122 Prof. K. Pearson on some Applications of the 



The following numerical results were obtained, still using 

 the same notation : — 



Mean Index = 77-3246. 

 Moments /jl 2 = 30*342,028, 

 yu 3 = 16-115,248, 

 fi, = 2261-284,715, 

 ^ = 3050-185,852. 

 Other constants X 4 = 1501'893,855, 

 X 5 = 5518-523,444. 



Patting p 2 = 10^;, the fundamental nonic is : — 



x 9 -17'522 % 7 H--389x 6 + 85-093x 5 -49'431 % 4 

 -207-i32x 3 -U-776 % 2 + 13-510x--017 = 0. 



A root was localized between — 1 and —2, and % was found 

 to be - 1-54599. This gave 



^=-15-4599, ^--5*0906, p i= -3290. 



Hence the quadratic determining the means of the com- 

 ponents is 



7 2 - -3290 7 -15-4599 = 0, 



which leads to y 1 = — 3*771 and y 2 = 4*100. 



Proceeding to the determination of the other quantities 

 we find 



First Component. Second Component. 



Mean Index 73*5536 81*4246 



Number of Skulls 59*383 54-617 



Standard Deviation ... 3*7397 3*9822 



Modal Frequency 6 '3-349 5*4719 



The equations of the two components referred to their 

 means are : — 



^ = 6-3349 ^-^27-9708^ 



y= 5'4719 £-* 2 /31*7130. 



The two components and their resultant, as well as the 

 smoothed observations, are plotted in fig. 3. I think they 

 ought to be considered as distinctly good, having regard to 

 the paucity of the material and the possibility that a certain 

 amount of the variation in it is due to distortion of the 

 skulls*. 



According to this resolution the population here classed 

 together as Ancient Britons consisted of two races mixed in 



* See -The Chances of Death,' vol. i. p. 3G2. 



