_Calycinal Theory._--The theory which had most influence on the conceptions of Echinoderms in the two concluding decades of the 19th century was that of Lovén, elaborated by P.H. Carpenter, Sladen and others. This, which may be called the _calycinal_ theory, will be appreciated by comparing the structure of a simple crinoid with that of some other types. A crinoid reduced to its simplest elements consists of three principal portions--(i.) a theca or test enclosing the viscera; (ii.) five arms stretching upwards or outwards from the theca, sometimes single, sometimes branching; (iii.) a stem stretching downwards from the theca and attaching it to the sea-floor (see fig. 1). That part of the theca below the origins of the free arms is called the "dorsal cup"; the ventral part above the origins of the arms, serving as cover to the cup, is known as the "tegmen." All these parts are supported by plates or ossicles of crystalline carbonate of lime. The cup, in its simplest form, consists of two circlets of five plates. Each plate of the upper circlet supports an arm, and is called a "radial"; the plates of the lower circlet, the "basals," rest on the stem and alternate with those of the upper circlet, i.e. are interradial in position. Some crinoids have yet another circlet below these, the constituent plates of which are called "infrabasals," and are situated radially. The tegmen in most primitive forms, as well as in the embryonic stages of the living _Antedon_ (fig. 2), consists of five large triangular plates, alternating with the radials, and called "orals," because they roof over the mouth. In addition to these three or four circlets of plates, two other elements were once supposed essential to the ideal crinoid: the dorso-central and the oro-central. The former term was applied to a flattened plate observed in the embryonic stage of a single genus (_Antedon_) at that end of the stem attached to the sea-floor, and comparable to the foot of a wine-glass (fig. 2). In some crinoids which have no trace of a stem (e.g. _Marsupites_) a pentagonal plate is found at the bottom of the cup, where the stem would naturally have arisen ("centrale" in fig. 1); and since it was believed that the stem always grew by addition of ossicles immediately below the infrabasals, it was inferred that this pentagonal plate was the centro-dorsal in its primitive position, as though the wine-glass had been evolved from a tumbler by pulling the bottom out to form the foot. The oro-central was, it must be admitted, a theoretical conception due to a desire for symmetry, and was not confirmed by anything better than some erroneous observations on certain fossils, which were supposed to show a plate at the oral pole between the five orals; but this plate, so far as it exists at all, is now known to be nothing but an oral shifted in position. The theory