LAW OF ANCESTRAL HEREDITY 113 
every ancestor of a particular individual contributes 
its quota to the heritable qualities displayed by that 
individual. The law also states that the average 
amount of resemblance between an individual and any 
particular ancestor is capable of definite numerical 
expression. Thus the mean amount of correlation 
between (x) the two parents and the offspring, (2) the 
four grandparents and the offspring, (3) the eight 
great-grandparents and the offspring, and so on, is 
believed to diminish in a geometrical series, which is 
the same for all organisms and for all characters. The 
actual amounts of these correlations were expressed by 
Galton in the form of the series 0°50, 0°25, 0125, etc. 
Pearson regards them as being more nearly represented 
by the more rapidly diminishing series 0°6244, 0°1988, 
0'0630, etc. 
Now, there can be no doubt that the law as stated 
above has been disproved in specific instances, and was 
indeed disproved by the work of Gregor Mendel before 
ever it was enunciated, although Mendel’s work was 
not generally known untillater. According to Mendel’s 
theory of inheritance, certain ancestors contribute 
nothing to the constitution of certain offspring in respect 
of certain characters. Furthermore, the modification of 
the law of ancestral heredity which applied to alterna- 
tive inheritance, and which was assumed in working 
out the inheritance of coat colour in thoroughbred 
horses, has recently been shown not to apply to that 
particular case. 
Unfortunately, most of the further biometrical 
generalizations which concern students of heredity 
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