Feb., 192 ll HARRIS AND OTHERS SEEDLINGS OF PHASEOLUS 
89 
The differences between the lines can best be seen from the figures. 
For a more critical comparison we must have recourse to statistical 
constants and their probable errors. 
The results for the hypocotyl of trimerous seedlings and their normal 
controls are set forth in table 12. Without exception the number of bundles 
in abnormal plants is higher than that in the control plants. The differences 
range from 1.7 to 3.9 bundles. These differences are many times as large 
as their probable errors and are unquestionably significant. The relative 
differences are about 16 percent in line 93, 30 percent in lines 75 and 98, 
41 percent in line 143, and 48 percent in line 139. 
Both the standard deviation and the coefficient of variation of the num- 
ber of bundles in the hypocotyl are lower in the abnormal than in the normal 
plants in lines 75, 93, and 98. In lines 139 and 143 the relationship of the 
standard deviations of the trimerous and dimerous plants is exactly reversed, 
that of the trimerous plants being somewhat larger than that of the dimerous 
series. The difference in line 143 is +.096 rb .056, which is nearly twice 
as large as its probable error and possibly statistically significant. In line 
139 the difference in standard deviation is +-285 =b .036. This difference is 
about 8 times as large as its probable error and unquestionably significant. 
The percentage differences in the standard deviations in lines 75, 93, and 98 
range from —40 to —56 percent. In line 143 the percentage difference 
is +8 percent, while in line 139 it is +70 percent. 
In line 143 the coefficient of variation is higher in dimerous plants (as 
it is in lines 75, 93, and 98), but in line 139 the trimerous show a slightly 
but perhaps not significantly higher relative variability. 
The results as a whole show that the difference in the variability of 
bundle number in the two types of seedlings in lines 139 and 143 is not the 
same as that in lines 75, 93, and 98. 
In interpreting these results we must remember that each primary 
double bundle at the base of the hypocotyl almost invariably divides to 
form two bundles at higher levels in the hypocotyl. Occasionally one 
of these branches may further divide into two. It is impossible in sections 
made in the central region of the hypocotyl to distinguish with certainty in 
every case between bundles originating through a division of the original 
protoxylem strands and those of intercalary origin. 
The simplest working assumption is that the number of bundles in the 
central region of the hypocotyl will be given by twice the number of primary 
double bundles demonstrated at the base of the hypocotyl plus the number of 
intercalary bundles found at the base of the hypocotyl; or the number of 
bundles, h, at the central region should be given by 
b = 2p -\- i 
where p = primary double bundles and i — intercalary bundles. 
