The Development, &c., of Diatomacez. By Dr. G.C. Wallich. 67 
gradatim in the direct line of descent, though of course all the 
pullulations successively taking place in the same half-frustule will 
be uniformly of the same size, holding the relation of cast to mould 
with respect to their developing cell. Seeing, therefore, 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 conju- 
gation 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 furnished us with the solution in his im- 
portant discovery that the sporangial frustule resulting from the 
process of conjugation is much larger than the parent cells... . 
Mr. Smith, in his work ‘The Synopsis of the British Diato- 
macex, p. 26, says that ‘the increase in the new valves, though 
slight, will, however, sufficiently account for the varying breadth 
of the bands of the filamentous species, and the diversity in size of 
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, Mr. Smith goes 
on to say, ‘it will be at once apparent that if the valves remain 
unaltered in size while the cell-membrane experiences repeated self- 
division, we shall have two frustules constantly retaining their 
original dimensions, four slightly increased, eight somewhat larger, 
and so on in a geometrical ratio.”” “I am afraid” (adds Dr. 
Macdonald) “ that this doctrine of a geometrical increase in the size 
of the frustules will not stand the test either of fair theoretical 
induction or comparison with natural fact; for although there 1s 
truth in a gradual diminution, even this does not take place in a 
geometrical ratio, which, in the nature of the case, can only apply 
to number, not to size.” 
In my paper “On Triceratium,” to which allusion has already 
been made, | pointed out that in this and many other genera the 
connecting zones, which consist invariably of ¢wo pieces, at first 
entirely overlap each other, but as the process of division advances, 
recede from each other, and whilst receding have the appearance 
of three distinct annular portions or rings, the central portion being 
less diaphanous than the portion on either side, and its markings 
confused, owing to its being, in reality, the overlapping double 
portion under notice. This appearance has led to great uncertainty 
and doubt in descriptions of the connecting zone, since, from the 
transparency of the uppermost layer, the markings on it and the 
one below are seen simultaneously. In those genera in which 
