girdle of the mother frustule gives way, and two distinct frustules
are formed, the siliceous valves in each of these new frustules being
one of the valves of the mother-cell, and a newly formed valve similar
and more or less parallel to it.

During the life of the plant this process of self-division is continued
with an almost incredible rapidity. On this subject the observation of
Professor William Smith, writing in 1853, is worthy of special
notice:--"I have been unable to ascertain the time occupied in a single
act of self-division, but supposing it to be completed in twenty-four
hours we should have, as the progeny of a single frustule, the amazing
number of 1,000,000,000 in a single month, a circumstance which will in
some degree explain the sudden, or at least rapid, appearance of these
organisms in localities where they were a short time previously either
unrecognized or sparingly diffused" (_British Diatomaceae_, vol. i. p.
25).

[Illustration: FIG. 6.--Formation of Auxospores.

A. _Navicula limosa._
B. _Achnanthes flexella._
C. _Navicula Amphisbaena._
D. _Navicula viridis._]

Individual diatoms when once produced by cell-division are incapable of
any increase in size owing to the rigidity of their siliceous
cell-walls, and since the new valves are always formed _within_ the
girdle of the old ones, it would follow that every succeeding generation
is reduced in size by the thickness of the girdle. In some diatoms,
however, this is not strictly true as daughter-cells are sometimes
produced of larger size than the parent-cells. Thus, the reduction in
size of the individuals is not always proportionate to the number of
cell-divisions.

On the diminution in size having reached a limit in any species, the
maximum size is regained by the formation of an auxospore. There are
five known methods of reproduction by auxospores, but it is unnecessary
here to enter into details of these methods. Suffice it to say that a
normal auxospore is produced by the conjugation of two parent-cells, its
distinguishing feature being a rejuvenescence accompanied by a marked
increase in size. These auxospores formed without conjugation are
parthenogenetic.

_Mode of Preparation._--The Diatomaceae are usually gathered in small
bottles, and special care should be taken to collect them as free as
possible from extraneous matter. A small portion having been examined
under the microscope, should the gathering be thought worthy