In 1871, Billings' specimen was examined by Professors James D. Dana (1871, p. 320), A. E. Verrill, and Sydney I. Smith, who agreed that the structures identified by Billings as legs were merely semicalcified arches of the membrane of the ventral surface, which opinion seems to have been adopted by zoologists generally in spite of the fact that the most elementary consideration of the structure of the thorax of a trilobite should have shown its falsity. While the curvature of the thoracic segments was convex forward, that of the supposed ventral arches was convex backward, and the supposed arches extended across so many segments as to have absolutely prevented any great amount of motion of the segments of the thorax on each other. Enrollment, a common occurrence in _Isotelus_, would have been absolutely impossible had any such calcified arches been present. Walcott, in his study of trilobites in thin section (1881, pp. 192, 206, pl. 2, fig. 9), obtained eleven slices of _Isotelus gigas_ which showed remains of appendages. He figured one of the sections, stating that it "shows the basal joint of a leg and another specimen not illustrated gives evidence that the legs extended out beneath the pygidium, as indicated by their basal joints." The second important specimen of an _Isotelus_ with appendages was found by Mr. James Pugh in strata of Richmond age 2 miles north of Oxford, Ohio, and is now in the U. S. National Museum. It was first described by Mickleborough (1883, p. 200, fig. 1-3). In two successive finds, a year apart, the specimen itself and its impression were recovered. Since I am redescribing the specimen in this memoir (see p. 35), it only remains to state here that Mickleborough interpreted the structures essentially correctly, though not using the same terminology as that at present adopted. His view that the anterior appendages were chelate can not, however, be supported, nor can his idea that the sole appendages of the pygidium were foliaceous branchial organs. Walcott (1884, p. 279, fig. 1) studied the original specimens and presented a figure which is much more detailed and clear than those of Mickleborough. By further cleaning the specimen he made out altogether twenty-six pairs of appendages. He stated that one of these belonged to the cephalon, nine to the thorax,[1] and the remaining sixteen to the pygidium. He showed that the endopodites of the pygidium were of practically the same form as those on the thorax, and stated that the "leg beneath the thorax of the Ohio trilobite shows seven joints in two instances; the character of the terminal joint is unknown." His figure shows, and he mentions, markings which are interpreted as traces of the fringes of the exopodites. [Footnote 1: The posterior one of these he believed to have been crowded forward from beneath the pygidium.]