HEREDITY 529 



individuals were found, thus furnishing additional evidence of 

 the remarkable agreement between theory and fact in matters 

 of breeding, and tending strongly to establish this law. 



All things considered, the fraction J- seems to be fairly well 

 established as the ratio of the intensity with which, on the 

 average, characters are transmitted at the several matings in 

 bisexual reproduction ; and if this be so, the law as stated by 

 Galton may be accepted as substantially correct, especially 

 when we recall the fact that this (^ -f- -J -f J- + -^Q . . . to infinity) 

 is the only infinite series whose ratio is ^ and that will add up 

 to unity, thus exactly accounting for the full heritage. 



Pearson's method. 1 Pearson has treated the same problem by 

 somewhat more complete mathematical methods, and arrives at 

 a somewhat more general result, but a result which may be said 

 to agree substantially with that of Galton. He begins by dealing 

 with the question of biparental inheritance. Then by extending 

 the results obtained he accounts for the total heritage from each 

 generation of back ancestry, taking into consideration the vari- 

 ability of the entire population to which each generation of the 

 ancestry belongs ; that is, he considers the variability of the 

 separate generations of ancestors, a factor which Galton did 

 not take into account. 



Biparental inheritance. Starting out with the question of bi- 

 parental inheritance, the problem, stated in general terms, is 

 as follows : What, on the average, is the character of offspring 

 of fathers whose deviation from the mean of fathers in general 

 is // 1} mated with mothers whose deviation from mothers in 

 general is /i 2 ? 2 



In the discussion of this problem let the deviation of this 

 offspring from offspring in general be // 3 , and its standard 

 deviation (in its own array) be denoted by 2. 



1 Proceedings of the Royal Society, LII, 1898, 386-412 ; also Pearson, Grammar 

 of Science, pp. 468-481. 



2 Stated in concrete terms, What is the height, on the average, of the children 

 from those fathers who are, for example, two inches above the average height of 

 fathers, mated with mothers who are one and a half inches below the average 

 height of mothers ? In discussions of this kind the student should remember that 

 males and females differ naturally in character valuations, and also that not all 

 males become fathers nor all females become mothers, so that the race descends 

 not from all but from a portion only of the preceding generations. 



