Correlation and Application of Statistics to Problems of Heredity 43 



Now I think this does not involve all the tricolour ancestry of the four 

 tricolour grandparents, for 0"21 of the great grandparents are non-tricolour, 

 and there will be (0-21) x (0*56) x (0-5)'x(079)x(0-5) 2 of thegreatgreat grand- 

 parents tricolour. At each stage a non-tricolour branch will split off, showing 

 in the next ascending generation some tricolour. It appears to me that 

 Galton has overlooked the sum of all these ancestral tricolour contributions 

 in estimating the tricolour in a . They may be considerably less than those 

 retained, but I do not think they can be disregarded without justification. 



"By a similar process," Galton writes, "the average tricolour contribution from the ancestry 

 of each non-tricolour grandparent is found to be - 0243." (p. 406.) 



It would seem that this is obtained from : 



(0-5) 3 x (0-56) {1 + (0-5) x (0-56) + (0-5) 2 x (0"56) 2 + etc.} = "0972, 

 for one-fourth of this is 0'0243. 



But the above expression is not, I think, correct, for after the great grand- 

 parental 0'56 of tricolour we must surely use not 0'56 but 079 to pass from 

 tricolour to tricoloured ancestry. Thus the result should be 



(0-5) :, x(0-56){l + (0-5) x (079) + (0-5) 2 x(079) 2 + etc.}= -1157, 



of which the fourth part is "0289. 



\Iere as before the non-tricoloured ancestors of earlier generations who 

 would themselves have tricoloured parents, etc., are neglected!^ 



Taking Galton's illustration (p. 406) of both parents tricolour, three 

 grandparents tricolour, and one lemon and white, Galton's factor of "8342 is 

 only changed to - 8388 by the above correction, but this gives 100 tricolour 

 hounds out of a total of 119 offspring in this category, while the observed 

 tricolours were 101, a remarkably close accordance. 



I illustrate the sort of accordance obtained in the following examples : 



The numbers in brackets denote total offspring. 



6—2 





