7O VISION WITH THE COMPOUND MICROSCOPE 



diffraction spectra arranged as in fig. 62, should, according to theory, 

 show markings in a hexagonal arrangement. For there will be one 

 set of lines at right angles to b a e, another set at right angles to 

 c af, and a third at right angles to y a d. These three sets of lines 

 will obviously produce the appearance shown in fig. 63. 



A great variety of other appearances may be produced with this 

 same arrangement of spectra. Any two adjacent spectra with the 

 central beam (as b c a) will form equilateral triangles and give 

 hexagonal markings. Or by stopping off all but gee (or bdf) we 

 again have the spectra in the form of equilateral triangles ; but as 

 they are now further apart, the sides of the triangles in the two 

 cases being as \/ 3 : 1, the hexagons will be smaller and three times 

 as numerous. Their sides will also be arranged at a different angle 

 to those of the first set. The hexagons may also be entirely 

 obliterated by admitting only the spectra y c or </ f or bf, tv c., when 

 new lines will appear parallel at right angles or obliquely inclined 

 to the median line. 



By varying the combinations of the spectra, therefore, different 

 figures of varying size and positions are produced, all of which cannot 

 of course represent the true structure. 



In practice, indeed, it lias been proved that if the position and 

 relative intensity of the spectra, as found in any particular case, be 

 given, what the resultant image will be can be reached by mathe- 

 matical calculations wholly, and with an exactness that may even to 

 some extent transcend the results of previous observation on the 

 actual image of the object whose spectra formed the mathematician's 

 data. 



If P. angulatum be illuminated by central light transmitted 

 from an achromatic condenser, and examined by means of a homo- 

 geneous lens of large aperture, Mr. Stephensoii points out T that 

 under ordinary conditions it would show, on withdrawing the eye- 

 piece and looking down the tube, one bright central light from the 

 lamp with six equidistant surrounding diffraction spectra, produced 

 by the lines (' if, indeed, lines they be ') in the object itself. But let 

 a stop made of black paper, which entirely excludes the central beam 

 of light, be placed at the back of the objective and close to the ] s 

 terior lens ; in the stop let six marginal openings be made through 

 which the diffraction spectra may pass. On examining the image 

 we find that in lieu of the ordinary hexagonal markings the valve 

 appears of a beautiful blue colour on a black ground, and covered 

 with circular spots, clearly defined, and admitting of the use of deep 

 eye-pieces. 



This is precisely what we learn from Abbe that the diffraction 

 llii-nry involves. In support of this, the philosophical faculty of the 

 University of Jena had proposed as a question to the mathematical 

 students the effect produced in the microscope by these interference 

 phenomena. One problem was that of the appearance produced by 

 six equidistant spectra in a circle ; they correspond precisely with 

 the spectra of 1' . (ciujtihtitnii, as accessible to us with our present 

 numerical aperture ; and the diagram of the diffraction image, de- 



1 Jo urn. li.M.S. vol. i. 187s, |> INC,. 



