ILLUMINATION OF OBJECTS; DARK FIELD 
41 
half of the mounting, while in the case shown in Fig. i8, 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 
o.8o to 0.95. 
Gage has recently shown ^ 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 ^ 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 j N.A. objective -(- j N.A. 
condenser, but Reinberger points out that on actual trial ^ 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.^ 
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 
^ Gage, S. H., Modern Dark-field Microscopy and the History of Its Develop¬ 
ment. Trans. Amer. Micros. Soc. 39 (1920) 95. 
^Conrady, J. Quekett Micro. Club, 11 (1912), 475. 
3 Reinberger, J. Quekett Micro. Club, 11 (1912), 503. 
* 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. 
