On Mendels Laws. 
201 
of the gra ;/<7parent. The only difference in result would probably 
he, that the constant B would be somewhat reduced as compared 
with its value for the parental heredity. If an individual have a 
given abnormality of character, his offspring will probably (or on the 
average) be abnormal, but rather less so, his grand offspring again 
divergent, but less abnormal still. This phenomenon, that the 
character of the grandparent (like that of the parent) enables one 
to estimate the mean character of the offspring more accurately 
than would be possible from a mere knowledge of the characters of 
the race, is, in a sense, “ ancestral heredity.” It is not, however, 
what the statistician generally means by that term. In the above, 
the parent’s character is supposed either unknown or neglected; 
we deal solely with grandparent and grandchildren. But supposing 
the character of the parent known, so that one datum for estimating 
the mean character of offspring is already given, a wholly new 
question arises, viz. will a knowledge of the grandparent’s character 
enable one to increase the accuracy of estimate ? If the answer 
to the question be in the affirmative, as it is in every case without 
exception which has yet been tried, then there is what may be 
termed a partial heredity from grandparent as well as parent, and 
it is to the existence of such partial heredity that statistical 
writers generally refer when they speak of “ ancestral heredity.” 
If Xj and X 2 be the parental and grandparental characters, Y the 
mean character of the offspring, then all the experience that we 
have shews that if an equation be formed giving Y as nearly as may 
be in terms of both X x and X 2 , e.g. 
Y = A + Bj. X, + B 2 . X a . ( 3 ) 
I 
the term B 2 has a very sensible value— i.e. the grandparent’s 
character very sensibly increases the accuracy of estimate. This 
law of partial heredity from the grandparent is known to hold for 
fertility, length of life, and eye-colour in man, for coat-colour in 
horses, for one character in a Daphnia, three characters in an Aphis , 
and I may add, from some recent work of my own, two or three 
characters in common duckweed (Lenina minor). The list is not a 
long one certainly, but the characters and the genera are so extra¬ 
ordinarily diverse that the law must be one of very great generality. 
Nor, of course, need we suppose investigations to cease with 
the grandparent. If a knowledge of the grandparental character 
increases the accuracy of estimate of the mean character of off¬ 
spring, it is natural to assume that the further knowledge of the 
great-grandparental,great-great-grandparental, etc., characters would 
