STATISTICAL AND PHYSIOLOGICAL LAWS z^^Z 



parents, smaller in the case of the grandparents, and so forth." 

 This, Darbishire somewhat sarcastically says, " is a very good 

 type of biological Law : it has the advantage of simplicity ; it 

 is also, except in a few cases, untrue." He is undoubtedly 

 right in distinguishing this physiological theory (in which there 

 is widespread belief) from Galton's statistical conclusion, " which 

 does not pretend to account for anything," but we are not 

 prepared to follow him in dismissing it as invalid. It appears 

 to us that there are not a few cases where Mendelian interpreta- 

 tions do not work, and where a theory of ancestral contributions, 

 more numerous and more conspicuous in proportion to the 

 nearness of the ancestors, is at present justiliable. Galton's 

 statistical conclusion may " not pretend to account for any- 

 thing," but there must be something in individual heredity 

 to account for it. And when Darbishire says, " Galton's Law 

 definitely states that on the average a half of the fihal generation 

 are like the parental, a quarter like the grandparental, and an 

 eighth like the great-grandparental, and so on," we venture 

 to think he is taking considerable liberties with Galton's own 

 statement of his Law. 



§ 8. Statistical and Physiological Laws 

 Darbishire has tried by means of a diagram to clear up 

 the prevalent confusion which opposes statistical and physio- 

 logical formulae. In the figure there is a diagrammatic representa- 

 tion of four successive generations ; a^, b\ x^ ; a'^, 5^, x'^, etc., 

 represent adult individuals of these generations ; a>, jS^, wi ; a2, 

 /S2, w2 ; 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^ 



