706 
which approach each other more and more. If the aperture of the 
projection-objective is MN and the wave-length of the light 2, the 
distance of the still distinguishable points or lines is generally 
assumed to be: 
a 
‘2 aN 
which for N= 0,95 and 42= 0,6 u yields the value of 0,31 u for /. 
The central diffraction-discs, which are formed in the image of each 
of the two luminous points, overlap for the distance of the length 
of the radius of the discs. 
On the other hand a thread of 0,2 u is represented sharply defined 
and contrasted with an objective of the same aperture. The edges 
are so sharply drawn that a number of small unevennesses becomes 
separately visible. 
6. When the same thread is represented with an objective the 
aperture of which is 0,18, the image becomes, indeed, less sharply 
contrasted and less detinite, but it remains clear enough to be useful 
for many purposes. In this the central diffraction discs formed of a 
luminous point on one edge of the thread, and of one of an opposite 
point on the other edge overlap to an amount of P= 94°/, of the 
diameter of the discs. 
7. In the direct observation of threads without application of the 
microscope we found as maximum values of P.... 98,2°/, and 
98,5°/,. Probably equally great and even greater values of P can 
be reached in the case of microscopic representation. 
8. There is every reason to assume that with commercial objectives 
a serviceable image may still be obtained of a thread of 0,04 uw. 
At the meeting photos were, in fact, exhibited of a bombarded quartz 
thread, the diameter of which was to all probability of the said 
order of magnitude. 
