LAW OF ANCESTRAL INHERITANCE 329 



generations, can seldom be measured with the accuracy pos- 

 sible in the case of a quality like stature ; and (3) that the 

 actual quota of any character which forms part of a heritage 

 is something different from the expression which that 

 quota finds in development for the expression depends in 

 part on the conditions of nurture. For these and similar 

 reasons it may seem suspicious that the fractions indicating the 

 average contributions of parents, grandparents, great-grand- 

 parents, etc., should be represents ble in such a simpte series 

 as i + i + i -f . . . . 



The general answer is, of course, that when the data are 

 large enough, the irregularities of result due to particular 

 peculiarities, such as a highly prepotent great-grandfather, are 

 smoothed out. 



While Galton sometimes spoke of his law in its physiological 

 aspect, there can be no doubt that he regarded it in the main as 

 a statistical description, dealing with average inheritances, and 

 applying to masses rather than to the component individuals 

 considered separately. Thus he distinctly says (1897, p. 402) : 

 " The neglect of individual prepotencies is justified in a law that 

 avowedly relates to average results." 



Darbishire has tried by means of a diagram to clear up the 

 prevalent confusion which opposes statistical and physiological 

 formulae. In the figure there is a diagrammatic representa- 

 tion of four successive generations ; a 1 , b l , x l ; a*, b z , X 2 , etc. 

 represent adult individuals of these generations ; a 1 , fp, to 1 ' ; a*, 

 /3 2 , o) 2 , etc., represent the germ-cells produced by those indi- 

 viduals. Now the statistical formulation contents itself with 

 keeping above the line A B, and deals with the successive 

 generations as generations, stating the relation of hereditary 

 resemblance which subsists between them. But the physio- 

 logical interpretation seeks to penetrate below the line A B, 

 and seeks to show by a theory of germinal contributions 

 how it is that a 1 gives rise to a 2 , which may be more or less 



