A. D. Darbishiiie 
17 
will result from unions of three kinds, of Avhich one will pi-obably be twice as 
frequent as the other ; there Avill be — 
QO^ X GG^ giving GG + 2(5(7/ + G^G^, 
2(GG,'xGG,') „ 2{GG + GG/ +GG.; + G/G,'}, 
GG,' X gg: „ GG + 2Gg: + g,'g:, 
the offspring of hybrids being a series of individuals represented in composition 
and in relative frequency by 
4(?(? + 4GG,' + 4<gg: + g;g; + 2G^g: x g:g:, 
where all the zygotes of constitution G'G' have pink eyes and some colour in the 
coat. The sum of these is a quarter of the whole population, and we have seen 
that this is compatible with the observed result ; but the three colours in the coat 
should occur with relative frequency 1:2:1, or among the 131 (possibly 134) 
individuals actually found there should be if we call a and /" Gi and G, — 
G^G,' 32-25 instead of 19 observed. 
(?/(?; 64'.50 „ 80 observed. 
G.!G.: 32-2 „ 32 or 3.5 observed. 
Taking either of the possible numbers of pink-eyed lilac mice we find that 
these results are not impossible on the hypothesis put forward, but the odds 
against results so divergent as these or more so are about 60 or 70 to 1. 
The distribution of pink-eyed young might therefore, if not very plausibly, be 
accounted for by a purely Mendelian hypothesis if that hypothesis did not involve 
the appearance of lilac individuals in the offspring of pure-bred waltzing mice 
when paired together. The absence of such individuals might be explained by a 
departure from the Mendelian statements such as that made by Bateson in several 
cases, and it might be assumed that the pure waltzing mice have their eye-colour 
and coat-colour determined by a compound allelomorph ((r/ -f G^) not resolved 
into its components during gametic-formation in a pure-bred individual. This 
view is consistent with the behaviour of the pure waltzing strain, but it does not 
lead to the observed frequencies among the offspring of hybrids. The hybrid 
zygote will on this view be of constitution GGi ■\- GGJ ; and two such hybrids 
when crossed will give in every 16 young 
GG +GG ... 
. .. once 
GG + GG/ 
GG +GG,' . . 
GG,' +GG,' ... 
GG, +gg; ... 
GG/ Gi'Gi . . . 
G,'G,' + G,'G,' ... 
GG + g;g/ 
. .. once 
GG -f g^g: 
Biometrika iii 
