M. A. Lewenz and K. Pearson 
369 
and guesses what he considers a suitable value for B\ He therefore (1) assumes 
that his line holds far beyond the range of any actual observation*, for his only 
ground for putting ^ = 0 must be, although he does not state it, that C vanishes 
with P ; (2) neglects the result of all observations hitherto made on human 
characters, for in no case, that we are aware of — and certainly more than 100 must 
now have been worked out — is A=0. When Dr Beddoe does not guess i? he 
obtains its value by giving G and P their mean values. Even here as he does not 
know the mean value of G, he guesses it ! 
" Je suis bien certain que la moyenne des pesees de cerveaux d'Anglais est un 
peu au dessous de 1400 grammes et que la moyenne de la capacite de cranes 
masculins anglais est voisine de 1500 c.c.f " 
The only reasonably long series of English skulls with which we are acquainted 
neither give a mean of 1500. This is the type of guesswork which has hitherto 
passed for science in anthropometry. Even if Dr Beddoe had found by actually 
examining data that a formula 
Probable C' = 5x Known P 
held for the skulls of one race, he ought before adopting it generally to have noted 
Dr Lee's warning about the changing degree of correlation between circumferences 
and capacity when we pass from one race to a closely allied race, and accordingly 
have tested it on other races. He has not attempted this, but finding it did not 
agree very well with observations on individuals attempted to modify it by 
introducing corrections depending on the cephalic index. This he has done 
notwithstanding Dr Lee's result that there is generally little correlation between 
cephalic index and capacity, and that what there is varies largely from race to racel. 
(3) We now turn to our own contribution to the subject. Dealing with the 
three circumferences U, S, Q defined above, which differ somewhat from Dr Beddoe's 
three, we have sought a linear relationship between their product P and the mean 
value of the corresponding G for four different races. We have used the following 
male crania : 
{a) Fawcett's measurements on 98 Naqada crania. 
(6) E. Schmidt's measurements on 164 Theban mummies. 
(c) Ranke's measurements on 78 Altbaierisch crania. 
(d) Macdonell's measurements§ on 72 English crania, 
and we have one series for female crania, 
(e) Macdonell's measurements on 76 English crania. 
* While the relation of the characters in man is closely linear for the range found in normal 
individuals of one race, it certainly ceases to be linear when we pass to 'dwarfs' and 'giants.' See 
Pearson : Phil. Trans. Vol. 192, A, pp. 169 — 214. There is no reason whatever for extending the 
linear relation like (i) to extreme ' dwarfs ' and putting ^=0. 
t Loc. cit. 286. t See loc. cit. p. 233. 
§ We have heartily to thank Dr Macdonell for providiug us not only with the data, but the actual 
reductions in cases (d) and (e). His own memoir on the English skull appeared in Biometrika, Vol. iii. 
pp. 191—244. 
Biometrika iii 47 
