Karl Pearson and David Heron 
209 
Again, an illustration from Mendelian dichotomy may be found in a paper 
by Hurst entitled "Mendel's 'Law' applied to Orchid Hybrids*." He desired 
to give a proof that the F 2 generation consists of 50 % of (DR)'s and 50 °/ c 
of "specifics," (DD)'s and (RR)'s. He recognised that the first cross gave an 
" intermediate," so he defined his (DD) as all those, which show § (DD) character 
and more, his (RR) as all those that show ^(RR) character and more, and the 
"intermediates" or apparently the (DR)'s all those that show character between 
%(DD) and f (RR). As a result his "specifics" came out as 2281 and his 
"intermediates" as 2267 in number, a plausible Mendelian 1 :1 ratio. Thus the 
classification into every one of the groups (DD), (DR) and (RR) in the F 2 
generation is by trisection of a continuous variate at arbitrary valuesf. 
Pearson has come across an exactly similar instance of the vagueness of the 
Mendelian unit in breeding dogs. If a short-muzzled dog be crossed with the 
long-muzzled dog, the hybrid would be described by general impression, and was 
so considered by him, as short-muzzled. The result was to indicate dominance 
of the short-muzzle. But when muzzle indices were formed and the dogs' heads 
measured in a variety of ways, the hybrids were found to be intermediates, and, 
crossed in again with the short-muzzled stock, they gave a group the mean of 
which had a position intermediate between the hybrid and that original stock. 
Each generation had very considerable variation. Dichotomy giving Mendelian 
ratios was possible, provided an arbitrary division was taken across the con- 
tinuous distribution. Mr Yule's unit difference, short-muzzle — not short-muzzle, 
would be a perfectly idle one across what in the F 2 generation is a continuous 
distribution. 
One of the most remarkable features, indeed, of the present situation is the 
assumption that in some mysterious manner Mr Yule's coefficients of association 
or colligation can be applied to Mendelian results. Mr Sanger, in his contribution 
to the discussion, said : 
" One additional reason why he welcomed the Paper was that the rise of 
Mendelian biology had made a great difference. There they were always dealing 
with things which were discrete, whereas according to all Galtonian laws they 
always dealt with things which were thought to be continuous. At present there 
was this difficulty that mathematicians had a prejudice in favour of more elegant 
mathematics, and the Mendelians had not yet learnt algebra ; but that day would 
come, and then Mr Yule's work would be the work for the Mendelians" (J.R.S.S. 
Vol. lxxv. p. 646). 
Mr Yule nowhere repudiated this application of his coefficients, and yet they 
are the last which can possibly be applied to Mendelian data ! We put on one 
* Journal of the Royal Horticultural Society, Vol. xxvi. Part 4. 
t Martin Leake has found continuity in the Fx generation with an intermediate mean in the ease of 
Indian cottons, Journal Asiatic Soc. of Bengal, N. S. Vol. iv. p. 13, 1908. Even more astonishing- 
frequency distributions for the F 2 generation for "tails" and "shorts," number of nodes and lengths 
of internodes may be obtained from Mr R. H. Lock's "Studies in Plant Breeding in the Tropics," 
Annals of Royal Botanic Gardens, Peradeniya, Vol. n. In these cases it is wholly impossible to speak 
of a unit difference between the members of either class. 
Biometrika ix 27 
