THE PRESIDENT'S ADDRESS. 21 



correctly remarks that " the hexagons are always turned 30° " 

 to their positions in Fig. 63, in the last edition of " Carpenter on 

 the Microscope," when the spectra at the back of the objective 

 are represented as in Fig. 62.* 



I think an explanation of the phenomenon will be found by 

 the examination of any hexagonal structure, such as a honey- 

 comb, fly's eye, or diatom ; by doing this we shall at once see 

 that the three directions of the rows of hexagons are at right 

 angles to the three directions of the sides of any particular 

 hexagon. In the above-mentioned erroneous Abbe-Eichhorn 

 figures the hexagons are turned, as Mr. Allan Dick has pointed 

 out, 30° from their proper position. These figures are, as I have 

 frequently remarked, incorrectly drawn. If you will examine 

 Figs. 63 and 64 you will observe that the directions of the rows of 

 hexagons are in an alignment with the angles of any particular 

 hexagon ; they are therefore 30° out of position. 



With regard to the spectra, it is well known that the spectra 

 assume a direction at right angles to those of the lines causing 

 the interference. Now it is the rows of hexagons which 

 cause the interference, and not the edges of the hexagons them- 

 selves. If, therefore, we draw three lines at right angles to the 

 three directions of the edges of any particular hexagon, they 

 will represent the three directions of the rows of hexagons ; and 

 if we draw a line at right angles to each of these, they will re- 

 present the proper position for the spectra. And also because 

 the angle subtended by a side at the centre of a hexagon is 60°, 

 and that angle and a half makes a right angle, the spectra will 

 therefore lie in the same direction as the corners of the hexagon. 

 The term used above, "rows of hexagons and not the edges 

 of the hexagons themselves," requires explanation ; it much 

 simplifies this question by regarding in the first instance the 

 inter-spaces rather than the lines. Of course it is the 

 intercostal material that diffracts the light, and in the case of 

 diatoms such intercostal silex has been isolated by our well- 

 known member Mr. T. F. Smith. This intercostal material 

 forms a wavy line, composed of short pieces inclined 120° to 

 each other, being the sides of contiguous hexagons. It is there- 

 fore this It.ng and ccntinr.cus wavy line that deteimines the 



* These figures, together with €4, are similar to tbcte in the "Journal 

 E. M. S." for 1881, p. 353-4, Figs. 1C5, ICG, and 107. 



