480 PROCEEDINGS OF THE SOCIETY. 



which I am concerned to uphold ; but at the same time, to prevent mis- 

 understanding, I wish distinctly to dissociate myself from many of 

 the chief deductions that have been drawn from this theory, notably, 

 that narrow cones of light are preferable to wide ones, and that there 

 are no reasons why a wide cone should yield a more correct projection 

 of the object. On the contrary, I hold that the Abbe school have not 

 correctly applied their own fundamental principles, and that the elimina- 

 tion or rather the contraction of diffraction fringes, etc., can be readily 

 shown to occur by the destructive interference of the elementary rays 

 of varying obliquity into which the cone of light can be analysed. 



This, however, is a digression, and I now revert to Mr. Gordon's 

 paper. 



In the first place we find certain arguments based upon the fact, 

 that the diffraction lines in the image are supposed to be images of the 

 light source, and that therefore these diffraction lines ought not to shift 

 so long as the light source is kept in its place, although we may shift 

 the object across the stage. Now this seems to be based on an entire 

 misconception. I think Mr. Gordon will find he has misinterpreted a 

 passage in Naegeli and Schwendener (p. 231), which, taken by itself, 

 might possibly suggest the above, but does not do so if read in connec- 

 tion with the context and the diagram to which it refers. This is the 

 only place in Naegeli and Schwendener which I can find as at all lend- 

 ing itself to the assumption made ; and in Dr. Zimmermann's book or 

 other works dealing with the Abbe theory, I have never seen it sug- 

 gested that the diffraction lines in the image plane of the Microscope 

 are images of the light source. The images of the light source in the 

 experiments referred to are near the upper focal plane of the objective, 

 and these images, as is well known, do not shift, which is in accordance 

 with theory. The rays forming the lines in the image plane may each 

 and every one have passed through the points in the upper focal plane of 

 the objective which constitute the images of the light source, and may, 

 in that particular sense, have been derived from these as secondary inter- 

 ference effects ; but that is quite a different matter. Suppose we project 

 the image of the object on a screen without using an eye-piece. Then 

 we should have images of the light source near the back focal plane of 

 the objective ; and if it were supposed that we again had images of the 

 light source on the screen, we should have two sets of images of the 

 light source, without so much as a lens of any sort between them to 

 form the one image from the other. 



The argument that we do not see candle-flame images in the image 

 plane, though we do in the focal plane of the objective, and all other 

 arguments based on the idea that the assumption above stated has been 

 held, do not therefore touch the Abbe diffraction theory.* 



We next come to Mr. Gordon's contention that the Abbe theory is 



* To avoid any possible misunderstanding, I wish to point out that I do not 

 contend that images of the light source can never be formed in the image plane 

 of the object, but only that under the conditions of the experiments under discussion 

 this is not the case. 



We can and do get diffraction images of the light source in the plane of the 

 image of the object, if the light is actually focussed on the grating or object ; 

 but unless the light source is confined to exceedingly small limits, its dioptric and 

 diffraction images overlie to such an extent that they cannot be separately dis- 

 tinguished. 



