The beginning of the search for the limbs of trilobites was coeval with the beginning of scientific study of the group, knowledge of the appendages being essential to the proper systematic allocation of the animals. The early search was so barren of results that negative evidence came to be accepted as of positive value, and it was for many years generally believed that such organs as may have been present beneath the dorsal test were so soft as to be incapable of preservation. This view is best expressed by Burmeister (1846, p. 43): There is good proof that the feet of trilobites must have been soft membranous organs, for the absence of the slightest remains of these organs in the numerous specimens observed is of itself evidence of the fact, and it can indeed scarcely be supposed that hard horny extremities should be affixed to a soft membranous abdominal surface; since they would not have possessed that firm basis, which all solid organs of locomotion require, in order that they may be properly available. Very well reasoned, and were it not for the discovery of new material in American localities, Burmeister's views would probably never have been proved incorrect. One can not escape the suspicion that some of the accepted hypotheses of today, founded on similar "proof," may yield in time to the weight of bits of positive evidence. The history of the study of appendages of trilobites may be divided into two periods. The first, in which there was a general belief that the appendages were soft organs, but during which numerous "finds" of limbs were reported, extended from the time of Linné to the year (1876) in which Walcott demonstrated the fact that the animals possessed jointed ambulatory and breathing organs. The second, much more fruitful period, began with Walcott's publication of 1881, descriptive of the appendages of _Ceraurus_ and _Calymene_, and for the purposes of this memoir, closes with his great contribution on the anatomy of _Neolenus_ (1918). Beecher's brilliant productions came in the middle of the second period. In the first period, there were at least two authentic discoveries of appendages, those of Eichwald (1825) and Billings (1870), but since neither of these men convinced his confreres of the value of his finds, the work of neither can be considered as having marked an especial epoch in the history. As all the authentic finds will be treated in detail on later pages, only a brief résumé of the first period will be given here. This has already been done by Burmeister (1843, 1846) and Barrande (1852, 1872), whose works have been my primary sources of information, but I have looked up the original papers, copies of nearly all of which are to be seen in the libraries in Cambridge and Boston. Brig.-Gen. A. W. Vogdes, U. S. A. (retired), has very kindly placed at my disposal a number of references and notes.