1921] ARBER—LEAVES OF HELOBIEAE 33 
ary veins, more or less parallel to themselves, and thus, without any 
essentially fresh departure, achieve a venation determining the 
auricled form of the leaf. It is probable, however, that such leaves 
do not form a transition to the arrowhead type, but that the 
latter is arrived at by a separate route. 
It will be seen on examining fig. 5 (Limnophyton obtusifolium) 
and fig. g (Sagittaria Greggii) that the principal veins are the 
midrib (a) and the two veins (0, 6’) passing into the cusps. In some 
species these cusps are very conspicuous; in S. longiloba they 
may be two or three times the length of the median segment. 
It is not probable that the arrowhead type of venation is derivable 
from that shown in fig. 8, which is, moreover, a rarity in the family. 
It is suggested that the veins } and b’ are, as it were, a repetition 
of the midrib, and have originated phylogenetically by its chorisis. 
Their morphological relation to the midrib would thus be equivalent 
to the relation borne by the tendrils of Smilax to the petiole, 
according to a hypothesis put forward in a previous paper in this 
journal (4). Of course it is impossible to offer any definite proof 
of such a theory, but it probably makes the nature of the arrowhead 
leaf a shade less obscure. It seems to account for the lack of 
any genuinely transitional forms between the types of venation 
characterizing the oval and arrowhead varieties of pseudo-lamina. 
It is true that the intermediate forms have very short cusps, but 
their venation is distinctly of the arrowhead type. 
Butomaceae 
The Butomaceae are so closely related to the Alismaceae that 
they are sometimes regarded merely as a tribe of the latter family. 
Among the Butomaceae we find examples of the three types of leaf 
enumerated under the Alismaceae. Butomus umbellatus L. has a 
leaf with a sheathing base, and an upper region which is triangular 
in section and phyllodic in anatomy (17). On the other hand, 
Hydrocleis Commersonii Rich. and H. parviflora Seub. have both 
ribbon leaves and leaves with a petiole and pseudolamina (10, 18, 
20). The published figures of these ribbon leaves suggest that they 
are equivalent to the ribbon leaves of Sagittaria, but I have not 
had the opportunity of examining their anatomy. 
