ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
101 
spectra ; this shows the intercostals, and is what I term a false diffrac- 
tion ghost. You will observe that the objective has been placed at a 
lower focus. If the same, i. e. the upper focus, had been used, then a 
picture similar to the true image taken with the large cone would bo 
seen, except that the walls of the hexagons would be considerably 
thicker, and in the centre of each areolation there would be a dark 
spot. 
If the illuminating cone be enlarged to a 3/4 cone the image will 
closely resemble the critical image (fig. 7) already shown, and more- 
over will be a true diffraction image, because it will go in and out of 
focus as a daisy under a 4-in. In examining the various images pre- 
sented by a hexagonal grating in focal alteration, when a small cone of 
illumination is used, I found that these false diffraction ghosts followed 
a certain sequence, and might be grouped in three classes, which I term 
degrees. The false diffraction ghost of the first degree requires spectra 
of the second order (fig. 2), for its production. It is the Eichorn 
intercostal image. 
The next experiment was performed with the narrow cone as before, 
but with the aperture of the objective reduced so that the second order 
of spectra (fig. 1), were cut out ; according to my theory no inter- 
costals should now be visible ; on taking the photograph, however, a trace 
of them could be distinguished (fig. 9). This is such an interesting result 
that I have printed the negative. The fact was that I had cut out 
the second order spectra visually but not photographically. On further 
cutting down the aperture quite up to the end of the spectra of the first 
order, no intercostals could either be seen or photographed (fig. 10). 
This is an additional proof that the intercostal image is a func- 
tion of the spectra of the second order. Further, if an intercostal on 
P. angiilatum is resolvable by means of spectra of the first order, which 
diverge about *5 N.A. from the central dioptric beam, as affirmed by 
Eichorn, Abbe, and the anonymous writer of the article on microscopic 
vision in the R. M. S. Journal,* then the theoretical limit tables at 
the back of the Journal had better be torn up. The intercostals would 
count about 95,000 per in., and according to those tables they would 
cause the spectra of the first order to diverge about * 99 N.A. from the 
dioptric beam. So it would require an aperture of nearly 2*0 N.A. to 
grasp all the six. Therefore all these years the tables at the back of 
the R. M. S. Journal, and the anonymous article on microscopic vision, 
which is a condensed summary of all their and Prof. Abbe’s teaching on 
the subject, are, as I have often pointed out, contradictory. This 
last experiment on the Triceratium with only the spectra of the 
first order admitted, shows that on focal alteration only a change 
from positive to negative diffraction images takes place, i. e. black 
to white dots ; in other words, a black hexagon with a white centre 
changes to a white hexagon with a black centre and vice versa. The 
word hexagon is here incorrect ; the pattern strictly speaking under 
these conditions is black or white circular dots arranged in a quincunx 
form. This experiment is most important, because it shows that when 
a small cone of illumination is used a more truthful image is secured by 
* R.M.S.J., Ser. 2, vol. i. pp. 354. 
