388 
Measurement of Internal Capacity of Skull 
above the best fitting line Dutch, English, Russians, Marquesans, will have their 
values as calculated altered for the worse by Dr Beddoe's correction for cephalic 
index, the French will remain unaltered (although they want most correction ! ) and 
the Altbaierisch and Malay will be slightly improved (although they stand least in 
need of correction ! ). Of the races below the line all but Finns would be improved 
by correction although in several cases they would be over corrected. But a very 
slight inspection shows that the corrections needed are in no way proportional to 
the defect of their cephalic indices from 80. Thus omitting Australians, the Ainos, 
Kanakas, Etruscans and Romans of Britain* (all over 75) want most correction; 
while Thebans, Naqadas, New Hebridians (all under 75) want far less correction. 
In fact we consider that if Dr Beddoe had formed a similar diagram he would not 
have laid any stress on his cephalic index correction. What does seem to us to 
follow from this diagram is the non-linearity of the inter-racial regression line. It 
is very markedly curved. We have therefore endeavoured to correct by aid of 
a curved line. Until more data are available, measured and reduced in a uniform 
manner, it is not worth spending much labour in calculating the constants of 
possible formulae, but we may roughly point out how we get far better results by 
correcting for non-linearity of the regression curve for inter-racial results than by 
attempting to " compensate " by cephalic index. Two hypotheses occurred to us, 
(i) the regression line instead of being C = ai + A.,P, where P is the product 
U X S X Q, may be taken 
G=a, + A,P + a,P' 
or as parabolic, (ii) the regression line may be taken as logarithmic 
P + cu = «5e"»*^. 
The only reason, and it is very slight, for the latter form is that it makes the 
increment of G not only directly proportional to the increment of P, but 
inversely proportional to the absolute magnitude of P measured from a certain 
value. A very similar curve has been found to suit the change in human physical 
measurements with age. The curve is here used merely as a form judged likely 
from the observations, and without at present any statement of a theoretical basis 
being suggested. We have found roughly the constants from the 10 races available. 
There result the two formulae, P being in cubic centimetres : 
C = - 15319-6 + •531,942P - 4-2075PV10'' 
C= 704-04 -I- 203-05 ]ogi„ (P - 55682). 
The disadvantage of the first formula is that with the constants selected, one 
reaches a value of P after which the capacity begins to decrease, but a very little 
change of the constants would suffice to throw this value up to, say 1550 cms.', a 
value exceeding any racial meanf hitherto observed. The logarithmic formula 
* We are inclined to doubt entirely the data for the Komans in Britain. It differs so widely from 
Eomans elsewhere. We hope that these skulls may be remeasured shortly. 
t We ask the reader to particularly note the words " racial mean," for our formulae are not to be 
transferred without further consideration to the calculation of individual capacities (or indeed to the 
female sex). 
