The growth of the memoir to its present size has been a gradual one. As first completed in 1917, it contained an account of the appendages only. Thoughts upon the probable use of the appendages led to the discussion of possible habits, and that in turn to a consideration of all that is known or could be inferred of the structure and anatomy of the trilobite. Then followed an inquiry into the relationships to other Arthropoda, which ultimately upset firmly established preconceptions of the isolated position of the group, and led to a modification of Bernard's view of its ancestry. During the progress of the work, I have had the opportunity of examining most of the known specimens retaining appendages. From the Marsh collection in the Yale University Museum were selected the forty-six specimens showing best the appendages of _Triarthrus_, _Cryptolithus_, and _Acidaspis_. Dr. Charles D. Walcott very kindly returned to the Museum of Comparative Zoology the slices of _Ceraurus_, _Calymene_, and _Isotelus_ which were the basis of his paper of 1881, and which had been loaned him for further study. He loaned also eight of the more important specimens of _Neolenus serratus_, and two of _Triarthrus becki_. At the United States National Museum I saw the specimens of _Isotelus_ described by Mickleborough and the isolated limbs of _Calymene_ from near Cincinnati. The _Isotelus_ at Ottawa I had already studied with some care while an officer of the Geological Survey of Canada. This memoir consists, as shown in the table of contents, of four parts. The appendages of _Neolenus_, _Isotelus_, _Ptychoparia_, _Kootenia_, _Ceraurus_, _Calymene_, and _Acidaspis_ are discussed, as fully as circumstances warrant, in the first part, and new restorations of the ventral surfaces of _Neolenus_, _Isotelus_, _Triarthrus_, _Ceraurus_ and _Cryptolithus_ are included It is not supposed that these restorations will be of permanent value in all of their detail, but they are put forward as the best approximations to the real structure that the writer is able to present from the materials so far discovered. I am greatly indebted to Doctor Elvira Wood for the care and skill with which she has worked up these restorations from my rather sketchy suggestions. She has put into them not only a great amount of patient work, but also the results of considerable study of the specimens.