THE THEORY OF APERTURE IN THE MICROSCOPE, 331 
angular aperture notation will be readily suggested by an examin- 
ation of the zumerical aperture table already referred to. 
Of the practical utility of wide-angled objectives every micros- 
copist knows something. However much we may differ as to the 
utility of wide angles for low or medium powers, we all know that 
the resolving capacity for such minute structure as the striz of 
diatoms in any given power is in direct relationship to the aperture. 
A half-inch dry objective of 60° will show the dotted structure of 
Pleurosigma formosum or P. hippocampus, which the same power 
of 40° will fail to resolve under any conditions of illumination of 
the object. This property is found in all lenses to increase with 
the aperture, until the highest numerical aperture is attained. 
The capacity for resolution, inherent in wide angles, was formerly 
supposed to rest upon the increase in the quantity of light trans- 
mitted by them, and in the obliquity of the marginal rays enabling 
us in some mysterious manner to see round the object. The 
researches of Professor Abbe have, however, proved that the 
microscopical vision of very minute structure depends upon other 
considerations than the ordinary laws of geometrical optics, and 
can be explained only by a reference to physical phenomena. 
There is, perhaps, no theory more firmly established on a 
physical basis than the undulatory theory of light. If a wave of 
light cannot actually be seen, it can be and has been measured. 
According to Angstrém, the length of a wave of monochromatic 
light varies from .7604, corresponding with the dark line A in the 
extreme red of the solar spectrum, to .3933 at the line H2 in the 
extreme violet (tu or micromillimetre = j>y'55 Of a millimetre, or 
rather more than sz, Of an inch); the line E near the centre of 
the luminous spectrum in the green having a wave-length of .5 269, 
or about z<4g5 of an inch, which is about the distance of the striz 
on P. angulatum. So long as the visible details of an object are large 
enough to be many multiples of the wave-length of light, the rays 
are propagated from them in rectilinear directions, as in ordinary 
vision, or as seen through the telescope; but when these details 
are only a few multiples of the wave-length, the rays are intercepted 
by the minute elements of the structure, diffracted from their rec- 
tilinear paths, and result in spectra or distorted images. The 
number of diffraction spectra proceeding from any minute struc- 
tural element will depend upon its morphological character ; and 
-the amount of separation of the spectra from the rectilinear direc- 
tion will depend upon the minuteness of the intercepting structural 
particles. The more complicated the structure the more numerous. 
the spectra ; the smaller the particles, the greater the separation. 
If an object containing minute structure be viewed through the 
microscope, and the image formed upon the retina be a combina- 
tion of all the diffracted rays, the real structure of the object may 
