20 Result of Crossing Japanese Waltzing ivith Albino Mice 
parents produce a markedly greater proportion of young in which whiteness 
predominates than are produced by the darker parents ; they also produce a larger 
proportion of pure albinos. 
In coat-colour the correlation between parents and offspring is much less, being 
about 0'2 for both parents. The cross-inheritance, as measured by the correlation 
between coat-colour of father or of mother and whiteness of young, is again 
positive (in accordance with the positive organic correlation between these two 
characters in the young), and its valwe is about 0'2. 
These various correlations cannot be adequately discussed without attempting 
a study of the effects due to the selection of parents during the experiment, too 
difficult for any but a trained mathematician. The hybrids were to a large extent 
paired together so that the members of a pair were of similar colours, the 
correlation between male and female members of a pair (weighted with the 
number of young produced) being about 0"4, so that the coefficient of assortative 
mating has changed from -|- 1 in the ancestors of the pure-bred mice, through — 1 
in the unions which produced the hybrids, to about 0*4 in unions resulting in the 
generation now described. The amount of whiteness in the coat of the hybrids 
was also selected, the correlation between male and female in the unions made 
being over 0"9 ; this difference in the degree of assortative mating may possibly 
account for the difference between the parental correlations in the two cases. 
We see, however, that both the colour and the amount of whiteness in the 
coat are variable characters, depending to a sensibly equal extent on characters 
transmitted by each of the pure-bred parents of the hybrids, so that there is no 
question of dominance on the part of one or other parent, and no possibility of 
regarding the characters of the generation examined as depending solely on the 
individuals paired in the original cross union, apart from their ancestry. In other 
words, we see that here, as in the hybrid generation, the phenomena observed must 
be formulated in some way or other in terms of the whole ancestry, and the idea 
of " gametic purity " is therefore excluded. 
Waltzing occurs in only 97 out of the 555 individuals resulting from the union 
of hybrids. When we compare this with the number of pink-eyed individuals 
(131 — 134) or of albinos (137) we see that the proportion of waltzing individuals 
cannot be regarded as a possible quarter. The probable error of the expectation 
that a quarter of the individuals will waltz is, on the Mendelian hypothesis, 
0-6745 X f X 555 = 6-88 only, and the observed deviation is 138-75 - 97 = 41-75, 
the odds against so great a deviation being rather more than 50,000 to 1. As 
the result here obtained differs from Mendelian expectation in the same direction 
as that already obtained by von Guaita* and to an extent consistent with the 
agreement of both, the evidence that the waltzing character does not segregate in 
Mendelian proportions is very strong. 
* " Versiichemit Kreuzungen von verschiedeuen llasseu der Hausmaus," Ber. d. naturforsch. Gesellscli. 
I'n'ilnirn, Bd. x. 1898, Bd. xi. I'JOO. 
