For the convenience of students the Catalogue is made in parts. The Syndics of the University Press printed last autumn as an example of the "Indexes to the Museum," an Index to the Pterodactyles, Birds, and Reptiles from the Secondary Strata. And this memoir is an example of the second kind of Catalogue, which explains the structures of the Pterodactyles of the Cambridge Greensand. In its progress questions have arisen which necessitated an examination both of the method, of research in comparative anatomy and of its results in classification. And in so far as the views here advanced differ from those commonly taught, the discrepancy is due to the writer's imperfect faith in the results of the inductive method of research, as commonly used by modern writers on Palæontology. It has not been consistent with the plan of this little work to do more than scatter through it a few hints upon method, a subject which will more fitly be discussed with a part of the Catalogue which forms a synopsis of the osteology of the fossil animals usually named Reptiles. The views here urged have however but little of novelty. The name Ornithosauria was proposed by the distinguished naturalist Prince Charles Bonaparte in 1838. The group as an order was recognized by Von Meyer in 1830. The affinities of the brain appear to have been detected by Oken, and the bird-like character of the respiratory system was expounded by Von Meyer. And most of whatever this memoir contains has been already thought or discovered by the German philosophers, who have had the Pterodactyles as fossils of their fatherland, though my own conclusions were arrived at separately and from different materials.