368 Transactions of the Society. 



call attention to it in this connexion ; for, although it is one of those 

 things which everybody knows, it is also a point which everybody 

 appears to have forgotten in the discussion of the Abbe theory and 

 phenomena. For example, among other extravagant inferences which 

 have been deduced from the Abbe theory, is the conclusion that 

 striated structure having centre distances less than half a wave-length 

 of light can never be microscopically resolved, because it is said such 

 a structure would produce such a wide dispersion of the diffracted rays 

 that no objective could possibly embrace both the direct beam and 

 even the nearest diffracted beam in its grasp, and Professor Abbe has 

 himself published a table which purports on this principle to set the 

 final limit upon the performance of various classes of objectives 

 deduced from their several angles of admitted light.* All such de- 

 ductions would be strangely precipitate even if the Abbe theory were 

 correct ; for, although it is quite true that you cannot extend the 

 angular aperture of any objective to include the first diffraction image 

 of such a structure formed by plane waves of light, it is equally true 

 that by substituting spherical waves of short radius for plane waves in 

 the illuminating light, you can bring not only the first but all the 

 rest of its diffraction images into the field of your objective. On Abbe's 

 own theory, therefore, there would be an alternative solution of the 

 problem of augmenting the resolving power of the Microscope. _ It 

 would be completely and absolutely solved for all kinds of objectives 

 by the simple expedient of critical illumination. 



But I have travelled back to the region of theory, and must 

 return to Dr. Zimmermann and his account of the Abbe experiments. 

 The object of the digression is to point out the great importance for 

 judging of the bearing of these experiments upon the Abbe theory of 

 realising and considering the conditions of illumination under which 

 the experiments are made. Bearing this in mind, we will submit once 

 more to Dr. Zhnmermann's guidance. 



" As has been already shortly stated," he writes (p. 47), " the 

 image of the object t arises from the interference of the light- waves 

 which originate in the diffraction spectra described in the last para- 

 graph, and lying in the upper principal focal plane of the objective. 

 It may in fact be shown by exact calculation for this simple case that 

 in this way a perfectly correct picture of a structure is produced so 

 soon as the entire diffraction image is taken up by any objective, and 

 that on the other hand nothing whatever is visible in the microscopic 

 picture unless, in addition to the direct (white) image of the source of 

 light, at least one diffraction spectrum passes into the given objective." 

 Having thus explained the nature of the theoretical demonstration, 

 he excuses himself from going into it upon the ground that the 

 calculations involved are too intricate for his book, and proposes as 



* Journal K.M.S., 1SS2. p. 463. 



t That is, the image in the upper focal plane — in this oase — of the diffraction 

 plate- 



