DARK-GROUND ILLUMINATION. 477 



the condenser to be used with it, thus enabling us to see the 

 light coming from the condenser. We then ask ourselves : Can 

 we realise the utmost resolving power just explained? The 

 obvious answer is that we could if we managed to bring the 

 iirst. spectrum to the position h in fig. 1, when, owing to 

 the equidistance theorem, the second spectrum would get into 

 position c, thus realising the theoretical limit ; but where does 

 this necessitate placing the direct light? Evidently at a as 

 far from 6 as 6 is from c. Therefore the condenser must have 

 an aperture at least as large as the outer dotted circle of 





Fig. 2. 



Fig 1, with a diameter obviously three times that of the 

 inner circle ; and as, again by Abbe's theory, these circles are 

 proportional to the numerical apertures of the lenses or con- 

 densers, we arrive at the first result : 



(1) In order to obtain the utmost resolving power with 

 dark-ground illumination the condenser must have not less than 

 three times the N.A. of the objective. As condensers are limited 

 to say 1-4:0 N.A. this means that it is impossible to obtain their 

 fullest resolving power with dark-ground illumination with any 

 objectives over 0*47 N.A. 



