(c) the history of the trilobites shows a considerable increase in the average number of segments in successive periods from the Cambrian to the Permian; (d) the simplest trilobites are nearly or quite blind. PART IV. DESCRIPTION OF THE APPENDAGES OF INDIVIDUAL SPECIMENS. Triarthrus becki Green. In order to make easily available the evidence on which the present knowledge of the appendages of Triarthrus and _Cryptolithus_ rests, it has seemed wise to publish brief descriptions and photographic figures of some of the better specimens preserved in the Yale University Museum. These specimens are pyritic replacements, and while they do not as yet show any signs of decomposition, it should be realized that it is only a matter of time when either they will be self-destroyed through oxidation, or else embedded for safe keeping in such a fashion that they will not be readily available for study. It is therefore essential to keep a photographic record of the more important individuals. Specimen No. 220 (pl. 3, fig. 2). Illustrated: Amer. Geol., vol. 15, 1895, pl. 4 (drawing); Amer. Jour. Sci., vol. 13, 1902, pl. 3 (photograph). This is one of the largest specimens showing appendages, and is developed from the ventral side. It shows some appendages on all parts of the body, but its special features are the exhibition of the shafts on the proximal ends of the antennules, the rather well preserved appendages of the cephalon and anterior part of the thorax, and the preservation of the anal opening. In the drawing in the American Geologist, the right and left sides are reversed as in a mirror, a point which should be borne in mind when comparing that figure with a photograph or description. The shaft of the left antennule is best preserved and is short, cylindrical, somewhat enlarged and ball-shaped at the proximal end. It is 1.5 mm. long. The posterior part of the hypostoma is present, but crushed, and the metastoma is not visible, the pieces so indicated in Beecher's figure being the rim of the hypostoma. Back of the hypostoma may be seen four (not three as in Beecher's figure) pairs of gnathites, the first three pairs broad and greatly overlapping, the fourth pair more slender, but poorly preserved. The inner edges of the gnathites on the right side are distinctly nodulose, and roughened for mastication.