4 Dr. J. D. Macdonald on the Structure of the 



to mould with respect to their developing cell. Seeing, there- 

 fore, that the smaller the frustules of the same species are the 

 more endogenous developments must have preceded them, and 

 therefore, as one would naturally suppose, the nearer must be 

 the fitness for conjugation to complete the genetic cycle, my 

 great difficulty at one time was to know how the frustules of 

 a given species ever regained their original size, or where this 

 gradual diminution should end; but Mr. Thwaites has fur- 

 nished us with the solution in his important discovery that 

 the sporangial frustule resulting from the process of conjuga- 

 tion is so much larger than the parent cells. In relation to 

 this subject we read {op. cit.) : — " A great difficulty meets us 

 here. The necessary consequence of the conjugation just de- 

 scribed is, that every species in which it occurs must be repre- 

 sented by two forms, one small and the other large, between 

 which a gap exists, over which we have at present no means 

 of bridging, except by supposing that the two new halves 

 formed in cell-division need not always be equal, and that by 

 dwindling away through a succession of steps of this kind 

 the progeny of the sporangial frustules may be reduced to the 

 original size." This may be very ingeniously conceived ; but 

 the true key to the difficulty does not appear to have been ap- 

 prehended by the writer. Mr. Smith, moreover, widens the 

 breach by assuming a diametrically opposite hypothesis, in 

 which, however, he only seems to account for difference of 

 size, without observing the dilemma into which he falls. 

 Thus he says at p. xxvi of his work, already alluded to, 

 speaking of self-division, that " a careful examination of the 

 process in the filamentous species has led him to conclude 

 that a slight enlargement occasionally takes place in the new , 

 valves, thus causing a widening of the filament ; " and reason- 

 ing upon this premiss, which, I humbly conceive, should have 

 been taken the other way, he proceeds as follows : — " The 

 increase in the new valves, although slight, will, however, suf- 

 ficiently account for the varying breadth of the bands of the 

 filamentous species, and the diversity of size in the frustules 

 of the free forms, without obliging us to suppose that a growth 

 or aggregation takes place in the siliceous valve when once 

 formed." Yet it is actually within the fully formed valve that 

 the new half-frustule is produced ; and if so, it must, as before 

 stated, be smaller than its parent by the whole thickness of 

 the siliceous coat. " Starting from a single frustule," he goes 

 on to say, " it will be at once apparent that if its valves re- 

 main unaltered in size while the cell-membrane experiences 

 repeated self-division, we shall have two frustules constantly 

 retaining their original dimensions, four slightly increased, 



