Bernard, who believed that the Crustacea had been derived through an Apus-like ancestor (1892, pp. 20, 85, 274), pointed out that four or less than four anal cirri were to be expected. Two well developed cirri and two rudimentary ones are present in Apus, and they are also to be found in other phyllopods and some isopods. It is, however, characteristic of the Crustacea as a whole to lack appendages on the anal segment. Caudal cirri (cerci) are much more freely developed in the hexapods than in the Crustacea, particularly in the more primitive orders, Palæodictyoptera, Apterygota, Archiptera, and Neuroptera. They are supposed, in this case, to be modified limbs, and therefore not homologous with the bristles on the anal segment of an annelid. Doctor W. M. Wheeler of the Bussey Institution has kindly allowed me to quote the following excerpt from a letter to me, as expressing the opinion of one who has made an extensive study of the embryology of insects:

I would say that I have no doubt that the cerci of insects are directly inherited from the insect ancestors. They are always highly developed in the lower insects, and only absent or vestigial in a few of the most highly specialized orders such as the Hemiptera, Diptera, and Hymenoptera. I have further no doubt concerning their being originally ambulatory in function. They are certainly not developed independently in insects. Embryologically they arise precisely like the legs, and each cercus contains a diverticulum of the mesoblastic somite precisely as is the case with the ambulatory legs and mouth parts.

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 appendifers and other rugosities for the attachment of tendons and muscles. It is conceivable that this migration backward of the mouth began very early in the history of the race, and that even before Cambrian times, the antennæ, probably originally biramous appendages like those on the remainder of the body, had dwindled away and become lost. If this is the case, then the first pair of biramous appendages of Triarthrus would be mandibles, the second pair maxillulæ, and the third pair maxillæ.

There remain the last pair of cephalic appendages, and they bring up the whole head problem of the trilobites. Beecher has stated (1897 A, p. 96) his conviction that the head of the trilobite is made up of five segments, representing the third, fourth, fifth, sixth, and seventh neuromeres of the theoretical crustacean. As a matter of fact, he really made up the head of seven segments, since he stated that the first neuromere was represented by the hypostoma and the second by the epistoma and free cheeks.