Sporangia simple; peridial wall simple, thin, breaking irregularly; capillitium formed of abundant, richly anastomosing tubules, filled throughout their entire length with calcareous granules; the nodes often feebly represented; stipe poorly developed or wanting entirely; columella, except in forms sometimes assigned to the sub-genus _Scyphium_, poorly developed or none; spores frequently adherent in clusters. The whole genus calls for careful and protracted study; and the present so-called species are like something new on the world; as full of vagaries as though but just entered upon their phylogenetic race. This genus is closely related to _Physarum_, but differs in having the capillitium calcareous throughout. Forms occur and are included here, in which the capillitium, especially in some parts, is physarum-like, physaroid. Nevertheless, the distinctions hold good as a rule, and are at once diagnostic. In capillitial differentiation the badhamias are definite and beautiful. The net in a typical species, as _B. papaveracea_, is throughout uniformly evenly tubular, the calcareous deposits delicate in the extreme, presenting, as the spores disappear, an elegant trabecular structure as if to support the persisting peridium if not the original content. In other forms the capillitium is physaroid, with swollen nodes, but heavily calcareous but not quite throughout. _Badhamia_, _Physarum_, _Tilmadoche_, _Craterium_ present a consistent group, of which _Physarum_ is the generalized expression. Berkeley's idea of the genus was expressed as follows: "Peridium naked or furfuraceous. Spores in groups, enclosed, at first, in a hyaline sack." Rostafinski, while accepting Berkeley's generic name, redefined it, emphasized the calcareous capillitium, and made reference to the spore-adherence only to assert that Berkeley's description was, in this particular, based on mistaken observation. In some species, the spores do, in fact, show a tendency to cling together, a characteristic which Badham was perhaps first to notice; but that this is occasioned by their being surrounded by a sac or common pellicle has not been proved nor even suggested, by any subsequent investigator. Berkeley's genus was therefore founded upon a slight mistake; but we may conserve his rights in the premises if we write _Badhamia_ (Berk.) Rost., and so keep history straight. =Key to the Species of Badhamia= _A._ Spores ovoid or ellipsoidal _a._ Spores free 1. _B. ovispora_ _b._ Spores adherent 2. _B. versicolor_ _B._ Spores spherical _a._ Sporangia yellow i. Spores free 3. _B. decipiens_ ii. Spores adhering 4. _B. nitens_ _b._ Sporangia grey, spores free i. Always sessile 5. _B. panicea_ ii. Stalked, at least some of them