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 ^, J, ^, 

 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 ^, ^, ^, 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. 



