Capacity of the Mioroscojoe, By Prof. HelmhoUz. 33 
For white light we may, as before, take the wave-length of the 
medium bright rays. • 
Ao = 0-00055 mm. 
If ao = 90^, then 
6 = ^ = 0-000275 ram. = mm., or inch. 
Were it possible to obtain with an immersion lens the trans- 
mission of rays = 180° of divergence aperture (in water), a would 
then = 90° and X nearly J X-o ; and hence 
According to measurements of Harting,* the magnitude of the 
smallest distances taken with No. 10 objective of Hartnack, reckoned 
by our formula, is 
« = 33T3 T^^- 
The figures s^tu Mini, given by Harting refer to the width of 
the dark space between the lines. In close accordance with the 
above are the measurements by Herr L. Dippel,t of fine diatoms, 
who found that the closest series of lines that he could distinguish 
= ^3\rF mm., and the finer Nobert lines = -^eV^ (^o^ttu inch). 
Earlier measurements, 1853, of Messrs. Sollitt and Harrison, i count 
much higher. Eecognizable lines of Navicula Arcus are said to have 
been counted at 5120 to the mm. (x^eWo- inch). This far exceeds 
the theoretical limits for objects in air. But since all later 
measurements remain much lower than these, I do not know that 
they are trustworthy. Harting also, who cites them, doubts their 
accuracy. 
Besides any possible further increase of angular aperture in the 
case of objects lying in water, the capacity of performance might 
perhaps be increased by employing blue rays only. § 
In photography, blue light is chiefly active, and photographs 
appear actually to perform more than the eye can with white light. 
In a photograph of Surirella gemma, executed by Dr. Stindi, with 
an objective of Gundlach's, giving -^-^ amplification, lines are 
visible which may be counted at 3800 to 4000 in the millimeter 
(tWow of English inch). 
Thus it appears to me beyond doubt that difiraction of the rays 
is the principal cause of the hmitation of sharpness of the micro- 
scope image. In comparison with difiraction, chromatic and spherical 
* Published in vol. cxiv. of Poggendorff 's ' Annals.' 
t In his work on the Microscope: Brunswick, 1867. 
i ' Quarterly Journal Microscopical Society,' vol. v. p. 62. 
§ Hartnack made an illuminating apparatus for use of blue rays only, and 
exhibited it in the Vienna Exhibition, 1874. 
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