170 DOMESTICATED ANIMALS AND PLANTS 
the grandparent in this particular character bring it suddenly 
into prominence. 
The number ‘*two.’’? The student cannot fail to be struck 
with the extent to which the number “two” figures in these 
affairs. The product of mixed breeding, if unrestricted, follows 
the binomial formula, giving definite mathematical proportions 
to the combinations of characters. The normal distribution 
when studying type follows the same formula, and the law of 
ancestral heredity is made up of fractions derived from the 
universal ‘‘ two.” 
This is not accidental, but perfectly natural. Inheritance 
everywhere is the result of combinations of characters from two 
parents ; not only that, but all growth is the result of cell divi- 
sion, which means parting into two, so that the number “ two’ 
lies at the very base of all affairs involving transmission. It is 
not strange, therefore, that the whole matter rests on a definite 
mathematical basis, that the chance combinations of characters 
can be predicted in the long run, or that the law of ancestral 
resemblances should be the very remarkable series 4, }, }, 
etc. It really could not be otherwise, with bisexual reproduc- 
tion and with growth by cell division involving a splitting 
of the chromosomes as the two characteristic attendants upon 
heredity. 
’ 
Summary. The offspring is a composite of all the blood of all his an- 
cestors in proportions fairly definite. We cannot predict what the individual 
may be, but of large numbers we can predict that their resemblances to ances- 
tral traits will follow the series 3, 1, 1, etc., in which the two immediate 
parents divide between them the chances of impressing the offspring ; and 
the other fractions are each divisible by the number of ancestors of the 
corresponding generation, so that of large numbers of offspring a certain 
definite number (25 per cent of all) will resemble the one parent with respect 
to any given unit character, 25 per cent will resemble the other parent in 
respect to the same character, and the remaining resemblances will be 
distributed proportionately among the back ancestors. The number “two” 
characterizes all reproduction, which therefore tends to conform to the 
binomial theorem. 
