32 
On the Limits of the Ojotical 
a dark field, or vice versa, for the reasons which I have already 
given in my ' Handbook of Physiological Optics ' (p. 217), in discuss- 
ing the capacity of the eye for distinct vision. For in the cases 
above mentioned the result depends not only on the proportional 
magnitudes of the images, but also on the susceptibility of the 
retina to slight difi'erences of light. The most suitable objects are, 
here also, fine gratings which show alternate clear and dark stripes. 
Such indeed are in common use, as in the examples of Nobert's 
lines, and the line systems of diatoms and insect scales. But as the 
light of the bright stripes is doubtless strongly dispersed before it 
becomes quite undiscernible, dependence can be placed only on the 
measurement of the space between the centres of two contiguous 
stripes, and not upon the measurement of space occupied by the 
stripes (wide or narrow) as originally distributed. I select, 
therefore, as the measure of the minutest distinguishable objects, 
that smallest appreciable interspace between the centres of two 
contiguous stripes by which these stripes can still be recognized as 
separate. 
When diffraction is caused by a fine network of square meshes, 
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. For 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 outermost fringes in 
the spectrum of a bright spot are of equal width, but the inner- 
most 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. For this reason I have, in the following demonstrations, 
taken the width of the outermost fringes of a circular meshwork as 
the lower Hmit of distinguishable distances in an object. It is not, 
however, impossible that by some fortuitous overlapping of images, 
objects of still 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 recognizable interspace, 
X wave-length of the medium, 
a divergence angle of the rays incident in that medium, 
Xq aQ the values of the last-named magnitudes (X and a) for air. 
Then by the formulae deduced in a subsequent page, 
2 sin. a 2 sin. Cp 
