A. Barrjngton, a. Lee and K. Pearson 
263 
the nature of its vai'iatioii and its relation to parental correlati(3n are still very 
obscure. 
(iv) That so far as work on the inheritance of pigmentation in the Biometric 
Laboratory at University College has yet gone, we find that for man, horse and 
dog in long series the results are in good agreement, and can be described by the 
statement that ancestral correlations diminish in a geometrical series and sensibly 
the same series. We hope shortly to publish two further long series of pigmen- 
tation inheritance statistics; should they give results in accordance with those 
already reached, no further reductions of this kind will be made by us, for we 
think the generality of the law will have been sufficiently demonstrated. In 
saying this we do not overlook the vast amount of material now being collected 
by Darbishire and others on inheritance of pigmentation in mice, but it is 
unfortunately not in a form to which it is easy to apply the mathematical 
processes required. The selection is so stringent, when two true breeding strains 
are crossed, that it is difficult to apply the complex equations for the influence 
of selection on correlation. WKat we should especially like to know would be : 
((() after hybridisation, do or do not the offspring of the hybrids, if mated at 
random inter se, give a stable population ? (b) If they do give a stable popu- 
lation, do the ancestral correlations diminish or not in a geometrical series ? 
and (c) If they do, are their numerical values sensibly or not the same as those 
we have found for man, horse and dog ? If these questions were answered in the 
affirmative, then it would be more possible to determine the relationship between 
so-called Mendelian Principles and the Ancestral Law. The latter seems to apply 
closely to any fairly stable population with random or nearly random mating, even 
in the matter of pigmentation. According to the Mendelian hypothesis developed 
by one of us, the offspring of the hybrids should, if mated at random, give a stable 
population, and this is likely to be true on many other hypotheses. What happens 
in such a population ? According to the view of some Mendelians both factors 
of the original cross are, as far as some one character at least is concerned, in 
appearance, elements of such a population ; this being so we ought to be able to 
see, once the stability of such a population of hybrid's offspring is established, 
much more clearly than at present the relation of the two views to each other. 
The differences between our man, horse and dog returns and Darbishire's mice 
returns seem to consist essentially in this : that in the three former or intra-racial 
results the intra-breeding between differently pigmented members has gone on for 
generations, while in the latter or inter-racial results there has been separation 
for generations. But if the offspring of hybrids mated at random give a ' stable ' 
population, then we ought to be able to predict at least certain phenomena with 
regard to the result of crossing its constituents. What is now quite clear about 
the mice is that ancestry can be no more neglected in their case than in the cases 
of man, dog or horse. 
