380 DUNCAN S. JOHNSON 
development is still greater as in the case caught by the somewhat 
oblique section shown in figure 119. All of the mature or nearly- 
mature twin sacs seen were of the collateral type shown in figure 120, 
in which each of the embryo sacs, except for the presence of but 15 
nuclei in the left one, has exactly the structure of the normal single sac 
at this stage. The lack of one nucleus out of the 16 in the last sac 
referred to exemplifies another type of abnormality not uncommon in 
the otherwise normal single sacs. It is possible of course that the fail- 
ure to find 16 nuclei in certain evidently mature sacs may be due to the 
difficulty of counting the crowded endosperm nuclei. This difficulty 
is increased by the fact that the nucleoli, which must be largely de- 
pended on in counting, may occasionally be displaced from the surface ^ 
of the section and lost. Embryo sacs are not uncommonly found in 
which but 13, 14 or 15 nuclei can be counted even when the egg and 
synergid are differentiated. Figure 121 shows such a sac in which but 
14 nuclei could be discovered, including those of the egg and synergid. 
The ultimate fate of the paired embryo sacs mentioned has not yet 
been determined. From the occurrence of a number of cases like that 
shown in figure 120 it seems probable that two eggs may be fertilized in 
one ovule and thus two embryos be formed. No case of this sort has 
been seen in P. hispidula, but seeds of P. pellucida have been seen from 
which two embryos protruded on germination. It may be discovered 
that these are developed from separate twin embryo sacs in the same 
ovule, such as have been described for P. hispidula but have not yet 
been reported for P. pellucida. 
The occurrence of these abnormal embryo sacs gives us no indi- 
cation of the phylogenetic origin of the peculiar composite sac normally 
found in this and other species of Peperomia. Neither of the two 
methods of doubling here found can be conceived of as in any way 
explaining the origin of the simple i6-nucleate sac from the 8-nucleate 
one characteristic of most angiosperms. This is evident from the 
fact that each of the twin mother cells, by itself, gives rise to a com- 
plete i6-nucleate embryo, and from the fact that in both the normal 
case and in the case of the twins it is one complete megaspore tetrad 
that gives rise to each complete individual sac. 
The widespread distribution among the angiosperms of the genera 
in which these multiple archesporial cells and embryo sacs occur is 
practically conclusive evidence that they can have no value as indi- 
cators of phylogeny aside from supporting the well-established view 
