This class shows much greater diversity of organization than any other, and the classifications proposed by recent writers, such as E. Haeckel, O. Jaekel and F.A. Bather, start from such different points of view that no discussion of them can be attempted here. Following the narrative given above, we recognize a primitive group--Amphoridea--represented by _Aristocystis_ (fig. 8). From this are derived the orders Diploporita (fig. 9) and Rhombifera (fig. 10) and the class Edrioasteroidea, all which have already been described as steps in the evolution of the phylum. But there were also side-branches leading nowhere, and therefore placed in separate orders--Aporita and Carpoidea. Order 1. _Amphoridea._--Radial symmetry has affected neither food-grooves nor thecal plates; nor, probably, nerves, ambulacral vessels, nor gonads. Canals or folds when present in the stereom are irregular. Families: Aristocystidae (fig. 8); Eocystidae. Order 2. _Carpoidea._--Theca compressed in the oro-anal plane and a bilateral symmetry thus induced, affecting the food-grooves and, usually, the thecal plates and stem. Food-grooves in part epithecal and may be continued on one or two exothecal processes. No pores or folds in the stereom. Families: Anomalocystidae, Dendrocystidae. These correspond to Jaekel's Carpoidea Heterostelea; he also includes, as Eustelea, our Comarocystidae and Malocystidae. Order 3. _Rhombifera._--Radial symmetry affects the food-grooves and, in the more advanced families, the thecal plates; probably also the nerves and ambulacral vessels, but not the gonads. The food-grooves are exothecal, i.e. are stretched out from the theca on jointed skeletal processes (brachioles). These either are close to the mouth or are removed from it upon a series of ambulacral or sub-ambulacral plates not derived immediately from thecal plates, or are separated from the oral centre by hypothecal passages passing beneath terminal plates. The stereom and stroma become arranged in folds and strands at right angles to the sutures of the thecal plates; in higher forms the stereom-folds are in part specialized as pectini-rhombs. Families: Echinosphaeridae; Comarocystidae; Macrocystellidae; Tiaracrinidae; Malocystidae; Glyptocystidae, with sub-famm. Echinoencrininae, Callocystinae, Glyptocystinae, of which examples are _Cheirocrinus_ (fig. 10) and _Cystoblastus_ from which Jaekel deduces the blastoids; Caryocrinidae. Order 4. _Aporita._--Pentamerous symmetry affects the food-grooves and thecal plates; probably also the nerves and ambulacral vessels, but not the gonads. Food-grooves exothecal and circumoral. The stereom shows no trace of canals, folds, rhombs or diplopores. Family: Cryptocrinidae.