92 Minnesota Algae 



in diameter, not constricted at joints; apex of trichome 

 straight, not tapering P. treleasei 



B Plant mass thin, membranaceous; trichomes i-i.S mic. in diameter, 

 not constricted at joints; apex of trichome straight, tapering; 

 transverse walls granulated P. laminosum 



C Plant mass thin, membranaceous; trichomes 1-2 mic. in diameter, 

 slightly constricted at joints; apex of trichome finally becom- 

 ing tapered and bent; transverse walls not granulated 



P. tenue 



D Plant mass thick, leathery; trichomes 2-2.5 mic. in diameter, not 

 constricted at joints; apex of trichome straight, obtuse 



P. valderianum 



E Plant mass lamellose; trichomes 2-2.8 mic. in diameter, slightly 

 constricted at joints; apex of trichome gradually tapering, bent 

 or twisted P. subuliforme 



2 Trichomes more than 3 mic. in diameter 



(1) Apex of trichome straight, not capitate 



A Apical cell obtuse conical 



a Plant mass encrusted with calcium carbonate 



P. incrustatum 



b Plant mass not encrusted with calcium carbonate 



(a) Filaments somewhat straight; trichomes 3-5 mic. in diame- 



ter; transverse walls covered by protoplasmic granules 



P. inundatum 



(b) Filaments flexuous; trichomes 3-4.5 mic. in diameter; cells 



3.4-8 mic. in length; transverse walls conspicuous 



P. corium 



(c) Filaments strongly flexuous; trichomes 3-5 mic. in diameter; 



cells 2-4 mic. in length; transverse walls conspicuous 



P. papyraceum 



(d) Plant mass membranaceous, mucous; trichomes 5-6.5 mic. in 



diameter, interrupted; apex of trichome straight, obtuse; 

 transverse walls sometimes finely granulated 



P. interruptum 



(e) Plant mass thin; trichomes 16-18 mic. in diameter, fre- 



quently interrupted P. naveanum 



B Apical cell not or scarcely tapering, truncate 



a Sheaths thin, fragile, soon diffluent; trichomes 4.5-12 mic. in 

 diameter; cells 4-9 mic. in length P. retzii 



b Sheaths firm, or mucous and diffluent, at times thick and lamel- 

 lose; trichomes 4-6 mic. in diameter; cells 1.5-2.7 mic. in length. 



P. ambiguum 



(2) Apex of trichome straight, capitate 



A Trichomes slightly constricted at joints P. submembranace- 



um 



