A. D. Darbishire 
15 
allelomorphic to a single unit character in the waltzing race ; that hypothesis 
leads us to expect that a quarter of the offspring of hybrids paired together will 
be albinos; and since = 13875, the observed result is in excellent accord with 
it; the difficulty in this, as in all attempts to apply Mendel's hypothesis, is to 
discover what are the unit characters concerned. 
In the preliminary account of the experiment it was evident that the pi'o- 
portion of pink-eyed individuals, with colour in the coat, was also nearly J ; the 
number now observed, namely at least 131 and possibly 134, is also a fair 
approximation to a quarter. So far then the results are not inconsistent with 
the truth of Mr Bateson's suggestion {Nature, March 19, 1903) that the character 
allelomorphic to albinism is pink eye with colour in the coat. 
Using Mr Bateson's original notation and denoting albinism by the symbol G, 
pinkness of eye with some colour in the coat by the symbol G', the generation is at 
first sight fairly represented by the formula 
GG + ^GG' + G'G' 
where GG' represents a heterozygous union between the albino and its allelo- 
morphic element — resulting, for some reason which the Mendelian hypothesis does 
not provide, in a dark-eyed mouse with a coat-colour variable and generally unlike 
that of either pure parent. 
The difficulties of this hypothesis are, however, great, even when we confine 
our attention to the frequency of the various kinds of individuals in the group, 
without considering the ancestral and fraternal correlations. In this as in the 
preceding generation the variability of the dark-eyed mice (heterozygotes of 
Bateson's hypothesis) is so great that it is impossible to regard each of them as 
resulting from the union of similar Mendelian elements ; and the relation between 
pinkness of eye and coat-colour is in the same way inexplicable on the view that 
there is only one kind of element G'. 
The 131 pink-eyed mice are all of colours a, b, or f, that is yellow, fawn-yellow, 
or lilac ; and these must on any Mendelian view represent more than a single kind 
of gametic element ; but if more than one such element be present, the original 
waltzing mice must have contained more than a single kind of unit G', and we 
have to consider Mr Bateson's second hypothesis {Nature, May 14), which is that 
in the formula already given the symbol G' must be regarded as denoting any one 
out of a series of different allelomorphic units, each leading, when mated with its 
like, to the production of a pink-eyed mouse with some colour in its coat. The 
hypothesis which involves the smallest number of kinds of elements is that one 
of the colours a, b, or / is a compound character resulting from the union of the 
other two : we should then have to consider the three kinds of pink-eyed mice 
with colour in the coat as of different gametic constitution : if we regard yellow 
and lilac as " pure," we should have to regard the yellow pink-eyed forms as " pure 
dominants," say of constitution G^'Gi, the lilac pink-eyed forms as pure, and of 
