It is of the first importance in Natural History to adopt a precise, and if possible a received terminology, and strictly to adhere to it. From the very different opinions that have been entertained regarding the nature of graptolites, a curiously mixed set of terms have been employed on their description, some being suggested by their supposed resemblance to plants, others being obtained from their affinities to animals. Discarding these I shall employ the terminology proposed by Allmann and Huxley for the Hydrozoa now generally adopted, asking the reader to take here for granted what I hope presently to establish, that these fossils have their nearest allies in this class, and consequently that the terminology is suited equally to both. As the terms, however, have not yet been generally introduced into text books, it is perhaps desirable to give definitions of those that I shall have to use in this paper.