ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
95 
On the Abbe theory the hinder part of the ray-path can be regarded 
as coming from a telescope objective, which, however, does not work 
with full aperture, but is rather covered up except for a row of little 
windows corresponding to the diffraction spectra. To these little 
windows must be ascribed an elementary surface. The achromatic un- 
diffracted centre is a primary maximum, and the lateral chromatic images 
the discontinuous diffraction appearances. Therefore, to produce mono- 
chromatic microscopic images no Microscope is necessary ; a telescope 
may be directed towards a point monochromatically illuminated, and 
the objective covered up except a large slit (primary maximum) and 
several small slits (secondary maxima). Such an arrangement works as 
a Microscope as soon as the totality of the wave-lengths is taken into 
consideration ; for in this case the secondary maxima have constant 
distances from the primary maximum, which distances in the Microscope 
are proportional to the wave-lengths. His treatment is an enlargement 
upon Eichhorn’s { Bestimmung dcr Interferenzcn von mehreren Iso- 
chronen und in gleicher Phase schwingenden Lichtzcntren,’ * both in 
depth and in scope : in depth, because Eiclihorn treated the diffraction 
spectra as lying in one plane instead of on a spherical surface ; in scope , 
because Strehl treats of the environment in space of the wave-centre, 
and includes spherical aberration, coma, cylindrical waves, distinction 
between direct and oblique light, and chromatic aberration. Moreover, 
he pays duo heed to the laws of conservation of energy neglected by 
Eichhorn. 
In discussing each subject he quotes the corresponding equations from 
liis ‘ Theorie des Fernrohrs,’ and deduces the following propositions. 
Aplanatic image-formation.— (1) If a definite group of diffraction 
spectra be displaced on the spherical wave-surface, the inner and outer 
proportions of the microscopical image thereby formed are left un- 
changed. 
(2) The microscopical image is achromatic in the focal plane, 
chromatic in the image plane and along the optic axis. 
(3) The fineness of delineation in the microscopical image is, both 
in the focal plane and in the corresponding image-planes and along 
the optic axis, proportional to the wave-length of the light source. 
(4) The fineness of delineation in the microscopical image is, in 
the focal plane and the corresponding image planes, inversely propor- 
tional to the linear extent of the group of ditfraction spectra. 
Chromatic aberration. — (5) The excellence of the microscopical image 
is attained by means of an integration over the various wave-lengths. 
Direct illumination. — (6) If a primary maximum lies in the midst of 
a circle of secondary maxima, then is the microscopical image along the 
cptic axis a regular simple periodic function of the spot — monochromatic 
light being assumed. 
(7) If a primary maximum lies in the middle of a circle of secondary 
maxima taken by pairs of opposiles, then complete images alternatj 
with images of exactly opposite character along the optic axis at constant 
distances — monochromatic light being assumed. 
(8) If a primary maximum lies in the midst of a regular polygon of 
secondary maxima, then the pattern of the microscopical image in the 
* Jena, 1878. 
