•278 



Prof. K. Pearson. On a Criterion which may [Mar. 4, 



horizontal or mean line of the " Ancestral Law " gives a better result 

 than the hyperbola. As a matter of fact in the small arrays at the 

 extremes we get as before very erratic results ; almost any value of 

 the standard deviation may be reached, not only because the probable 

 errors are so large, but because the appearance of any single abnormality 

 or of any slip due to measurement or classification becomes so very 

 disturbing in these small arrays. Even then we only find four cases 

 in seventeen which deviate by more than twice the probable/error from 

 the mean line. In this case the mean error of the " Ancestral Law " for 

 the seventeen arrays is 0*31, and of Dr. Boas's hyperbola CK9.* 



*o u 1st 73 1T~1& 77 73 T3 GO GX S» <S3 G& GS &6 37 



Diagram II. 



(12.) It may be asked how Dr. Boas has reached the conclusion 

 that in the case of cephalic index the "Ancestral Law" does not apply 

 and that the children break up into " mothers' offspring " and " fathers' 

 offspring " "? He has used the measurements of Dr. Maurice Fishberg 

 of New York, on forty-eight families of "East European Jews." 

 Now, I think it may be reasonably questioned whether a population 

 defined as " East European Jews" can be considered as homogeneous. 

 I mean by this : Would any such category breed true to itself % Is it 

 to be looked upon as a " race " in the sense used by met of a popula- 



* If the large values often found for the variability of the extreme arrays of a 

 correlation table have real significance, which I doubt, I personally am inclined to 

 think it is due to deviation from true linear regression, the regression curve being 

 a cubic curve with its inflexional portion representing the regression line of the 

 ordinary range. 



f ' Biometrika,' vol. 2, p. 511, and compare with the stable Mendelian popula- 

 tion discussed in my paper, ' Phil. Trans.,' A, vol. 203, pp. 58 — 60. 



