20 The Problems 



Here again Gallon applied his method with remarkable 

 success. Referring to the progenitors of A and It, deter- 

 mining how many of each type there were in the direct 

 pedigree of A and of B, he arrived at the same formula as 

 before, with the simple difference that instead of expressing 

 the probable average intensity of one character in several 

 individuals, the prediction is given in terms of the probable 

 number of 4's and j5's that would result on an average 

 when particular A'& and It's of known pedigree breed 

 together. 



The law as Galton gives it is as follows :- 

 "It is that the two parents contribute between them 

 on the average one-half, or (0*5) of the total heritage of 

 the offspring; the four grandparents, one-quarter, or (0'5) 2 ; 

 the eight great-grandparents, one-eighth, or (0'5) 3 , and so 

 on. Then the sum of the ancestral contributions is ex- 

 pressed by the series 



{(0-5) + (0'5) 2 + (0-5) 3 , &c.}, 



which, being equal to 1, accounts for the whole heritage." 



In the former case where A and a are characters which 

 can be denoted by reference to a common scale, the law 

 assumes of course that the inheritance will be, to use 

 Galton's term, blended, namely that the zygote resulting 

 from the union of A with a will on the average be more 

 like a than if A had been united with A ; and conversely 

 that an Aa zygote will on the average be more like A than 

 an act zygote would be. 



But in the case of A' 8 and 's, which are assumed to 

 be mutually exclusive characters, we cannot speak of 

 blending, but rather, to use Galton's term, of alternative 

 inheritance. 



Pearson, finding that the law whether formulated thus, 



