334 ! COMPOSIT 
43 Helianthus Achenes thick, quadrangular-compressed or with the 
sides convex and the angles obtuse: pappus a pair of caducous chaffy 
scales or awns. 
SUBTRIBE Iv, BIDENTIAEZ Heads radiate, the rays neutral or 
pistillate. Receptacle chaffy with flat or barely concave decidu- 
ous chaff. Achenes all obcompressed Pappus of 2-4 teeth or 
awns from the angles, or none. ; 
44 Coreopsis Achenes never rostrate-attenuate nor with retrorsely barb- 
ed awns. 
45 Bidens Achenes neither winged nor beaked, 2-5-awned with retrorse- 
ly barbed persistent awns. 
SuBTRIBE y, GALINSOGEZ Heads heterogamous with the ray- 
flowers. when present, fertile; disk-flowers either perfect and 
fertile or sterile. Achenes neither compressed nor obeompressed. 
Pappus in both ray- and disk-flowers few to numerous chaffy 
scales. | 
46 Blepharipappus Heads radiate; the rays pistillate: pappus of 12-20 
thin scales with a stout midrib. 
SuBTRIBE v1, Maprrm Heads heterogamous; ray-flowers, when 
present, fertile; disk-flowers either perfect and fertile, or sterile. 
Involucre a series of bracts, each subtending and more or less en- 
closing a ray-achene. Receptacle chaffy only at the margin, the 
chaff forming a sort.of inner involucre or else subtending some or 
all of the disk flowers 
* Achenes all laterally compressed ; those ef the ray wholly enclosed 
in the carinate strongly infolded bracts of the involucre. 
47 Anisocarpus Rays conspicuous and mostly numerous, fertile; disk- 
flowers numerous, sterile or tne exterior ones fertile; with pubescent 
corolla and a pappus composed of fimbriate or plumose-lacerate scales, 
48 Madaria Rays numerous and conspicuons: disk-flowers without pap- 
pus, either ail or only the central ones sterile. ; 
49 Madia Rays 1-12 or none, short and more or less inconspicuous: disk- 
flowers numerous or few, all fertile, destitute of pappus. 
50 Harpeearpus pay 4-8, very short and inconspicuous; disk-flower 
solitary, fertile, enclosed in a 3-5-toothed herbaeeous cup: pappus none. 
* * Achenes of the ray-flowers turgid. more or less oblique or incury- 
ed, never laterally compressed but mostly somewhat obcompressed : 
bracts of the involucre each investing an achene, rounded on the back. 
51 Hemizonella Involucre stronglg 4-5-sulcate by the complete enwrap- 
ing of the 4 or 5 achenes: disk-flower solitary in a sort of inner inyo- 
lucre: pappus none. 
52 Hemizonia Achenes of the ray-flowers obovate-triangular, with de- 
pressed terminal areola; disk flowers numerous, with abortive achenes : 
pappus none. . . 
53 Calyeadenia Achenes of the ray-flowers obovoid, the terminal areola 
little if at all oblique, triangular; of the numerous disk-flowers well 
formed, and sometimes truly fertile. surrounded by a cirele of herba- 
ceou bracts; pay pus of conspicuous chaffy scales. 
