251 



of a much finer structure than the real one, the fine lines being doubled 

 and the coarse ones quadrupled. 



Proceeding to the examination of more complex phenomena, it was 

 pointed out that the spectra were formed in a direction perpendicular to 

 the lines producing them, and conversely the spectra produced lines per- 

 pendicular to their own direction. The phenomena were interchangeable 

 and reversible. 



Two series of lines crossing each other at right angles produced a very 

 complex arrangement of spectra, but it would be easily understood by 

 keeping in mind what had been said about the spectra of a series of lines in 

 one direction only. 



By using a diaphragm with a slit which admitted the spectra in one 

 direction only, say a horizontal series, it was found that the vertical lines 

 of the grating alone were visible ; on rotating the slit 90° the horizontal 

 lines only were seen, and by selecting spectra at an angle of 45° the hori- 

 zontal and vertical series were invisible, being replaced with spurious 

 diagonal lines. A diaphragm with a cross-slit enabled two sets of lines to 

 be seen, false or true according to its position and consequent selection of 

 spectra. 



The experiments demonstrated the importance of admitting all the 

 diffraction spectra which the object gave rise to, in order to see truly the 

 details under the microscope. 



The important bearing of the subject with reference to the markings on 

 diatoms was alluded to. One of the series on Professor Abbe's diffraction 

 plate consisted of lines intersecting each other at an angle of 60°; the 

 diffraction spectra produced by this object closely resembled those pro- 

 duced by Pleurosigma angulation. 



When with this series of rulings the dioptric beam alone is admitted, the 

 lines disappear as in the preceding experiments, the conditions closely re- 

 sembling those of Pleurosigma angulatum viewed with an objective, say of 

 50° or 60°, incapable of resolving it. If the examining eye-piece be used, 

 it will be found that no diffraction spectra are contained in the field ; there- 

 fore, as before shown, no markings are visible. Changing the objective for 

 one of larger aperture, say 80° or 90°, so long as the light is central, the 

 appearance of the emitted pencil is the same as before ; but by pushing 

 the mirror aside the dioptric beam can be moved to the margin, and one or 

 two of the diffraction spectra brought into view near the other side. If the 

 diatom is now viewed, one or two series of cross lines can be seen. This 

 explains how, by the old process of skilfully dodging with the mirror, a 

 diatom could be resolved. The peculiar qualities of immersion objectives 

 were briefly alluded to, especially the fact discovered by Professor Abbe 

 that although their angular aperture might be smaller than that of a dry 

 lens, yet they were larger in real and effective aperture, and their capa- 

 bilities of including diffraction spectra and consequently giving greater re- 

 solving power were enormously in advance of any dry objective that could 

 possibly be constructed. 



