38 HEREDITY [ch. 



deviations of the fathers is then the coefficient of 

 correlation between father and son for this character^ 

 This is more clearly seen in diagram form. 



If a square is made with its sides divided into 

 equal lengths corresponding to equal increments in 

 stature from 60 to 76 inches, the top may represent 

 the scale of statures of fathers and the side the scale 

 of mean statures of sons for each class of fathers. If, 

 then, there were complete correlation between fathers 

 and sons, the mean stature of sons of fathers 62 inches 

 high would be 62, of fathers of 63 inches, 63, of 64, 

 64 and so on. If on the other hand there were no 

 correlation, the means of the sons of every class of 

 father would be the mean of the population (68). 



In the first case the line joining the points repre- 

 senting the means of the sons would be a diagonal 

 running from corner to corner (AB), in the second 

 case a horizontal line running across the middle (CD). 

 But if the correlation is between these extremes the 

 line would lie between the diagonal and the horizontal 

 (EF), and the greater the correlation the steeper 

 would be the slope of EF. The steepness of this line 

 is thus a measure of correlation, and since all these 

 lines pass through in the middle of the square, the 



1 It is assumed throughout that the variahiHty of the sons is similar 

 to that of the fathers. If their variability were different this would 

 have to be allowed for. The variation is also assumed to be normal, 

 so that the mode in each case coincides with the mean. 



