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increase it still more, though probably in a diminishing ratio. 
It would he very unlikely, to say the least, that an absolute dis¬ 
continuity should come in at any one generation, and that the «th 
ancestor should sensibly increase the accuracy of estimate while the 
(n + 1) th should not. In the absence of such discontinuity the 
law of heredity (of intra-racial individual heredity) must be of the form 
Y = A + B L . X t + B 2 . X 2 + B 3 . X 3 -j- B 4 . X 4 + ... ( 4 ) 
where X x X 2 X 3 , etc. are the characters of the successive ancestry 
andBj B 2 B 3 , etc. a series of diminishing fractions. No investigations, 
so far as I am aware, have been published, that give the values of 
B’s beyond the grandparents, but my own experiments on a small 
scale on Lenina minor give sensible positive values up to B 4 —as far 
as I could carry the observations. Moreover such a form of law is 
in obvious accordance with the practice of breeders of pure stock, 
who judge the value of an animal for breeding purposes not by its 
own characters alone, nor by that and the characters of its imme¬ 
diate parents, but by its whole pedigree. The pedigree would be 
completely valueless if there were no “ partial heredity ” from 
ancestry; if B 2 B 3 , etc. were all zero two animals with equally 
desirable values of X 1 would be equally likely to produce good off¬ 
spring, even if the one had bad or mediocre ancestry and the other 
a good pedigree. It is difficult to suppose that the weight attached 
to pedigree is based on nothing but illusion, yet it is only reconcilable 
with a law of partial ancestral heredity such as (4). This law then, 
that the mean character of the offspring can he calculated with the 
more exactness, the more extensive our knowledge of the corresponding 
characters of the ancestry, may be termed the Law of Ancestral 
Heredity. 
Little work has yet been done on the intra-racial inheritance of 
attributes, but the form which the law of ancestral heredity would 
take in such a case is fairly obvious. It might be written in the 
form (to use as nearly as possible the same words )—the percentage 
of A's and a’s amongst the offspring can he calculated with the more 
exactness, the more extensive our knowledge of the corresponding 
characters in the ancestry. For instance, one may presumably take 
it for a fact that the percentage of insane amongst the offspring 
of the insane is larger than amongst the offspring of normal 
individuals i.e. insanity is inherited. Does the law of “ ancestral 
heredity ” hold ? If we assume that it does, we are assuming that 
the percentage of insane amongst the ultimate offspring is greater 
and greater the more of the ancestry were insane; if we assume on 
