The appendages of _Neolenus_ 21 Historical 21 _Neolenus serratus_ (Rominger) 21 Cephalon 21 Thorax 22 Pygidium 23 Epipodites and exites 23 Description of individual specimens 23 Restoration of _Neolenus_ 30 _Nathorstia transitans_ Walcott 31 The appendages of _Isotelus_ 32 Historical 32 _Isotelus latus_ Raymond 34 _Isotelus maximus_ Locke 35 Restoration of _Isotelus_ 37 _Isotelus gigas_ Dekay 37 _Isotelus arenicola_ Raymond 39 The appendages of _Triarthrus_ (see also Part IV) 39 _Triarthrus becki_ Green 39 Historical 40 Restoration of _Triarthrus_ 42 Relation of cephalic appendages to marking on dorsal surface of glabella 43 Anal plate 44 The appendages of _Ptychoparia_ 45 _Ptychoparia striata_ (Emmrich) 45 _Ptychoparia cordilleræ_ (Rominger) 45 _Ptychoparia permulta_ Walcott 45 The appendages of _Kootenia_ 46 _Kootenia dawsoni_ Walcott 46 The appendages of _Calymene_ and _Ceraurus_ 46 Historical 46 Comparison of the appendages of _Calymene_ and _Ceraurus_ with those of _Triarthrus_ 47 Spiral branchiæ 48 Ventral membrane 50 Appendifers 51 _Calymene senaria_ Conrad 52 Cephalic appendages 52 Thoracic appendages 53 Pygidial appendages 54 Relation of hypostoma to cephalon in _Calymene_ 55 Restoration of _Calymene_ 56 _Calymene_ sp. ind. 56