126 Sfeil. — Apogamy in Nephr odium hirtipes , Hk. 
Miss Allen’s figures of the sporogenous cells of Aspidium falcatum are 
so similar to many of those which I have obtained in Nephr odium hirtipes as 
to make it seem probable that a further study of the former species may 
show that in it also the divisions first initiated at the stage of the eight sporo- 
genous cells are, except in very rare cases, never completed. Her Fig. 44, 
PL III, representing an early stage in fusion, may be interpreted as showing 
a completed nuclear division and a nearly completed cell division, and if 
this be a correct interpretation the division shown in this case has progressed 
farther than any I have observed in N ephrodium. However, in some instances, 
as in Fig. 33, PL VI, my preparations show a near approach to a complete 
division of the cell and its nucleus. 
In three cases Miss Allen found more than eight spore mother-cells in 
a sporangium of Aspidium falcatum. The larger number of spores was 
accounted for by the failure of some of the sporogenous cells to fuse in pairs. 
In two instances I found that more than eight sporogenous cells must have 
been produced in a sporangium of N ephrodium hirtipes . If in these 
instances any of the sporogenous cells complete their divisions, more than 
eight spore mother-cells will be formed. No evidence has been presented 
by either Miss Allen or myself to indicate that the spore mother-cells which 
do not possess the diploid number of chromosomes have the power to 
divide. Six of the eleven tetrads found in a single sporangium of Nephro- 
dium (Fig. 53, PL VII) showed that abnormalities had occurred in the 
division of the mother-cells, which, as has been previously suggested, may 
have been produced from sporogenous cells that completed their divisions 
and hence did not have the diploid number of chromosomes. Since more 
than four spores are sometimes produced from a single spore mother-cell of 
N ephrodium hirtipes , no conclusion can be drawn from the number of spores 
in a sporangium in regard to the possibility of the division of the super- 
numerary spore mother-cells. It is evident, however, that spores may be 
formed with nuclei which have not received the haploid number of chromo- 
somes (Figs. 50, 51, and 52, PL VII). 
The formation in many instances of a spindle, and not seldom of 
a cell plate extending part way across the cell, and the distribution of the 
chromosomes from the equatorial plate exclude the possibility that the 
irregular nuclear figures which I have found in the eight sporogenous cells of 
Nephrodium hirtipes can in any case represent amitotic division. Amitosis, 
also, cannot occur at any later stage, since in such a case more than thirty- 
two spores would then be produced. 
In apogamous ferns three cases have been reported in which ‘ substitu- 
tion fusions ’ are thought to occur — that is, fusions of cells (or nuclei) other 
than those which are morphologically gametes, by means of which the 
diploid number of chromosomes is established. In the two Lastraea varieties 
studied by Farmer and Digby ( 1907 ), in which the fusion is between nuclei 
