53. Verbesina. Involucral scales closely imbricated in 2 or more rows. 54. Actinomeris. Scales few, soon deflexed. Achenes obovate, squarrosely spreading. [*] 4. Rays few, neutral, or wanting. Achenes obcompressed, i.e., flattened parallel with the scales of the involucre (rarely terete). Involucre double; the outer spreading and often foliaceous. Receptacle flat. Leaves opposite. 55. Coreopsis. Pappus of 2 (or rarely more) scales, teeth, or awns, which are naked or barbed upward, sometimes obsolete or a mere crown. 56. Bidens. Pappus of 2 or more rigid and persistent downwardly barbed awns or teeth. 57. Thelesperma. Inner involucre connate to the middle. Achenes terete. Awns retrorsely bearded. [*] 5. Heads radiate or discoid; disk-flowers all perfect and fertile. Achenes turbinate, 5-angled; pappus of several chaffy scales. [+] Leaves alternate, entire. Disk-flowers purplish. 58. Baldwinia. Rays numerous, long, neutral. Involucre much imbricated. Receptacle deeply honey-combed. 59. Marshallia. Rays none. Involucre of narrow leafy equal scales. Receptacle chaffy. [+][+] Leaves opposite, serrate. Disk-flowers yellow. 60. Galinsoga. Rays few, short, pistillate, whitish. Involucre of 4--5 thin ovate scales. Receptacle chaffy. Tribe VI. HELENIOIDEÆ. Nearly as Tribe V., but receptacle not chaffy (somewhat so in n. 64). In our genera, the disk-flowers perfect and fertile; the pappus a row of several chaffy scales (bristly-dissected in n. 65); the involucre hardly at all imbricated (partly scarious in n. 61). [*] Involucral scales distinct, not glandular-punctate. 61. Hymenopappus. Rays none. Receptacle flat. Involucre colored. Western. 62. Actinella. Rays fertile, 3-toothed. Receptacle elevated. Involucre appressed. Western. 63. Helenium. Rays fertile or sterile, 3--5-cleft. Receptacle elevated. Involucre small, reflexed. Leaves decurrent. 64. Gaillardia. Ray 3-toothed, or none. Receptacle usually beset with fine fimbrillate chaff. Outer involucral scales loose and leafy. Pappus-chaff tipped with the projecting midvein. Western. [*][*] Dotted with oil-glands. Involucral scales united into a cup. 65. Dysodia. Pappus a row of chaffy scales dissected into many bristles. Tribe VII. ANTHEMIDEÆ. Distinguished from the last two tribes by the more or less dry and scarious imbricated scales of the involucre. Heads radiate (ray mostly white) or discoid, the perfect flowers sometimes sterile and the pistillate rarely tubular. Achenes small; pappus a short crown or none.--Mostly strong-scented; leaves alternate. [*] Receptacle chaffy, at least in part. Heads radiate, many-flowered. 66. Anthemis. Achenes terete, angled or ribbed. Heads hemispherical, rather large. 67. Achillea. Achenes obcompressed. Heads small, campanulate or obovate. [*][*] Receptacle naked. [+] Heads rather large, pedunculate, radiate or rarely rayless. 68. Matricaria. Receptacle conical. Rays pistillate or none. Pappus crown-like or none.