258 



Among the remarkable forms found, although not considered to 

 belong to the Diatomacese, are the two varieties of Bacteriastrum, 

 the discs of which, it may be observed, were three or four times the 

 diameter of those described by Mr Shadbolt, from Port Natal, and 

 the radiations more numerous. 



Attention was directed to the structure of the Diatomacese as af- 

 fording some of the most beautiful examples of geometric arrange- 

 ment 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 a plane surface, namely, the equi- 

 lateral triangle, the square, and the hexagon ; these forms and their 

 angles are accordingly found to prevail in the structure of the tis- 

 sues. By constructing the polygons, it was shewn that they ar- 

 ranged 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 run 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 position 

 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 accord- 

 ance with it has divided his genus Pleurosigma into two sections. 



The above arrangements will be found to prevail in the structures 

 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 

 centre 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. 



These divisions are seen very conspicuously in Actinocyclus and 

 Actinoptychus. In the large species of Coscinodiscus, the number of 

 sectors appeared to be twelve, from the groups of rows at the centre, 

 and in it was shewn the very beautiful arrangement of the cells in 

 radiating and intersecting spiral lines. Eupodiscus Kalfsii was re- 

 ferred to as affording an example of the division of the circle into 

 sectors, within which the lines of cells are arranged synmietri- 

 cally on each side of a single radiating row, to which the rest are 



