He suggested that, in relation to other plants, Eulichens approach Pezizae, Hysteriaceae and Sphaeriaceae; Epiconiaceae have affinity with Lycoperdaceae, while Collemaceae are allied to the algal family Nostocaceae. These three groups of Eulichens, he held, advanced on somewhat parallel lines, but reached a very varied development, the Discocarpeae attaining the highest stage of thalline form. Müller accepted as characters of generic importance the form and structure of the fruiting body, the presence or absence of paraphyses, and the septation, colour, etc. of the spores. A few years later (1867) the composite nature of the lichen thallus was announced by Schwendener, and, after some time, was acknowledged by most botanists to be in accordance with the facts of nature. Any system of classification, therefore, that claims to be a natural one, must, while following as far as possible the line of plant development, take into account the double origin of lichens both from algae and fungi, the essential unity and coherence of the class being however proved by the recurring similarity between the thalline types of the different phyla. As Müller had surmised: “they are a series of parallel detached though convergent groups.” _g._ REINKE. The arrangement of Ascolichens on these lines was first seriously studied by Reinke[1026], and his conclusions, which are embodied[1027] in the _Lichens of Schleswig-Holstein_, have been largely accepted by succeeding workers. He recognizes three great subclasses: 1. Coniocarpi; 2. Discocarpi; 3. Pyrenocarpi. The Coniocarpi are a group apart, but as their fruit is at first entirely closed—at least in some of the genera—the more natural position for them is between Discocarpi and Pyrenocarpi. It is in the arrangement of the Discocarpi that variation occurs. Reinke’s arrangement of orders and families in that sub-class is as follows: Subclass 2. Discocarpi. Order I. _GRAMMOPHORI_: Fam. _GRAPHIDACEI_ and _XYLOGRAPHACEI_. Order II. _LECIDEALES_: Fam. _GYALECTACEI_, _LECIDEACEI_, _UMBILICARIACEI_ and _CLADONIACEI_. Order III. _PARMELIALES_: Fam. _URCEOLARIACEI_, _PERTUSARIACEI_, _PARMELIACEI_, _PHYSCIACEI_, _TELOSCHISTACEI_ and _ACAROSPORACEI_. Order IV. _CYANOPHILI_: Fam. _LICHINACEI_, _EPHEBACEI_, _PANNARIACEI_, _STICTACEI_, _PELTIGERACEI_, _COLLEMACEI_ and _OMPHALARIACEI_. The orders represent generally the principal phyla or groups, the families subordinate parallel phyla within the orders. The first three orders are stages of advance as regards fruit development; the Cyanophili are a group apart.