The simplest trilobite 138 _Naraoia compacta_ Walcott 139 The ancestor of the trilobites, and the descent of the Arthropoda 140 Evolution within the Crustacea 142 Summary 144 Evolution of the Merostomata 146 Evolution of the "Tracheata" 147 Summary on lines of descent 147 Final summary 151 Part IV. Description of the appendages of individual specimens 152 _Triarthrus becki_ Green 152 _Cryptolithus tessellatus_ Green 158 Bibliography 163 LIST OF ILLUSTRATIONS. 1. _Triarthrus becki_ Green. Diagram of limb to show nomenclature employed 20 2. _Neolenus serratus_ (Rominger). Two thoracic appendages 24 3. The same. An exopodite 26 4. The same. A so-called "epipodite" 26 5. The same. The so-called "exites" 29 6. The same. A cephalic limb 29 7. The same. Restoration of a transverse section 30 8. The same. Restoration of the ventral surface 31 9. _Isotelus_. Restoration of the ventral surface 38 10. _Triarthrus becki_ Green. Restoration of the ventral surface 41 11. The same. Median appendage 44 12. _Ceraurus pleurexanthemus_ Green. Slice showing an exopodite 49 13. _Calymene senaria_ Conrad. Slice showing cephalic coxopodites 53 14. The same. Another similar slice 53 15. The same. Slice showing method of articulation of the appendages 53 16. The same. Restoration of the ventral surface 55 17. _Ceraurus pleurexanthemus_ Green. Slice showing the method of articulation of the appendages 58 18. The same. Slice showing an exopodite above an endopodite 58 19. The same. Restoration of a transverse section 60 20. _Cryptolithus tessellatus_ Green. Restoration of the ventral surface 63 21. _Ceraurus pleurexanthemus_ Green. Slice showing the abdominal sheath 79 22. The same. Slice showing the large alimentary canal 79 23. _Calymene senaria_ Green. Slice showing the large alimentary canal 79