Ma thematical Contributions to the Theory of Evolution, 141 



guishing between three diverse types of heredity, namely (i), Blended 

 Inheritance, (ii) Exclusive Inheritance, and (iii) Particulate Inherit- 

 ance. 



In a memoir printed in vol. 62, pp. 386 — 412 of the ' Proceedings,' . 

 I have dealt at length with the theory of blended inheritance, general- 

 ising for this purpose Mr. Galton's Law of Ancestral Heredity. 



Allowing for a certain degree of variation in the constant y, or 

 " coefficient of heredity," there discussed, I consider that this theory 

 gives a fairly good first approximation to the facts hitherto observed in 

 this field. But blended inheritance certainly does not cover the whole 

 field of heredity. When a character blends, then this law of ancestral 

 heredity tells us the most probable blend for the offspring of given 

 ancestry. It shows us the offspring of exceptional parents regressing 

 towards mediocrity, owing to the fact that without stringent selec- 

 tion the great bulk of their ancestry must be mediocre and not 

 exceptional.''^ Thus the main feature of the law of ancestral heredity 

 is regression. Such regression is not what most biologists would un- 

 derstand by reversion. In fact, when the inheritance from a variety of 

 ancestry is blended, the idea of reversion becomes very obscure ; I venture 

 to think meaningless. 



Let us suppose stature a blended character, then the array of off- 

 spring of a definite short statured ancestry will have a mean regressing 

 (here progressing) towards the population mean and a definite vari- 

 ability. Hence the theory of chance enables us at once to determine 

 the frequency of a very tall man born of such short ancestry. The 

 frequency may be small, but sooner or later the tall man will appear. 

 Now let us suppose one distant ancestor in the otherwise short ancestry 

 to have been tall. Clearly his existence will hardly affect at all the 

 mean of the array of offspring. 



He will not materially influence the chance of a very tall man 

 appearing among the offspring ; yet a superficial observer might easily 

 describe the appearance of the very tall man as a case of reversion to 

 the distant tall ancestor. The absurdity of this attribution is mani-, 

 fest when we remember that persons like him would have had sensibly 

 equal frequency with or without the distant tall ancestor. In fact, 

 it seems to me that in the case of characters which continuously 

 vary, and which blend their inheritance, it is hopeless to look for any 

 evidence whatever of reversion. The term is, then, meaningless. 



To find reversion we must investigate cases in which characters do not 

 blend, i.e., the individual takes exclusively after some one member of the 

 ancestry. In this case the appreciation of reversion becomes possible 

 and its meaning intelligible. Cases of this kind are by no means un- 



* An individual has 1024 If tli great parents, and these can hardly be anything 

 else but a fair sample of the population of their generatioA, if there has not been 

 an excessive amount of in-and-in breeding or much selection. 



VOL. LXVI. N 



