436 



THE GRAMMAR OF SCIENCE 



i.e. if there be no homogamy, our measure is zero. If 

 e = ^N, then P falls on O and PM = QO = unity, i.e. if 

 there be complete homogamy, our measure is unity. 

 Thus all degrees of homogamy are included in the range 

 o to I. If the reader asks why PM is taken as our 

 measure, I reply, because if the characters were quanti- 



FiG. 31. 



tatively measurable and followed what the mathematicians 

 term the " normal law " of distribution (see footnote, p. 

 397), PM would be exactly the coefficient of correlation, 

 which we have previously used as a measure of assortative 

 mating.^ We now return to our statistics of eye-colour, 

 and form our scheme. We have : — 



Husbands. 



> 



Thus e/N = .01597 ; the angle POX = 5°45'.04 and PM 

 the sine of this angle = .1002. There is a probable error 

 of ±.0378. 



Now these results are very striking ; for two quite 



1 The method here discussed is perfectly general, and may be applied to 

 all problems in correlation. It is based on a theorem of Mr. W. F. 

 Sheppard's Phil. T7-ans., vol. cxcii., A., p. 141. 



