diagonally forward and outward. (pl. 21, fig. 6; pl. 22.) _Pygidium._ The pygidium of _Neolenus serratus_ is large, and usually shows five rings on the axial lobe and four pairs of ribs on the sides. There are five pairs of biramous appendages belonging to this shield, and behind these a pair of jointed cerci. That the number of abdominal appendages should correspond to the number of divisions of the axial lobe rather than to the number of ribs on the pleural lobes is of interest, and in accord with other trilobites, as first shown by Beecher. The endopodites of the pygidium have the same form as those of the thorax, are long, and very much less modified than those of any other trilobite whose appendages are known. On some specimens, they extend out far beyond the dorsal test, so that nearly all the segments are visible (pl. 17, fig. 3; pl. 18; pl. 19; pl. 20, fig. 1), but in these cases are probably displaced. The segments are short and wide, the whole endopodite tapering gradually outward. The dactylopodite bears terminal spines, and the individual segments also have outward-directed spines. The cerci appear to have been long, slender, very spinose organs much like the antennules, but stiff rather than flexible. They are a little longer than the pygidium (pl. 17, figs. 1, 2), and seem to be attached to a plate on the under surface of the posterior end and in front of the very narrow doublure. The precise form of this attachment can not be determined from the published figures. They bear numerous fine spines (pl. 17, fig. 3). _Epipodites and Exiles._ Doctor Walcott has found on several specimens of _Neolenus_ remains of organs which he interprets as epipodites and exites attached to the coxopodites. A study of the specimens has, however, convinced me that both the large and small epipodites are really exopodites, and that the exites are badly preserved and displaced coxopodites. Detailed explanation of this interpretation is given below in the description of the several specimens involved. _Description of Individual Specimens._ Doctor Walcott was kind enough to send me eight of the more important specimens of _Neolenus_ figured by him, and since my interpretation of them does not agree in all respects with his, I have thought it fairer to the reader to present here rather full notes explaining the position I have taken. I understand that since I communicated my interpretation of the epipodites and exites to him, Doctor Walcott has submitted the specimens to several palæontologists, who consider that epipodites are really present. Since I am not able to convince myself that their conclusion is based upon sound evidence, I give here my own interpretation. There is of course, no a priori reason why trilobites should not have had epipodites. Specimen No. 58589.