The interest excited by the discovery, in 1869, of that remarkable flexible Echinoderm, Asthenosoma or Calveria , in the deep Atlantic, is increased by the fact noticed by Mr. J. Young∗ and other palæontologists, that certain other forms, whose day ended far back in geological time, also possessed the same overlapping plates and consequent flexibility. This structure was first described by Prof. J. Hall in Lepidechinus , and has since been noticed by Meek and Worthen in another American genus, Lepidesthes , and by Mr. Young in the scattered plates of Archæocidaris from our own Carboniferous rocks. This character I have also detected in other genera of the same group of Perischoechinidæ from Co. Wexford, Ireland. It is worthy of note that whereas in the more modern (Cretaceous and Recent) group of flexible Echini (Echinothuridæ) the interambulacral plates imbricate from above downwards, and the ambulacral from below upwards, in these Palæozoic forms (Perischoechinidæ) the opposite arrangement obtains. 1. Perischodomus. Pl. III. figs.1–5. Since the first notice of the genus Perischodomus by Prof. McCoy, in the ‘Annals of Natural History,’ vol. iii (1894) p. 251, this specimen, which is one of McCoy's two types, seems to have been lost sight of by palæntologists; for we find Mr. Etheridge, Jun., observing † that “very little is known regarding this genus,” and Meek and Worthen say ‡ “only a single very imperfect specimen of it has, we believe, yet been found.” McCoy's diagnosis of this genus is:—“Spheroidal, depressed, subpentagonal; ambulacra narrow, of two rows of small