5. Eupatorium. Involucre of more than 4 scales and the flowers few or many. Stems not twining. [+][+] Achene 10-ribbed; involucral scales striate-nerved. 6. Kuhnia. Pappus very strongly plumose. Scales of the involucre few. 7. Brickellia. Involucral scales in several series. Pappus merely scabrous. 8. Liatris. Pappus plumose or only barbellate. Corolla red-purple, strongly 5-lobed. Heads spicate or racemose, the involucre well imbricated. 9. Trilisa. Pappus minutely barbellate. Corolla rose-purple. Heads corymbed or panicled, the involucre little imbricated. Tribe III. ASTEROIDEÆ. Heads discoid, the flowers all alike and tubular; or else radiate, the outer ones ligulate and pistillate. Anthers not caudate at base. Branches of the style in the perfect flowers flat, smooth up to where the conspicuous marginal stigmatic lines abruptly terminate, and prolonged above this into a flattened lance-shaped or triangular appendage which is evenly hairy or pubescent outside.--Leaves alternate. Receptacle naked (destitute of chaff) in all our species. [*] 1. Ray-flowers yellow (in one species of Solidago whitish), or sometimes none at all. [+] Pappus of not numerous slender bristles. Heads radiate. Involucre of firm scales with greenish tips, commonly coated with resin. West of the Mississippi. 10. Gutierrezia. Heads small, numerous. Ray and disk-flowers 3 or 4 each, all fertile. Pappus of several short chaffy scales. Suffrutescent; leaves very narrow. 11. Amphiachyris. Heads small. Ray-flowers 5--10; pappus coroniform. Disk-flowers infertile; pappus of several bristle-like scales. Annual; leaves very narrow. 12. Grindelia. Heads large, many-flowered. Flowers all fertile. Pappus of 2--8 rigid caducous awns. Coarse herbs with toothed leaves. [+][+] Pappus (at least of the disk) of copious slender or capillary bristles. [=] Pappus double. 13. Heterotheca. Resembling Chrysopsis, but the achenes of the ray thicker than those of the disk and without pappus or nearly so. Western. 14. Chrysopsis. Heads many-flowered; rays numerous. The outer pappus of very small chaffy bristles, much shorter than the inner of copious capillary bristles. [=][=] Pappus simple. 15. Aplopappus. Heads many-flowered, many-radiate. Involucre hemispherical. Pappus of many unequal bristles. Western. 16. Bigelovia. Heads 3--4-flowered; rays none. Receptacle awl-shaped. Pappus a single row of capillary bristles. 17. Solidago. Heads few--many-flowered; rays 1--16. Pappus of numerous slender and equal capillary bristles. 18. Brachychæta. Heads 8--10-flowered, clustered; rays 4 or 5. Pappus a row of minute bristles shorter than the achene. [*] 2. Ray-flowers white, blue, or purple, never yellow. [+] Pappus none or very short, with or without a few awns. [++] Receptacle conical. Awns none. 19. Bellis. Achenes marginless, flattened; pappus none. Involucral scales equal. 20. Aphanostephus. Achenes prismatic; pappus coroniform. Outer scales shorter.