254 PLANT HYBRIDIZATION BEFORE MENDEL 



It is interesting to note that Galton endeavors by means of his 

 statistical method to arrive at a conclusion concerning what he 

 termed sex-prepotency, and that he recognized the fact that some 

 single character, color in this case, might operate in a special 

 manner in the inheritance. 



Galton's manner of calculating the influence of the tricolor 

 factor is interesting. He found from the data that 79 per cent of 

 the parents of tricolor hounds were tricolor also, and that 56 per 

 cent of the parents of non-tricolor hounds were tricolor. Suppos- 

 ing all the four grandparents, A2, to be tricolor, then only 0.79 

 per cent of A3 will be tricolor also; (0.79)" of A^ and so on. The 

 several degrees of ancestry will respectively contribute an average 

 of tricolor to each ao, amounting to (o.^)^y((o.jg)-\-( i-\-(o.^) 

 X(o.79) + (o.5)-X(o.79)-+etc.)=o.i632. His conclusion there- 

 fore is that the average tricolor contribution from the ancestry 

 of each of the four tricolor grandparents will be equal to one- 

 fourth of this, viz., 0.0408. 



Similarly, the average tricolor contribution from the ancestry 

 of each non-tricolor grandparent is found to be O.0243. When the 

 furthest generation known is that of the great-grandparents, the 

 formula differs from the preceding only by substituting (0.5)'* X 

 (0.79) for (o.5)"X (0.79). Thus the average tricolor contribu- 

 tion from the total of the eight tricolor great-grandparents is 

 found to be O.0816, and the contribution from each of them 

 0.0102. Similarly the contribution from each non-tricolor great- 

 grandparent is found to be 0.0061. 



On the same basis of these calculations, and taking the number 

 of tricolors in the parents in the classes of 2, 1, and o, respec- 

 tively, and the number of tricolors in the grandparents as 4, 3, 

 2, and 1, respectively, Galton was able to calculate coefficients 

 for tricolor occurrence in the offspring. Thus, taking the case of 

 tricolor in both the parents, combined with tricolors in 4, 3, 2, 

 and 1 of the grandparents, respectively, the multiplying co- 

 efficients are found to be as follows: 0.91, 0.83, 0.76, and 0.68. 

 Multiplying the number of cases, 119, 119, 28, and 11 in the 

 four categories, by the four respective coefficients, gives the cal- 

 culated numbers of the tricolor offspring as 108, 99, 21, and 8, 

 respectively. How closely this calculation fitted the actual cases, 

 is proved by the fact that the observed tricolor cases in the off- 



