210 
On Theories of Association 
side what Mr Sanger can possibly mean by " all Galtonian laws " dealing with 
things thought to be continuous — he has clearly never read the treatment of eye- 
colour in man nor of coat-colour in Bassett hounds by Sir Francis himself, who 
distinctly treated them as discrete quantities and applies "his laws" to them. But 
we must indicate the fallacy of applying coefficients of association and colligation 
to Mendelian characters. The reason for applying them is the assumption made 
that a Mendelian character is a discrete unit. But if this be so, fourfold, and 
three by three Mendelian tables should be treated as discrete tables and true 
product moments formed of them. We believe that one of us was absolutely the 
first to apply these methods, treating the Mendelian theoretical characters as 
units*, and his work has been followed up by a whole series of workers in the 
Biometric Laboratory f. There was thus no question with the Biometric School 
of how Mendelian theoretical problems should be dealt with, and Mr Yule wholly 
misses the point when he states that Dr Snow's " recent comments in Biometrika 
on the use of the normal coefficient for Mendelian tables in Dr Brownlee's paper" 
were "a much stronger condemnation of Professor Pearson's than Dr Brownlee's 
work" (J. R. S. S. Vol. lxxv. p. 651). Pearson has never used a normal corre- 
lation coefficient on a true fourfold tablej, which he believed to be Mendelian in 
character. He has only applied such coefficients when he believed the character 
under consideration to be at bottom continuous, and as far as eye-colour is con- 
cerned, the many dissections of eyes he has been able to examine in his recent 
investigations as to albinism have confirmed rather than weakened that stand- 
point. But even had he done so, although the use of such a normal coefficient 
might be criticised on the ground of the labour involved in determining it.it cannot 
be condemned on any other ground, for it is in all respects as good a coefficient of 
association as Mr Yule's Q or a>, and possesses the important property that it is 
subject to selection — in opposition to the wholly fictitious merit which Mr Yule 
claims for his coefficients, namely that they are uninfluenced by selection. 
This point is so well illustrated by Mendelian theoretical tables, that we stay 
to demonstrate it here. Let us consider the correlation of father and offspring 
when a population represented symbolically by the fathers 
I (A A) + m (A a) + n (aa) 
is crossed at random with a population of mothers given by 
V ( A A ) + m (Aa) + n (aa). 
Here we can put N = I + m + n = total of fathers, /' + m' + n = N' = total 
mothers, and the fundamental Mendelian formulae 
(AA) x (aa) = *(Aa), 
(AA) x (Aa) = 2 (.4.1) + 2 (.4a), 
(Aa) x (Aa) = (AA) + 2 (Aa) + (aa) 
* Phil. Trans. Vol. 203 A, pp. 53—86, and R. S. Pruc. Vol. 81 B, p. 225. 
+ Jacobs, R. S. Proc. Vol. 84 B, p 23 ; Snow, R. S. Proc. Vol. 83 B, p. 37, and Biometrika, 
Vol. vin. p. 420. 
J The error of Dr Brownlee's work was that he went back on all this and applied continuous 
methods to theoretical Mendelian tables ; see Proc, Boy. Soc, Edin. Vol. xxk. p. 473. 
