ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
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such cameras. Focusing is effected by clamping the stage so that 
the object is approximately in focus, and then moving the back of 
the camera as found necessary. This apparatus, which I designed 
and had made early in 1881, has been found to work very well with 
low powers, the illumination being effected by a paraffin lamp with 
one wick, the flame of which is focused on the object by stand con- 
densers, with a blue cell interposed.” 
(5) Microscopical Optics and Manipulation. 
Determination of the Focal Length of Optical Systems.* — Prof. Abbe 
describes a very convenient apparatus for determining focal lengths. 
Most of the methods for this purpose depend on the determination of 
the position or displacement of the images formed by the system to bo 
tested. Such processes, besides being very difficult of application 
to systems of great focal length, are subject to considerable uncer- 
tainty. The method here suggested depends on the determination of 
the ratios of the apparent magnitudes of objects which are first observed 
directly and then by the system under examination. If this ratio for 
two objects at a distance from each other A is p 1 and p 2 , the focal length 
/ = A (p 2 — Pi). To obtain great exactness a Microscope with Abbe 
diaphragm is used, in which only pencils with axes parallel to the axis 
of the Microscope are effective in the production of the image. The 
complete apparatus consists of a Microscope, with the adjustable stage 
of which two glass scales at a determined distance apart are rigidly 
connected. The system to be tested is mounted between the Microscope 
and scales. In passing from one scale to the other, separated from it 
by a distance of 50 mm., the objective is changed in order to facilitate 
the adjustment. 
Microscopic Image of Transparent Bodies, f — Prof. Abbe explains 
the peculiarity of the phenomena which take place in the microscopic 
representation of bodies illuminated by transmitted light. In general, 
for each point of the object there is a corresponding point in the 
image. For bodies illuminated by transmitted light this is no longer 
the case. The rays from the source of light will on emergence from 
the object convert each point of its surface into a luminous point from 
which pencils are emitted in all directions. If, in the formation of 
the image, all of these pencils are made use of by the instrument, the 
image will then correspond to the object. This will happen when 
the angular aperture of the objective is sufficiently large to include all 
parts of the diffraction spectra formed on the boundary of the object. 
But where this is not the case different images may be obtained from 
the same object by blocking out certain of the diffraction spectra forming 
the image. It is also possible to obtain similar images from two differ- 
ent objects, if only those parts of the pencils which are common to both 
objects are made effective in the formation of the images, while the rest 
are blocked out. 
Dr. Czapski demonstrated the truth of these remarks by some ex- 
periments on gratings made with a projection apparatus. By blocking 
out those spectra which resulted from the effect of every second line, the 
* Zeitschr. f. Instrumentenk., xi. (1891) p. 44G, f Tom. cit., p. 447. 
