2 NATURAL INHERITANCE. [chap. 



generations. The large do not always beget the large, 

 nor the small the small, and yet the observed propor- 

 tions between the large and the small in each degree of 

 size and in every quality, hardly varies from one gener- 

 ation to another. 



A second problem regards the average share con- 

 tributed to the personal features of the offspring by each 

 ancestor severally. Though one half of every child 

 may be said to be derived from either parent, yet he 

 may receive a heritage from a distant progenitor that 

 neither of his parents possessed as personal character- 

 istics. Therefore the child does not on the average 

 receive so much as one half of his personal qualities 

 from each parent, but something less than a half. The 

 question I have to solve, in a reasonable and not merely 

 in a statistical way, is, how much less % 



The last of the problems that I need mention now, 

 concerns the nearness of kinship in different degrees. 

 We are all agreed that a brother is nearer akin than a 

 nephew, and a nephew than a cousin, and so on, but 

 how much nearer are they in the precise language of 

 numerical statement % 



These and many other problems are all fundamentally 

 connected, and I have worked them out to a first degree 

 of approximation, with some completeness. The con- 

 clusions cannot however be intelligibly presented in 

 an introductory chapter. They depend on ideas that 

 must first be well comprehended, and. which are now 

 novel to the large majority of readers and unfamiliar 

 to all. But those who care to brace themselves to a 



