372 Transactions of the Society. 



that question, for the second head of criticism leads to matter of much 

 greater consequence and less debatable significance. 



Suppose, then, that it had occurred to Dr. Zimmermann to chauge 

 the curvature of his illuminating light-waves, and so to bring the 

 excluded spectra into the field of view ; what would he have seen ? 

 Take for example his first experiment — that illustrated by figs. 73 

 and 74. He passes, in fact, from this to the condition of illumination 

 illustrated in fig. 75 by substituting a diaphragm with a wider opening 

 for that used in the first experiment. He might equally well have 

 passed to this second arrangement by giving to his light-waves, at 

 the point where they pass the diffraction plate, a cylindrical form with 

 a suitable radius of curvature. 



This implies only the placing of the stop a little farther from the 

 substage condenser, and of the substage condenser itself at a suitable 

 distance below the stage. Then, upon withdrawing the ocular and 

 looking down the tube of the instrument, he would have seen the 

 group of diffraction images figured in group B of fig. 72, of course 

 more closely packed, through the narrower opening in the diaphragm 

 of fig. 73. Here then are all the conditions for producing the image 

 of fig. 76 ; but on replacing the ocular and looking again at the object 

 •on the stage, he would have detected no change. It would still pre- 

 sent to his view only the blank field of fig. 7f. In the same way he 

 might with either of the diaphragms figs. 73 and 75 have produced 

 the conditions of illumination shown in group C of fig. 72. But 

 again, he would not thereby have changed the appearance of the 

 diffraction plate. He would have observed, on the contrary, that in 

 every case the microscopic picture assumed the features determined 

 by the shape and dimensions of the opening through which the image- 

 forming beam was passed, and independent wholly of the particular 

 grouping of diffracted rays which passed that aperture. 



The line of observation so suggested might have been pursue 1 in 

 experimenting with the diaphragm figured in fig. 79, and with the 

 same general result. He would have found that, however he varied 

 the selection of diffraction spectra passed through its apertures, he 

 made no difference in the resulting picture. But he might also have 

 made another observation of great interest with this piece of apparatus, 

 had he simply rotated it slowly around the axis of the instrument, and 

 noted down the changes which occurred in the image as it revolved. 

 He would have found that in passing from the pattern which he has 

 depicted to the true representation of the actual form, the image 

 developed a number of phases, some of which are, by reason of the 

 small scale of the object, difficult to see, but among which the trebling 

 of the coarse ruling and the doubling of the fine are clearly dis- 

 cernible. 



Now all these phenomena are not only unexplained by the Abbe 

 theory ; they are plainly incompatible with it. They show undeniably 

 that the pattern of the image formed in the Microscope of the 



