412 



Mr. F. Galton. 



[May 27, 



the two parents, and 15 among the four grandparents; making 90 pos- 

 sible classes altogether. The number of observations are of course by 

 no means evenly distributed among the classes. I have no returns at 

 all under more than half of them, while the entries of two light-eyed 

 parents and four light- eyed grandparents are proportionately very 

 numerous. (I shall not here discuss the question of marriage selec- 

 tion in respect to eye-colour, which is a less simple statistical question 

 than it may appear to be at first sight.) 



Calculation. — I have now to show how the expectation of eye- 

 colour among the children of a given family is to be calculated on the 

 basis of the law laid down for stature, so that those calculations of 

 the probable distribution of eye-colours may be made, which fill the 

 three last columns of Tables III and IY, which are headed I, II, and 

 III, and which are placed in juxtaposition with the observed facts as 

 entered in the column headed "Observed." These three columns 

 contain calculations based on data limited in three different ways, in 

 order the more thoroughly to test the applicability of the law that it 

 is desired to verify. Column I contains calculations based on a 

 knowledge of the parents only ; II contains those based on a know- 

 ledge of the grandparents only ; III contains those based on a know- 

 ledge both of the parents and of the grandparents, and of them only. 



I. Eye- colours given of the two parents — 



Let the letter M be used as a symbol to signify the person for 

 whom the expected heritage is to be calculated. Let P stand for 

 the words "a parent of M ;" G x f or "a grandparent of M;" G 2 ^ or 

 " a great-grandparent of M," and so on. 



Now suppose that the amount of the peculiarity of stature pos- 

 sessed by P is equal to r, and that nothing whatever is known with 

 certainty of any of the ancestors of M except P. "We have seen* that 

 though nothing may be actually known, yet that something definite 

 is implied about the ancestors of P, namely, that each of his two 

 parents (who stand in the order of relationship of G 1 to M) will on 

 the average possess -|r. Similarly that each of the four grandparents 

 of P(who stand in the order of G 2 to M) will on the average possess 

 |-r, and so on. Again we have seen that P, on the average, transmits 

 to M only | of his peculiarity ; that G x transmits only ; G 2 only , 

 and so on. Hence the aggregate of the heritages that may be ex- 

 pected to converge through P upon M, is contained in the following 

 series : — 



=rl—+ 1 + 1 + &c. \ =rxO30. 

 * Ante, p. 42 (No. 242). 



