_Sarcodina with no central capsule or distinction of ectosarc; the pseudopodia fine, branching freely, and fusing where they meet to form protoplasmic networks, or the outermost in the pelagic forms radiating, but without a central or axial filament: sometimes dimorphic, reproducing by fission and by rhizopod or flagellate germs in the few cases thoroughly investigated: all marine (with the exception of some of the Allogromidiaceae), and usually provided with a test of carbonate of lime ("vitreous" calcite, or "porcellanous" aragonite?), or of cemented particles of sand ("arenaceous"); test-wall continuous, or with the walls perforated by minute pores or interstices for the protrusion of pseudopodia._ The classification of Carpenter (into _Vitreous_ or _Perforate_, _Porcellanous_ or _Imperforate_, and _Arenaceous_), according to the structure of the shell, had proved too artificial to be used by Brady in the great Monograph of the Foraminifera collected by the "Challenger" Expedition,[75] and has been modified by him and others since then. We reproduce Lister's account of Brady's classification.[76] We must, however, warn the tyro that its characterisations are not definitions (a feature of all other recent systems), for rigid definitions are impossible: here as in the case, for instance, of many Natural Orders of Plants, transitional forms making the establishment of absolute boundaries out of the question. In the following classification we do not think it, therefore, necessary to complete the characterisations by noting the extremes of variation within the orders:— 1. Allogromidiaceae: simple forms, often fresh-water and similar to Rhizopoda; test 0, or chitinous, gelatinous, or formed of cemented particles, whether secreted platelets or ingested granules. _Biomyxa_, Leidy = _Gymnophrys_, Cienk.; {59}_Diaphorodon_, Archer; _Allogromia_, Rhumbl. (= _Gromia_, auctt.[77] nec Duj.) (Fig. 14, 1); _Lieberkühnia_, Cl. and Lachm. (Fig. 12); _Microgromia_, R. Hertw. (Fig. 11); _Pamphagus_, Bailey. 2. Astrorhizidaceae: test arenaceous, often large, never truly chambered, or if so, asymmetrical. _Astrorhiza_, Sandahl; _Haliphysema_, Bowerb.; _Saccammina_, M. Sars (Fig. 13, 1); _Loftusia_, Brady. 3. Lituolidaceae: test arenaceous, often symmetrical or regularly spiral, isomorphous with calcareous forms: the chambers when old often "labyrinthine" by the ingrowth of wall-material. _Lituola_, Lam.; _Reophax_, Montf.; _Ammodiscus_, Reuss; _Trochammina_, Parker and Jeffreys.