H4 BIOMETRY 



are based upon the assumption that the law of ancestral 

 heredity is strictly true. So that whilst we have 

 spent some time in considering the facts of normal 

 variability and of correlation between relatives, 

 because these facts are quite independent of any 

 theoretical assumption, the remainder of our review 

 must be passed over at a more rapid rate. Until 

 the theoretical conclusions now to be described have 

 been revised by their authors in the light of recent 

 knowledge, it is difficult to say how much reliance is to 

 be laid upon them, but it seems quite likely that they 

 will hold good as approximations. Indeed, though 

 not applying to individual cases, the law of ancestral 

 heredity does seem to hold good as a statistical state- 

 ment of general results, so that there would be no objec- 

 tion to it on either theoretical or practical grounds if 

 only it had been enunciated in some such terms as ' a 

 law of average ancestral resemblance.' Thus it is quite 

 possible that the total contribution of the eight great- 

 grandparents of an individual maybe on the average 

 correctly represented by Pearson's fraction, even 

 though their individual contributions are not always 

 the same. 



Let us, then, briefly examine some of the further 

 conclusions which have been drawn from the data of 

 the biometricians. 



Assuming the law of ancestral heredity, Pearson has 

 arrived at very interesting conclusions with regard to 

 the effects of artificial selection when the correlation 

 coefficients have those values which have been actually 

 found for them in the case of the human race. In the 



