The sporangial frustules vary in shape and size, some being long and slender, others clavate, but they are all more or less tumid in the middle, with costæ more indefinite than in perfect valves. All gradations occur, one end becoming shorter until the valve has the shape of the variety known as constrictum. It would seem, therefore, that the non-constricted form is a passage from the sporangial to the smaller or adult form, or is of no specific importance. All forms are found living together. The adult frustules are the smaller ones; it is from them that the sporangia are produced. Meridion intermedium H. L. Smith (Amer. Quart. Mic. Jour., Vol. 1, p. 12) is characterized by less evident costæ and is more delicate in general appearance. Some forms are capitate and others are not. Prof. Smith compares the M. intermedium with Peronia erinacea Bréb. and Arnott which he has named M. erinaceum, hitherto found only in Europe, and points out the relation of the two forms to Licmophora. An examination of the H. L. S. type slides of the two diatoms proves that Peronia has very delicate costæ and a distinct pseudoraphe not noticeable in Meridion. On the slide of Peronia are frustules exactly similar to certain of the sporangial variations of M. circulare. The fan-like arrangement of Licmophora, the marine form, and the circular chains of Meridion, the fresh-water genus, are similar. Both are stipitate at the beginning of their growth. (_c_) FRAGILARIEÆ Divided into three sections: _Diatominæ._--Valve circular, elliptical to linear, quadrate or cruciform, with transverse costæ; without raphe, a pseudoraphe sometimes wanting. _Fragilariinæ._--Valve elongate, with small central and terminal elevations, without costæ but with transverse punctate striæ; without genuine central nodule. _Eunotiinæ._--Valve lunate; a raphe sometimes partially formed with terminal nodules near the edges. DIATOMINÆ _Diatoma._--Frustules in filaments. Valve linear or elliptical, costate. _Plagiogramma._--Frustules in fasciæ or free. Valve costate. _Opephora._--Valve costate, with an inner punctate stratum. DIATOMA DE CANDOLLE (1805) em. HEIB. (1863) (diatemno, I cut in two) Frustules oblong or quadrate, adnate in filaments, attached by alternate angles and finally separating. Valve linear or elliptical, with transverse costæ and rows of puncta and a pseudoraphe. Chromatophores large granules without definite arrangement. (See Pl. 40, Fig. 11.) {42}DIATOMA VULGARE BORY. Valve elliptical-lanceolate, with apices sometimes rostrate or capitate; pseudoraphe narrow; costæ, 5 in 10 µ. Common everywhere in pure fresh water and extremely variable. Pl. 10, Figs. 9 and 10. Var. elongatum (Ag.) = var. ehrenbergii (Kuetz.)--elliptical-lanceolate, constricted near the apex. Var. grande (Wm. Sm.) Grun.--linear, elongated, constricted near the apices. Pl. 10, Fig. 4.