74 
WILLIAM H. BROWN 
given in Table IV, in which are recorded the results of hourly measure- 
ments made during this period. 
The average increase in the distance between the first and last 
dot on the lower leaf surface, for the entire period of closing and 
reopening, may be calculated by adding the average percentage in- 
crease during closure (6.7 percent) to the average percentage during 
opening (1.4 percent), the result being 8.1 percent. In the case of 
the upper leaf surface, the average percentage of shrinkage during 
closure (1.5 percent) is to be subtracted from the average percentage 
of expansion during opening (9.4 percent) leaving 7.9 percent as the 
total percentage of increase in the transverse direction for the upper 
surface. These two values are very nearly alike and their average, 
which is 8.0 percent, may be taken to represent the transverse enlarge- 
ment of the lobe during the entire period of closing and reopening. 
It is worthy of note that the average transverse shrinkage of the 
upper surface during closure (1.5 percent) is nearly equal to the 
average expansion of the lower surface during opening (1.4 percent). 
As has been seen, the former of these apparent changes is probably 
to be explained as due to an error in measurement, resulting from the 
curvature of the leaf lobe when closed, and it seems equally probable 
that the measurement of the lower surface during opening is subject 
to a similar error, ,but of opposite direction resulting from the straight- 
ening of the leaf lobe, which makes the dots appear farther apart in 
rectihnear distance. It is therefore not unlikely that all of the 
apparent expansion of the lower surface during opening is attributable 
to this error. 
It remains to enquire whether the rate of transverse enlargement 
of these leaf lobes is greater during the period of closing and opening 
than at other times. As shown above, this enlargement amounts to 
about 8.0 percent. To answer this question three leaves of different 
ages were selected and one lobe of each was marked on the lower 
surface, with a row of ink dots reaching from the midrib to the margin 
as in the previous cases, the distances between the dots being then 
measured at intervals of from i to 8 days. The results of these 
measurements are given in Table V. 
The last column of Table V presents the total amount of enlarge- 
ment for the entire period of observation, on the basis of the original 
measurements. The first of the experiments here referred to con- 
tinued 18 days, and the total transverse enlargement, from the first 
