_Paired biramous appendages._--Behind the antennules all the appendages except those on the anal segment are biramous, consisting of a coxopodite with an inward-directed endobase and an outward-directed pair of branches, the exopodite above, and the six-jointed endopodite beneath. The basipodite really bears the exopodite, but the latter also touches the coxopodite. This structure has been seen in _Triarthrus_, _Cryptolithus_, _Neolenus_, _Kootenia_, _Calymene_, _Ceraurus_, and _Ptychoparia_. In _Triarthrus_, _Neolenus_, _Acidaspis_, _Ptyclioparia_, and Kootenia, the appendages extend beyond the margins of the dorsal test. In _Cryptolithus_ and _Isotelus_ none (other than antennules) does so. In _Isotelus_ and _Acidaspis_ only the endopodites have been seen. In _Triarthrus_, _Calymene_, _Ceraurus_, and _Neolenus_ there are four pairs of appendages behind the antennules. The other genera probably had the same number, but the full structure of the under part of their cephala is not known. In _Triarthrus_ the endopodites of the cephalon are slender, the individual segments parallel-sided, the inner ones flattened, the outer ones cylindrical in section. They project slightly beyond the edge of the cephalon when fully extended, and each terminates in three small spines. In _Cryptolithus_ the endopodites of the cephalon are longer than those of the thorax, but with the possible exception of the first pair, are bent backward at the carpopodite, and do not ordinarily project beyond the brim of the test. In _Neolenus_ the endopodites of the cephalon are rather thick and wide, but are long, project forward, and extend beyond the brim. The individual segments are flattened, probably compressed oval in section. The terminal segment of each is furnished with three strong spines at its distal end. In _Calymene_ and _Ceraurus_ the endopodites appear to consist of slender segments which are oval or circular in section. In _Calymene_ Walcott believed the three distal segments of the last endopodites of the head to be greatly enlarged, giving these appendages a paddle-like form similar to some of the appendages of eurypterids. The evidence for this does not seem to me to be good. The cephalic endopodites of _Isotelus_ are entirely similar to those of the thorax, and are rather short, consisting of a series of short cylindrical segments which do not taper greatly toward the distal end. The endopodites of the cephalon of _Acidaspis_, _Kootenia_, and _Ptychoparia_ are still unknown. The exopodites of the cephalon seem in all known cases (_Triarthrus_, _Cryptolithus_, _Neolenus_, and Ceraurus) to be like those of the thorax. They point more directly forward in most cases, project beyond the margin of the head normally only in Triarthrus, and usually occupy the region under the cheeks (fixed and free).