14 
Influence of Weight of Seed on Plant 
different purpose. The tables are very large and need not be given here. The 
physical constants deduced from them appear in Table I. The distribution of the 
seed weight is shown in the frequency columns of the reduced correlation tables. 
The physical constants* for seed weight are given in Table II. 
III. Analysis of Data. 
1. Number of pods per plant in Navy, White Flageolet and Ne Plus Ultra f. 
From Tables III to VI the value of the rough product moment %{w' p) about 
0 as origin may be calculated straight away by multiplying up the total pods by 
the number of the weight class (in parentheses) and summing. The coefficient of 
correlation, r, is then deduced from the formula 
_ 2 (w p')/N '— wp 
while the equation for the regression straight line is given by 
p=(p- r wp ^-w)- r wp w, 
where p and w represent weight of seeds and pods per plant, the bars denote the 
population means of the respective characters, and the sigmas their standard 
deviations. The variable p is integral and there is no need for grouping; the 
unit of w is '025 gram, with class 1 ranging from 0 to "025, and centered at 
•0125 gram. 
The correlation coefficients and regression equations are given in Table VII. 
The straight line regression equations being available for all series, it is only 
necessary to determine the empirical means for number of pods per plant to test 
by graphical methods the linearity of the regression of pods per plant on weight 
of seed planted. 
It is not feasible — because of the rather great labour demanded, and the com- 
plexity of the diagrams — to do this for all the series. In the diagrams (Figures 
1 — 3) the slope of all the twenty lines given by the equations is shown. In the 
case of certain of these lines, selected quite at random, the values of the empirical 
means are indicated in the usual way. 
. The empirical means are scattered with some irregularity and from inspection 
alone one might suspect that regression is not strictly linear j. In other words, 
* Sheppard's correction was applied in calculating the moments for seed weight, but not in obtaining 
those for number of pods per plant, since the latter varies discretely. 
f Other series of material, and the relationships for seed weight and characters other than number 
of pods are being reduced. 
J The sensitiveness of the number of pods per plant to environmental conditions (and consequently 
the great variability in the means, especially near the ends of the range of seed weight) is so great that 
it has seemed inadvisable to attempt more refined mathematical treatment of the problem of linearity 
of regression. I hope to do this later on larger series of material. 
