88 Transactions of the Royal Microscopical Society. 
Further illustrations of the formation of hexagonal markings 
may be found on the same diatom. 
On bringing into focus a good specimen of P. angulatum flat 
and with distinct-looking lines, using a broad beam of central light, 
the six diffraction spectra before alluded to may be distinctly seen 
within the margin of the back lens of the objective (Fig. 12). Any 
two adjacent spectra combined with the central cone of light will 
form an equilateral triangle, and produce the well-known hexagonal 
markings; but as any other pencils forming an equilateral tri- 
angle will also produce hexagonal markings, a new set on a dark 
field may be formed by excluding the central and each alternate 
diffraction ray: the sides of this triangle being longer than in the 
common figure, in the proportion of ,/3: 1, the new hexagons 
will be three times as numerous as those usually seen, and with 
their sides at a different angle to the median line. The three 
pencils producing the interference in this case are g, ¢, e, or b, d, f, 
and the hexagons will have their sides normal to the axis of the 
scale, not parallel as in the common image. Not only is this so, 
but it follows from the theory that there must be visible three 
other sets of lines, bisecting the angles between the common lines, 
and corresponding to the combinations of the spectra, g, ¢, or f, d— 
b, f, or c,e—b, d, or g,e. All these phenomena may be observed 
by stopping off the pencils which are to be excluded. It is easy to 
get the lines bisecting the angles of the common rows, one after 
the other, and of these one set parallel to the axis of the scale. 
For that purpose oblique light must be used, and the central beam 
and one of the peripheral rays must be stopped out, leaving for 
instance b and f, or ¢ and e (i. e. two spectra parallel to the median 
line). 
In conclusion, I can only express my sincere regret that Pro- 
fessor Abbe’s recent visit to London took place during our recess. 
Had it been otherwise, the Society would have been gratified by 
an account of his most important investigations and experiments 
from his own lips, very much more perfectly than I can possibly 
have done. But my object has been accomplished if, in bringing 
before the Society this wonderful contribution to microscopic science, 
I have induced the Fellows to appreciate the important considera- 
tions to which it necessarily gives rise. 
