680 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
None of the measuring arrangements, however, at present known 
would sufficiently satisfy the third requirement by presenting a large 
enough part of the image for measurement. To obviate this difficulty a 
micrometer-Microscope may be made to move parallel to itself, and to 
the axis of the system from one end of the image to the other, e. g. from 
the ray E to the ray G. Different parts of the image are thus brought 
Fig. 78. 
into the field of view, and the magnitude of the displacement required 
in order to bring certain parts of the image into a determined part of 
the field, is equal to the distance between those parts of the image. 
When the micrometer-Microscope is provided with cross- wires in the 
eye-piece, a further simplification follows. For if the axis, i.e. the line 
joining the centre of the cross wires to the hinder principal focus of the 
micrometer-objective, is parallel to that of the system to be measured, 
and keeps parallel to it during the displacement at right angles to that 
axis, then only pencils, the axes of which are parallel to that axis, come 
to a focus. Thus by this arrangement the telecentric path of the rays is 
obtained without the necessity of inserting a diaphragm in the front 
focal point of the system. 
An arrangement however to effect the exact parallel displacement of 
the Microscope, if technically possible, would render the instrument 
costly and perhaps detract from its functional exactness. To avoid this, 
Prof. Abbe, instead of making the measuring arrangement (the Micro- 
scope) displaceable with respect to the objective, has made the latter 
movable at right angles to its axis and parallel to itself, while the 
Microscope and scale remain fixed. The displacement Y of the objective 
necessary to pass from the image of one point of the object to another is 
then the magnitude of the image ; the magnitude of the object to be 
compared with this is equal to this displacement, minus the real 
distance y of the two points of the object which were successively 
adjusted, i. e. to Y — y. If then /3 X and /i 2 denote the reciprocals of 
the magnifications N x and N 2 , we have 
/ = 
a 
where /3 1 = 
y 1 D — ^ 2 V2 
Y x ’ ^ - Y a * 
The apparatus itself (figs. 79 and 80) is essentially a large Microscope. 
Almost the only difference is that in the lower part there is a metal 
frame for the reception of a glass seal© T, A second more finely 
