98 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
three images, viz. the true diffraction image, and the true and false 
diffraction ghosts. You will naturally ask, how do jmu distinguish 
between these three images ? A true diffraction image goes in and out 
of focus like a daisy under a 4 in. In other words, a true diffraction 
image is one out of which it is impossible to make another image by 
focal adjustment. A diffraction ghost, on the other hand, is one which 
changes into other images on focal adjustment, a false diffraction ghost 
being an image which is dissimilar to the original, and a true diffraction 
ghost one in which it is fairly in accordance with the original. 
A true diffraction image is produced by a large cone of illumination, 
except in those cases where the structure is so fine, in relation to the 
aperture of the objective, that the large cone does not cause the spectra 
to overlap one another and the dioptric beam. 
True and false diffraction ghosts are produced by small cones, except 
in those cases where the structure is either so coarse that the spectra 
overlap, even with the small cone, or so fine that only spectra of the 
first order are taken up by the objective ; in this latter case a false 
diffraction ghost becomes impossible. Taking the ghosts first, the 
reason why there is a change of image on alteration of focus may be 
seen on reference to plate II. fig. 3. Let 0 be an object having about 
20,000 interference elements per inch, let DD be an infinit-ely thin diop- 
tric beam in the optic axis, then S and M will be the spectra of the first 
order, and T and X those of the second. If the object be examined by 
an objective whose aperture is greater than the angle T 0 N, i. e. upwards 
of 100°, a diffraction ghost will be seen, because at the longer focus the 
spectra S and M will be united with D, and a representation similar to 
the true structure will be produced ; but on shortening the focus the 
spectra T and X will be united with D, and a picture having double the 
fineness of the original structure will be seen. (You require no stop at 
the back of your objective to perform this experiment ; the spherical 
aberration, which is always present, even in the best corrected lenses, 
will be sufficient to prevent the union of S and M with T and N. 
See Mr. Leroy’s results on applying the Foucault test to Microscope 
objectives, E.M.S.J., 1890, p. 224: the spherical aberration varied 
from tenths of mm. to several mm.) It is therefore a diffraction 
ghost, because the image alters on focal adjustment ; it is a true ghost 
at the upper focus and a false ghost at the lower focus. 
Let us now see what takes place when a large cone is used. Let 
PP be an isolated pencil of such a cone, then HQ will be spectra of 
the first order, and R a spectrum of the second, and K one of the third 
order. These dotted lines are drawn at a little distance from the 
others for the sake of clearness, but they are supposed to be either 
coincident with or very near the others. Here we see at the upper 
focus that a spectrum of the second order R is combined with a dioptric 
beam P, and a first diffraction spectrum Q, and this takes place in 
addition to the combination of S and M with D mentioned above. 
Bringing in a diffraction spectrum of the second order will tend to 
improve the image. At the lower focus even now there will be a first 
diffraction spectrum H, combined with a third order spectrum K, together 
with the combination of H and X with D as above. This combination 
■would give a confusion of images, so it comes to pass that images with 
