GENETICS: PEARL AND SURFACE 
225 
ation of these observed distributions from the most probable distribu- 
rion of such measurements on the theory of chance. The tables of 
these constants are too extended to be given here, but the figures show 
that in every case (except one) the deviation from the theoretical mean 
is very much greater than would occur on the basis of chance. The 
deviation of the very small and the very large plants (quintiles I and V) 
are much greater than any of the others. Thus there is a much more 
marked tendency for the extreme plants to remain in the extreme classes 
than for the medium sized plants to remain in a particular medium 
sized class. There is a similar, though less marked, tendency for the 
plants ending in a given quintile to have remained in or near that quin- 
tile throughout their growth. 
The second step in the analysis was to study the mean quintile position 
of each group of plants in the successive growth stages. Here the main 
conclusion is entirely clear. Extreme variants at the beginning of the 
season tend strongly, on the whole, to remain extreme variants during 
the whole season. At the same time such extreme variants regress 
slightly towards the general population mean as growth continues. 
This second tendency is, however, by no means so strong as the first. 
The third step in the analysis of the variation curves was a study of 
the average relative size (mean quintile position) of the individual 
plants and of the variability of individual plants with respect to rela- 
tive size. Definite quantitative evidence is presented showing that: 
1. The observed differences in the manner of growth of individual 
plants and of groups of plants cannot be explained as the effect of ex- 
ternal, environmental factors. 
2. These differences are rather to be looked upon as the effect of in- 
ternal factors. 
3. The distribution of the average relative size (mean quintile posi- 
tion) of individual plants is such as to suggest the random distribution 
of these factors among the plants. The same thing is brought out by 
the distribution of the relative measurements of plants starting or end- 
ing with a given relative size (quintile). 
4. The simplest method of explaining these facts is to regard the 
differences in the manner of growth as due to independent Mendelian 
factors which are distributed at random in any population of open fer- 
tilized maize plants. These factors would occur in the proportions found 
in a stable Mendelian population mating at random. 
5. By assuming the presence of two independent growth factors and 
weighting each with the proper value, it is possible to obtain a theoreti- 
cal distribution agreeing very closely with the observed distribution. 
