1909.] NATURAL SCIENCES OF PHILADELPHIA. 189 



of an hour's experimenting was a tired eye and the conviction that it 

 was absolutely impossible for anyone with eyesight good enough to 

 use the microscope at all to perform this experiment with the results 

 claimed. Nevertheless, devoid as it is of the slightest basis in either 

 fact or deduction, it is offered as one-half of all the evidence necessary 

 to refute so well considered a theory as that of Abbe. As it should 

 succeed under the dioptric theory, it indicates the inadequacy of that 

 theory alone to account for microscopical image formation. 



One more experiment, of the many made, may be worth mention- 

 ing. For this will be required an objective that will stand full cone 

 illumination, and a Nobert test plate or other series of rulings will 

 supply the object. No objective of more than very low power and 

 aperture will fully fill the specifications, which would require resolu- 

 tion with a full cone, equal to that with oblique light, but an old Spen- 

 cer one-half inch of 70°, which approaches perfection more closely than 

 any other objective I have seen, was found to answer the purpose. 

 If illuminated with a cone completely filling its aperture, it will be 

 found that the seventh band of the Nobert plate is well resolved, and 

 if the aperture of the illumination be cut down as far as the iris will 

 close, so the dioptric beam seen at back of objective will not exceed 

 one-twenty-fifth of the diameter of the back lens, the third band, 

 which is just twice as coarsely ruled as the seventh, will still be easily 

 and distinctly resolved. Now the aperture of the illuminating cone 

 has been cut to one-twenty-fifth, and by a strict interpretation of the 

 dioptric theory the resolution should be impaired to a similar extent, 

 but it is found to be one-half as great as with the full aperture. This 

 will be answered by the statement that the image is now formed by 

 refracted rays, outside the dioptric beam. Very well, if that is the case, 

 then one-half of the aperture of the objective is sufficient to resolve 

 the third band, and it can therefore do no harm if we contract the 

 aperture just a little, say 10 per cent., by means of an iris back of it. 

 It will be found, however, that as soon as this is done the lines com- 

 pletely disappear. In fact, just as soon as two minute diffracted 

 beams, visible at margin of objective, are partially eclipsed resolution 

 is at an end. 



This experiment, dealing with the "mystery of the dark space" 

 which led Abbe to evolve a new theory, is introduced not to demon- 

 strate that the unilluminated portion of an objective's aperture assists 

 in image formation, which every microscopist must already know, 

 but to call attention to the fact that it does so in a definite manner. 

 Under the explanation given by the advocates of the dioptric theory 



