DATA FOR THE PROBLEM OF EVOLUTION IN MAN. 
253 
In this way we find : 
s C = ‘000,337 Ixh xh ^ 140'13| 
? C = '000,400 I X h X h - 80-62J. 
This formula merely assumes that the factor multiplying the product of length, 
breadth, height remains the same, whether these quantities are measured on the head 
or the skull. 
We now turn to the discovery of linear formulae corresponding to ( 8 ) of pp. 234, 236. 
Here we are met by the very obvious difficulty that unlike formula (9) the constants 
of formula ( 8 ) change much from local race to local race. If we take the formula for 
the Germans as being nearest akin to tlie English, we are met by the ol^vious fact 
that the constants change widely when we pass from a brachycephalic to a dolicho¬ 
cephalic race; the English, indeed, have a cephalic index nearer to the Ainos than 
to the Germans. Accordingly, in default of more amj^le data for striking a mean 
formula, I have Inserted in (A) ofqx 250, the mean values of the German and Aino 
constants. We tlius have :—• 
c? C - Co = 10-1025 (/ - Q + 8-0345 (5 - b^) -j- 3‘709 {h - /g, 
? G - Co = 7-222 {I - Iq) + 8-4605 {h - h^) -f 6-300 {h - /q,). 
Inserting the British Association mean values for Iq, and /^-o, as well as the mean 
capacities found from (14), we have ; — 
d C = 10-1025 I + 8-0345 h + 3-709 k - 2237-52 1 
? C= 7-222/ + 8-4605 6-f 6-300 /^ - 2071-22 ) . 
Another linear formula may be obtained in an entirely diderent manner ])y taking 
the tangent plane at the mean to the surface in (14). Thus the skull measurement 
surface is :— 
C = eLBH + 7 }, 
and the tangent plane is 
C - Co = eLoBoHor^ ^ 
L J-'o * *0 -*^0 
How introduce the British Association values, remembering that Lo = /o — H, 
Bq = 6o — 11, Ho = Hq — 11, and we find :— 
J C = 5-8185 /-f 7-5600 /> + 9-0796/;, - 2017-96-1 
? C = 6-4006 / d- 8-1992 6 + 9-5192/; - 2294-46J • • - - i G- 
Equation (17) will be found to give results excellently in accord witli (14) ; it is the 
linear formula most comparable witli (14), yet the coefficients differ very widely 
from those of (16), the height which is least influential in (16) being now the most 
influential factor. It would have been satisfactory to find (17) more closely iii agree- 
