_Body_ much depressed into an oblong ellipsis not contractile into a sphere. _Buckler_ edged, a slight longitudinal furrow arising from its anterior extremity. Posterior angles elongated into points. _Without any tubercles_ except the eyes, which are neither prominent nor reticulated. _Longitudinal lobes_ slightly prominent. _Abdomen_ with 8 articulations. _Genus Fourth._ Paradoxides. _Body_ depressed not contractile. _Flanks_ much broader than the middle lobe. _Buckler_ nearly semicircular three transverse furrows on the middle lobe. _Eye-shaped tubercles_ none. _Abdomen_ with 12 articulations. _Arches_ of the lateral lobes, more or less prolonged beyond the membrane which sustains them. _Genus Fifth._ Agnostus. _Body_ ellipsoidal--semicylindrical. _Buckler and flanks_ edged--the edges being slightly elevated. _Middle lobe_ with two transverse divisions, each composed of a single piece. _Two glandular_ tubercles on the anterior part of the body. In 1824, Dr. J. E. Dekay added a sixth genus to the family of the trilobites, which he describes in the following manner. _Genus Sixth._ Isotelus. _Body_ oval oblong, often contracted, not unfrequently extended. _Head_ or _buckler_ large and rounded, equalling the tail in size, with but two oculiform tubercles. _Abdomen_ with 8 articulations. Frontal process beneath, with two semilunar terminations. _Post-abdomen_ or _tail_ broad, expanded with indistinct divisions, as large as the buckler. _Longitudinal_ lobes very distinct. This genus, he remarks, will be sufficiently distinguished from the five genera proposed by _M. Alexandre Brongniart_ in his valuable and truly philosophical work on the trilobites by the following particulars. From _Calymene_. By the presence of but two tubercles on the buckler not reticulated; by the abdomen with but 8 articulations. From _Asaphus_. By the middle lobe, which is double the size of the lateral ones; by the absence of a membranaceous expansion on the sides; by the non-reticulation of the eyes, &c. From _Ogygia_. By the rolled form, the rounded posterior angles of the buckler, and the distinct articulation of the longitudinal lobes. From _Paradoxide_ and _Agnoste_ by characters too obvious to be enumerated. (See Annals of N. York Lyceum, Sec. Vol. I. pp. 174-5.) In 1826, J. W. Dalman published in the Transactions of the Swedish Academy, and also in a separate work, an account of the trilobites found in the North of Europe, in which he has enriched the family by a number of fine species, and with the following genera, which he modestly proposes merely as subdivisions. _Genus Seventh._ Nileus. _Body_ short, capable of contraction into a sphere, smooth, convex. _Abdomen_ with about 8 articulations, without any dorsal longitudinal furrows. _Buckler_ sub-lunate, with large lateral eyes. _Tail_ expanded, not so large as the buckler, without lobes. _Genus Eighth._ Illænus. _Body_ ovate oblong, contractile.