208 
On Theories of Association 
with the result that the segregating generation F 2 shows 222 (RR)'s, a very 
plausible Mendelian quarter. 
Prof. East does not do this, although it was a step absolutely compatible 
with current impressionist classifications by Mendelians. All he says is that 
" each species was absolutely reproduced by recombination in the F 2 genera- 
tion " and " I do maintain that the Mendelian notation satisfies the facts of 
size inheritance as well as it satisfies the facts of qualitative inheritance " 
(I.e. p. 639). 
Well, the fourfold Mendelian table of somatic characters would give in the 
F 2 generation (RR) = 222, (DD) + (DR) = 606 *. Now will anything be discovered 
by assuming that those two groups differ by a unit ? This is the " dichotomy" of 
Mr Yule's association. We contend that, while theoretically (RR) differs from 
(DR) by having no D as against one D and from (DD) by the latter's having 
two D's, this theory is idle when pushed into actual Mendelian statisticsf. The 
division at 60 is not a dichotomy of things differing by a unit, except in name, 
but an arbitrary cut across a continuous distribution, and the application of either 
the Boas-Yulean <f> or such coefficients as those of association and colligation is 
entirely misleading. We are told that "short" is "dominant" over "tall" as 
a result of experiment, and the importance of dividing at 60 mm. to get our 
tables is dropped out of sight. 
Piebaldism is another unit character of the Mendelians, and doubtless 
Mr Yule would be content to take his dichotomy between piebald and whole 
colour. Now here are 2314 mice classified according to the ratio of pigmented 
area of coat to whole area of coatj. Where shall we make the division between 
Total 
•10, -15 
■20, -25 
■SO, -35 
•Ifi, -45 
■50, -55 
■60, -65 
■70, -75 
■80, -85 
■90, -95 
■975 
1-00 
2314 
6 
31 
60 
81 
126 
111 
138 
176 
79 
393 
1113 
the piebald and the whole colour ? The group '975 largely refers to individuals 
with a very small white area on belly; but as a matter of fact the TOO group 
has been divided into three sub-groups of individuals who, without having white 
areas on belly, have or have not somewhat lighter pigmented areas there. Where 
is the true dichotomy, especially when we can show that each grade of pie- 
baldism is hereditary? Mr Yule would no doubt apply his association to 
piebalds and whole colours as giving a Mendelian unit, but in doing so he 
will be applying his dichotomy to words, to class-indices and not to the real 
things represented by them. 
* Whether this means anything or not would of course depend on the 105 at 60 never in later 
generations giving anything below 60 ! 
t Take the division at 35 mm. and we have dominance of long corolla, but the Mendelian quarter 
now fails. 
X From the late W. F. It. Weldon's mice data now at press. 
