ID., 1921] 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 

 lonstants and their probable errors. 



The results for the hypocotyl of trimerous seedlings and their normal 

 jrntrols are set forth in table 12. Without exception the number of bundles 

 fii abnormal plants is higher than that in the control plants. The differences 

 I nge from 1.7 to 3.9 bundles. These differences are many times as large 

 i their probable errors and are unquestionably significant. The relative 

 (inferences are about 16 percent in line 93, 30 percent in lines 75 and 98, 

 4 percent in line 143, and 48 percent in line 139. 



Both the standard deviation and the coefficient of variation of the num- 

 !fer of bundles in the hypocotyl are lower in the abnormal than in the normal 

 j.ants in lines 75, 93, and 98. In lines 139 and 143 the relationship of the 

 sandard deviations of the trimerous and dimerous plants is exactly reversed, 

 Hat of the trimerous plants being somewhat larger than that of the dimerous 

 sries. The difference in line 143 is +.096 .056, which is nearly twice 

 .5 large as its probable error and possibly statistically significant. In line 

 i$9 the difference in standard deviation is +.285 .036. This difference is 

 bout 8 times as large as its probable error and unquestionably significant, 

 &quot;he percentage differences in the standard deviations in lines 75, 93, and 98 

 inge from 40 to 56 percent. In line 143 the percentage difference 

 + 8 percent, while in line 139 it is +70 percent. 



In line 143 the coefficient of variation is higher in dimerous plants (as 

 is in lines 75, 93, and 98), but in line 139 the trimerous show a slightly 

 ut perhaps not significantly higher relative variability. 



The results as a whole show that the difference in the variability of 

 undle number in the two types of seedlings in lines 139 and 143 is not the 

 ame as that in lines 75, 93, and 98. 



In interpreting these results we must remember that each primary 

 ouble bundle at the base of the hypocotyl almost invariably divides to 

 Drm two bundles at higher levels in the hypocotyl. Occasionally one 

 f these branches may further divide into two. It is impossible in sections 

 aade in the central region of the hypocotyl to distinguish with certainty in 

 very case between bundles originating through a division of the original 

 irotoxylem strands and those of intercalary origin. 



The simplest working assumption is that the number of bundles in the 

 entral region of the hypocotyl will be given by twice the number of primary 

 louble bundles demonstrated at the base of the hypocotyl plus the number of 

 ntercalary bundles found at the base of the hypocotyl; or the number of 

 mndles, b, at the central region should be given by 



b = 2p + i 

 vhere p = primary double bundles and i = intercalary bundles. 



