EVOLUTION 



435 



a and b we have the a and b groups equally numerous, or 



n. 



= n^ = in„ = in,, = i-N. Thus our table becomes : — 



Husbands. 



C/5 



> 



Now clearly the number e, which the most elementary 

 investigation will disclose {i.e. we have only to discover 

 the number of husbands with eye-colour above the median 

 tint who marry wives with eye-colour above the median 

 tint, and their excess over ^N is e), really determines the 

 correlation. If e be zero there is random mating. Gener- 

 ally 2e is the total number of individuals who, instead of 

 mating with their unlikes, prefer to mate with their likes, 

 and so 2e/N, the relative proportion of such individuals, 

 may be used as a measure of homogamy. If e = <?, there 

 is no assortative mating, if e = ^N it is absolute. It is 

 found, however, better to measure the intensity of assorta- 

 tive mating by taking an expression closely related to 2e/N, 

 and this is obtained in the following manner : Describe a 

 circle of unit radius OP, and suppose its circumference 

 divided into N equal parts. Take PX equal to e of these, 

 then the angle POX at the centre is e/N of four right 

 angles, or 2e/N of two right angles. Thus the ratio of 



the angle POX to two right angles is our first measure of 

 homogamy. It is clear then that the angle POX might 

 also be used as our measure. Or, again equally well any 

 method of measuring this angle. Drop the perpendicular 

 PM on OX, then PM is termed the sme of the angle 

 POX, and this sine will be used as a proper measure of 

 homogamy.^ If e = ^, then PX is zero and PM vanishes, 



1 In the language of trigonometiy if r be the measure : — 



e 



r = sin i^27r. 



