PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 269 
These results have been reached by Mr. Galton in his work on £ Natural 
Inheritance.’ He, however, supposes the population to be stable, and makes the 
mean and variation of successive generations the same, i.e., ay is measured from the 
mean of the general population of parents, and oq taken equal to oq. It seems better 
to keep our formulae perfectly general, and allow for possible natural selection of the 
secular kind as well as for possible reproductive selection. 
(b.) Special case of Stature in Man .—In order to get some idea of the nature of 
direct and cross inheritance, of assortative mating, &c., in man, I have, in conjunction 
wich Professor W. F. It. Weldon, issued a circular and card appealing for help in 
collecting family measurements. We hope eventually to procure 1000-2000 families 
with data of height, span, and arm-length, but it may be many months, or even 
years, before sufficient material has been accumulated to allow of fairly definite state¬ 
ments being made. Meanwhile, Mr. Galton, with his accustomed generosity, has 
placed at my disposal the family data on which his work on ‘Natural Inheritance’ 
was based. These data contain statistics with regard to one organ, height , for about 
200 families. The number is not sufficiently great to make the probable error of 
quite small enough dimensions in several cases, and so allow of definite conclusions. 
The data do not offer, as those we are collecting, material for the treatment of cross 
as well as direct inheritance. Nevertheless, the drift of Mr. Galton’s statistics is in 
many cases obvious enough, and even in other cases, where the weight of the numerical 
results is not great, the conversion of our formuke into numbers will still assist the 
reader to understand their significance, and serve to some extent for comparison when 
wider series of statistics are forthcoming.^ Hence, in the numerical results of this 
paper, I wish more to draw attention to method than emphasise general laws. Mr. 
Galton’s families appear to have been drawn from the upper middle classes, and 
therefore any conclusions formed must not be hastily extended to the whole 
community. 
* Only those who have attempted to get the measurements of, say 20 families, will appreciate the 
difficulty of the task of completing even 200 for one organ. Parents and children must be alive and 
fall within suitable limits of age; and what is more, their interest must be aroused. 
