PLANT HYBRIDIZATION BEFORE MENDEL 249 



seldom be medium eye-coloured, like the children of medium eye- 

 coloured parents." (p. 139.) 



"if notwithstanding this two-fold difference between the qualities of 

 stature and eye-colour, the shares of hereditary contribution from the 

 various ancestors are alike in two cases, as I shall expect to show that 

 they are, we may with some confidence expect that the law by which 

 those hereditary contributions are found to be governed may be widely 

 and perhaps universally applicable." (p. 139.) 



The data for eye-color were drawn from the same collection of 

 family records referred to for the data for statures. Taking the 

 fraternities in which the eye-color is known for the two parents 

 and the four grandparents, there are 211 of such groups, with a 

 total of 1,023 children. Letting S stand for the individual subject 

 of the investigation, F for the parent of the individual, G^ for his 

 grandparent, Go for his great-grandparent, etc., the transmission 

 to the individual is F, 1/4; G^, 1/16; Go, 1/64; etc. 



Supposing that the amount of any peculiarity possessed by F 

 is equal to D, then, as Galton has shown, each of the immediate 

 ancestors of F, who stand in the relation of G^ to S, will on the 

 average possess 1/3 D. Similarly, each of the four grandparents 

 of F (who stand in the order of Go to S) will, on the average, 

 possess 1/9 D and so on. Now F transmits to S only 1/4 of his 

 inherited peculiarity; G^ transmits only 1/16; Go only 1/64 and 

 so on. Hence the aggregate total of the inheritance of any peculi- 

 arity in the heritage that may be expected in S is as follows: 



D^ i/4+2(i/3Xi/2^)+4(i/9Xi/2'^)+&c. [ = 



I J 



D(i/22+i/23.3+i/2M-+&c.)=DX0.30 



where the eye-colors of the two parents are given. 



This means that each parent must contribute 0.30 to the heri- 

 tage of the offspring in question, or the two parents taken to- 

 gether, 0.60, leaving a residue of O.40 due to the influence of an- 

 cestry about which nothing is known or implied. 



By a similar calculation Galton shows that the aggregate of 

 the probable heritages from G^ are expressed by DX0-l6 

 (0.1583), where the eye-colors are given of the four grand- 

 parents. Similarly, where the eye-colors are given of the two par- 

 ents and four grandparents, the aggregate contribution of each 

 grandparent is DX3/40=DXO-075, taken as 0.08. 



