Lister has examined Rostafinski's type of _C. reticulatum_ and declares that it has the usual didermic characters. Hence there is no doubt that our small-spored American specimens are covered by Rostafinski's description, No. 72. On the other hand, Lister makes _C. difforme_ (Pers.) Rost. a _Didymium_, by its crystalline coat. That species therefore is removed from consideration in this connection. _C. calcareum_ remains as applicable to American forms having the spores 10-12 mu, but according to the author of the species the capillitium is abundant and definitive. Unhappily the type of _C. calcareum_ is lost (Lister, _Mon._, p. 95), so that there is no other means of verification than the description and Rostafinski's figure. Under these circumstances we consider the name _calcareum_ inapplicable to any American forms we have so far seen. See next species. As to the American species which have been distributed as _C. calcareum_ (Lk.) Rost., they are, so far as seen, referable to _D. reticulatum_ (Rost.), Morg. Here also belongs No. 1217, Ellis, _N. A. F._ New York, Pennsylvania, Ohio, Iowa, Nebraska. Probably to be found throughout the eastern United States. 2. DIDERMA SPUMARIOIDES _Fries_. 1829. _Diderma spumarioides_ Fries, _Syst. Myc._, III., p. 104. 1833. _Physarum stromateum_ Link., _Handb._, III., p. 409. 1876. _Chondrioderma stromateum_ (Lk.) Rost., _App._, p. 18. Sporangia sessile, crowded, spherical, or by mutual pressure irregular, white; the peridium plainly double, but the layers adhering, the outer more strongly calcareous, but very frail, almost farinaceous; hypothallus more or less plainly in evidence, white or pale alutaceous; columella distinct, though often small, globose, yellowish; capillitium variable in quantity, sometimes abundant, brown, somewhat branching and anastomosing outwardly, the tips paler; spores minutely roughened, dark violaceous, about 10 mu. This species has the outward seeming of a didymium, but is plainly different as that genus is here defined, since the calcareous crust, although inclined to be pulverulent, is made up of minute granules, not crystals, of lime. The hypothallus is sometimes hardly discoverable, anon well developed, out-spread, rugulose, far beyond the limits of the fructification. In his _Monograph_, p. 175, Rostafinski includes here _Physarum stromateum_ Link. In the Appendix he is inclined to raise Link's form to the dignity of a distinct species, basing the diagnosis upon the superposition of the sporangia in certain cases, a feature entirely unknown to Link's description and of extremely uncertain value, since by their crowding the sporangia are liable always to be pushed above each other. We therefore regard _C. stromateum_ (Link) Rost. as a synonym of the present species, as the description, Link, Handb., III., 409, indicates, so far as it goes. 3. DIDERMA SIMPLEX (_Schroet._) _Lister._