CH. I] MICROSCOPE AND ACCESSORIES 21 



(2) The illuminating power of an objective of a given focus is 

 found to vary directly as the square of the numerical aperture (N. A. ) 2 . 

 Thus if two 4 mm. objectives of N.A. 0.20 and N.A. 0.40 were compared 

 as to their illuminating power it would be found from the above that 

 they would vary as o.20 2 :o.40 2 = 0.0400:0.1600 or 1:4. That is the 

 objective of 0.20 N.A. would have but /^th the illuminating power of 

 the one of 0.40 N.A. 



(3) The penetrating power, that is the power to see more than one 



plane, is found to van- as the reciprocal of the numerical aperture— — -r- 



so that in an objective of a given focus the greater the aperture the 

 less the penetrating power. 



Of course when equivalent focus and numerical aperture both differ 

 the problem becomes more complex. 



While all microscopists are agreed that the fineness of detail which 

 can be seen depends directly on the numerical aperture of the objective 

 used, the general theory of microscopic vision has two interpretations : 



(A.) That it is as with the unaided eye, the telescope and the 

 photographic camera. This is the original view and the one which many 

 are favoring at the present day (see Mercer, Proceedings of the Amer. 

 Micr. Soc. 1896, pp. 321-396). 



(B) The other view originated with Professor Abbe, and in the 

 words of Carpenter-Dallinger, pp. 62, 43 : "What this is becomes ex- 

 plicable by the researches of Abbe. It is demonstrated that micro- 

 scopic vision is sui generis. There is and can be, no comparison between 

 microscopic and macroscopic vision. The images of minute objects 

 are not delineated microscopically by means of the ordinary laws of 

 refraction ; they are not dioptrical results, but depend entirely on the 

 laws of diffraction. These come within the scope of and demonstrate 

 the undulatory theory of light, and involve a characteristic change 

 which material particles or fine structural details, in proportion to their 

 minuteness, effect in transmitted rays of light. The change consists 

 generally in the breaking up of an incident ray into a group of rays 

 with large angular dispersion within the range of which periodic alter- 

 nations of dark and light occur. ' ' 



For a consideration of the aperture question, its history and sig- 

 nificance, see J. D. Cox, Proc. Amer. Micr. Soc, 1884, pp. 5-39 ; 

 Jour. Roy. Micr. Soc, 188 1, pp. 303, 348, 365, 388 ; 1882, pp. 300, 

 460; 1883, p. 790; 1884, p. 20 ; 1896, p. 681; 1897, p. 71 JlJjfS^yiPP 1 -, 

 354, 362, 592 ; Mercer, Proceedings Amer. Micr. Soc, 1896VPP. 321- 



