The endobases of the coxopodites of the appendages of the cephalon probably in all cases function as mouth-parts (gnathites), and are especially modified for this purpose in Triarthrus, being flattened, shoe-shaped in outline, and so arranged that they work over one another in a shearing fashion. While the more anterior of the coxopodites are attached in front of the posterior tip of the hypostoma, the gnathites of Triarthrus bend backward so that all are behind the hypostoma. In _Calymene_ and _Ceraurus_, two or three pairs of the gnathites are back of the hypostoma, and one or more pairs may be beside or under the hypostoma. In these genera the mouth is probably in front of the tip of the upper lip. In _Isotelus_, the mouth seems to have been situated in the notch between the two branches of the hypostoma, and the gnathites of two or three pairs of the appendages probably worked under its forks. Since the length of the hypostoma differs in the various species of _Isotelus_, there would be a variable number of gnathites projecting under its forks, according to the species. In this genus the gnathites are of the same long form, cylindrical in cross-section, as the endobases of the thoracic segments, but each is bowed back considerably from the point of attachment. The gnathites of _Neolenus_ are like the endobases of the thorax, but broader. The great length of the hypostoma makes it probable that the mouth was far back and that some of the gnathites were in front of it. The gnathites of _Cryptolithus_ are unknown. Professor Beecher in his drawing shows some fragments with toothed ends near the hypostoma, and it may be that they are inner ends of gnathites, but I see nothing to substantiate such an interpretation. If, as some suppose, _Cryptolithus_ was a mud feeder, the gnathites were probably poorly developed. Of the gnathites of _Kootenia_, _Ptychoparia_, and _Acidaspis_ also nothing is known. _Thorax._ In each genus there is a pair of appendages for each segment of the thorax. When the axial lobe is narrow, the endobases of the coxopodites are small and short (_Cryptolithus_, _Ceraurus_, _Calymene_). When the axial lobe is wide, the endobases are long and stout (_Isotelus_, _Triarthrus_). The exopodites always lie above and in front of the corresponding endopodites. In Triarthrus the two branches are of practically equal length. In _Cryptolithus_ the exopodites are much the longer. In _Neolenus_, _Calymene_, _Ceraurus_, _Kootenia_, and _Ptychoparia_, the exopodites are shorter than the endopodites.