140 REPORT OF THE CONFERENCE ON GENETICS. 
ON THE THEORY OF INHERITANCE OF QUANTITATIVE 
COMPOUND CHARACTERS ON THE BASIS OF MENDEL’S 
LAWS—A PRELIMINARY NOTE. 
By G. Upny Yuus, University College, London. 
In his memoir of 1904 “ Ona generalised theory of Alternative Inheritance 
with especial reference to Mendel’s laws”’ (Phil. Trans. Roy. Soe. A, vol. 
203) Professor Pearson laid the foundation of the theory of inheritance 
of a quantitative character determined by 7 allelomorphic pairs, in a race 
of which the individuals mate at random. Distinguishing the three types 
of couplet that can occur as “ protogenic,”’ “ heterogenic,”’ and “ allogeniec,”’ 
he discussed only the theory of inheritance of the number of pairs of the 
first or last type. Parents containing, say, m allogenic couplets will, he 
showed, give rise to offspring containing on the average only 4 of m such 
couplets ; that is to say, as the variability of the two successive genera- 
tions is the same, the coefficient of correlation between parents and 
offspring is, for this character, +. The similar coefficients between 
erandparents and grandchildren, great-erandparents and great-grand- 
children were found to be 7, 74, and so on, all these values being quite 
independent of the total number of couplets by which the character was 
determined. But the coefficients of correlation between parents and off- 
spring that have been determined from actual data are for the most part 
greater than 4, and moreover appear to exhibit significant differences as 
compared with one another. Professor Pearson concluded, accordingly, 
that the theory was “not sufficiently elastic to cover the observed facts” 
(p. 78); that “when. we come to the actual numerical values for the 
coefficients of heredity deducible from such a theory of the pure gamete, 
they do not accord with observation. They diverge in two ways. First, 
they give a rigid value for these coefficients for all races and characters— 
a result not in reasonable accordance with observation. Secondly, they 
give values distinctly too small, as compared with the average values, or 
with the modal values of large series of population observations.’’ (p. 85). 
There does not appear to be any justification in the memoir, however, 
for the very wide statement in the second passage cited regarding “all 
races and characters.” The only character there dealt with is the 
number of allogenic or protogenic couplets, and no reason is shown for 
supposing that this is typical of all characters. There did not appear to 
me, moreover, to be any obvious reason for making such a supposition, 
and I accordingly endeavoured to work out a slightly more general, 
though still quite limited case. Imagine a length to be made up of a 
number of distinct segments, the length of each of which is determined 
by an independent allelomorphic pair. Let each segment take the length 
a, b, or c, according as the corresponding protozygote, heterozygote, or 
allozygote is present; then the total length L is related to the number of 
