Correlation and Application of Statistics to Problems of Heredity 107 



Number of Kinsfolk. This question of the "Average Number of Kinsfolk 

 in each Degree" was raised by a paper with this title published in Nature, 

 September 29, 1904 (Vol. lxx, p. 529). Galton tells us that the simplest 

 conditions for a general theory are those which suppose (i) the population to 

 be stable, i.e. its numbers statistically constant in successive generations; 

 (ii) that the generations do not overlap; (iii) that they are completed by 

 passing wholly into history ; and lastly (iv) that any individual is taken into 

 account at whatever age he or she may have died. Galton further supposes 

 that the numbers of the two sexes may be taken as roughly equal. Thus he 

 considers it only needful to work out the results for a single sex. Suppose 

 the average number of females born to a woman who is a mother to be d, 

 then he says that on the average only one of her female children will be 

 fertile of female children, or the chance that any one of these females will be 

 fertile of females is l/d. Any mother has d female and d male children and 

 therefore any one of these children will have d — \ brothers and d — ^ sisters 

 on the average. Galton uses a dash to denote a female relative who is fertile 

 of females. Thus the number of sisters (si) is d — %, but the number of fertile 

 sisters (si') is only (d — \)/d, and each of these produces d daughters (da). 

 Accordingly the number of sisters' daughters (sororal nieces) of a woman 

 will be (a — \)fdxd = d — \. In this way the following table is reached: 



Further explanatory letters were published by Galton, October 27, 1904, 

 November 10, 1904, and January 12, 1905. These note one or two misprints 

 and also reply to an objection raised by Professor G. H. Bryan. The reader 

 will find an interesting paradox to solve, if he asks why his wife's sisters' 

 daughters are on the average slightly less numerous than those of his own 

 wife! 



Kinsfolk of Fellows of the Royal Society. The main purpose of several 

 of the notes by Galton discussed above becomes clear when we read the 



14—2 



