552 Transactions of the Society. 



only the outermost zone of an object-glass, a large central portion 

 of the aperture is capable of yielding a good image of such a coarse 

 structure, which is only " fogged " by the scattered light which has 

 passed through the marginal zone. The dots, on the other hand, 

 are brought out by the regular diffraction-spectra corresponding to 

 them, and in accordance with figs. 127a to 127d, combinations of 

 these can only enter through the marginal zone ; the image of the 

 dots therefore is formed by, and indicates the focus of, the marginal 

 zone, whilst the image of the outline is due to light passing through 

 the axial portion of the object-glass. 



This peculiarity of the image formed by an under- or over- 

 corrected objective may therefore be claimed as constituting a 

 proof that objects do not behave as if they were self-luminous. 



An even more remarkable fact bearing on the subject is men- 

 tioned in our standard handbook of Microscopy.* It is that with 

 difficult diatoms resolution is sometimes emphasised when an 

 analyser is interposed between the object and the eye. As it is 

 universally accepted as a criterion of a self-luminous object that 

 the light from it is quite free from any trace of polarisation, this 

 observation again proves that the object does not behave like a 

 self-luminous body. At the same time it is a remarkable piece 

 of evidence in favour of the Abbe theory ; for when the effect of 

 gratings is studied more rigorously than by the usual more or less 

 elementary approximation, the result is arrived at that the diffracted 

 pencils are polarised, the amount of the polarisation depending 

 largely on the angle between the direct and the diffracted light, 

 but also on the nature of the edges of the slits, etc. This observa- 

 tion, which in the above quoted passage is put forward as a 

 puzzling one, is therefore a direct refutation of the spurious disk 

 theory and an equally direct proof of the correctness of the Abbe 

 theory. 



The chief results of this inquiry into the theory of microscopical 

 vision may now be summarised as follows : 



1. The spurious disk theory, being based on the inadmissible 

 assumption that microscopical objects could be made to behave as 

 if they were self-luminous, must be abandoned. 



2. The images obtainable from plane gratings of various types 

 can be fully accounted for by the Abbe theory, provided that the 

 phase-relation as well as the intensity of the diffraction-spectra is 

 taken into consideration. 



3. The advantages derivable from so-called aplanatic cones of 

 light are : 



(a) That the image acquires that fixity of focus which is 

 desirable and indeed necessary in order to distinguish 

 spurious " ghosts " from the image formed in the plane 

 of the geometrical image. 



* Carpenter, Dallinger, 8th edition, bottom of page 381. 



