Correlation and Application of Statistics to Problems of Heredity 9 



distribution. This is the earliest appearance of the symbol r as a coefficient 

 of " reversion" ; the reasoning by which the result is obtained is only true, if 

 parental and offspring generations have the same variability; in that case r 

 is what we now term the coefficient of correlation, and Galton here deduces 

 the relationship between the constant array variability and this coefficient. 



In the course of his work he introduces the ideas of natural selection and 

 of differential fertility. This section of the discussion is somewhat difficult to 

 follow. Galton further supposes selection to take place symmetrically round 

 the population mean or type. Finally to obtain the above result Galton 

 supposes the selection and the fertility to be non -differential, or gives them 

 mere percentage values for all parents alike*. 



Fig. 2. Oalton's Quincunx illustrating the nature of Regression. 



The third point in this paper of Galton's is the ingenious " Quincunx " by 

 which he illustrates the phenomenon of reversion and the continual main- 

 tenance by aid of inheritance of a stable population. Galton at first indicates 

 how closely certain measured characters are given by a normal distribution 

 and how such a normal distribution may be produced by a stream of pellets 



* A paper in which this matter is more fully dealt with by the present writer will be found 

 in Biometrika, Vol. vn, pp. 258-275, "On the Effect of a Differential Fertility on Degeneracy: 

 A New Year's Greeting to Francis Galton, 1910." 



p G III 2 



