The Abbe Diffraction Theory. By J. W. Gordon. 3 73 



diffraction plate does not in any way depend upon the particular 

 diffraction spectra which contribute rays to its formation, and they 

 forcibly suggest that the features of this image are profoundly 

 affected by diffraction arising in the diaphragms themselves. 



This last suggestion points to a fresh line of experiment. If the 

 Abbe phenomena take their rise in the diffraction produced by the 

 Abbe diaphragm behind the objective, they should be slightly modified 

 by changes in the length of tube. For the scale of the diffraction 

 image produced by the diaphragm will vary directly with the distance 

 between the diaphragm and the visible image. Suppose then that 

 we displace the diaphragm from its position in the Abbe apparatus 

 and drop it actually upon the top of the objective. We can, as we 

 know, by a very slight alteration of the position of the stop beneath 

 the substage condenser, alter the angle of diffraction so that the same 

 spectra shall pass the apertures in this position as in the original 

 position. No difference will be made therefore in the conditions 

 required by the Abbe theory, but the diffraction image produced by 

 the diaphragm itself will be enlarged in the proportion of about one- 

 twentieth. This is not a great change, but it is visible, since it disturbs 

 the exact superposition or apposition of the outlying parts of adjacent 

 diffraction images upon which the Abbe phenomena really depend. 

 But this will appear more clearly at a later point in the present 

 paper. Suffice it at this point to say that the changes are such as 

 entirely to confirm the hypothesis on which the experiment is based.* 



Enough has now been said to show that observations upon the 

 Abbe diffraction plate, when made in a critical spirit, lend no 

 support to the Abbe theory, but even show it to be untenable. But 

 in order to cover, so far as I am able to cover it, all the ground of this 

 investigation, I desire, before parting from these experiments, to draw 

 attention to certain exhibitions of these same Abbe phenomena by 

 objects which are incapable of producing any diffraction spectra at all. 



First Experiment. — In the first place I propose to use the Abbe 

 apparatus of diaphragms upon a self-luminous object which Professor 

 Abbe himself places in a class apart, and which in fact is quite in- 

 capable of producing a diffraction spectrum of any sort. For this 

 purpose I take a ruled glass plate in which are a number of lines 

 traced at a distance of -,-^q in. apart in a film of soot. The lines 

 have the same proportional diameter — 1 to 7 — relatively to their dark 

 interspaces that the lines of the coarser ruling in the Abbe Diffraction 

 Plate have to their intervening spaces. This glass plate is arranged 

 at a suitable distance behind the substage condenser, and its image is 

 focussed upon the stage of the Microscope, side by side with the 

 ruling on the Abbe Diffractions Platte. By a little management the 

 aerial image of the carbon film may be made to assume the exact 



* This is a difficult experiment in any case, and is simplified if the tube of the 

 Microscope be shortened as much as possible. It is much easier to succeed with 

 six inches than with ten inches of tube-length. 



