MENDELISM AND BIOMETRY 231 
Consequently Pearson’s treatment of the subject does 
not justify his statement that the Mendelian theory 
gives a rigid value for the coefficients of parental cor- 
relation for all races and characters—a conclusion 
which he regards as fatal to this theory, because the 
coefficients for different characters and races, as found 
statistically, show considerable individual differences, 
and seem to cluster round a value considerably higher 
than that indicated by his elaboration of the theory of 
the pure gamete. Yule thereupon discusses a somewhat 
more general case, and considers the inheritance of a 
length made up of a number of distinct segments, each 
of which is determined by an independent pair of 
allelomorphs. Supposing each segment to take the 
length a, b, or c, according as the corresponding proto- 
zygote, heterozygote, or allozygote is present, Yule 
arrives at an equation from which the correlation 
between parent and offspring may be found. From 
that equation the following results are deducible : 
If there is dominance—+.e., if a=), or b =c, the corre- 
lation coefficient is the same as that found by Pearson 
—i.é., one-third. 
But if the heterozygote always gives rise to a 
length exactly intermediate between those due to 
the respective homozygotes, the correlation is found 
to be one-half. 
Cases of partial dominance will give an intermediate 
value. Consequently, according to the degree of 
imperfection of dominance, and without assuming any 
other disturbing circumstances, values of parental 
correlation varying from 0°33 to 0°5 are to be expected 
