4 THE AMERICAN MONTHLY [Jaimary, 



original valves y^/j'/' equal to the smaller valve which the larger origin- 

 ally overlapped or enclosed. The result, therefore, of multiplication 

 by division is not that eacJi of the succeeding -pair of frustules is 

 smaller than the frustule from which it originates, but that only one of 

 each pair is. And thus there will always be some frustules which rep- 

 resent the typical or original size of the diatom ; just as many in fact as 

 there are individuals of the species at the time the multiplication takes 

 place. One of the new frustules, however, is smaller than the original 

 frustule, and so it must be at each new division. So that we shall 

 have, or ought to have, as many frustules of the original size as there 

 were individuals of the species at the time of division, and any number 

 of the next smaller size. For each original frustule holds its own as 

 to size by simply restoring itself at each division, and it can produce 

 as many frustules of the size next smaller as the vitality of the orignal 

 frustule will allow. I mean, that the larger valve can keep reproducing 

 valves of the size of the smaller valve and letting them go at each 

 division. Thus let a represent the larger valve of a frustule and b the 

 smaller valve. It is plain that a can always reproduce b^ in other 

 words produce a second (5, and let the first b separate itself And so 

 the original frustule keeps restoring itself and at the same time sending 

 off a valve of the size of b^ which has formed within itself a smaller 

 opposing valve, c, and become also a complete frustule, and b in turn 

 can do the same. So that there will always be one representative in 

 size of the original frustule for each of the individuals of a given 

 species at the beginning of the process of division, and as many rep- 

 resentatives in size of the frustule of which b is the larger half as there 

 are divisions of the original frustule of which a is the larger half. For 

 that frustule does not simply divide once and then stop, but keeps on 

 dividing again and again after each reproduction of itself. That is to 

 say, it is not as if b separated from a and then b alone produced c, and 

 c in turn separated from b and c alone produced d. In short, it is not 

 like the Japanese c^^ which encloses a smaller egg and so on ad infi- 

 nitum. 



I emphasize this point, because Carpenter says that " It seems to be 

 in this way that the normal size is recovered, after the progressive dim- 

 inution (the italics are my own) which is incident to repeated binary 

 multiplication," * leading us to infer that one of the valves loses its vi- 

 tality at each division, or at each after the first, for he also calls atten- 

 tion to the fact that " in those newly-formed frustules which have been 

 just produced by binary subdivision * * * one of the valves is 

 always older than the other." f But there is no apparent reason why one 

 valve should have anv more vitality than the other, for the two origi- 

 nal valves form one and the same diatom cell to begin with, and each 

 half produces another half within itself. Neither of the two resulting 

 frustules therefore will have any more vitality than the other. In other 

 words, for all I can see, one frustule can produce as many pairs of frus- 

 tules as any other from the original down, and if so the size does not 

 progressively diminish ; there will always be as many frustules of the 

 original size as there were at the start, and the number of the next size 

 smaller will be equal to the number of times the original frustule divides. 



* p. 337, 6th edit. t P. 328. 



