This section is from the book "An Illustrated Flora Of The Northern United States, Canada And The British Possessions Vol1", by Nathaniel Lord Britton, Addison Brown. Also available from Amazon: An Illustrated Flora of the Northern United States, Canada and the British Possessions. 3 Volume Set..
Annual, bright green or somewhat yellowish-tinged, similar to P. ramosissimum in habit, but smaller, stem rather sparingly branched, usually 2°-4° tall. Leaves mostly oblong or elliptic or slightly broadened upward, 4"-14" long, acute, rather persistent; ocreae becoming very much lacerate; flowers sparingly clustered, short-pedicelled; sepals mostly 5, yellowish-margined, 1/2"-3/4" long; stamens mostly 5; achene 3-angled, acute, about 1" long, broadly ovoid.
Polygonum tenue Michx. Fl. Bor. Am. 1: 238. 1803.
Annual, glabrous, somewhat rough about the nodes, stem very slender or filiform, erect, simple or branched, somewhat 4-angled, 4'-12' tall. Leaves linear or linear-lanceolate, sessile, acuminate at the apex, 2"-12" long, articulated to the ocreae, 1-ribbed with a lateral impression on each side of the rib, the margins minutely scabrous or serrulate; ocreae fun-nelform, soon lacerate; flowers several in the axillary clusters, green, subsessile; sepals whitish; stamens 8; fruit erect; achene 3-angled, black, 1"-1 1/2" long, reticulated on the angles, the centre of its faces smooth.
Dry soil, Ontario to Minnesota, Nebraska, Georgia and Arkansas. July-Sept.
Annual, similar to the preceding species, glabrous, somewhat rough at the nodes, sometimes slightly glaucous, stem erect, 8'-18' tall, simple or usually much branched, almost terete. Leaves oblong or narrowly lanceolate, 1/2'-2r long, sub-sessile, rather thin, flat or revolute, with no lateral impressions parallel to the midrib; ocreae, oblique, short, soon lacerate; clusters axillary, several-flowered; the flowers and fruit deflexed; sepals green with white or rose-colored margins; stamens 8; achene 3-angled, 1 1/4"-2" long, oblong or ovoid-oblong, black, smooth and shining.
Northwest Territory and British Columbia to New Mexico, Nebraska and Oklahoma, east through Ontario and New York to Vermont. June-Sept.