C. D. Fawcett 
461 
of the mean values of the chief cranial characters in 50 to 100 races would be a 
most valuable investigation, breaking practically untrodden ground. We want an 
interracial as well as this intraracial correlation, to show us how far it is safe to 
generalise from what occurs within a race to what will happen when we compare 
races together. If platyrrhiny is associated with chamaeconchy for individual 
Naqadas, is it right to generalise and say that the platyrrhine races of men 
are also chamaeconchic ? Probably, but there is no proof, until someone has 
actually worked out interracial coefficients of correlation. 
Cephalic Indices and Length, Breadth and Height. 
The correlations of the cephalic indices are of such importance that a special 
consideration of them as well as their relationships to length, breadth and height 
was desirable. For comparative purposes the Paris catacomb crania were worked 
out at the same time. The formulae used in the investigations were those given 
by Professor Pearson in his paper " On a form of Spurious Cori'elation which may 
arise when Indices are used in the Measurement of Organs*." In every case where 
it exists, the value of spurious correlation has been calculated : see Table XIV. 
p. 456. In order, however, to test the accuracy of the results reached by the.se 
formulae from the recorded values (if the coefficients of variation (Table XI.) 
and the length, breadth and height correlations (Table XIII.), in two cases the 
correlations were worked out ab initio, namely from the data given in the 
Appendix of measurements to this memoir. There resulted : 
Correlated Pair 
From Formula 
From Measurements 
B/L and H/L S 
B/L and H/L ? 
•490 + -018 
•576 ±-024 
•500+ •O 18 
•572 ± -025 
The results are in such good agreement, well within the limits of the probable 
errors, that it seems unnecessary to deduce in future any such correlations 
directly from the measurements. 
Now turning to our results themselves, Table XIV., we see that where the 
spurious correlation exists it is at least of the same order and very frequently 
sensibly larger than the gross correlation. In fact the organic correlation between 
L, B and H often tends to reduce the result considerably below the value it 
would have if the lengths, breadths and heights had been selected from the 
records in random triplets, i.e. below the spurious correlation. Thus the cor- 
relation of the two chief cephalic indices for male Naqada is reduced from '604 
to •284<. In the case of the French males it is raised from '464 to "489, which 
is fairly in keeping with Professor Pearson's result for Bavarians (/, i.e. '401 to 
■486-f, the only other comparable values at present known. 
* R. S. Proc. Vol. 60, p. 493. Formula (iv) and (vi). 
t R. S. Proc. Vol. 60, p. 495. 
