height of their sons is 70.8 inches, or a regression towards 

 the mean of the general population. On the other hand, 

 fathers with a mean height of 66 inches give a group of sons 

 of a mean height 68.3 inches, or a progression towards the 

 mean of the general population of sons. The general re- 

 sult is a sensible stability of type and variation from genera- 

 tion to generation" (Pearson, Grammar of Science). 



The following chart shows graphically the results ob- 

 tained by Pearson in his investigation where more than a 

 thousand pairs of fathers and sons were measured. \^The 

 line AB joining the points in the chart is nearly straight but 

 not horizontal, — in fact about half way to 45°. 



PIG. 7. 

 Chart to illustrate Galton's and Pearson's 



(after Watson). 



Law of Kilial Regression 



The interpretation is:— if the line were horizontal / e 

 It the angle with the horizon be 0°, all the sons would be of 

 same average height, and the inheritance would be zero 

 (tan =0) : if the line were inclined 45° all the sons would be 

 of the same average height as the fathers and inheritance 

 would be unity (tan 45° =1). As the line is about 2.3° the 

 average height of the son is about half way between the 

 height of the father and the mean height of the race This 

 traction is termed the co-efficient of heredity, and is expressed 



4S 



