The "pygidial antennæ" seem to be as fully developed in _Neolenus_ as in any of the other arthropods, and may suggest a common ancestry of the phyllopods, isopods, and hexapods, in the trilobites. They were doubtless tactile organs, and while the evidence is chiefly negative, it would seem that they proved useless, and were lost early in the phylogeny of this group. Possibly the use of the pygidium as a swimming organ proved destructive to them. HOMOLOGY OF THE CEPHALIC APPENDAGES WITH THOSE OF OTHER CRUSTACEA. The head of the typical crustacean bears five pairs of appendages, namely, the antennules, antennas, mandibles, and first and second maxillæ, or, as they are more properly called, the maxillulæ and maxillæ. As Beecher has pointed out, the "antennæ" of the trilobites, on account of their pre-oral position and invariably uniramous character, are quite certainly to be correlated with the antennules. The second pair of appendages, the first pair of biramous ones, Beecher homologized with the antennæ of other crustaceans, and that homology has been generally accepted, though Kingsley (1897) suggested that it was possible that no representatives of the true antennæ were present. In preparing the restorations in the present study, the greatest difficulty has been to adjust the organs about the mouth. In _Triarthrus_, numerous specimens show that without question there are four pairs of gnathites back of the hypostoma, and that all four belong to the cephalon. In forms with a long hypostoma, however, there was no room on the cephalon for the attachment of four pairs of gnathites, neither were there enough appendifers to supply the requisite fulcra. At first I supposed I had solved the difficulty by assuming the mouth to be in front of the posterior tip of the hypostoma, as it really is in Ceraurus and _Calymene_, and allowing the gnathites to play under the hypostoma as Walcott (1912) has shown that they do in _Marrella_. Finally, when I came to study in greater detail the slices of _Calymene_ and _Ceraurus_, they seemed to show that the anterior one or two pairs of appendages became degenerate and under-developed. This was probably a specialization due to the great development of the hypostoma in trilobites, that organ being much more prominent in this than in any other group. As the hypostoma lengthened to accommodate the increasing size of sub-glabellar organs (stomach, heart, etc.), the mouth migrated backward, leaving the anterior appendages ahead of it, with their gnathobases, at least, functionless. That such migration has taken place, even in Triarthrus, is shown by the fact that the points of articulation of the first biramous appendages are pre-oral, and it is more obviously true of _Ceraurus_. Correlated with the weakening of the appendages on the lower surface is the loss of glabellar furrows on the upper surface. The glabellar furrows mark lines of infolding of the test to form the