110 
Miscellanea 
Series," in which he has taken the correlation coefficients with a single parent or a single grand- 
parent etc., as I have deduced them for man and horse as if thej' were quantities in the least 
comparable with the number of individual offspring. He remarks: 
"Comparing Pearson's series with that of Galton, we see that the parental influence is 
reckoned as substantially the same by both Galton and Pearson, but that Pearson assigns a much 
greater influence to the more remote ancestors than does (lalton*." 
Had Professor Castle merely added up the numbers he gives in this " Pearson's Series " he 
would have realised that they could not possibly represent what he states them to do ; for the 
four grandparents alone would have had more offspring " like " themselves than the total number 
of offspring ! 
Now the Law of Ancestral Heredity as stated by me gives absolutely no means of ascertaining 
the number of offspring "like any given ancestor" ; and if we measure parental influence by 
intensity of correlation, we should have : 
Pearson's Series Gallon's Series 
Parental Influence 1/2 1/3 
Grandparental Influence ... 1/3 1/9 
Great grandparental Influence ... .. 2/9 1/27 
Great grejit grandparental Influence ... 4/27 1/81 
whence the complete misrepresentation of Professor Castle will be obvious. 
After calculating a table which he says gives the distribution of the oft'spring of a cross between 
grey and white mice for 7 generations on Galtoii's Law, Professor Castle continues : 
" The observed numbers, it is evident, agree no better with one of Pearson's series than with 
that of Galton. The discrepancies noted between observed and calculated will remain and even 
be accentuated if we replac^e Galton's series with one of those t suggested by Pearson. For the 
result will be unchanged in generation II, but the calculated numbers will in most cases diverge 
still more ft-om the observed ones, in the later generations, because Pears(jn attaches more weight 
to the remoter ancestors than does Galton." 
Now I sui)pose Professor Castle had some idea in his mind when he penned these lines, but 
so far as I can understand the Law of Ancestral Heredity as I have myself enunciated it, the 
produce of a grey mouse and a fawn mouse might be on the average a green mouse without 
that Law having anything to say on the point. From it you cannot possibly deduce what 
number of the offspring of any generation will be like this or that ancestor. It is not a law of 
types, but of the distribution of deviations from type, and this is a very different thing indeed. 
The Law of Ancestral Heredity, as I have repeatedly stated J, makes no ass\imption as to the 
mean character of any generation ; it gives no statement whatever as to the number of offspring 
who are like any individual ancestor. What it does give us is this : the means of determining 
the probable deviation of any individual from the type of his own generation, when we know the 
deviations of some or all his ancestry from the types of their respective generations. What then 
is the simple rehxtion of my Law of Ancestral Heredity to Galton's series of j, J, etc. ? It lies in 
the following hypotheses : (i) Galton supposes the type of each generation to remain the same, and 
* p. 224, loc. cit. 
t Professor Castle quotes the two series I have given in Biometrika, Vol. ii., p. 222, the one as 
the best geometrical series, and the other as a close series, in which round numbers were taken. 
ij: It. S. Pioc. Vol. 62, pp. 387 et seq., where all the deviations are expressly said to be measured 
from the type of each generation, so that any modification of the type may be allowed for. Also in 
Biometrika, Vol. ii., p. 217, where we are again told that the deviation is from the type of its 
generation, and are expressly warned (p. 226) that no assumption is made that the mean of the fore- 
cnsted character is identical or not with any of the means of the foreknown characters. These papers 
are actually cited by Professor Castle. 
