GALTON'S THEORY 119 



are constantly being recorded between species and genera 

 of fishes. 



Galton's theory of heredity l supposes that the individual 

 derives half of its total heritage of characters from its im- 

 mediate parents, one-quarter from its grandparents, one- 

 eighth from its great-grandparents, and so on in a lessening 

 degree from its more remote ancestors. In a comparatively 

 few generations, according to this theory, we find that the 

 amount derived by an individual from its remote ancestors 

 almost vanishes. This has been put in a slightly different 

 way, taking into account the individual variations of the 

 offspring. " Suppose, for the sake merely of a very simple 

 numerical example, that a child acquired one-tenth of his 

 nature from individual variation, and inherited the remaining 

 nine-tenths from his parents. It follows that his two parents 

 would have handed down only nine-tenths of nine-tenths, 

 or -j^j- from his grandparents, /^ from his great-grand- 

 parents, and so on ; the numerator of the fraction increasing 

 hi each successive step less rapidly than the denominator, 

 until we arrive at a vanishing value of the fraction. The 

 part inherited by this child in an unchanged form from 

 all his ancestors above the fiftieth degree, would be only 

 one five-thousandth of his whole nature." 2 



This interpretation appears to be directly contrary 

 to the theory of recapitulation "which supposes that the 

 ancestors (i.e. mid-ancestors) are represented not en masse 

 but in orderly succession beginning with the first and 

 ending with the last." 3 



Now according to what we actually observe, it would 



1 Galton, Proc. Roy. Soc., vol. Ixi. p. 402. 



2 Galton, writing on Darwin's theory of Pangenesis, in Hereditary Genius. 



3 Archdall Reid, op. cit., p. 63. 



"The word 'mid-parent' . . . expresses an ideal person of composite sex 

 whose stature is half-way between the stature of the father and the transmuted 

 stature of the mother" (Galton, Natural Inheritance, p. 87). 



' ' Similarly a mid-grandparent is a conception obtained by striking an average 

 between the characters of the four grandparents, and a mid-ancestor of any 

 generation by striking an average between all the ancestors of that generation " 

 (Archdall Reid, op. cit., p. 48). 



