ordered Tables of measurement. 
Biometrika i 46 
