

8 Life and Letters of Francis Galton 



the variability constant of the equivariable arrays in order that the popula- 

 tion may owing to the laws just stated repeat in the filial the parental 

 distribution. 



Now there are two points to be regarded here. Galton first states that 

 he is going to suppose no sexual selection at work, and further he next 

 supposes every female to be reduced to an equivalent adult male standard. 

 It is true that he does this by the aid of percentiles, but what it really 

 amounts to is this : If to 2 be the female mean character, o- 2 the standard 

 deviation and A, the deviation of an individual female from type, to, , cr, and 

 A, corresponding quantities for the male, then Galton replaces the female 

 to 2 + A 2 by a male to, + A, , where A, has the same percentile value p for males 



as A 2 for females. This really amounts to taking A, = — A 2 ; it appears to me 



cr 2 



that this reduction of female to male value is more correct than that which 



he adopted later in his memoir of 1886 and in Natural Inheritance (see our 



p. 15). Having got his midparental value as the mean of the father's and 



mother's characters, the last reduced to male value, Galton correctly asserted 



that if there be no sexual selection and the original population followed a 



normal distribution, the midparental distribution also would be normal with a 



standard deviation -p cr, . He next introduces an ingenious artifice ; instead 



of supposing the offspring to " revert " he supposes the midparent to revert 

 and then to have offspring whose type (i.e. mean value) is that of the 

 original parentage. In other words, if X be the character in a midparentage, 

 then r'X, where r 1 is the reversion coefficient, will be the same midparentage 

 after reversion. This really signifies a uniform " squeeze " in the ratio of 

 r 1 to 1 of the normal curve of midparentages, or the new curve of reverted 



midparentages will be a normal curve of standard deviation — = o-, x r'. We 



have lastly to distribute the offspring of these midparentages about their 

 mean values with a constant variability, which we will represent by 2 ; thus 

 the standard deviation a 1 of the distribution of offspring will be given by 



(T 



3 = 1^2,/2 



a 



o-,V 2 + 2 2 . 



But, if this standard deviation of the final normal curve is to repeat the 

 original population, cr' must equal cr,, or we have 



Here / is the " reversion " of the midparent and is equal to -f2r, if r be the 

 reversion on a single parent*. In other words, if r be the reversion of 

 offspring on parent then the constant standard deviation of the array of 

 offspring fox a given parent must be ct,n/i — r 2 , if the population starts with 

 a normal distribution and when reproduced is to have the same normal 



* If the standard deviation of the "reverted" single parent be rv x , then v2ro-, will be the 

 standard deviation of the reverted midparent, but if this be taken as r'a l clearly r' = *J2 r. 



