69 



VARIATION IN THE GENUS EREBIA. 



By Geoffrey Smith. 



(Continued from p. 9.) 



Sufficient stress has not been laid upon the fact that when 

 the mean (M) of a normal scheme of distribution of certain 

 variations is preserved from generation to generation, the 

 measures of those variations will tend to converge toward that 

 mean. It was on this ground that the acquisition of constancy 

 by some character was stated to occur, when both sexes were 

 variable, and all prepotent tendencies to reversion were theo- 

 retically eliminated. 



One of the properties of M of a normal scheme was stated to 

 be that the most probable value of any unknown measure in a 

 group is M. This results from the following consideration, in 

 the words of Prof. Galton, " that if N be one of the measures, 

 and U be the value of the unit in which the measure is recorded, 

 then the number of measures that fall between iN — |- U) and 

 (N + J U) is greatest when N — M." Or from a somewhat dif- 

 ferent point of view, the idea of mediocre may be extended away 

 from the mean so as to include more measures ; but the idea of 

 extreme cannot be so extended, since by the nature of things it 

 is strictly limited. It must also be remembered that as a matter 

 of fact in a normal scheme the mediocre is always the commonest 

 condition, and that the numbers of individuals possessing the 

 various degrees of the character on each side of the mean (M) 

 graduate away, and become less as the extremes are approached. 

 Hence it is that in schemes of distribution applied to the same 

 group from generation to generation a centripetal tendency would 

 hold good, with the final theoretical result that the mean would 

 be established as a constant measure of the character under con- 

 sideration. Moreover, this tendency to converge toward the 

 mean is increased in the process of sexual reproduction ; for, if 

 we take an extreme male, the chance is small of its pairing with 

 a female which is extreme in the same direction, as against the 

 combined chances of its pairing with a female either of the oppo- 

 site extreme or of the mediocre. In this way, too, the extremes 

 would tend to merge into the mediocre. Of course, all these 

 considerations only hold absolutely, supposing that the scheme 

 is normal, that the selection of mates is made entirely by chance, 

 and also ex hypothesi that the numbers of the sexes are pro- 

 portional. 



We will now go on to consider the numerical proportions of 

 the sexes with reference to the genus Erehia. 



In chap. viii. part ii. of the 'Descent of Man' (2nd edition), 

 Darwin has written on this subject : the point of view taken is 

 that normally equal numbers of the sexes should be produced, 



