126 DAVENPORT. [VOL. II. 



To apply the normal law of inheritance it is convenient to 

 assume it and to compare the theoretical heritage with the 

 empirical. If the two agree, the validity of the law is estab- 

 lished in this case ; conversely, if the two do not agree, the law 

 does not hold. This method of testing the law is the same as 

 that employed by Galton ('98) in the case of Bassett hounds. 

 It may be illustrated by the calculation of the theoretical num- 

 ber of albinos in the sixth generation. Let us take the first 

 column. If one of the two parents were an albino, we should 

 expect at least \ x 50^0 of the progeny to. be such. If both 

 parents were A, | x 50/0 of progeny at least should be A. 

 If, in addition, all of the grandparents (Gen. IV) were A, we 

 should expect at least | x 50^0 + | x 25/0 of the VI Gen. to 

 be A. In general, if ;/ v , w iv , 7/ iU , etc., represent the number of 

 times an albino appears as ancestor in the different genera- 

 tions, then the proportion of albinos in the sixth generation 

 should be : 



=-^ x 50/0 + Wiv x 2$fi + -i" x I2.5'/, +--1 x 6.25/0 . 

 24 1 6 



+ x 3. 1 25/0 + i x 3-125/0. 



*J "^ 



The last term is got by observing that the ancestors of half 

 of the first generation were exclusively albinos for many gen- 

 erations, while the ancestors of the other half were exclusively 

 walzers. The value of A is similarly calculated for each column, 

 and the theoretical number of individuals for each column 

 is found. Their sum should be equal to the observed number, 

 or, when reduced to percentages, to the observed percentage 

 of total. The closeness of theory to observation is some- 

 times striking. Thus if we compare column by column the 

 observed and theoretical frequencies of walzers in the fifth 

 generation we get : 



'"|.UMN i 2 3 4 5 6 TOTAL PERCENT 



Observed 2 7 i 3 o o 13 n 



Calculated 2.19 6.00 1.13 4.88 o o 14.19 12.5 



In the following table are given for each generation the 

 observed and (in parenthesis) the corresponding calculated 

 percentages for each color : 



