38 TUFTS COLLEGE STUDIES, VOL. IV, No. 7 



less commonly flat with concave sides; short sides 14-16 ft, 

 longer sides i6-i8fi, isthmus of former 13-14 /x, of latter 7-9 /x 

 wide; spines 7-8 /* long, usually slightly curved. Wis.. G. M. 

 Smith. liuropf. 



Var. TORSUM (W. B. Turner) Brunnthaler in Pascher, 1915, 



p. 150, fig. 169 ; Polycdrium tctracdricum var. torsum W. B. 



Turner, 1892, p. 158, PI. XX, fig. 15. Angles prolonged and 

 twisted. Wis., G. M. Smith. Asia. 



Page 80 of supplement, after T. CAUDATUM, add, 



Var. LONGISPINUM Lemmermann, 1898, p. 151 ; 18993, p. 1 17, 

 PI. I, figs. 8-9. Cells 10-12 /t diam., spines 8-10 /* long, each 

 bent at a right angle with the plane of the cell body. Wis., 

 G. M. Smith. Europe. 



Page 166, after description of T. ENORME, add, 



1 8. T. OBESUM (W. & G. S. West) Brunnthaler in Pascher, 

 1915, p. 154 ; Reinschiella obcsa W. & G. S. West. 19018, p. ioo, 

 PI. IV, figs. 53-54. Cells serai-circular to ovate with one side 

 more convex than the other, about 30 X 14 M. each end with a 

 strong spine about 7 p. long, curved towards the convex side ; 

 cells often in pairs. Me., F. D. Lambert. Siam. 



19. T. TORTUMW.&G.S. West, i895b, p. 52. Cell irregularly 

 triangular, twisted, sides convex or concave or nearly straight ; 

 angles slightly prominent, each ending in a sharp spine about 

 30 fi long. Membrane thick. Cell without spines, 73-81 /A 

 diam., 42-44 /* thick. " North America " West. 



20. T. PENTAEDRICUM W. & G. S. West, 18958, p. 84, PI. 



V, figs. 15-16. Cells pentagonal, sides concave, angles rounded, 

 each with a curved or hooked spine. Cells 10-15 /* diam., 

 without spine ; spine 4.5-5.5 M long. Wis., G- M. Smith. 



Madagascar. 



21. T. SPINULOSUM Schmidle, 1896, p. 193; Brunnthaler in 

 Pascher, 1915, p. 154, fig. 188 ; Polyedriopsis spinulosa Schmidle 

 in Lemmermann, 18993, p. 118. Cells 4-5-angled, up to 20 M 

 diam., angles somewhat prolonged, each bearing 4-10 irregularly 

 placed, slender, somewhat tapering spines, 30-40 n long. Wis., 

 G. M. Smith. Europe. 



The habit, small body with many very long slender spines, is 

 quite different from the other species of the genus, and perhaps 

 most writers would accept Schmidle's second thought, and 

 make a separate genus for it. But when one begins to divide 

 up Tttraedron, it is hard to stop, and for the present Polyedriop- 



