The exopodite on this same specimen was evidently cut diagonally across near the setiferous edge, showing a section through the shaft and the bases of seven setæ (fig. 18). This section is so exactly what would be obtained by cutting similarly an exopodite of either Neolenus or _Triarthrus_ that it should in itself dispose of the "spiral-exopodite" theory. Several sections have already been illustrated showing sections across the setæ of the exopodites (pl. 3, figs. 4-6, 1881; pl. 27, figs. 3, 4, 9, 1918), and similar sections are not uncommon. Only a very few, however, show sections in the plane of the exopodite. If only No. 111, described above, were known, it would be inferred that the exopodite had a slender shaft as in _Calymene_, but another good slice, No. 80 (fig. 12, ante) shows that the blade was rather broad, though not so broad as in Neolenus. The other specimen is No. 22, which has already been discussed. The thoracic exopodite of this specimen has been very incorrectly figured by Walcott, as it shows no such palmate shaft as he has indicated, but a long blade-like one is outlined, though its entire width is not actually shown. _Pygidial Appendages._ Sections 14 and 18 (pl. 2, figs. 4, 8, 1881) prove the presence under the pygidium of three pairs of appendages, the coxopodites and fragments of endopodites of which are shown. Nothing is known of the exopodites. _Relation of Hypostoma to Cephalon._ In Ceraurus the body portion and posterior end of the hypostoma are roughly oval, about as wide as the glabella at its broadest part, and the posterior edge extends back to within 0.5 to 1 mm. of the neck furrow. The posterior pair of appendifers are behind the hypostoma, while the second pair are in front of its posterior end but escape being covered by it on account of its oval shape. At the anterior end the hypostoma is widened by the presence of two side lappets which extend beyond the boundaries of the glabella. In both Ceraurus and Cheirurus the anterior edge of the hypostoma fits against the doublure at the anterior margin of the head and the epistoma is either entirely absent or is so narrow as not to be seen in specimens in the ordinary state of preservation. A section across the cephalon of _Ceraurus pleurexanthemus_ at the horizon of the eyes shows the sides of the hypostoma fitting closely against the sides of the glabella (Walcott's pl. 1, fig. 1). Further back on the head it is not in contact with the dorsal test, and the gnathobases extend beneath it. Restoration of _Ceraurus pleurexanthemus_. (pl. 11; text fig. 19.) The restoration of the appendages of _Ceraurus pleurexanthemus_ is a tentative one, based upon a careful study of the translucent sections prepared by Doctor Walcott. In no case among these sections is the actual test of any appendage preserved, and the real form of each part is generally obscured by the crystallization of the calcite which fills the spaces formerly occupied by animal matter.