[++][++] Receptacle flat or convex. Pappus usually with awns. 21. Chætopappa. Achenes fusiform; pappus of 5 or fewer thin chaff and alternating awns. Western. 22. Boltonia. Achenes very flat, thick-winged; pappus of short bristles and usually 2--4 awns. [+][+] Pappus of a single row of awns or coarse rigid bristles, or in the ray scale-like. 23. Townsendia. Low or stemless, with linear-spatulate leaves and large aster-like flowers. [+][+][+] Pappus of numerous long and capillary bristles; receptacle flat. 24. Sericocarpus. Heads 12--20-flowered; rays 4 or 5. Involucre oblong or club-shaped, imbricated, cartilaginous. Achenes short, narrowed downward, silky. 25. Aster. Heads many-flowered, on leafy peduncles. Involucral scales unequal, loosely or closely imbricated. Achenes flattish; pappus simple (rarely double), copious. 26. Erigeron. Heads many-flowered, on naked peduncles. Involucre of narrow equal scales, little imbricated. Achenes flattened; pappus simple and rather scanty, or with some outer minute scales. [*] 3. Rays none. Heads diœcious (all pistillate or all staminate). 27. Baccharis. Heads many-flowered. Pappus capillary. Smooth glutinous shrubs. Tribe IV. INULOIDEÆ. Heads discoid (radiate only in Inula), the pistillate flowers mostly filiform and truncate. Anthers sagittate, the basal lobes attenuate into tails. Style-branches with unappendaged obtuse or truncate naked tips. Pappus capillary or none. [*] 1. Receptacle naked. Involucre not scarious, imbricated. Not woolly. 28. Pluchea. Heads containing a few perfect but sterile flowers in the centre, and many pistillate fertile ones around them. Pappus capillary. [*] 2. Receptacle chaffy. Involucral scales few, mostly scarious. Low floccose-woolly annuals; flowers as in n. 28. 29. Evax. Receptacle convex. Achenes obcompressed. Pappus none. Western. 30. Filago. Receptacle subulate. Achenes terete. Outer flowers without pappus. [*] 3. Receptacle naked. Involucral scales many, scarious. Floccose-woolly herbs. 31. Antennaria. Heads diœcious. Pappus of sterile flowers club-shaped, of the fertile united at base and deciduous together. 32. Anaphalis. Heads diœcious or nearly so. Pappus not thickened above nor at all united at base. 33. Gnaphalium. Heads all fertile throughout. Pappus all capillary. [*] 4. Corollas all somewhat broadly tubular and lobed. Involucre not scarious. Receptacle naked. Pappus none. 34. Adenocaulon. Head few-flowered and scales few; outer flowers pistillate. Somewhat woolly. [*] 5. Heads radiate. Receptacle naked. Involucre herbaceous. Pappus copious. 35. Inula. Heads large, many-flowered. Flowers yellow. Stout perennial. Tribe V. HELIANTHOIDEÆ. Heads radiate or discoid. Involucre not scarious (nut-like in fruit in n. 43, 44). Receptacle chaffy. Pappus never capillary, sometimes none. Anthers not caudate. Style-branches truncate or hairy-appendaged.