16 Result of Crossing Japanese Waltzing with Albino Mice 
constitution G.^G.^, the fawn-yellow pink-eyed forms being heterozygotes of 
composition G^G.^. 
This hypothesis fails in several ways to meet the facts ; and since the objec- 
tions to this apply with greater force to any Mendelian hypothesis involving a 
larger number of allelomorphic units, it is worth while to consider them in some 
detail. The two kinds of elements G-^ and G^, which are here assumed to be 
manifested in the pink-eyed young with coloured coats, must be derived from the 
waltzing grandparents, for the hypothesis of gametic purity at once excludes any 
attempt to derive them from the albino ancestors : hence either each original 
waltzer used must have been a heterozygote of composition G^'G^', or two kinds 
of pure waltzers G-^G^ and G^G^ must have been employed. I am convinced 
that neither of these consequences of the hypothesis considered is true. Two 
mice of constitution G^G^^ paired together should have given young of character 
and relative frequency indicated by 
G^G^ + ^G^G^ + G;G^, 
so that all three of the colours observed among the pink-eyed offspring of hybrids 
must have appeared among the offspring of waltzing mice paired together. Now 
I am aware that lilac and white waltzing mice are bred by dealers, and I am 
familiar with their characters ; I am absolutely sure that no one among the many 
young bred from the waltzing mice used in these experiments was lilac in colour. 
The second hypothesis that two kinds of waltzing mice were employed involves 
the belief that one of these was lilac ; and this is also untrue. 
The known history of the waltzing mice used is therefore incompatible with 
the view that a andy (yellow and lilac) represent pure gametic elements of which 
b (fawn colour) is the heterozygote. It is similarly impossible to regard a or/ as 
a character of a heterozygote, b and the remaining character being pure ; for this 
hypothesis also would involve the appearance of lilac individuals in a quarter 
(or in the whole) of the young produced by waltzitig mice bred together. The 
behaviour of the waltzing mice when bred together is alone sufficient to destroy 
the validity of any hypothesis, involving numerous elements G', which does not 
depart from Mendel's doctrines. 
Mr Bateson has already proposed {Nature, April 23, 1903) to regard the 
waltzing mice used as heterozygous ; if he has once refused to accept the state- 
ments as to their purity he or others may well do so again. Let us therefore see 
what happens under these circumstances. The hybrids produced by pairing a 
heterozygous waltzing form (r/G^a' with a homozygous albino GG will be of two 
kinds, GGi and GG^ ; it is said that these will be dark-eyed and have some colour 
in the coat, but at present there is no means of distinguishing between them : all 
we know on this hypothesis is that the hybrids are of two kinds which are 
present in equal numbers. These hybrids, being indistinguishable, will be paired 
at random by any experimenter ; so that the offspring of hybrids now considered 
