K. Pearson 
365 
still in long series foi- a variety of characters in man, horse, and dog the parental correlation 
certainly approaches a value about -5. If Mr Punnett's values were for a long series I think we 
should have to conclude that the intensity of heredity could vary very much from species to 
species, and perhaps admit even considerable variation in the same species for the same character 
at difi'erent periods. Hitherto, however, we have found that when we replace our short and 
doubtful series by longer and more carefully measured or observed data — as we have done in 
several of the cases referred to above — we approach closer to the value '5 for parental heredity. 
Further, the coniirmation of Mr Punnett's statements on p. 333, as to growth changes in post- 
embryonic life (and perhaps during embryonic life itself ?) would certainly lead us to expect a 
weakened parental correlation (and in the latter case a weakened fraternal correlation). Anyhow 
values like '3 for parental and "4 for fraternal correlation cannot discriminate between the 
ancestral law and any form of Mendelian theory, for the former with Mr Galton's value of the 
constants actually leads to these values. A value like '5 would be opposed to one fairly compre- 
hensive Mendelian theory, but possibly not to every such theory. 
A possible test between the ancestral law and my generalized Mendelian theory is given in 
my paper : On a Criterion which may serve to test various Theories of Inheritance*. It is there 
indicated that we should expect the variability of the several arrays in the latter case to be 
given by a parabola, while with anything like a normal distribution of variations it would in 
the former case be a straight line. Dr Lee and I applied this test to Mr Punnett's five parental 
correlation tables, we calculated the s.D.'s of each array and plotted them to the magnitude 
of the parental character. But the numbers in the arrays were so small, and therefore their 
probable errors so large, and there were so few points (especially if we omitted those which 
belonged to arrays of 6 to 10 members only, and therefore were absolutely untrustworthy), that 
we got nothing but wild zigzags of three to four lines ; these differed between the wide limits of 
random sampling from neither straight line nor parabola, and were quite insufficient to serve 
as any criterion. In fact they only again emphasized the lesson we had already learnt from 
short series that 25, 50, or even 100 families are insufficient to adequately determine the bio- 
metric constants of a correlation surface for heredity. In saying this I do not for a moment 
undervalue the importance of Mr Punnett's work ; he has shown for the first time how heredity 
in one species of fish can be dealt with, and this is a great step onwards. I quite realize the 
difficulty of dealing with 1000 mothers, but this is, I believe, the sort of ideal we must bio- 
metrically propose if we are to reach data sufficiently smooth to give final values to the heredity 
coefficients, and so available for testing between current theories. 
* R. S. Proc. Vol. 73, pp. 262—80. 
