Part II is a discussion of the internal anatomy of the trilobite and a brief statement of some of the possible habits and methods of life of these animals. Part III, which begins with a survey of the relationships of the trilobites to other Arthropoda, is largely taken up with an attempt to demonstrate the primitive characteristics of the former, and their probable ancestral position. The form of the ancestor of the trilobite is deduced from a study of the morphology, ontogeny, and phylogeny of the group, and evidence adduced to indicate that it was a depressed, flattened, free-swimming animal of few segments. In Part IV are included somewhat detailed descriptions of a few of the best specimens of _Triarthrus_ and _Cryptolithus_. Professor Beecher, while an observer of the minutest details, believed in publishing only the broader, more general results of his investigations. This method made his papers brief, readable, and striking, but it also resulted in leaving in some minds a certain amount of doubt about the correctness of the observations. In a matter so important as this, it has seemed that palæontologists are entitled to the fullest possible knowledge of the specimens on which the conclusions are based. The last part is, therefore, a record of the data for the restorations of _Triarthrus_ and _Cryptolithus_. The illustrations in the plates were nearly all made by or under the supervision of Professor Beecher, as were also text figures 45 and 46. In conclusion, I wish to express my thanks to Mrs. Charles E. Beecher for the use of drawings which were the personal property of Professor Beecher; to Doctor Charles D. Walcott for photographs of the limbs of _Calymene_, and for his kindness in sending me the slices of trilobites from Trenton Falls and specimens of _Neolenus_ and _Triarthrus_; to Doctor R. V. Chamberlin for suggestions and criticisms in regard to the relationship of trilobites to Insecta, Arachnida, Chilopoda, and Diplopoda; to Mr. Samuel Henshaw, Director of the Museum of Comparative Zoology, for permission to use the time which has been devoted to this work; and to Miss Clara M. Le Vene, for assistance in the preparation of the manuscript. My greatest debt is to Professor Charles Schuchert, to whom the work owed its inception, who has assisted in many ways during its prosecution, and who read the manuscript, and arranged for its publication. To him I can only express my warmest thanks for the favors which I have received and for the efforts which he has put forth to make this a worthy memorial to our friend and my teacher, Professor Charles Emerson Beecher. Harvard University, Cambridge, Mass. November, 1919. TABLE OF CONTENTS. Historical review 17 Part I. The appendages of trilobites 20 Terminology 20