A. D. Darbisiiihk 
I!) 
produce hybrids with darker coat-colour ; betweeu waltzing grandparents and the 
offspring of hybrids the sign is, however, positive for the same arrangement of 
colours, so that while the intermediate hybrid offspring of waltzing mice with a 
large amount of white coat arc darker than the average of hybrids, the young 
produced by such offspring paired together are on the whole lighter than the 
average. 
It must be remembered that this relation between the amount of white coat 
in one generation is a relation of cross inheritance, depending on (though not 
always simply proportional to*) the product of the coefficients of direct inheritance 
and of organic correlation. We have seen that the coefficient of organic correlation 
between amount of whiteness and coat-colour is negative in the hybrids them- 
selves ; in their offspring it has changed its sign and become positive, so that we 
see the way in which the sign of the coefficient of cross grandparental inheritance 
has become changed. We see then tliat both the colour of the coat and the 
amount of white fur in the offspring of hybrids are correlated about as strongly 
with characters of one set of grandparents as with those of the other; neither 
the waltzing grandparents nor the albinos are dominant in the sense that they 
alone determine the characters of the generation, neither are recessive in the 
sense that they take no part in such determination. It may be urged that the 
correlations just determined are without value because the offspring of hybrids 
are obviously divisible into two groups, albinos and others — and perhaps into 
three. There is some indication that the correlations between the albinos and 
their Avaltzing grandparents is negative, the grandchildren of the whiter waltzers 
containing a distinctly smaller percentage of albinos than the grandchildren of 
waltzers with a larger amount of coat-colour: the numbers descended from the 
various waltzing grandparents are shown in Tables XXIV. and XXV., and it 
will be seen that the deviation from Mendelian expectation is only great enough 
to be suggestive among the 112 offspring of hybrids whose waltzing grandparents 
were both of type a. The number of albinos which should be found in this group 
is 28, and the probable error of the expectation is 0-6745 V ^ x f x 112 = 3-09; 
the number of albinos actually found is 18, shoAving a deviation from the most 
probable result equal to more than three times the probable error, the chance of a 
deviation so great as this being about 0"0015, or the odds against it about 370 to 1. 
If, however, we exclude the albinos, and calculate the correlation between the 
coat-colour or the amount of white fur in the remaining individuals, and the 
whiteness of their waltzing grandparents, we obtain values very closely similar 
to those already given, so that in this case at least the apparent dimorphism of 
the young has no effect upon the grandparental correlations. 
The parental correlations are considerable, and curiously different for different 
characters. The correlation between the amount of white coat in hybrids and in 
their offspring is about 0'7 for both father and mother, showing that the whiter 
* Cf. Pearson, " Ou the Laws of Iiihei-itauce in Man,'' Biomctrika, Vol. ii. Part iv. pp. 38i — 5. 
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