Order 5. _Diploporita._--Radial symmetry affects the food-grooves, and by degrees the thecal plates connected therewith, but not the interradial thecal plates; probably also the nerves and ambulacral vessels, but not the gonads. The food-grooves are epithecal, i.e. are extended over the thecal plates themselves without intermediate flooring; they are also prolonged on exothecal brachioles, which line the epithecal grooves. The stereom of the thecal plates may be thrown into folds, but the mesostroma does not so much tend to lie in strands traversing the sutures, nor are pectini-rhombs or pore-rhombs developed; diplopores are always present in the mesostereom, but often restricted to definite tracts or plates, especially in higher forms. Families: Sphaeronidae; Glyptosphaeridae, e.g. _Fungocystis_ (fig. 9); Protocrinidae; Mesocystidae; Gomphocystidae. The Protocrinidae lead up to _Proteroblastus_, in which the theca is ovoid, sometimes prolonged into a stem, the plates differentiated into (a) smooth, irregular, depressed interambulacrals, (b) transversely elongate brachioliferous adambulacrals, to which the diplopores, which lie at right angles to the main food-groove, are confined. This leads almost without a break to the Protoblastoidea. Class II. BLASTOIDEA.--Pelmatozoa in which five (by atrophy four) epithecal ciliated grooves, lying on a lancet-shaped plate (? always), radiate from a central peristome between five interradial deltoid plates, and are edged by alternating side-plates bearing brachioles, to which side-branches pass from the grooves. Grooves and peristome protected by small plates, which can open over the grooves. The generative organs and coelom probably did not send extensions along the rays into the brachioles; but apparently nerves from the aboral centre, after passing through the thecal plates, met in a circumoral ring, from which branches passed into the plate under each main food-groove, and thence supplied the brachioles. The thecal plates, however irregular in some species, always show defined basals and a distinct plate ("radial") at the end of each ambulacrum; they are in all cases so far affected by pentamerous symmetry that their sutures never cross the ambulacra. All Palaeozoic. Division A. _Protoblastoidea._--Blastoidea without interambulacral groups of hydrospire-folds hanging into the thecal cavity. Families: Asteroblastidae, Blastoidocrinidae. The former might be placed with Diploporita, were it not for a greater intimacy of correlation between ambulacral and thecal structures than is found in Cystidea as here defined. They form a link between the Protocrinidae and--