110 
Mycologia 
cia. Thus it appears that these fungi can live without the algae, 
but are benefited by the association with them. Trentepohlia is 
known to live commonly in the periderm. Therefore, it seems 
certain that this alga is often there and enters into the hostal 
relation with the lichen soon after the lichen spore germinates 
and penetrates the periderm, though Frank seems to have sup- 
posed that these lichens were always independent of the alga 
during a good portion of their course. More of Frank’s results 
are given toward the close of this paper. 
Lindau (8i) accepted, in the main, the conclusions of Frank 
and passed on to a profitable consideration of the same or similar 
lichens and the algae which grow with them. He found Trente- 
pohlia filaments on the surface of the bark entwined by hyphae 
of Arthopyrenia punctiformis (Pers.) Mass.; but the portion of 
the fungus within the periderm was wholly free from the algal 
filaments. He concludes that this Arthopyrenia lives without 
other than an accidental relation with the alga. 
These researches are interesting and instructive in many ways. 
Frank decided that typical lichens are Ascomycetes which live in 
symbiotic relationship with algae ; but he regarded all of these 
plants which belong to the same genus lichens, whether all or 
only part of them live with the algae. Lindau, on the other hand 
thinks that those that live outside the symbiotic relation are not 
lichens. These studies also indicate that the lichen is benefited 
by the association with the alga quite as plainly as do the cultural 
experiments with higher lichens ; and this makes sure the position 
that those fungi which live during all or part of their life in para- 
sitic relation with algal hosts are lichens, provided that they sus- 
tain, at the same time, the usual relation with an external sub- 
stratum. Lindau thinks the Arthopyrenia considered above is not 
a lichen, since the alga does not grow more luxuriantly because 
of association with it. We can not accept this view, but believe 
that the fungus is a lichen if it is benefited by the association with 
the alga instead of using it merely as a support about which to 
twine. We agree with Lindau that those species which do not 
enter into parasitic relation with algae are not lichens, even though 
they belong to the same genus with others that enter into relations 
beneficial to themselves and are lichens. Whether a fungus 
