Miscellanea 
243 
It is a remarkable fact that many biologists have accepted Galton's theory of regression, 
without seeing that there is no regression whatever on Galton's hypothesis after the first 
generation, at which selection is stopped ! This misunderstanding arises from the common 
belief that a word carries its own definition and that it is not needful to study its algebraical 
significance. 
Looked at as a whole it appears to me that the theory of multiple correlation is the natural 
manner in which to approach the theory of ancestral inheritance. The work done on man shows 
that for all sorts of types of measurable characters we have true linear regression, and that 
our correlations of measurable characters in all species hitherto dealt with are singularly 
constant. Further these correlations appear for the same grades of relationship to be the same 
for measurable and non- measurable characters. We are largely compelled to measure ancestral 
correlations by colour characters as no other data are available, but the equality of pigmental 
and of measurable-character correlations for grades we can compare gives us confidence , in 
testing the decadence of resemblance on pigmental characters. And the law of geometrical 
decadence being once established we have a multiple regression formula which may be legiti- 
mately applied to all measurable characters. 
The fact that the Mendelian gametic correlations approach in some respects those found by 
observation on populations, is not a justification of Mendelism. It is only an indication that for 
such special cases as "unit" characters, even if they exist, there is no absurdity in our geometrical 
law of decadence. Most biometricians, however, who have measured and observed characters in 
man or animals have not been able to classify into A and not- J, but believe that there are many 
grades of A and not- A and that probably every one of these are capable of selection and of 
inheritance. Thus they look to continuous or at least multiple variations of the germ-plasm 
with regard to any single character, and not to the mere presence or absence of a single 
determinant. 
LITERATURE. 
F. Galton : Natural Inheritance, 1889, pp. 133, 135 — 7. 
Galton's correlation values (parental J, grandparental J, etc.) are not in accord with wider 
observation, and they are opposed to the ^, j, g, etc. of his own law of " contributions." 
K. Pearson : On the Law of Ancestral Heredity, Royal Soc. Proc. Vol. 62, 1898, pp. 386 — 412. 
This is the first attempt to apply the formulae of multiple regression to the problem of 
heredity. It endeavours to show how Galton's correlations must be brought into touch with his 
" contributions." 
The paper is now inadequate because : (i) we now know much better values of the ancestral 
correlations — we had then only very few data ; and (ii) there are one or two bad algebraical slips. 
These are corrected in 
K. Pearson : The Law of Ancestral Heredity, Biometrika, Vol. II. p. 211. 
But another stupid blunder is made in this paper on p. 224, where by an oversight a and r 
are given the individual and not the mid-parental values. I hope this has been finally put right 
in this note. 
Galton contributed a paper, R. Soc. Proc. Vol. 61, p. 402, on the Ancestral Law in Basset 
Hounds, but this is really written from a somewhat different standpoint ; that standpoint has 
been considered by me in a paper on the Law of Reversion, R. Soc. Proc. Vol. 66, p. 140. 
There has been a great deal of perfectly idle criticism of the Law of Ancestral Heredity 
(Archdall Reid, Bateson, Darbishire) principally based on a crude application of Galton's original 
5, j, \, ... contributions to individuals with selected ancestry (Darbishire, Castle, etc.). The least 
that can be said of these criticisms is that the writers had not grasped the fundamental idea 
of correlation before they started to criticise the ancestral law. 
31—2 
