The Arthropoda, to make the simplest possible definition, are invertebrate animals with segmented body and appendages. The most primitive arthropod would appear to be one composed of exactly similar segments bearing exactly similar appendages, the segments of the appendages themselves all similar to one another. It is highly improbable that this most primitive arthropod imaginable will ever be found, but after a survey of the whole phylum, it appears that the simpler trilobites approximate it most closely. That the trilobites are primitive is evidenced by the facts that they have been placed at the bottom of the Crustacea by all authors and claimed as the ancestors of that group by some; that Lankester derived the Arachnida from them; and that Handlirsch has considered them the progenitors of the whole arthropodan phylum. Specializations among the Arthropoda, even among the free-living forms, are so numerous that it would be difficult to make a complete list of them. In discussing the principal groups, I have tried to show that the essential structures can be explained as inherited from the Trilobita, changed in form by explainable modifications, and that new structures, not' present in the Trilobita, are of such a nature that they might be acquired independently in even unrelated groups. The chief objections to the derivation of the remainder of the Crustacea from the trilobites have been: first, that the trilobites had broad pleural extensions; second, that they had a large pygidium; and lastly, that they had only one pair of tactile antennæ. It has now been pointed out that many modern Crustacea have pleural extensions, but that they usually bend down at the sides of the body, and also that in the trilobites and more especially in _Marrella_, there was a tendency toward the degeneration of the pleural lobes. A glance at the Mesonacidæ or Paradoxidæ should be convincing proof that in some trilobites the pygidium is reduced to a very small plate. In regard to the second antennæ standard text-books contain statements which are actually surprising. A compilation shows that the antennæ are entirely uniramous in but a very few suborders, chiefly among the Malacostraca; that they are biramous with both exopodite and endopodite well developed in most Copepoda, Ostracoda, and Branchiopoda; and that the exopodite, although reduced in size, still has a function in some suborders of the Malacostraca. The Crustacea could not possibly be derived from an ancestor with two pairs of uniramous antennæ.