1900 | SPOROPHYLLS AND SPORANGIA OF ISOETES 231 
of unusual thickness may be again ruptured, but no considerable 
increase in their number ever occurs after their first formation. 
It is easy with the low power of the microscope to count the 
diaphragms in leaves floating upon a little water on a slide. 
The usual number is from fifty to seventy, and is quite as many 
in young leaves three fourths of an inch long as in leaves fully 
formed. It is instructive, too, as proving the absence of a defi- 
nite meristematic zone, to count the average number of super- 
ficial cells which intervene between the diaphragms. In very 
young leaves this is from three to six or eight throughout the 
whole length, but in older leaves it is much greater, varying 
from twelve to twenty in the tip region to forty to sixty in the 
middle and basal regions, which remain longest in the meristem- 
atic condition. 
The diaphragms, I think, are quite functionless, and their 
existence merely incidental to the manner of origin of the air 
chambers. They are too delicate to serve for mechanical sup- 
port, which is sufficiently secured by the four longitudinal bands 
already described. The position of the air chambers and longi- 
tudinal bands between them in relation to the axis of the plant 
is always the same as that indicated in figs. 10,71, 44. Near 
the ligule the air spaces are less regular, and instead of four 
of them symmetrically placed we find many irregular ones. 
Behind the sporangium the dorsal longitudinal band of living 
cells, and sometimes the two lateral ones, are well marked, but 
there are no large distinct air spaces. The vascular bundle of 
the leaf is as characteristic as that of the stem. My observations, 
referring chiefly to the changes of form of the bundle, were made 
with the view of discovering whether there is any definite relation 
between it and the sporangium or the ligule, and whether it 
Presents any evidence that the leaf of.Isoetes has been reduced 
from amore complex type. The leaf trace can first be recognized 
in the base of the young leaf and in thestem region below it towards 
the central bundle. The xylem elements are first differentiated, 
and consist of five or six tracheids grouped into a cylinder and 
Surrounded by a sheath of parenchymatous cells with dense 
