322 Proceedings of tlie Royal Society of Edinburgh. [Sess. 
the individual molecules, and yet to develop the general laws as to the 
behaviour of gases, leaving but a few fundamental constants to be deter- 
mined by experiment. 
In the second place, it was widely believed that the results of bio- 
metrical investigation ran counter to the general acceptance of the 
Mendelian scheme of inheritance. This belief was largely due to the 
narrowly restricted assumptions as to the Mendelian factors, made by 
Pearson in his paper of 1903 (6). It was there assumed that the factors 
were all equally important, that the allelomorphs of each occurred in equal 
numbers, and that all the dominant genes had a like effect. The effect of 
homogamy was also left out of consideration, and it is to this that must be 
ascribed the much lower correlations given by calculation, compared to 
those actually obtained. When the more general system came to be 
investigated, it was found to show a surprisingly complete agreement with 
the experimental values, and to indicate with an accuracy which could not 
otherwise be attained, how great a proportion of the variance of these 
human measurements is to be ascribed to heritable factors. 
At the time when the paper of 1918 was written, it was necessary, 
therefore, to show that the assumption of multiple, or cumulative, factors 
afforded a working hypothesis for the inheritance of such apparently 
continuous variates as human stature. This view is now far more widely 
accepted : Mendelian research has with increasing frequency encountered 
characters which are evidently affected by many separate factors. In 
some fortunate circumstances, as in Drosophila, it has been possible to 
isolate and identify the more important of these factors by experimental 
breeding on the Mendelian method ; more frequently, however, and especially 
in the case of the economically valuable characters of animals and plants, 
no such analysis has been achieved. In these cases we can confidently 
fall back upon statistical methods, and recognise that if a complete analysis 
is unattainable it is also unnecessary to practical progress. 
This fact is meeting with increasing recognition in the United States, 
and a considerable number of mathematical investigations have been 
published dealing with the statistical effects of various systems of mating 
(Wentworth and Remick, 1916 ; Jennings, 1916, 1917 ; Robbins, 1917, 1918). 
A number of the simpler results of my 1918 paper have since been 
confirmed by independent American investigators (Wright, 1921). The 
present note is designed to discuss the distribution of the frequency ratio 
of the allelomorphs of dimorphic factors, and the conditions under which 
the variance of the population may be maintained. A number of points 
of general interest are shown to flow from purely statistical premises 
