PROCEEDINGS OF THE SOCIETY. 
145 
there is no evidence that they are not, and if we can derive this from 
another quarter in favour of their existence, I do not see why we should 
reject it. I think this evidence in favour of their truth is found in the 
fact that fractures occur at the point where the dark lines divide one 
from another, as we shall see by at least two examples from different 
valves. 
I have called the appearances produced in my photographs, inter- 
costals, but I may state that they differ from what has hitherto gone 
under that name, both in character and their mode of production. 
Having carefully examined the whole series from the Eichhorn pattern 
to those produced purposely by Mr. Nelson from Triceratium favus and 
the eye of the fly, I find that they all possess this common character- 
istic ; that they seem to be miniature images of the centre spot, thrown 
off in a circle around it and are light or dark as that is ; and that they 
are all the production of a small aperture. In mine, however, the centre 
is dark but the intercostals light, and the divisions between them are 
only shown with the widest aperture of an oil-immersion objective of 
at least 1 * 40 N.A. Two slides will well show this. In the first, taken 
with the condenser stopped down, there is no appearance of a division 
of the bars, while in the second are shown thin dark lines cutting them 
in two. 
In the June number of the Journal of this Society for 1892, p. 428, 
there is a review of Dr. Van Heurck’s work on the Microscope, where 
in speaking of test-objects the writer of the article says, ‘ What we now 
need are objects which will specially differentiate the qualities of the 
apochromatic objectives from their achromatic predecessors, especially 
when it is considered that for lined (or dotted) objects the table so long 
and usefully printed at the back of this Journal gives the theoretical 
power of any lens.’ 
Now, with all deference I submit that this evidence of the minute 
division of structure around the dark hexagons of the inner layer of 
P. angulatum is just the test-object required to fulfil this purpose, as 
far as oil-immersions are concerned, and one that proves at least that 
the apochromatic with which this structure was taken works to the 
theoretical limit of its aperture (1*40). Mr. Nelson has kindly worked 
out the measurements for me, and assuming the diameter of a hexagon 
to be 1/50,000 in., each side would be 1/86,600 in., and the intercostal 
itself 1/173,200 in. in diameter. Indeed, the diameter is considerably 
iess than this, there being a space to divide one intercostal from another. 
Unfortunately, while within the photographic, it is without the 
visual limit of the resolving power of the lens, and unless the aperture 
of *he objective can be considerably increased by true monochromatic 
light, we cannot hope to see them. Of course, the dimensions given 
will depend upon the size of the hexagons being correct, but anyway 
the dividing up of the interspaces seems to point to a great advance of 
definition on any objective of pre-apochromatic days. 
As to the nature of the structure, I consider that its unit consists of 
short bars of silex of the same character as that on the outer side of the 
valve, only much more minutely divided, and with sufficient aperture 
we should find them square instead of round. 
Eecurring to the question of the hexagons, I do not think that on 
1894 
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