356 SUMMARY OF CURRENT RESEARCHES RELATING TO 



delineated hy means of one or a few diifraction beams, is in general 

 a more imperfect and incomplete image than another which is 

 depicted by means of a greater part of the total diffraction group. 

 The images of coarse objects are perfectly similar to the objects, 

 because even small apertures are capable of admitting the ioJiole group 

 up to the limit of vanishing intensity of the deflected rays. 



To put it in another way. The interference image of any object 

 must become more and more similar to a simple dioptric image when 

 the elements become coarser and coarser, and the breaking up of the 

 rays by diffraction is confined to smaller and smaller angles. When- 

 ever these angles of the diffraction groups are very small compared to 

 the aperture angle of the objective, the result of the interference effect 

 is the same as if there were no diffraction at all, and the object were 

 dejncted as if self-luminous. 



(2) The Delineating Power of Objectives and Aperture. — So 

 far we have not supposed the existence of immersion objectives or of 

 npertures exceeding the equivalent of 180'' angular in air, indeed 

 Prof. Abbe's views were developed at a period when opticians had not 

 recognized the possibility of constructing objectives with so large 

 apertures. 



The two considerations with which we have however dealt— the 

 existence of apertures in excess of 180° in air, and the function of 

 increased aperture — may now be combined. 



The beams of diffracted light which emanate from any structure 

 are, as we have seen, by no means indifferent and accidental things in 

 the action of the Microscope, the efficiency of the instrument depend- 

 ing essentially on their admission. Unless at least one of these 

 diffracted beams is admitted by the objective, together with either 

 another beam or the direct incident pencil, no indication of structure 

 is visible in the microscopical image. It will be important therefore 

 to consider the conditions upon which this admission depends, that is, 

 the aperture of objectives. If aperture is of any general scientific 

 interest at all, and not a mere matter of abstract dioptrical doctrine, 

 its definition must afford a clear and correct indication of so important 

 a function of the objective as the admission or non-admission of rays on 

 which the effect of the Microscope is based, that is, of its delineating power. 

 1. Suppose any object composed of minute elements in regular 

 arrangement, such as a diatom valve ; and to confinf the con- 

 „ ^.„ sideration to the most simple case, sup- 



pose it illuminated by a narrow axial 

 pencil of incident rays. If this object 

 is observed successively in air and bal- 

 sam, or any other dense medium of 

 refractive index n, the radiation from 

 every point of the object is, in conse- 

 quence of the diffraction effect, com- 

 posed of an axial pencil S, Fig. 108 

 (the direct continuation of the incident rays), and a number of bent- 

 off pencils S,, Sj . . . inclined at the angles jCj, W2 the first, 

 second . . . deflected beams on all sides. Denoting by A the wave- 



