The Abbe Diffraction Theory. By J. W. Gordon. ""T' 1 



to the rotation of the axis of the antipoint produced by rotating 

 the diaphragm as indicated in the figure, and no doubt can be 

 entertained as to their origin. If now the modified apparatus used 

 for this experiment be replaced by the original Zeiss apparatus, all 

 these phenomena will be found to be exhibited by the Diffractions 

 Platte when viewed through the diaphragm with three slits. The 

 gradual disengagement of the phantom lines from the true lines as the 

 rotation of the diaphragm proceeds, the serrated edge along the top 

 and bottom of the figure, and the strengthening up of the phantom 

 lines to a brightness approximately equal to that of the true lines — 

 all these marks identify the Abbe experiment with the one last 

 described, and show that the Abbe phenomena take their rise in the 

 form of an antipoint, which resembles that depicted in fig. 8Q. 



It is now apparent that for the discussion of all questions involving 

 the resolving power of the Microscope, and indeed of any other optical 

 instrument, the form of the antipoint is of capital importance. Until 

 we know the form and dimensions which it takes, the degree of 

 correspondence between an object and its optical image must remain 

 unknown. The practical determination of this point presents no 

 difficulty. It is only necessary to take a luminous object sufficiently 

 small to be sensibly a luminous point, and to view it under the given 

 conditions, when the antipoint will actually appear in the field oi 

 view. But the mathematical law connecting point and antipoint 

 will be found to have been very fully investigated, and also to be 

 susceptible of a very exact statement. The first investigation of this 

 most interesting topic was, so far as I am aware, undertaken by 



