ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
679 
system. Prof. Abbe makes the angle zero by the use of a sufficiently 
small diaphragm in the front focal plane of the system, the effect of 
which is to make the system on the side of the image “ telecentrisch,” 
i. e. the axes of all the pencils emerging from the system, as seen in 
fig. 77, are parallel to the axis of the system. 
(3) The third requirement in any method of precision depends on the 
following considerations ; — 
It is in the nature of dioptric systems that in general the images are 
not in all parts proportional to the objects, but that the ratio of the 
Fig. 77. 
magnitudes of the two is a function of their dimensions. For this 
reason, if conclusions on the fundamental properties, e. g., the focal 
length, are to be drawn from the magnification which a system has in 
any two conjugate points, only a very small central part of the image 
must be used in the measurement. On the other hand, however, the 
measurement of the magnification is always more exact, the greater the 
object and image. 
The simplest way to satisfy these somewhat conflicting requirements 
is to take several measurements on large images, gradually diminishing 
in size, and from the result of these relatively exact measurements, to 
calculate the fundamental value of the magnification, i. e. that value 
which would be found for the infinitely small central part of the image. 
The author shows how these three requirements are fully satisfied in 
the Abbe method for determining focal lengths. 
In this method, the determination of the focal lengths depends upon 
the magnifications which the system gives of two objects at a determined 
distance apart. 
If/ is the focal length of the system, the magnification for one 
pair of conjugate points, N 2 that for another pair, and a the distance of 
the object planes apart, then (fig. 78) 
N, N 2 
Two exactly divided scales in and 0 2 serve as objects. The first 
requirement is satisfied by the fact that it is the distance of the objects 
and not that of the images which has to be measured. 
In order to satisfy the second, a small diaphragm may be brought 
into the front focal plane F of the system, and measuring arrangements, 
for determining the magnitude of the images, in the planes Pj and P 2 , 
behind the system. 
