Wainio[1028] rendered great service to Phylogeny in his elaborate work on Cladoniaceae, the most complicated of all the lichen phyla. He also drew up a scheme of arrangement in his work on Brazil Lichens[1029]. There is in it some divergence from Reinke’s arrangement, as he tends to give more importance to the thallus than to fruit characters as a guide. He places, for instance, Gyrophorei beside Parmelei and at a long distance from his Lecidei. The Cyanophili group of families he has interpolated between _Buelliae_ (Physciaceae) and _Lecideae_. Many workers approve of Wainio’s classification but it presents some difficult problems. _h._ ZAHLBRUCKNER. The systematist of greatest weight in recent times is A. Zahlbruckner, who is responsible for the systematic account of lichens in Engler and Prantl’s _Natürlichen Pflanzenfamilien_. It is difficult to express the very great service he has rendered to Lichenology, in that and other world-wide studies of lichens. The sketch of lichen phylogeny as given in the present volume owes a great deal to the sound and clear guidance of his work, though his conclusions may not always have been accepted. The classification in the _Pflanzenfamilien_ is the one now generally followed. The class _Lichenes_ is divided by Zahlbruckner[1030] into two subclasses, I. Ascolichens and II. Hymenolichens. He gives a third class, Gasterolichens[1031], but as it was founded on error[1032], it need not concern us here. The Ascolichens are by far the more important. These are subdivided into: Series 1. =PYRENOCARPEAE=, with perithecial fruits. Series 2. =GYMNOCARPEAE=, with apothecial fruits. These are again broken up into families, and in the arrangement and sequence of the families Zahlbruckner indicates his view of development and relationship. They occur in the following order: SERIES 1. =PYRENOCARPEAE= ALGAL CELLS PROTOCOCCACEAE OR _PALMELLA_. I. _MORIOLACEAE._ } } II. _EPIGLOEACEAE._ } Thallus crustaceous, perithecia solitary. } III. _VERRUCARIACEAE._ } IV. _DERMATOCARPACEAE._ Thallus squamulose or foliose. V. _PYRENOTHAMNIACEAE._ Thallus fruticose. ALGAL CELLS _PRASIOLA_. VI. _MASTOIDIACEAE._ ALGAL CELLS _TRENTEPOHLIA_. VII. _PYRENULACEAE._ } } Thallus crustaceous, perithecia occurring VIII. _PARATHELIACEAE._ } singly. IX. _TRYPETHELIACEAE._ } } Thallus crustaceous, perithecia united X. _ASTROTHELIACEAE._ } (stromatoid). XI. _MYCOPORACEAE._ Thallus crustaceous, perithecia in compact groups with a common outer wall. XII. _PHYLLOPYRENIACEAE._ Thallus minutely foliose. ALGAL CELLS _PHYLLACTIDIUM_ OR _MYCOIDEA_. XIII. _STRIGULACEAE._ Tropical leaf-lichens. ALGAL CELLS _NOSTOC_ OR _SCYTONEMA_.