Correlation and Application of Statistics to Problems of Heredity 103 



exceptional parents is only one man in fifty-four. We have now to determine 

 what is the variability of this array of sons about the mean and how many sons 

 in that array will equal or exceed the father in exceptionality. The variability 

 of such sons is '8133cr, and the deviation from the filial mean of the father 

 is (3-100-2-086) 0-= l-014o-, or the deviation is 1'014/'8133 = 1'25 nearly in 

 terms of the sons' variability. From which we ascertain that only 1 1 times 

 in 100 occasions would the son equal or exceed his father's exceptionality, i.e. 

 one in nine sons. Granting an average of three sons to each father we have 

 to examine the cases of three exceptional fathers before we come across a son 

 equal to his father in ability. 



But Galton was considering a much higher degree of exceptional ability ; 

 he suggests seven or eight times the quartile for his excess above mediocrity. 

 Let us take one man in 100,000, and suppose a nearer approach in the mother 

 to Galton's view, say she was one woman in fifty, then the deviations of the 

 parents would be 4'27<x and 2'05cr respectively. The genetic centre would be 

 2'32cr, and the deviation of the filial mean from the father in terms of filial 

 variability would be (4'27 -2'32)/'8133 = 2'40 nearly, or 8 sons out of 1000 

 would reach or exceed their fathers' level or 1 son in 125, or allowing three 

 sons to a father only 1 son would arise in the case of 40 fathers of distinction 

 who would be at least his father's equal. 



In a population of 10,000,000 adult men there would be 100 of this ex- 

 ceptional ability each producing able sons at the rate of '025 apiece. The 

 remaining 9,999,900 produce 97'5 or nearly at the rate of 1 per 1000, or '001 

 apiece. That is to say 39 exceptional men are produced by non-exceptional 

 fathers to one produced by exceptional fathers, but the latter produce 

 exceptional sons at 25 times the rate of the former. This is the paradox 

 which Galton tried in vain to make people understand. It has quite recently 

 been again confusing the minds of Professors Raymond Pearl and Leonard 

 Hill, who cannot grasp how great ability is inherited, because the majority 

 of distinguished men have not distinguished fathers. 



Pedigrees. Few of those who have had the task of making pedigree charts 

 have not been worried by the unmanageable size to which they are apt to grow, 

 but still more by the difficulty of indexing in a connecting form the material 

 on which pedigrees are ultimately to be based. Galton in a paper entitled 

 "Pedigrees," published in Nature, April 23, 1903 (Vol. lxvii, pp. 586-7), 

 suggests a method of what may be termed an "index pedigree" — or as he 

 himself termed it a "pedigree based on fraternal units." This consists in 

 giving a numbered page to each family group. The family group consists of: 

 (i) Father and (ii) Mother with reference to their family group numbers; 

 (iii) their offspring, with any facts the purpose of the pedigree is to illustrate 

 stated about them; thus the main information is to be found on the page, 

 where an individual is one of the offspring, i.e. under his family group number ; 

 (iv) the. wife or husband of each child with their family group numbers; and 

 (v) the family group number which gives the offspring of each marriage in 

 the first family group. The birthdays of the parents in every family group are 



