112 
Miscellanea 
precision that it is impossible to measure the deviations from the mean of any generation and 
so obtain the correlations. Not until far more precise classifications are made than von Guaita 
provides would the material be " available." 
In the next place, to what material can the ancestral law at present be applied '] It was 
perfectly open to Professor Castle to examine the conditions under which its results so far have 
been reached. They are stated with perfect precision in my memoir of 1898, and are (i) the 
absence of assortative mating, (ii) the absence of in-breeding and of selection. Now in von Guaita's 
experiments he got mice in which the ancestry had been a.?sortatively mated for generations: he 
first put like to like or made a perfect coefficient of assortative mating ; and then he crossed like 
with unlike, or made the coefficient of assortative mating negatively perfect. 
This coefficient is taken zero throughout my memoir on the law of ancestral heredity, and the 
reader is told that the author hopes to deal in a later paper with the influence of assortative mating 
and in- and in-breeding. Notwithstanding this direct warning Professor Castle does not hesitate 
to speak of the Law of Ancestral Heredity as applicable to von Guaita's data, and while the pro- 
pounder of that law has not yet been able to master the difficulties of the analysis which arises 
when intense assortative mating and generations of in-breeding are taken into account, the 
biologist remarks that the observed numbers, "it is evident," disagree with Pearson's series. Had 
I been able to master the analysis, von Guaita's data would not have provided the material upon 
which the correlations could be based, and so the law itself tested ; they are simply not "complete 
and precise" enough. 
Professor Castle, as I have already stated, reaches his result by taking my correlation 
coefficients for inheritance in man and horse, and asserting that they give the proportions 
of offspring who will be " like the ancestors." As I have before indicated, the typical ancestor 
might be blue and the typical off'spring yellow without this having any bearing at all on the 
correlation coefficients. Personally I have no means of determining whether the law of ancestral 
heredity holds or does not hold for coat colour in mice. The theory has not yet been worked 
out in a form covering von Guaita's cases, and data are only at present being collected complete 
and precise enough for the purpose. 
In the face of these facts I directly challenge Professor Castle to confess that he did not 
when writing his paper know what a coefficient of correlation was, and that he was thus 
incompetent to discuss the application of the law of ancestral heredity to mice ; or else to show 
that either the correlation coefficients, or, if he likes better, the multiple i-egression coefficients, 
which lie hidden in von Guaita's data can really be extracted therefrom and are inconsistent 
with the values which I ha\e found for man, horse and dog, when allowance is made for 
assortative mating and selection. I do not see that any other course is open to Professor 
Castle, after his statements that " it is evident " that the numbers do not fit my series and that 
"it is evident" that some fundamental defect exists in the "law of ancestral heredity." It is 
time that some check should be administered to this irresponsible and ignorant criticism of 
biometric methods, a criticism which can confuse a gi-oup-frequency — i.e. a number of individuals 
— with a correlation coefficient, a relation between deviations from type in individuals ; and I 
therefoi-e directly challenge Professor Castle to justify his statements, or failing that I call 
upon him to retract them. 
These statements are as follows : 
(ti) Pearson's Law of Ancestral Heredity can be applied to test von Guaita's data for 
mice, and, 
(6) When so applied, " it is evident " that it does not fit them. 
K. P. 
