Tlieory of Chance to Racial Differentiation. 11.9 



Using the same notation as before we find for the funda- 

 mental constants : — 



Mean = 78-846.. 



Moments : fi 2 = 21*268,109, 

 ^3=^ 51081,613, 

 ^=1438-723,449, 

 Ms = 8358-086,377. 



Other Constants : \ 4 = -245-177,507, 

 \ 5 = 7519*938,389. 



The fundamental nonic, writing p 2 = 10^;, is 



% 9 + 2-86x 7 + 3*914 % 6 -35*911 x 5 -7*669 % 4 



+ 129-429 % 3 +95-675 % 2 -22*262 % -17*772 = 0«. 



A root of this was localized between and —1, and by 

 successive approximation was found to be —'9685. Hence 

 /? 2 =-9-685. Thus p 3 = -49-637 and ^ = 5-125. The quad- 

 ratic for the means of the two components is 



T 2 - 5-125 r f -9-685 = 0, 



which leads to «/!= — 1*4685 and y 2 — 6*5935.. Working out 

 the other constants for the components we have, finally, the 

 following results : — 



First Component. Second Component- 

 Mean Index 77-3775 85*4395 



dumber of Skulls 552*05 122*95 



Standard Deviation . . . 3*3926 3*4518 



Modal Frequency 64*917 14*210 



The equations of the two components referred to their means 

 are : — 



y = 64*917 6?-*7*3-020 



y = 14*210 *-r723-830. 



The frequency-distribution, the two components, and their 

 compound curve are given in fig. 2, and it will be seen that 

 the result is very satisfactory*. We have a mixture of a 

 mesocephalic and a hyperbrachycephalic race in the pro- 

 portions of 81*8 and 18*2 per cent. The second component 

 is remarkably high ; it stands between the modern German 

 83-84 and the so-called Disentis type of His and Rutimeyer 

 (Crania Helvetica, p. 25). The first component is almost 

 identical with that of His and Rutimeyer's Sion type with 



* Much more so than the fit of a skew-frequency curve which I have 

 also tested on these data. 



