10 Result of Crossing Japanese Waltzing with Albino Mice 
And since every measure of association or correlation becomes zero with the 
difference of the products of diagonally opposite squares of such a table, we see 
that whatever measure be adopted must in this case give a value = 0, since the 
difference of the cross products = (a + c) (6 + (i) — (a + c) {h + d) = 0. 
It is of course evident that this important result is a necessary arithmetical 
consequence of the way in which the parents have been mated and of the identity 
between reciprocal crosses ; it does not depend on any theory of the nature of 
inheritance, and it involves no statement about the mean character of the young 
produced; the young may be intermediate between their two parents, or exactly 
like one or the other, or wholly unlike both. 
A further effect of breeding experiments, which involve sudden (and generally 
great) changes in the correlations between male and female, is a condition of 
instability during the first few generations. A race may become stable with any 
constant amount of assortative mating, but a sudden change results in a condition 
of instability, making it peculiarly difficult to discuss those first generations which 
are too often the only experimental data available. 
These considerations, usually forgotten by those who criticise the law of 
ancestral inheritance, must be carefully borne in mind by anyone who wishes to 
realise the questions actually at issue. 
We have seen that a process of crossing, such as that performed with the mice 
described, involves a total absence of correlation between parents of either sex and 
offspring if the individuals of either race are chosen with equal frequency as male 
and as female parents. It must be pointed out that many of the tables which 
accompany this paper are not tables showing correlation between all parents of 
one sex and their offspring; but tables of correlation between all parents of one 
character, whatever their sex, and their young. 
An examination of the full list of hybrids given in Table A, Appendix I., will 
show that the results of reciprocal crosses are so nearly identical as to justify the 
neglect of sex in the treatment of the data : a table of the correlation between the 
coloured waltzing mice or the albino mice and their hybrid young such as any of 
the Tables IV. — VII., may therefore be considei'ed to give approximately the same 
result as if each referred to half the whole crosses from random unions between 
waltzing mice and albinos — that half namely in which all the parents are of one 
sex. 
• 
Such a way of regarding the tables is at best only an approximation to the 
truth ; a fuller discussion of the parental and indeed of all correlations observed 
during the experiments must be published later : in the meantime the present 
way of regarding them may be useful as a preliminary test of their compatibility 
with the law of ancestral inheritance. 
On the view suggested Tables VI. and VII. may be regarded as showing the 
result of two operations; it may be considered that first one parent has been 
