vii.] DISCUSSION OF THE DATA OF STATURE. 119 



hopeful case among my 18 schemes, but found the gain, 

 if any, to be so small, that I did not care to go on 

 with the experiment. It did not seem to deserve the 

 additional trouble, and I was indisposed to do anything 

 that was not really necessary, which might further 

 confuse the reader. But had I possessed better data, 

 I should have tried the Geometric Mean throughout. 

 In doing so, every measure would be replaced by its 

 logarithm, and these logarithms would be treated just 

 as if they had been the observed values. The conclusions 

 to which they might lead would then be re-transmuted 

 to the numbers of which they were the logarithmic 

 equivalents. 



In short, we have dealt mathematically with an ideal 

 population which has similar characteristics to those of 

 a real population, and have seen how closely the 

 behaviour of the ideal population corresponds in every 

 stage to that of the real one. Therefore we have 

 arrived at a closely approximate solution of the problem 

 of statistical constancy, though numerous refinements 

 have been neglected. 



Natural Selection. — This hardly falls within the 

 scope of our inquiry into Natural Inheritance, but it 

 will be appropriate to consider briefly the way in 

 which the action of Natural Selection may harmonise 

 with that of pure hereclhty, and work together with it 

 in such a manner as not to compromise the normal 

 distribution of faculty. To do this, we must deal 

 with the case that best represents the various possible 



