35* BOTANICAL GAZETTE [MAY 
side was found to be less than that of the average length of the 
normal cells in many examples beside those quoted led Sachs to 
the conclusion that the discrepancy was due to faults in obser- 
vation. The fault is in the system of obtaining the measure- 
ments, however. If only the same factors were operative in the 
production of curvature that are to be found in normally elon- 
gated roots, this method of obtaining the average stature of the 
normal cells would be allowable. This is not the case, however, 
as the curvature is produced by an excessive elongation of the 
convex side, which might be due to growth or ductile stretch- 
ing, but in either case would be followed by after effects that 
would destroy the normal relations. Even if this system of 
measurements were applied to forming or newly formed curva- 
tures, the rapidly increasing and unequal rate of growth of the 
motor zone would destroy the proportions of the average. A 
glance at the tables given above shows that the increase in the 
length of the cells in the basal direction is by no means uniform. 
In order to obtain the stature of normal cells in my own 
observations the measurements were made upon a region corre- 
sponding in distance from the apex and stage of development 
with the curvatures with which comparison was to be made. 
This region, from which the data in table XI were obtained, cor- 
responds to the region of curvature of the root curved through 
105° (see table V). Identical methods of preparation were 
used and the cells measured from a radial longitudinal plane 
eight cells in length and eight cells in width radially. 
In a comparison of the data obtained from the normal root 
with the figures of a root curved through 105° after twenty 
hours of geotropic excitation (table V), the following facts are 
to be noted. The average lengths of the cells of the normal 
root are 11.35 and 14.82. The average length of the cells of 
the concave side in the root bent at an angle of 105° after 
twenty hours’ excitation is 24.7, and of the convex side is 48. 
If it is supposed that the error has been made in measuring the 
region in the normal root nearer the tip than in the curved root, 
the lengths of the cells in the curvature of a root three hours” 
