218 BOTANICAL GAZETTE [MARCH 
VN . I 
£/Eg= ers Bi’ & Se ey OT ay eae 
0.67449 V 1+-(1—77)?—(1—-7°’) 
This gives 
For 1906, £=.o1000, §&/Es=3.38 
1907, €= .03762, ¢/E:=5.19 
In both cases €/E;> 2.5, and regression cannot be safely regarded 
as linear.%4 Physiologically this indicates that after a certain 
number of seeds have been formed, the rate of increase in the stimu- 
lus to development exerted on the fruit falls off. Something of 
the same nature has been noticed in Cercis,%5 where it appeared that 
while for the central region of the seed distribution a straight line 
expressed the change in the pod length very well, pods with a 
_ single seed and those with the maximum number of seeds seemed a 
little smaller in comparison with their number of seeds than the 
pods of the population as a whole. When better data are avail- 
able, it will be interesting to investigate this problem in greater 
detail, but considering the sources of error which have been 
emphasized above, I see no advantage in further grinding in the 
mathematical mill. The time would be more profitably spent in 
collecting other series of data for comparison. The sensibly higher 
coefficients for total seeds per fruit, as compared with those for 
seeds per locule, evidence for a direct influence of the seed upon 
the fruit. 
4 From the graphs one would almost have expected a higher value for £/E¢, but 
one of the difficulties in testing linearity of regression in these series is the fact that 
the frequencies are so concentrated into a few classes. Pods with 1, 2, 3, and 4 seeds 
form 91.3 per cent of the total in 1906, and g1.1 per cent in 1907. With so few pods 
falling in the extreme classes, it is difficult to get arrays sufficiently large to give trust- 
worthy averages for testing the goodness or fit of means to any equation. In 1906 
there are only 15 classes for 2050 pods, while in 1907 there are 17 classes for 1218 pods. 
Consequently the mean number of pods per array is less in 1907, and the probable 
error attaching to these means is greater, thus increasing the value of 7 by an amount 
depending on the magnitude of the probable errors. For 1906 the average number 
for arrays with entries is 157.7 pods, while for 1907 it is only 81.2. The probable 
errors of the means of arrays, therefore, is much higher in 1907 than in 1906, but there 
is no method of freeing » from their influence; perhaps these facts explain why §/£¢ is 
greater in 1907 than for 1906. 
ts Compare the figure in Bor. Gaz. 50:122. 1910. 
CARNEGIE STATION FOR EXPERIMENTAL EVOLUTION 
Cc SprING Harpor, N 
