Mathematical Contributions to the Theory of Evolution. 281 



(6) Turning to the results for daughters, we have the following 

 table for the coefficients of correlation and regression : 



Table III. Inheritance of Stature by Daughters. 



Fathers and elder daughters 



Fathers and younger daughters 



Mothers and elder daughters 



Mothers and younger daughters . . . 



0-4829 0-0220 

 0-4376 0-0236 

 0-3953 0'C250 

 0-4542 0-0230 



E. 



-4528 

 -396L 

 -4293 

 -4763 



These results, more numerous than those for sons, are, for reasons 

 which I am unable to explain, much more divergent. We may note 

 the following points : 



(i) There is a sensible difference between the coefficients of corre- 

 lation for either parents with younger and elder daughters. Thus, 

 the difference of the coefficients for fathers with elder and younger 

 daughters is 0*0453, and the probable error of this only 0*032 ; while 

 for mothers the corresponding difference is 0*0589, and the probable 

 error of the difference only O0328. The difference, however, is 

 in the opposite sense. We are thus face to face with an increasing 

 maternal and a decreasing paternal influence on the stature of 

 daughters. In other words, our statistics are entirely opposed to any 

 steady telegonic influence on the sfcature of daughters. If such a 

 thing were conceivable, we should be confronted with the case of the 

 mother influencing the father, the reverse of telegony. 



(ii) The mean correlation of fathers and daughters is very slightly 

 higher than that of mothers and daughters (0*4602 as compared with 

 0*4247) . Thus, to judge by the mean coefficients of correlation, the 

 father is slightly more prepotent than the mother in heredity. The 

 mean coefficients of regression are for fathers 0*4244, and for mothers 

 0'4528, or in the ratio of 1 : T067, but the ratio of the paternal to 

 the maternal stature is T083, or this slight prepotency is still pre- 

 served if we judge the matter by regression coefficients. Again, we 

 notice an immense increase (0*2841 to 0'4247) in the correlation 

 between mothers and daughters when we compare the present results 

 with those of my earlier memoir. As an explanation of this, I have 

 already suggested the possibility of a law exhibiting a relation 

 between fertility and hereditary influence in mothers ( 4 (ii) ). 



(iii) The mean coefficient of correlation in stature between either 

 parent and a daughter may be taken to be 



0*440'02. 



