374 Transactions of the Society. 



dimensions of the Abbe ruling, so that here you have in the same 

 field two objects visibly alike, but differing, from the present point of 

 view, in the important particular that the one can and the other 

 cannot be made to yield a diffraction spectrum. Now we can repeat 

 Dr. Zimmermann's experiments and the other Abbe tests upon both 

 these objects simultaneously, and in all cases it will be found that 

 there is no difference between the behaviour of the one and that of the 

 other. When the one is blurred the other is blurred ; when the 

 ruling appears doubled in the one, it appears doubled in the other ; 

 when it appears trebled in the one, it appears trebled in the other ; 

 and so forth. Whatever results the diffraction plate can be made to 

 yield, this ghostly grating, with no diffracted rays to be manipulated, 

 contrives to yield also. 



Second Experiment. — Yet another experiment of the same sort, 

 and this time I propose to cut loose from the Microscope altogether, 

 and ask you to observe the Abbe blurring, the Abbe doubling, and all 

 the other Abbe phenomena, upon an object as large as the diagram 

 which stands as fig. 70 in this paper. This time the optical instru- 

 ment with which I propose to work is the eye itself, and it is, of 

 course, necessary to modify the Abbe diaphragm if it is to be applied 

 direct to the eye, in accordance with the reduced focal length of the 

 instrument. In the Microscope the distance between the Abbe dia- 

 phragm and the plane of the image is about 9 in., in the eye it is 

 effectively about f in., or perhaps less. The exact distance, of course, 

 depends on the distance at which the diaphragm is held in front of 

 the eye, and must be measured between a corresponding point within 

 the eye and the retina. Somewhere between fifteen and twenty will 

 be the proper numerical ratio between the two sets of diaphragms ; 

 and as nothing turns on a very exact reproduction, I have prepared a 

 number of diaphragms in which the apertures and their spacing have 

 dimensions -Jg- of those of the Abbe diaphragms. If now you will 

 take one of these diaphragms, and, holding it close to the eye, look 

 through it at fig. 70, holding the paper at a full arm's length from 

 the eye, you will see that all Dr. Zimmermann's phenomena are 

 reproduced. 



The significance of these results is wholly unmistakable. It 

 cannot indeed be said of fig. 70, as of the grating last described, that it 

 cannot yield a diffraction spectrum at all. Theoretically it would no 

 doulit give off diffracted rays at extremely small angles to the prin- 

 cipal ray. But their angles of deviation would be insensibly small 

 and their brightness insensibly feeble : they cannot, therefore, enter 

 into the explanation of the strongly marked phenomena which you 

 have just witnessed. These are due, as are the analogous phenomena 

 of the diffraction plate, to diffraction in the diaphragm itself. 



It is easy to perceive, when once this point is realised, that the 

 Abbe phenomena may be exhibited by a modified form of the Abbe 

 apparatus on a much larger and more easily intelligible scale than in 



