The exact contour of this species cannot be perfectly ascertained from our specimen; it seems, however, to have been lunate. The horns of the crescent which form the posterior angles, are very distinct, and they project like curved spines, some distance on each side of the head. The middle lobe or front is faintly scalloped on each side along the cheeks. The cheeks are rather large, and are furnished with two small oculiform tubercles, very remote from each other, and quite near to the anterior portion of the buckler. The abdomen is composed of twelve articulations. The lateral lobes of the abdomen are flat, and each of the ribs, at about half their extent, is marked on the upper surface, with an elevated pimple. These little pustules are nearly on a line with the oculiferous tubercles of the buckler, and present two parallel ranges down the body, one on each side of the middle lobe, and are terminated by a curved spine, which projects to some distance beyond the tail of the animal. Length one inch and a fourth. This remarkable organic relic was found near Newport, in the State of New York. It is embedded in black limestone shale, and so exceedingly depressed is this animal, that a very thin lamen of the slate removed from the surface would destroy every vestige of its appearance. I am indebted to my early friend, Professor T. R. Beck, for the use of this valuable petrifaction, which now belongs to the cabinet of the Albany Institute. Genus Triarthrus. _Green._ _Body_, slightly convex; contractile? _Buckler?_ _Abdomen_, with three articulations, side lobes longitudinal, narrow, and wedge-shaped. _Tail_, broad, rounded, without any membranaceous expansion. The name of this genus is derived from the circumstance, that the abdomen has but _three_ articulations; an organization which is very peculiar. These curious fossil animals are very abundant in the rocks in which they are found; but though I have examined a multitude of specimens from different localities, no vestige of the head or buckler could, on the most minute examination, be discovered. Whether these animals, during their petrifaction, were so contorted or rolled up, as to bring the extremities of the body together, in such a manner as to present the posterior folded part only to the view; or whether the buckler has been destroyed by the process of mineralization, as appears frequently to happen with the asaphs, we are at a loss to determine. The animal remains which belong to the genus Triarthrus, differ so much in their' form and general characters from all the other trilobites, that we perhaps ought to regard them as forming another race of beings. They are, however, more nearly allied to this family than the Agnosti of Professor Brongniart. Triarthrus Beckii. _Green._ Cast No. 34. Fig. 6. Cauda subrotunda, bipunctata; articulis abdominis tribus, absque lobis lateralibus consuetis, sed lobo arcuato utrinque apposito.