The specimens of figures 1-3, plate 5 (1881) show the form of the ventral membrane more distinctly than any of the others. The section of figure 1 was cut just inside the dorsal furrow on the right side, and figure 2, which is on the opposite side of the same slice, is almost exactly on the median line. Figure 3 shows a section just inside the left dorsal furrow. Section 2 did not cut any of the appendages, and the ventral membrane is shown as a thickened, probably chitinous sheet thrown into low sharply crested folds equal in number to, and pointing in a direction just the reverse of, the crests of the segments of the thorax. Under the pygidium, where there would of course be less wrinkling, the folds are hardly noticeable. In the actual specimens one sees more plainly than in the figures the line of separation between the ventral membrane and the appendages, but the state of preservation of everything beneath the dorsal shell is so indefinite that one does not feel sure just what the connection between the appendages and the membrane was. In the original of figure 5, plate 2, which seems to have been cut so as to cross the appendages at their line of junction with the ventral membrane, there appear to be narrow chitinous (?) plates extending from the ventral membrane to the dorsal test. Appendifers. In Ceraurus there are regular calcareous processes which extend down from the dorsal test just inside the line of the dorsal furrow, and which undoubtedly serve as points of attachment of the appendages. These processes, which for convenience I have designated as "appendifers," are broken off in most specimens showing the lower surface of _Ceraurus pleurexanthemus_, but on certain ones cleaned with potash they are well preserved. Doctor Walcott showed them well in his figures of the lower surface of this species (1875, pl. 11; 1881, pl. 4, fig. 5), while the attempt of Raymond and Barton (1913, pl. 2, fig. 7) to show them by photography was not so successful.