18^8.] MICROSCOPICAL JOURNAL. 101 



means really good moderate powers can be used up to 

 their full aperture, rendering the very finest hairs as 

 tapering to a perfect point, with entire absence of the 

 diffraction-fringes shown round such details with a 

 narrow pencil. Where and why " resolution " often 

 fails with high powers as regards some objects ho illu- 

 minated, belongs to the question before us, and is dealt 

 with presently ; but the method can be carried much 

 farther than many would suppose. The diatom P. 

 angulatiim (45,000 to the inch) is resolved by it beauti- 

 fully with a dry lens ; and this self-luminous resolution 

 has the cardinal superiority over Abbe's with a narrow 

 pencil, that by no possibility can any images be pro- 

 duced by it other than the small white disks on dark 

 ground, or black spots on white ground, at different foci, 

 which can be produced in the same way from a sheet of 

 perforated zinc. By grinding the back of the slide itself* 

 even an immersion-lens can be more or less filled with 

 direct rays, and in this way all the spots can be seen 

 (a.9 spots, and not falsely as spherules) in A. Lindheimerii 

 (69,000 to the inch). With a flrst-rate apochromatic and 

 one of the slides mounted in sulphate of arsenic, I have 

 seen the strisB in A. pellucida ; though with such objects 

 as these the method comparatively fails. 



13. We may also compare the results of mathematical 

 analysis with those of experiment. We have two kinds 

 of possible image, for the Abbe or '* spectrum " image is 

 a real fact enough under the necessary conditions; our 

 inquiry here is simply what proportion and value must be 

 assigned to it in ordinary research. Lord Rayleigh's 

 articles here and elsewhere seem to supply useful criteria 

 as regards that question. He shows that according to 

 the " spectrum " theory a square and circular aperture 

 of the same width give the same resolution for points or 

 short lines. On the other hand, respecting the resolu- 

 tion of self-luminous 1 ines of sensible length, another 



