Miscellanea 
187 
only raise the correlatiou to '0359 against a single parental correlation of "5000 ; if tlie correlati(.)n 
was "05 instead of "03, we should have the total possible environmental multiple correlation '0598 
as against "5000. Even if we raise the average environmental correlation to "1 and the inter- 
envirormiental factor correlation be reduced to '5, the multiple correlation of an infinity of factors 
is only ■1414 as against the single factor of hereditj^ 'SOOO. Even if we could pick out one 
hundred environmental factors which had no inter-correlations — which experience shows is 
wholly impossible — and each of these independent factors was correlated to the extent of '05 
with the mental or 2Jhysical characters of an individual they would only just reach the hereditary 
influence of a single character in a single parent. 
Now let us su2Jpose an absolutely idle case, namely that the environmental factors had the 
same correlation as a parent, i.e. "5, with the chai'acter of the individual, and only a correlation 
of "6 with each other, then if we could use an indefinitely great numbei' of such factors the 
multi2Jle correlation would only he ■5/v/'6 = "6455, while the correlation with two ]Darents, with 
no assortative mating, would be '7071. Even with assortative mating, it sufl&ces to take only 
the four grandparents into account to show that heredity acts in excess of an environmental 
scheme even so jareijosterous as is suggested above. If we take the i)arental correlations '50, the 
grandparental '25, and those of assortative mating '15, we have for the determinant: 
1, 
•50, 
•50, 
•25, 
•25, 
•25, 
•25 
■50, 
1, 
•15, 
•50, 
•50, 
0, 
0 
•50, 
■15, 
1, 
0, 
0, 
•50, 
•50 
■25, 
•50, 
0, 
1, 
•15, 
0, 
0 
■25, 
•50, 
0, 
•15, 
1, 
0, 
0 
•25, 
0, 
•50, 
0, 
0, 
1, 
■15 
■25, 
0, 
•50, 
0, 
0, 
•15, 
1 
Add together the second and third rows multijilied by ■3951, and the fourth, fifth, sixth and 
seventh multijjlied by -0456 and subtract the result from the first. The first row then becomes 
I -5593, 0, 0, 0, 0, 0, 0 | 
the others of course remaining the same. 
Hence A = -5593 x Aii,,, 
and R-=l - A/A„„= 1 - -5590= ■4407. 
Therefore /?==^6639. 
Or together grandparents and jjarents would influence a man's character more than an 
infinitij of environmental factors of the same gi'ade of correlation, because the latter factors 
are far more highly correlated together than several of our relatives. 
Actually of course we are dealing with average values ; the average value of environmental 
correlation with individual character being in our experience of the order OZ to •OS and the 
inter-environmental factor correlations of the order ^5 to But these averages enable us to 
appreciate the total effect. 
The doctrine taught by the ^xriters in the Eugenics Review, that we know nothing of the 
relative intensity of environment and heredity and that it is unwise " to use words in scientific 
literature without endeavouring to attach a definite meaning to them " only demonsti'ate how far 
the Editors of that Journal are removed from any apijreciation themselves of modern stati.stical 
methods. How far the doctrine is removed from the very strong views held on this point by 
Francis Galton, only those who have studied his writings and know how strongly he felt jjerson- 
ally on the subject are in the least comjjetent to appreciate. 
■24—2 
