(142) 
selection tends to increase the probable error of the mean. 
Second, the selection exercised in the operated series is sim- 
ilar to that in the normal series of the same experiment and 
the difference between the averages is therefore less than it 
would have been if the individuals had been chosen entirely 
atrandom. We are therefore justified in concluding that the 
difference between the averages represents a real change 
when it is greater than the sum of the probable errors of the 
mean. Further, when we get similar results for all three 
species iene can no longer be any doubt of the validity of the 
conclusions.* 
Tue Data. 
The following six tables (Tables I to VI) will in a large 
measure explain themselves after the foregoing discussion. 
There are two tables for each species, one giving the posi- 
tion and length of the leaflets in the normal series and the 
other in the operated series. The letters at the tops of the 
columns indicate the leaflets occupying the various positions 
zn the leaf, the removed leaflet being represented by a letter 
enclosed in parentheses. At the bottom of the columns are the 
averages and below them the probable errors (P.E.M.). In 
Table VI the average positions as given are not necessarily 
the averages of the figures as they stand in the columns 
because some of the leaflets fluctuate between the two sides 
of the petiole. It is of course necessary to assume that 
the rotation has in each case been through the shorter arc 
of the circle. The figures in the first column of each table 
have no significance except as catalogue numbers. The 
dates of operation and of measurement are given below the 
tables. 
I wish to express my obligation to Professor C. B. Davenport for sug- 
gesting the determination of the probable errors of the averages. 
