208 SEMI-CENTENNIAL OF TORREY BOTANICAL CLUB 
In the winter of 1915 an experiment bearing on this point was 
planned and the data recorded are from thirty-eight plants of the 
Longfellow variety of string-bean grown in the summer of 1916. 
The plants had 736 pods and 3,462 beans. The individuality of 
the bean pod and of the bean plant chosen for expression is the 
shape of the beans. An index, the thickness of the bean divided 
by the width measured from the hilum to the opposite side, has 
been used not because any particular importance is to be attached 
to this measure, but because it was convenient. An index of this 
sort is preferable to weight or to a single measurement as thickness 
or length because purely physiological differences due to nutrition 
are more probably eliminated. It was observed that the beans 
varied considerably in form, some being flat and others much 
thicker. This is expressed in the index, which varies from about 
70 to about IIo. 
If all the pods on a plant were alike and the variations among 
the individual beans of a plant purely chance variations, the 
average index of each pod, assuming each pod to contain a large 
number of beans, would be the same as the average index for the 
plant as a whole. There would then be no variation among the 
pods or, in other words, they would all be alike. If, however, 
there are differences among the averages for the pods, the pods 
show individuality. 
e have first to consider in how far the plants are alike or dif- 
ferent. As we might expect, the average index is not the same for 
all plants. It ranges from 86 to 98, the average being 94 with a 
standard deviation of + 3.4. Іп other words, the plants are not all 
alike, but have individuality, some with thicker and others with 
flatter beans. 
We may treat the separate pods on a plant in the same way. 
The fact that the pods contain a small number of beans and not all 
pods the same number must be taken into account in the calcula- 
tion, in order that the results obtained may be comparable. If 
the variability of the individual beans on a plant is expressed by 
с, Ше correlation between the beans in a pod Бу г, and the number 
of beans in a pod by л; then s, the observed variability of the beans 
іп a pod, is expressed Бу the following formula: 
