100 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
W e must now return to the Eiehorn intercostals ; the history re- 
garding these is as follows : — 
The six spectra of the first order of P. angulatum (fig. 1) were set 
to a student who had never seen a diatom, and he calculated the pre- 
sence of an intercostal. These intercostals were afterwards seen hy 
Mr. Stephenson, and the student’s discovery was likened to that of 
Neptune. There is a double error here. The first is that the inter- 
costal is a function of the spectra of the second order, and can neither 
be calculated, originated, nor seen by those of the first order. 
Secondly, the intercostal is not a true diffraction image, but is a false 
diffraction ghost, and is caused by the reunion of the spectra of the 
second order, and the exclusion of the first order. 
The very data given to the student have to be excluded before an 
intercostal can appear or be calculated ! 
The error in connection with the exhibition of the intercostals of 
the P. angulatum is that no sufficient checks were imposed to render it 
absolutely certain that no spectra of the second order were present at 
the time the intercostals were seen. The intercostals have also been 
accounted for by a fallacious geometrical picture. Thus, the six spectra 
(fig. 1) account for three sets of lines ruled at 60° to each other. Now, 
as I pointed out in the ‘ English Mechanic,’ v »1. xliii., No. 1108, p. 337, 
two very different pictures are produced according to whether the third 
line be ruled through the apices of the rhombs (fig. 4) or not. It is 
for those who uphold the truth of the intercostals to show which 
spectrum or what arrangement of the six spectra determines that the 
third line does not pass through the apices of the rhombs (fig. 6). 
The contrary is really the fact, viz. that if there is any truth at all in 
the diffraction theory, then with a spectral arrangement as set to the 
mathematical student the third line must pass through the apices of the 
rhombs (fig. 5). Figs. 4, 5, and 6 show the rhombs and the formation 
of the two kinds of pictures. In passing, it is as well to note that 
objectives being for the most part spherically undercorrected, generally 
show the intercostals at the lower focus. In other words, you have to 
lower your objective in order to obtain the reunion of the spectra of the 
second order by means of the outer zone of the objective. Intercostals 
are due to illumination by means of a narrow cone, which allows and 
aids zonal differences to operate on the spectra, uniting those of the 
second order, whilst excluding those of the first. 
Illumination by a large cone neutralizes the effect of these zonal 
differences, and intercostals disappear. 
I have given much attention to diffraction ghosts, and have made 
several photographs of them for your inspection. Instead of confining 
my investigations to P. angulatum, as has been usually done, I thought 
ft better to select very coarse structures, concerning the true appearance 
of which all microscopists are entirely agreed. In the first instance, I 
experimented with the coarse hexagonal structure of a Triceratium, 
which measured 1/3600 in. A photograph x 387 taken with a large 
cone I will now project (fig. 7). The illuminating cone was now cut 
down by closing the iris diaphragm, and the aperture of the objective 
stopped down until the spectra at the back of the objective appeared as 
in fig. 2. The next photograph (fig. 8) shows the image due to those 
