102 THEORY OF THE MICROSCOPE. 



XI. 



DIFFEACTIONAL ACTION OF THE ATERTUEE OF 

 THE LENSES. 



IF we view a luminous point, say the reflexion of the sun on a 

 thermometer bulb, through an aperture of about *5 nun., e.g., a 

 needle-hole in a card, it will appear as a bright circular disc, 

 surrounded by alternately bright and dark rings. If we substitute 

 for the luminous point a bright image-surface of fine markings, 

 the diffraction figures of adjacent luminous points will encroach 

 on each other similarly to the dispersion circles in the dioptric 

 image of non-aplanatic systems of lenses. The action is therefore 

 identical ; the fine details disappear in both cases, and the image 

 appears faint. 



A similar diffractional action takes place in high-power objective- 

 systems, in which the clear aperture decreases more and more with 

 the focal length. This action is entirely independent of other 

 deficiencies of construction ; it takes place in objectives that are 

 as free as possible from aberration, just as necessarily as in those 

 of inferior construction, and attains such a degree in the highest 

 powers, that any further increase of magnification must be entirely 

 useless. 



The absolute measure of these disturbances may be theoretically 

 determined. 1 We can prove that its influence is universally pro- 

 portional to the magnitude of the last aperture-image above the 

 eye-piece, and that its action is exactly equivalent to viewing the 

 microscopic picture, regarded as free from the difiractive eifect, 

 through a small aperture of the size of the aperture-image. From 

 what we have already shown, the diameter d, of the aperture- 

 image, is found by the formula 



1 See Helmholtz : " Pogg. Ann., Jubelband," p. 557, and specially p. 579. 

 A generally applicable mathematical explanation of these phenomena has been 

 promised by E. Abbe (" Archivfiir mikr. Anat." Bd. ix. p. 432). 



