162 TUFTS COLLEGE STUDIES, VOL. II, No. 3 



2. Angles entire and unarmed. 3. 



2. Angles spinous or forked. 6. 



3. Membrane finely granulate-punctate. 5. T. pundulatum. 



3. Membrane with a network of ridges. 6. T. reticulatum. 



3. Membrane smooth. 4. 



4. Cells triangular. 2. 7". mnticum. 



4. Cells quadrangular. 5. 



5. Cells 15-21 /j. diam. 3. 7 1 . tetragoniun. 



5. Cells 6-1 1 ft diam. 4. T. minimum. 



6. Angles prolonged into many fine divisions. 8. T. gradle. 



6. Angles mucronate or spinous only. 7. 



7. Angles mucronate. i. T. tngonnm. 



7. Angles spinous. 8. 



8. Quadrate. 9. 



8. Polygonal. 10. T. angnlositin. 



9. Regularly quadrate, with short spines. 7. T. quadratum. 



9. Irregularly 3- or 4-sided, with long spines. 



9. T. quadricuspidatum. 



10. Angles unarmed and undivided. n. 



10. Angles spinous or prolonged and divided. 12. 



ii. Cells 17-26 p. diam. n. T. pachydermum. 



ii. Cells 65 /x or more in greatest diam. 13. 7". gigas. 



12. Angles spinous but not lobed. 13. 



12. Angles lobed or divided. 14. 



13. Membrane thick, lamellate; sides plane or slightly concave ; one 



stout spine at each angle. 12. T. regulare. 



13. Membrane thin ; sides convex, unequal ; i or 2 spines at each angle. 



14. T. armatum. 



14. Angles forked with rounded sinus and two sharp teeth. 



15. T. bifnrcatntn. 



14. Angles several times lobed or forked. 16. T. cnorme. 



i. T. TRIGONUM (Nag.) Hansgirg, 1888, p. 130; Polye- 

 drinm trigonum Nageli, 1848, p. 84, PI. IV. B, fig. i ; Reinsch, 

 1888, p. 497, PI. IV, fig. i. Cells triangular, 12-37 /* diam.; 

 thickness 6-16 ^ ; sides slightly sinuate, angles rounded, mucro- 

 nate. Fig. 47. Mass., 111., Pa., Neb., Porto Rico. 



Europe, Asia. 



Reinsch gives four forms of this species, distinguished only by 

 dimensions ; the American plant comes under forma majus 

 Briigger, with diam. of 36 ^. 



Var. PUNCTATUM (Kirchner), Hansgirg, 1888, p. 130; Polye- 

 diium trigonum var. punctatum Kirchner, 1878, p. 104; Wolle, 

 1887, p. 184. Membrane granulate, mucro small, papilla-like. 

 N. j., Pa., Neb. Europe. 



