ILLUMINATION OF OBJECTS; DARK FIELD 41 



half of the mounting, while in the case shown in Fig. 18, the 

 long tubular diaphragm is inserted into the objective from above 

 without necessitating any separation in the mounting of the 

 objective lenses. By means of these diaphragms the numerical 

 apertures of the objectives are reduced to between approximately 

 0.80 to 0.95. 



Gage has recently shown l that the reduction of the numerical 

 aperture should in most cases be as low as 0.80 and further that 

 in critical work it is desirable to have several diaphragms avail- 

 able so that the numerical aperture may be altered at will from 

 0.85 to as low a value as 0.70, since some preparations are best 

 studied with lower and some with higher numerical apertures. 



In order to obtain the maximum resolving power with dark- 

 field illumination Conrady has shown 2 that the condenser must 

 have not less than three times the numerical aperture of the 

 objective. He suggests that the practical resolving power obtain- 

 able may be expressed as equal to \ N.A. objective -f- J N.A. 

 condenser, but Reinberger points out that on actual trial 3 the 

 Conrady formula gives results about 25 per cent too low. The 

 inexperienced observer, however, will find that the resolving 

 power obtainable in his work will conform rather closely with 

 the Conrady formula. It is therefore well to bear in mind that 

 in dark-field illumination studies fine details of structure are 

 to be discerned only with the greatest difficulty and will require 

 extreme care in adjusting the illumination and in selecting the 

 proper objectives. 4 



It is evident that with a properly selected optical combination, 

 the field of view will appear black or very dark, while any objects 

 present will appear to be bright and self-luminous. 



The more oblique the rays the more minute the particles 



1 Gage, S. H., Modern Dark-field Microscopy and the History of Its Develop- 

 ment. Trans. Amer. Micros. Soc. 39 (1920) 95. 



2 Conrady, J. Quekett Micro. Club, 11 (1912), 475. 



3 Reinberger, J. Quekett Micro. Club, 11 (1912), 503. 



4 Siedentopf and Zsigmondy have shown (Ann. d. Phys. [4] 10 (1903), 14) that 

 in the ultramicroscope the brilliancy of the diffraction disks is proportional to the 

 product of the squares of the numerical apertures of the image-forming and illu- 

 minating objectives. 



