192 PROCEEDINGS OF THE ACADEMY OF [March; 



requires the presence of both dioptric and diffracted beams. Fur- 

 thermore, he lays stress on the fact that diffraction in the aperture 

 of the objective will result in every point being imaged by a "disper- 

 sive circle" (the "antipoint" of Gordon) of greater or less size accord- 

 ing to circumstances, and recommends the examination of a brightly 

 illuminated object through a pinhole one-two hundred and fiftieth of 

 an inch in diameter in a card or piece of tinfoil, to secure an idea 

 of what must be the appearance of the best image that could be pro- 

 duced through a microscope magnifying five thousand diameters, 

 even if the construction was perfect. 



If his later application of the diffraction theory to the images of 

 coarser details, earlier termed "absorption images," could be inter- 

 preted as a denial that any refracted rays, outside the dioptric beam, 

 entered into the image at all, then indeed some modification is neces- 

 sary, as most objects unquestionably refract light outside the dioptric 

 beam; and not only do the simplest laws of refraction require that these 

 rays find a place in the image, but there is no other way of accounting 

 for what becomes of them. It is more likely, however, that Abbe 

 regarded this fact as self-evident. At any rate, the important work 

 he undertook was not to refute the dioptric theory, but to supplement 

 it by accounting for phenomena which it then, as now, failed to ex- 

 plain. He has done this in so eminently satisfactory a manner that it 

 would appear that his theory, in all essential details, must be accepted, 

 unless someone can bring indisputable experimental proof of the 

 formation of a microscopical image that goes beyond its possibilities. 

 Any experiment that merely demonstrates failure to fully realize the 

 possibilities of the Abbe theory, on account of interference with image 

 formation due to diffracted rays arising in the aperture of objective, 

 or anywhere except in the object itself, is not pertinent, as this 

 unavoidable limitation was evidently fully recognized in evolving 

 the theory. 



