A CONTRIBUTION TO THE STUDY OF THE SCOTTISH SKULL. 403 



there is no evidence now, and the walls are of average thickness. The norma verti- 

 calis presents an elongated elliptical form and the cephalic index is 74'5. I had 

 not enough shot to estimate the capacity in the usual way, as after the introduction 

 of fully 1950 c.c. there was still left a considerable space to be filled, but I was able 

 to calculate the capacity by using Lee's formula, and found it to be well over 2050 c.c. 

 It thus seems possible for a skull from a dolichocephalic group to attain to the 

 above capacity without in any way " tending towards sphericity." If future stages 

 of evolution therefore should be characterised by an increase in the cranial capacity, 

 it would seem that this end is attainable in a dolichocephalic type of skull without a 

 necessary change in the prevailing form of the latter. There would seem to be some 

 factors exercising an influence over skull form when the capacity is increased which 

 are not demonstrable by the aid of a " mechanical appliance." The shape of this 

 large skull is proof of such an influence, at least till the skull capacity reaches 

 2000 c.c. 



I have also calculated the correlation existing between several of the indices, 



T> TT T T> IT T 



namely, 100 £ with 100 ^ ; 100 ^ with 100 £ ; and 100 ^ with 100 ^. 

 L L H H i> a 



As has been pointed out by Pearson (23), even though there is no correlation 

 between the absolute measurements taken in pairs, in arranging them in the above 

 manner and correlating two indices with the same denominator a form of correlation 

 exists to which he applies the term " spurious correlation," and suggests that this 

 correlation value should be deducted from the whole value or gross correlation 

 obtained by correlating the indices in the usual way to get the real measure of 

 correlation between those indices or what is called " organic correlation." 



Having found it somewhat arduous to calculate the correlation between indices 

 by the method, said to be the most reliable, of multiplying the deviation from the 

 means in pairs and summing the products (which requires to be done over 400 times 

 in each calculation in the male group), and then applying the requisite formula to 

 obtain the coefficient of correlation, I decided to apply the formula which Karl 

 Pearson has provided for calculating the coefficient of correlation between indices 

 with the same denominator in terms of the coefficients of correlation and coefficients 

 of variation of the three absolute measurements. I had already calculated the 

 coefficient between the cephalic and vertical indices by the previous method, and 

 found, as stated in a former table, that the coefficient had a value in the male of 

 "301 ±'030 and in the female of '316±'061. By the formula above mentioned the 

 values obtained were '302 and '317 respectively, quantities practically identical with 

 those obtained by the other method. I applied the formula to find the correlation 



TD T TT T 



existing between the ^ and = indices and the ^ and r- indices, and also calculated 



H rl d Jj 



the spurious correlation values. The results are arranged in the following table, with 



corresponding values from other races for comparison. 



TRANS. ROY. SOC. EDIN., VOL. LI, PART II (NO. 9). 5 " 



