The third genus, _Sphaerophorus_, is cosmopolitan; three of the species are British and are fairly common on moorlands, etc. They are fruticose in habit, being composed of congregate upright branching stalks, either round or slightly compressed and varying in height from about 1 to 8 cm. The structure is radiate with a well-developed outer cortex, and a central strand which gives strength to the somewhat slender stalks. The fruits are lodged in the swollen tips and are at first enclosed; later, the covering thallus splits irregularly and exposes the hymenium. Coniocarpineae comprise only a comparatively small number of genera and species, but the series is of unusual interest as being extremely well defined by the fruit-formation and as representing all the various stages of thalline development from the primitive crustaceous to the highly evolved fruticose type. With the primitive thallus is associated a wholly fungal fruit, both stalk and capitulum, which in the higher forms is surrounded and protected by the thallus. Lichen-acids are freely produced even in crustaceous forms, and they, along with the high stage of development reached, testify to the great antiquity of the series. _c._ THALLUS OF GRAPHIDINEAE. As formerly understood, this series included only crustaceous forms with an extremely simple development of thallus, fungi and algae—whether Palmellaceae, etc., or more frequently Trentepohliaceae—growing side by side either superficially or embedded in tree or rock, the presence of the vegetative body being often signalled only by a deeper colouration of the substratum. The researches of Almquist, and more recently of Reinke and Darbishire, have enlarged our conception of the series, and the families Dirinaceae and Roccellaceae are now classified in Graphidineae. Arthoniaceae, Graphidaceae and Chiodectonaceae are all wholly crustaceous. The first thalline advance takes place in Dirinaceae with two allied genera, _Dirina_ and _Dirinastrum_. Though the thallus is still crustaceous, it is of considerable thickness, with differentiation of tissues: on the lower side there is a loosely filamentous medulla from which hyphae pierce the substratum and secure attachment. _Trentepohlia_ gonidia lie in a zone above the medulla, and the upper cortex is formed of regular palisade hyphae forming a “fastigiate cortex.” It is the constant presence of _Trentepohlia_ algae as well as the tendency to ellipsoid or lirellate fruits that have influenced the inclusion of Dirinaceae and Roccellaceae in the series.