Perianth[3] funnel-shaped, with oblanceolate[4] segments, falcate[5] only at the apex. Leaves heart-shaped, ovate, and stalked, 1. _Cordifolium._ 2. _Giganteum._ SECTION II.—_Eulirion._ Perianth same as _Cardiocrinum_. Leaves linear or lanceolate, not stalked. (_a_) Tube scarcely widened from base to middle. 3. _Philippinense._ 4. _Wallichianum._ 5. _Longiflorum._ 6. _Neilgherrense._ (_b_) Tube widened from neck to base, (α) Leaves scattered. 7. _Japonicum Odorum._ 8. _Brownii._ 9. _Krameri._ 10. _Nepaulense._ 11. _Candidum._ 12. _Belladonna._ (β) Leaves in whorls. 13. _Washingtonianum._ 14. _Parryi._ SECTION III.—_Archelirion._ Perianth open and funnel-shaped. Segments deeply spreading and broadest about the middle. Stamens diverging from the style, which is curved. (_a_) Leaves sessile. 15. _Tigrinum._ 16. _Oxypetalum._ (_b_) Leaves stalked. 17. _Speciosum._ 18. _Auratum._ SECTION IV.—_Isolirion._ Perianth erect. Segments falcate, but not revolute. Stamens diverging on all sides. (_a_) Leaves in whorls. 19. _Philadelphicum._ 20. _Medeoloides._ (_b_) Leaves scattered, (α) Style shorter than ovary. 21. _Concolor._ (β) Style longer than ovary. 22. _Bulbiferum._ 23. _Croceum._ 24. _Davuricum._ 25. _Elegans._ 26. _Catesbaei._ SECTION V.—_Martagons._ Perianth cernuous with the segments very revolute. Stamens diverging on all sides. (_a_) Leaves in whorls. (α) American species; bulbs annual bearing rhizomes. 27. _Canadense._ 28. _Pardalinum._ 29. _Superbum._ 30. _Lucidum._ 31. _Roezlii._ 32. _Columbianum._ 33. _Humboldti._ (β) Old world species. 34. _Martagon._ 35. _Avenaceum._ 36. _Hansoni._ (_b_) Leaves scattered, (α) Leaves lanceolate. Many-nerved. (i.) Perianth falcate above middle. 37. _Monadelphum._ (ii.) Perianth revolute to below middle. 38. _Polyphyllum._ 39. _Ponticum._ 40. _Carniolicum._ (β) Leaves narrow. With one or few nerves. (i.) Segments of the perianth from six to twelve lines broad in the middle. 41. _Testaceum._ 42. _Leichtlini._ 43. _Batmanniae._ 44. _Pseudo-Tigrinum._ 45. _Wallacei._ (ii.) Segments of the perianth from three to six lines broad in the middle. 46. _Pomponium._ 47. _Chalcedonicum._ 48. _Callosum._ 49. _Tenuifolium._ SECTION VI.—_Notholirion._ 50. _Hookeri._ 51. _Roseum._ We said that in all divisions of natural objects there were “aberrant” types which refused to be located in any one group and remained sitting on the wall between several of the divisions. And in this group there are likewise some which stick upon the wall. The chief reasons we have for not using this classification will be apparent from the following criticism of it. The first section, _Cardiocrinum_, forms a very natural group. _L. Cordifolium_ and _L. Giganteum_, though distinct species, are yet very near akin and are totally different from any other lilies.