98 BIOMETRY 



tion is the degree of slope of the line AB. This is 

 expressed mathematically as tan a, a being the angle 

 which the line in question makes with the horizontal. 



When there is positive correlation this angle falls 

 between o and 45 degrees, and tan a between o and i. 

 In the present instance tan a is 0-5. This value is 

 known as the coefficient of correlation, and affords 

 the basis of a numerical comparison with other similar 

 coefficients obtained for other characters besides 

 stature, and in the case of other pairs of relatives 

 besides fathers and sons. 



It ought now to be clearly understood that a com- 

 plete resemblance between each class of fathers of a 

 particular stature and the average stature of the 

 corresponding array of sons would be indicated by 

 the close approximation of our plotted points to a 

 straight line making an angle of 45 degrees with the 

 base line a line, that is to say, having a slope of 

 i in i, or unity ; whilst the entire absence of correlation 

 Would be represented by a line having no slope that 

 is to say, a horizontal line. The actual result in the 

 example given is represented by a line having a slope 

 of nearly i in 2, or 0-5.* 



* Correlated Variability. A precisely similar method is 

 employed to measure the correlation of two parts or organs of 

 the same individual. For example, the lengths of the right 

 and left arms of men are very closely correlated. In order to 

 attach a numerical value to this correlation the lengths of 

 the right arms of a number of men are treated in the same 

 way as the statures of fathers in the example given, and the 

 lengths of their left arms in the same way as the statures of 

 sons. The proper correlation coefficient can then be found 

 by plotting the result ; or the labour of plotting may be 

 obviated by a process of calculation. 



