LAW OF ANCESTRAL INHERITANCE 329 



generations, can seldom be measured with the accuracy possible 

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

 quota of any character which forms part of a heritage is some- 

 thing different from the expression which that, quota finds in 

 development — for the expression depends in part on the con- 

 ditions of nurture. For these and similar reasons it may seem 

 suspicious that the fractions indicating the average contributions 

 of parents, grandparents, great-grandparents, etc., should be 

 representable in such a simple series as \ -f- \ -f \ -f- . . . . 



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

 large enough, the irregularities of result due to particular pecu- 

 liarities, 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 it 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 x , x 1 ; a 2 , b 2 , x 2 , etc., 

 represent adult individuals of these generations ; a 1 , /3 1 , w 1 ; a 2 , 

 [i 2 , (o 2 , etc., represent the germ-cells produced by those individuals. 

 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 physiological inter- 

 pretation seeks to penetrate below the line A — B, and seeks to 

 show by a theory of germinal contributions how it is that a> 

 gives rise to a 1 , which may be more or less different, how a 2 

 gives rise to rt 3 , which again may be more or less different, 



