The first announcement of the discovery of actual appendages in _Ceraurus_ and _Calymene_ was made by the same investigator in a pamphlet published in 1876 in advance of the 28th Report of the New York State Museum of Natural History, the publication of the whole report being delayed till 1879. The results were obtained by the process of cutting translucent slices of enrolled trilobites derived from the Trenton limestone at Trenton Falls, New York. Since he summarized all the results of this study in one paper at a later date, it is not necessary to follow the stages of the work. A second preliminary paper was published in pamphlet form in September, 1877, and in final form in 1879, when the first figures were presented. In his important paper of 1881, Walcott reviewed all that was known of the appendages of trilobites to that time, and gave the results of seven years of study of sections of enrolled specimens. Slices had been made of 2,200 individuals from Trenton Falls, which resulted in obtaining 270 which were worthy of study. Of these, 205 were from _Ceraurus pleurexanthemus_, 49 from _Calymene senaria_, 11 from _Isotelus gigas_, and 5 from _Acidaspis trentonensis_. Walcott's views on certain portions of the anatomy can best be set forth in the form of a few extracts (1881, pp. 199-208): _The Ventral Membrane._--In those longitudinal sections in which the ventral membrane is most perfectly preserved, it is shown to have been a thin, delicate pellicle or membrane, strengthened in each segment by a transverse arch, to which the appendages were attached. These arches appear as flat bands separated by a thin connecting membrane, somewhat as the arches in the ventral surface of some of the Macrouran Decapods.... In by far the greater number of sections, both transverse and longitudinal, the evidence of the former presence of an exterior membrane, protecting the contents of the visceral cavity, rests on the fact that the sections show a definite boundary line between the white calcspar, filling the space formerly occupied by the viscera, and the dark limestone matrix. Even the thickened arches are rarely seen. The mode of attachment of the leg to the ventral surface is shown [in transverse and longitudinal sections of _Ceraurus_ and _Calymene_]. These illustrations are considered as showing that the point of articulation was a small, round process projecting from the posterior surface of the large basal joint, and articulating in the ventral arch somewhat as the legs of some of the Isopods articulate with the arches in the ventral membrane. The arches of the ventral membrane in the trilobite ... afford a correspondingly firm basis for the attachment of the legs.