Since the remarkable paper by Professor Lapworth “On an Improved Classification of the Rhabdophora” was published in the Geological Magazine for 1873, a great deal of fresh information has been gathered as to these interesting fossils; but the classification given in that paper, though to some extent confessedly artificial, is still generally adhered to. Observations made by the authors in recent years lead them to suppose that that classification will in the future undergo considerable modification; but in the present state of our knowledge it serves a purpose so useful, that it is not our intention to propose any immediate change in it. Our object, on the other hand, is to bring forward certain conclusions which we have independently reached, and which will, we believe, enhance the value of Graptolites to the stratigraphical geologist, and lead to results important to the biologist. Our conclusions are based upon an examination of a large number of forms generally referred to the family Dichograptidæ; but, as we propose very briefly to indicate, they affect the relationships of Graptolites belonging to other families also.