60 GENERAL HISTORY OF THE rNFTJSORIA. 



between the new valve and the parent one with which it is united in the 

 newly-created frustule. The newly- developed segment occasionally acquires 

 slightly greater dimensions, — a fact best exhibited in the filamentous genera, 

 since in them it gives rise to an evident irregularity in the chain, affecting its 

 width. Yet, as Prof. Smith remarks (i. p. xxvi), " This increase is so small, 

 that in a filament of many hundred frustules, the enlargement is scarcely 

 appreciable. The rapid attenuation represented by some authors in the 

 filaments of the FragilaricB must therefore be attributed to the deceptive 

 appearance presented by a compressed band when slightly twisted, the sem- 

 blance of attenuation being thus given to the portions which are presented 

 in an oblique direction to the eye of the observer .... Starting from a single 

 frustule, it will be at once apparent, that if its valves remain unaltered in 

 size, while the cell-membrane experiences repeated self-di\ision, we shall 

 have two frustules constantly retaining theii' original dimensions, four slightly 

 increased, eight somewhat larger, and so on in a geometrical ratio, which 

 will soon present us with an innumerable multitude containing individuals in 

 every stage, but in which the larger sizes preponderate over the smaller ; and 

 such are the circumstances ordinarily found to attend the presence of large 

 numbers of these organisms." 



Mr. Balfs has favoured us ^ith the follomng remarks on this subject in 

 letters. He writes (March 1856) — *' In a recent number of the Ann. Nat. 

 Hist, Mr. Carter expresses his belief that the fnistules of Diatomaceae gra- 

 dually become smaller by division, and that it requires the sporangial frustule 

 from time to time to keep them the proper size. This I cannot admit ; for 

 any person who will take the trouble to watch a species of Gomphonema 

 from its fii'st appearance in spring, as a scarcely \isible fringe to aquatic 

 plants, will observe not only increase of mass, but also enlargement of the 

 frustules. If Mr. Carter is right, the filament in Fragilaria would be veiy 

 unequal : for instance, as the first-formed frustule could not decrease, and as 

 its segments after division would always form the two ends of the filament, 

 they should be the largest, then the adjacent valves of the two central frustules 

 of the filament the next largest, and so on." In a subsequent letter the 

 same distinguished authority writes : — '' I see that Prof. Smith, in his 

 Synopsis, p. xxvi, takes the contrary view to Mr. Carter, and considers that 

 the frustules do not grow after they are fully formed, but that, in dividing, 

 the new frustules may slightly increase in size. It is thus that he accounts 

 " for the varying breadth of the bands in the filamentous species, and the 

 diversity of size in the frustules of the free forms." If he is correct, his 

 opinion is still more adverse to Mr. Carter's views respecting the frustules 

 formed after self- division. But I doubt also the correctness of Mr. Smith's 

 views. He himself states that " the enlargement is scarcelj^ appreciable ;" 

 and yet we find a vast difference of size in the frustules of the same gather- 

 ing. The filaments are so fragile in Fragilaria, and even in Himantidium, 

 that it is very difficult to determine whether the frustules in the same fila- 

 ment do diff'er much ia size, and whether, if they do, the variations are alter- 

 nating or irregular, as would be the case if either Prof. Smith or Mr. Carter 

 be correct. 



The rate of production of specimens of Diatomeae, even by this one pro- 

 cess of simple self-division, is something really extraordinary. So soon as 

 a frustule is divided into two, each of the latter at once proceeds with 

 the act of self- division ; so that, to use Prof. Smith's approximative cal- 

 culation of the possible rapidity of multiplication, supposing the process 

 to occupy, in any single instance, twenty-four hours, " we should have, as 

 the progeny of a single frustule, the amazing number of one thousand 



