On 17th December 1868 I presented to the Society a large Cephalopod which, judging from its external characteristics, which were very imperfect, and not having the advantage of comparing it with other specimens, I named Orthoceras fusiforme. The specimen is very much defaced and crushed. Dr Page, on seeing it, said he thought it was an Ascoceras, and very like those he had seen in certain museums in the West of Scotland. It was accordingly named by the Society Ascoceras, and was supposed to have come from one of the carboniferous limestones of the west, probably Lanarkshire. An abstract of my paper appeared in the ‶Geological Magazine,″ which attracted the attention of M. Barrande of Prague, the distinguished author of the ‶Systeme Silurien de Boheme,″ and on the 17th of March I received a communication from that gentleman requesting me to send him a sketch of this interesting fossil with any observations I might make upon it. He remarked, that the re-appearance of a class, after so long an intermittance in time, interested him very much, because, he continued to say, ‶I have recently drawn the attention of the scientific world to this subject in a small brochure which I now send you on the re-appearance of the class Arethusina (Trilobite). In the case of your Ascoceras the long interval of this class is still greater than that of the Arethusina, of which an account is given in my memoir.″ Accordingly, after receiving this letter, I put myself in communication