The "annelid" theory of the origin of the Crustacea and therefore of the trilobites, originating with Hatschek (1877) and so ably championed by Bernard (1892), has now been a fundamental working hypothesis for some years, and has had a profound influence in shaping thought about trilobites. This hypothesis has, however, its weak points, the principal one being its total inhibition of the workings of that great talisman of the palæontologist, the law of recapitulation. Its acceptance has forced the zoologist to look upon the nauplius as a specially adapted larva, and has caused more than one forced explanation of the protaspis of the trilobite. When so keen a student as Calman says that the nauplius must point in some way to the ancestor of the Crustacea (1909, p. 26), it is time to reëxamine some of the fundamentals. This has been done in the preceding pages and evidence adduced to show that the primitive features of a trilobite indicate a swimming animal, and that the adaptations are those which enabled it to assume a crawling mode of existence. It has also been pointed out that in Naraoia there is preserved down to Middle Cambrian times an animal like that to which ontogeny points as a possible ancestor of the trilobites. _Naraoia_ is not the simplest conceivable animal of its own type, however, for it has built up a pygidium of fourteen or fifteen somites. One would expect to find in Proterozoic sediments remains of similar animals with pygidia composed of only one or two somites, with five pairs of appendages on the cephalon, one or two pairs on the pygidium, a ventral mouth, and a short hypostoma. Anything simpler than this could not, in my opinion, be classed as a trilobite. What the ancestor of this animal was is mere surmise. It probably had no test, and it may be noted in this connection that _Naraoia_ had a very thin shell, as shown by its state of preservation, and was in that respect intermediate between the trilobite and the theoretical ancestor. Every analysis of the cephalon of the trilobite shows that it is made up of several segments, certainly five, probably six, possibly seven. Every study of the trilobite, whether of adult, young, or protaspis, indicates the primitiveness of the lateral extensions or pleural lobes. The same studies indicate as clearly the location of the vital organs along the median lobe. These suggestions all point to a soft-bodied, depressed animal composed of few segments, probably with simple marginal eyes, a mouth beneath the anterior margin, tactile organs at one or both ends, with an oval shape, and a straight narrow gut running from anterior mouth to terminal anus. The broad flat shape gives great buoyancy and is frequently developed in the plankton. Inherited by the trilobites, it proved of great use to the swimmers among them.