38 Transactions of the Society. 



the objective. If the particular object under examination requires 

 light of extreme obliquity for its resolution, that light is present, 

 and it is by that light that the resolution actually takes place, just as 

 if we had shut out all the strictly " central " light by a diaphragm, 

 and had used the oblique light alone undiluted (so to say) by the 

 central rays. 



Applying these considerations to the case of an objective of 

 1-50 N.A., illuminated by strictly "central" light, the aperture 

 is reduced to • 75, with which the resolution of A. pellucida having 

 a striation of some 95,000 to 100,000 lines to the inch, is impossible. 



By increasing the width of the illuminating beam to one- 

 third of the diameter of the back lens, we increase the available 

 aperture of the objective from 0'75 to 1*00 N.A Still further 

 increasing its width, by making it equal to one-half the diameter 

 of the back lens (still keeping it concentric with the objective), we 

 raise the available aperture to 1"125 N.A., which exceeds the 

 theoretical limit for the resolution of A. pellucida. 



The resolution, however, instead of being effected by " central " 

 light, is, under these conditions, effected by ohlique light emanating 

 from peripheral portions of the illuminating beam, not only un- 

 assisted by the central rays, but in spite of the diluting action of 

 the more central light with which the field is flooded. 



It may be useful to show diagrammatically the positions of the 

 diffraction pencils of J., pellucida relatively to the effective portions 

 of tie illuminating beam under the different conditions which I 

 have assumed. 



Fig. 1, with a beam of quasi " central " light. A, shows the 

 virtual positions of the two diffraction pencils a a, outside or 

 beyond the back lens, which are therefore useless. 



Fig. 1. Fig. 2. 



Fig. 2 shows the wider illuminating beam (equal to one-third 

 of the diameter of the back lens), the more effective portions of 

 which are indicated by the two small circles A and B, and their 

 respective diffraction pencils by a and h, partly within the limits of 

 the back combination ; either pair A a or B & being sufl&cient to 

 resolve if the more refrangible rays, which alone are assumed to be 

 admitted, give sufficient intensity to the image. 



