II4 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 may be 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 
