A point in which Walcott differs from Beecher in the interpretation of specimens is in regard to the development of the endopodites of small pygidia. Beecher (1894 B, pl. 7, fig. 3) illustrated a series of endopodites which he likened to the endites of a thoracic limb of _Apus_. Doctor Walcott finds that specimens in the United States National Museum show slender endopodites all the way to the back of the pygidium, and thinks that Beecher mistook a mass of terminal segments of exopodites for a series of endopodites. On careful examination, however, the specimen shows, as Beecher indicated, a series of endopodites in undisturbed condition (No. 222, our pl. 4, fig. 5). _Restoration of Triarthrus._ One of the more important points noted in the later studies of _Triarthrus_ is that the gnathites of the cephalic appendages are much less like the endobases under the thorax than Beecher earlier thought, and showed in his restored figures and in his model. The four gnathites of each side are curved, flattened, not club-shaped, and so wide and so close together that they overlap one another. The metastoma is somewhat larger and more nearly circular than Beecher's earlier preparations led him to suppose. The restoration here presented is modified only slightly from the one designed by Professor Beecher, and the modifications are taken principally from figures published by him. The gnathites are drawn in form more like that shown by the specimens and his figures in the American Geologist (1895 A), and the metastoma is taken from one of the specimens. On the thorax the chief modification is in the addition of a considerable number of spines to the endopodites. In spite of the trivial character of most of these changes, they emphasize one of the important characteristics of _Triarthrus_ the regional differentiation of the appendages. It should be pointed out that although _Triarthrus_ is usually considered to be a very primitive trilobite, its appendages are more specialized than those of any of the others known. This is shown in their great length, the double curvature of the antennules, the differentiation of four pairs of endobases on the cephalon as gnathites, and the flattening of the segments of the posterior endopodites. These departures from the uniformity existing among the appendages of the other genera lead one to question whether the genus is really so primitive as has been supposed. _Relation of the Cephalic Appendages to the Markings on the Dorsal Surface of the Glabella._