PREFATORY NOTE. 



The present paper is an attempt to apply a rigorous theory of probable 

 inference to a question of genetic biology, taking statistical data as the 

 basis of the inquiry. If, in making such an investigation, the author 

 may seem to stray outside his professional field, he would reply that the 

 discussion of a biological question was by no means the sole object with 

 which the work has been undertaken. It has appeared to him that the 

 treatment of statistical data generally on a large scale, by the rigorous 

 methods of probable induction, leads one into a field the cultivation of 

 which promises important results to the science of the future; and he 

 hopes the work will show how it is possible by such methods to reach 

 conclusions on questions which elude all direct investigation. 



The author has to acknowledge his indebtedness to the Trustees of the 

 Bache fund, who made him a grant to pay the expenses of the necessary 

 examination of genealogical data, and to the Census Bureau, through Mr. 

 W. C. Hunt, chief statistician for population, who supplied statistical 

 data relating to several thousand families culled from the Census records. 



WASHINGTON, November, 1903. 



