1 64 TUFTS COLLEGE STUDIES, VOL. II, No. 3 



angles somewhat rounded ; membrane thin, covered with a net- 

 work of very delicate ridges. Cuba. Europe, Africa. 



7. T. QUADRATUM (Reinsch) Hansgirg, 1889, p. 18; Polye- 

 drium quadratum Reinsch, 1888, p. 499, PI. IV, fig. 7. Cells 

 regularly quadrate, sides straight or slightly convex, angles 

 obtuse, each with a single spine ; membrane rather thick, dis- 

 tinctly of two layers; diam. 17-34 ft; membrane 2-4.5 ft thick. 



The type occurs in Europe ; we have only forma minus 

 acutum ; cell 17-18 p. diam.; angles subacute ; membrane only 

 indistinctly lamellate. 111. 



8. T. GRACILE (Reinsch) Hansgirg, 1889, p. 19 ; Polyedrium 

 gracile Reinsch, 1888, p. 502, PI. VII, fig. i. Cells four-angled, 

 sides equal, emarginate or deeply and obtusely incised, angles 

 prolonged, three times forked, divisions divergent, ultimate 

 divisions very slender, acute ; prolongations from the angles as 

 long as the diam. of the cell; cell in side view narrowly 

 elliptic, with prolonged ends; total diam. of cell 35-46 /x ; dis- 

 tance between centers of sides 18-20 ft. Mass. 



Var. tenue (Reinsch) nov. comb. ; Polycdrium gracile we. tenue 

 Reinsch, 1888, p. 502, PI. VII, fig. la. Sides very deeply in- 

 cised, lobes of the angles in all orders very slender. Mass. 



9. T. QUADRICUSPIDATUM (Reinsch) Hansgirg, 1889, p. 18 ; 

 Polyedrium quadric2ispidatum Reinsch, 1888, p. 500, PI. VI, fig. 

 2. Cells 50-95X36-63 ft, with 3 or 4 unequal sides, convex or 

 concave, each angle ending in a long, acute, stout spine, 13-14^ 

 long ; membrane th'in, thickened at the angles ; cells in side 

 view narrowly elliptic, with attenuate, spinous ends. Mass. 



Europe. 



Quite irregular in outline of the cell, but characterized by the 

 four stout spines ; in Mass, is reported the type, also forma 

 inaequale Reinsch, which seems to differ only in having spines 

 of unequal length. 



10. T. angulosum (L/arsen) nov. comb. ; Polyedrium angu- 

 losum L/arsen, 1904, p. 104, fig. 8. Cells more or less irregu- 

 larly polygonal, with rounded angles, each with two short 

 spines. Greenland. 



Possibly identical with Polyedrium irregulare Reinsch, 1888, 

 p. 508, PI. VII, fig. 3. 



11. T. PACHYDERMUM (Reinsch) De Toni, 1889, p. 603; 

 Polyedrium pachydcrmum Reinsch, 1888, p. 504, PL V, fig. 2. 

 Cells 6-8-angled, 17-26 ft diam., sides usually equal and sym- 

 metrical, emarginate, angles rounded, obtuse ; in side view 



