APPLICATION OF EVOLUTIONARY THEORY 11 
were regarded as more advanced (Osmundaceae, Schizaeaceae, Marattiaceae). 
But this, which was little better than an assumption, needed to be tested 
on other grounds, such as comparison with other Pteridophytes, and 
reference to the results of physiological and palaeontological enquiry. It 
is now pointed out, first, on the comparative basis, that the Leptosporangiate 
Ferns are isolated from other plants by the simplicity of their sporangia, 
and that.the link in sporangial character with other early types is to be 
found more probably through the Eusporangiate than through the Lepto- 
sporangiate types. Secondly, it can be shown experimentally that reduction 
of complexity of leaf-structure follows the shade-habit; and the “filmy” 
character of the leaf in the Hymenophyllaceae is probably only an extreme 
case of this, while the smaller ‘size of the individual sporangia shows some 
degree of parallelism with this adaptation: certainly it is so in the genus 
Todea. There is also some experimental basis for the conclusion that 
the thin-leaved habit is a derivative condition following on a shade-habit. 
Thirdly, the Palaeontological evidence shows that whereas the Eusporangiate 
Ferns were the characteristic Ferns of the primary rocks, while Lepto- 
sporangiate Ferns were certainly rare, the Leptosporangiates were in the 
ascendant in later strata, and are the dominant Ferns of the present day. 
From such evidence, which will be seen to be convergent along three 
lines of argument, the conclusion is drawn that the general series of 
Ferns has not been one of advancing complexity of sporangial structure, 
but of reduction. This case will serve as an illustration how the prima 
facie probability of advance may be overruled by the cumulative effect 
of other evidence. As a consequence perhaps of such proof of reduction 
in this and other cases, the tendency of the moment among Botanists 
is to look with general mistrust upon ascending series. For my own 
part, I think this tendency has been allowed too free scope: the primd 
facie probability of a series being truly progressive should be kept clearly 
in mind until it is disproved on more exact grounds. 
Wherever a linear series of forms is recognised these two alternatives, 
of the series being an ascending or a descending one, will present them- 
selves. But there is also the third alternative, viz. that the series may 
have been one of divergent development from some central point. It will 
be apparent that this is in truth merely a combination of the two pre- 
ceding cases, and the lines of argument will be the same, though necessarily 
more complicated. As a consequence such divergent series are less readily 
substantiated than simple series would be. 
But there remains the still more serious question whether a series which 
may have been laid out on ground of form as a presumable evolutionary 
sequence reflects actually any line of evolution at all. It may be composed 
of members of distinct phyletic lines, which have converged in respect of those 
characters which lie at the foundation of our comparison. It has long been 
known that similarity of form may be arrived at along distinct evolutionary 
_ routes: this is designated parallel, or polyphyletic development, and examples 
