1. Submersed leaves linear, mostly more than 10 times as long as wide (2) 



1. Submersed leaves lanceolate to ovate, mostly less than 10 times as long as 



wide (12) 



2(1). Stipules united with the base of the leaf for a distance of 7 mm. or more; 

 floating leaves often absent (3) 



2. Stipules free from the leaf or united for a distance of less than 6 mm. (6) 



3(2). Plants with submersed leaves only; fruiting spikes slender (4) 



3. Plants with long-petioled floating leaves and sessile linear submersed leaves; 



if floating leaves absent the fruiting spikes of submersed parts 



capitate and sessile or on very short peduncles 



9. P. diversifolius. 



4(3). Leaves more than 1 mm. broad, the apex rounded to broadly obtuse and 

 apiculate, the veins 3 to 7 1. P. latifolius. 



4. Leaves all linear-filiform, less than 1 mm. broad (5) 



5(4). Stigma disc-shaped, sessile or short-stalked; leaves blunt or submucronate 

 2. P. filiformis. 



5. Stigma not discoid, the stigmatic tip prolonged and with little evident swelling; 



leaves acute at the apex 3. P. pectinatus. 



6(2). Floating leaves absent (7) 



6. Floating leaves usually present, with broad blades and long petioles (11) 



7(6). Fruits with dorsal keel prominent, thin, alate, undulate or toothed (8) 



7. Fruits with dorsal keel rounded or acute but never thin and alate (9) 



8(7). Leaves 1.4—2.7 mm. wide, the veins 3 to 5; fruits 2-2.5 mm. long 



5. P. foliosus var. foliosus. 



8. Leaves 0.3-1.5 mm. wide, the veins 1 to 3; fruits 1.8-2.3 mm. long 



5. P. foliosus var. macellus,. 



9(7). Fruits tuberculate (especially at base), 2.5-2.8 mm. long, the lateral keels 

 prominent 7. P. clystocarpiis. 



9. Fruits smooth, 2-2.5 mm. long, the lateral keels rounded or obscure (10) 



10(9). Stipules connate when young; peduncles 1.5-8 cm. long; spikes 6-12 mm, 

 long, of 3 to 5 separated whorls 6. P. pusillus. 



10. Stipules not connate; peduncles rarely more than 3 cm. long; spikes 2.8 mm. 



long, of 1 to 3 adjacent whorls 



8. P. Berchtoldii var. tenuissimus. 



11(6). Submersed leaves linear, usually bladeless and filiform, 0.8-2 mm. wide; 

 blade (when present) linear-lanceolate and on a very long petiole; 



floating leaves broad, many-veined, base of blade subcordate 



15. P. nutans. 



1 1 . Submersed leaves linear to linear-obovate, often very unequal in size, usually 



tapering to tip and base, 3-12 cm. long, to 15 mm. wide 



14. P. gramineus. 



12(1). Leaves mostly all submersed and essentially alike; petioles short or ab- 

 sent (13) 



12. Leaves of two kinds, submersed and floating, the floating leaves with broad 



blades and long petioles (14) 



13(12). Leaves broadly lanceolate-attenuate, large, serrulate only at tip 



13. P. illinoensis. 



13. Leaves oblong and crisped, serrulate throughout, rounded at tip 



4. P. crispus. 



14(12). Submersed leaves ovate-lanceolate, arcuately folded or falcate in outline, 

 sessile or on short petioles; floating leaves mostly with more than 

 30 nerves 11. P. amplifolius. 



97 



