207 
fered somewhat from the figures and descriptions given of them, being 
provided with two spines placed close to the projecting terminations 
or angles of the valve, and which were always present in the examples 
that had come under observation. The surfaces of the valves were 
also seen to be dotted over with small nodules, which gave them a 
very remarkable appearance, and might be seen to project from the 
surface when the valve was suitably placed. These appearances 
might be attributable to a more matured developing of the silicious 
structure. 
Among the remarkable forms found, although not considered to 
belong to the Diatomacez, are the two varieties of Bacteriastrum, the 
disks of which, it may be observed, were three or four times the dia- 
meter of those described by Mr. Shadbolt, from Port Natal, and the 
radiations more numerous. 
Mr. Dallas directed attention to the structure of the Diatomacee, 
as affording some of the most beautiful examples of geometric arrange- 
ment of cells with which we are acquainted. It was pointed out that 
there are only three of the regular polygons that can be employed 
alone to fill up the space about a point in plane surface, namely, the 
equilateral triangle, the square, and the hexagon: these forms and 
their angles are accordingly found to prevail in the structure of the 
tissues. By constructing the polygons it was shown that they 
arranged themselves in straight lines, determined by the shorter axis 
of the figures, the quadrilaterals having two directions in which the 
lines run, and the hexagons three. With the hexagonal structure, 
when one set of the lines passing through the axis is referred to a 
centre, the cells then appear to radiate in straight lines from the 
centre ; while the other two directions in which they appear to rnn 
will be spiral lines, having a definite character according to the size 
of the cells. Much of the character of the tissue depends on the posi- 
tion of the axis of the polygon, with respect to an axis of the 
valve; that is, whether the longer or shorter axis is parallel to it. 
Mr. Smith, in his ‘ Synopsis,’ has noticed this peculiarity ; and, in 
accordance with it, has divided his genus Pleurosigma into two sec- 
tions. 
The above arrangements will be found to prevail in the structure 
of the tissues of the valves; and the influence of the living principle 
might generally be seen in the repetition of like spaces, about a cen- 
tre in each species, and always in the same numerical relations in 
each individual of the species, multiples of the numbers 2, 3, and 5, 
and also.7, seeming to prevail. 
