156 THE FIRST PRINCIPLES OF HEREDITY 



other. There is a certain amount of correlation between 

 the length of the legs and that of the arms, but less than 

 in the previous case ; and there exists less correlation still 

 between the length of the limbs and that of the face. 

 In short, we see that when one organ varies, the other 

 correlated organ varies with it to a certain extent. What 

 we want to find is a measure of how much the second organ 

 varies ; in other words, we want to know the degree of 

 correlation between the organs. But correlation exists, 

 not only between the organs of the same individual, but 

 it extends also to characteristics belonging to separate 

 individuals. For instance, we can compare the height of 

 fathers with that of their sons or that of brothers. In 

 all these cases the method of determining the degree of 

 correlation is the same. 



For this purpose we proceed in the following manner : 

 We measure, let us say, the heights of a certain number of 

 fathers and the heights of the same number of sons, taking 

 one son for each father, and arrange all fathers of equal 

 heights into groups (each group forming what is called a 

 " class"), so that we get a class of fathers of 62 inches, 

 63 inches, and so on up to 76 inches height. We find, then, 

 that the fathers have sons of varying heights. For 

 instance, in an imaginary example given by R. H. Lock we 

 have, out of 4,503 fathers and their respective sons, fourteen 

 fathers with a height of 62 inches. Their sons have 

 different heights, distributed as follows : 



*.***. /ro /c /Mean height of sons, 



i 04 OS DO O7 Do OQ-l &*.,. ;,,/>V>,a<, 



^ 05 5 inc/iieb. 

 Frequency i 2 3 4 2 i i I 



Such a series of sons, giving the frequency of sons of 

 different heights for a given class of fathers, is called an 

 " array." The mean height for the whole array of sons 

 can easily be calculated it is 65-5 inches. We see that, 

 though the fathers of 62 inches height have sons ranging in 

 height from 62 inches to 69 inches, the average or mean 



