430 LIMITS OF OPIICA-L C\PACITY OF THE MICROSCOPE. 



it can be proved that the network must appear as a uniformly 

 illuminated surface when the breadth of fringe of diffracted light is 

 equal to that of the open space of the network. Por circular 

 meshes, the integration for calculating the distribution of light is 

 tediously diffuse. When the diameter of a circular mesh is equal to 

 the length of one side of a square mesh, the outmost fringes in the 

 spectrum of a bright spot are of equal width, but the innermost 

 fringes are wider in the circular meshwork. If, therefore, the 

 fringes of the square meshes are so broad as to efface all impression 

 of separate bright lines of the network when the measured widths 

 of fringe and mesh are equal, the same thing must happen with the 

 circular meshwork, a portion of whose diffraction-fringes is still 

 wider. Tor this reason I have, in the following demonstrations, 

 taken the width of the outermost fringes of a circular meshwork as 

 the lower limit of distinguishable distances in an object. It is not, 

 however, impossible that by some fortuitous overlapping of images, 

 objects of stni smaller dimensions might, occasionally, be half seen, 

 half guessed at. But safe and certain recognition will scarcely be 

 possible. 

 Let now — 



e be the magnitude of the smallest recognisable interspace 



\ wave length of the medium, 



a divergence angle of the rays incident in that medium, 



Xo Uo the values of the last named magnitudes (A. and a) for air, 

 Then by the formulae deduced in a subsequent page — 



e = — ^— = — ^°— 



2 sin a 2 sin a^ 



For white light we may. as before, take the wave length of the 

 medium bright rays. 



Xo = 0.00055 mm. 



If a^ = 90° then £ = ^° = 0*000275 mm. ^ — i-^ mm. or 

 2 3,636 



— inch. 



92,000 



