On the Estimation of Aperture. By Prof. E. Abbe. 4l1\ 



illumination is shown to be solely based on the fact that with an 

 oblique incident beam, diffraction beams can be taken-in by the 

 objective which are lost for the same aperture with a direct pencil. 

 It has been ascertained by various experiments that the peculiar 

 effects which arise from oblique illumination are always manifested, 

 even if the objects, from their well-known structure, cannot possibly 

 admit of shadow or similar effects. Moreover, it has been directly 

 shown that the benefit of this kind of illumination by no means 

 depends on obliquity quel obliquity. For if it were so it v?ould 

 necessarily involve the consequence that the same benefit must be 

 obtained by means of a direct pencil if the preparation were inclined 

 to the axis of the Microscope. The fact, however, is, that when 

 we have a structure (of any kind whatever) which is not depicted 

 in the ordinary position with direct light by an objective of given 

 aperture-angle, say 40^, it is never depicted by that objective when 

 the object is inclined at any angle, even if it is depicted in the 

 former position hy another objective of slightly increased aperture 

 only. 



Apart from all experiment, the first principles of undulatory 

 optics lead to the same inference. The laws of rectilinear propaga- 

 tion of the luminous rays, of reflection and refraction, are not 

 absolute laws. They arise from and depend on a certain relation 

 between the wave-lengths and the absolute dimensions of the objects 

 by which the luminous waves are intercepted, or reflected, or re- 

 fracted. They do not hold good unless these objects represent large 

 multiples of the wave-length. With minute elements, measuring a 

 fraction of X,, or a few wave-lengths only, we have nothing like 

 shadows or similar effects of solidity (and nothing hke prismatic or 

 lenticular refractions), for the same reason that we have no per- 

 ceptible acoustic shadow behind the trunk of a tree, except for 

 notes of a very high pitch. Luminous as well as sonorous waves 

 go all round obstacles whose dimensions are not large multiples of 

 their own length. 



The suggestion of a peculiar efficiency of obliquity in micro- 

 scopical vision, taken from the analogy of oblique vision and 

 oblique illumination in ordinary visual observation, is thus devoid 

 of any sound basis. 



Eegarding the other suggestion, illustrated by the analogy of 

 the 100 eyes around the object, this also has some very weak 

 points. Particularly, it overlooks one little difference. Suppose 

 these 100 eyes to be simultaneously used, and to receive on their 

 retinas the 100 different aspects of the object; and suppose, now, 

 all these various images collected upon the same retina — as is done 

 in the Microscope ; then you will conceive what would be the benefit 

 of such all-round or solid vision. In the same degree as there 

 would be a real difference among the various images, in the same 

 degree the total image would become more and more confused, and 



