84 THE AMEKICAN MONTHLY [April, 



decrease in size after subdivision, and they must decrease both ways — in 

 length as well as in breadth. The frustules ought to become shorter 

 as well as narrower, for the outer hoop limits the inner all the way 

 round. But according to the drawings they do not decrease in length 

 in a number of cases. 



Take, for example, the drawings of Licmophora (fig. 172, p. 342, 

 Carpenter's 6th edition ; Nave's Handy Book, pi. vii ; Wolle, Diatom- 

 aceae, pi. xxix, fig. i), or look at Meridion circulare (fig. 170, Car- 

 penter; Wolle, pi. xxxvii, figs. 24, 25, 26; Micrographic, pi. 17, fig. 

 7 a); Bacillaria paradoxa (fig. 171, Carpenter ; Wolle, pi. Ixviii, 

 figs. 32-34) ; Eunotia pectinalis (Wolle, pi. xxxvi, fig. 19) ; Synedra 

 .pulchella and supcrba (Wolle, pi, xli, figs. 26, 32) ; Odontidium ., 

 Sphenosira^ Tabellaria^ T^e/racyc/z/^ (Micrographic, pi. 17, figs. 14 a, 

 26 b, 27 a, 28 ; Wolle, pi. 1) ; Asterionella, Diatonia (Wolle, pi. xlvi, 

 figs. 5 -S, 14. 21-27); Fragilaria (pi. xlvii, figs. 1-7); Striatella 

 (Wolle, pi. li, fig. I ; Micrographic, pi. 17, fig. 20 b) ; Stylobiblium 

 (Micrographic, pi. 18, fig. 50 b; Wolle, pi. Ixii, fig. 25) ; Achnanthes 

 (Wolle, pi. xxvii, figs. 22, 29, 33). In fact the instances are so many 

 that I am getting tired of citing the references. If you will look at these 

 figures you will see that after several subdivisions the frustules do not 

 vary In le7tgth at all in many cases, and that in some they vary, if any- 

 thing, the wrong way, the frustules becoming longer instead of shorter. 

 The radius of the spiral of Meridio7i or of the fan of Licmophora is 

 represented as constant. In Fragilaria., Himantidium., Tabellaria., 

 and Tetracyclus., the upper and lower lines of the filament are di-awn 

 parallel. One frustule is just as long as another, and so it is with 

 Asterionella and Diatoma. It would seem, therefore, as if there must 

 be something wrong about the theory or else about the figures. Either 

 the frustules in many cases do not decrease as the text-books say they 

 do, or else the figures do not correctly represent the facts. They ought 

 to become shorter, whereas they are figured as being all equally long, 

 or the difference is so slight as to be inappreciable. Certainly any one 

 looking at the figures would say the frustules were of the same length 

 in the majority of the cases I have cited. 



And now comes the climax ; for in turning to the Rev. Mr. Smith's 

 synopsis on this point of multiplication by division, I find to my amaze- 

 ment that he not only asserts that in many cases they do not decrease, 

 but that they actually increase I 



"The new valves" he says "formed during the process of self- 

 division ordinarily appear exact counterparts in form and size of the 

 valves of the original frustule ; but careful examination of the process 

 in the filamentous species has led me to conclude that a slight enlarge- 

 ment occasionally takes place in the new valves, thus causing a widen- 

 ing of the filament. 



'' This increase is, however, so small that in a filament of many 

 hundred frustules the enlargement is scarcely appreciable. The rapid 

 attenuation represented by some aiithors in the filaments of the Fragi- 

 larice must, therefore, be attributed to the deceptive appearance pre- 

 sented by a compressed band when slightly twisted, the semblance of 

 attenuation being thus given to the portions which are presented in an 

 oblique direction to the eye of the observer. 



"The increase in the new valves, although slight, will, however, 



