504 J. RHEINBERG ON RESOLUTIONS OBTAINED WITH DARK-GROUND 



interest, for taken in conjunction with Mr. Nelson's results they 

 enable us to get a very good idea of the relative role which refrac- 

 tion plays in dark-ground images. Clearly if Mr. Conrady's 

 limits hold good without refraction, and we are able to obtain 

 results in excess, we have but to deduct the one from the other 

 to enable us to judge how refraction as such is acting. 



Now this brings out a striking fact which reference to 

 Mr. Stokes's table, reproduced here in part, shows : 



From the last column, added by myself, it will be seen that the 

 percentage steadily increases with increased ratio of the N.A. 

 of the objective to that of the illuminator. In other words, 

 given the same illuminator the effects of refraction as such are 

 increasingly in evidence the higher the power of the objective. 

 This I believe to be a fact which has not hitherto been 

 recognised. 



Personally I am inclined, indeed, to assign an even greater 

 proportion of the effects obtained in dark-ground illumination to 

 refraction than is brought out by the above table, for the reason 

 that we never do in practice obtain the full limit of resolution 

 which theory predicts. Moreover, it will be seen that with the 

 first two low-power objectives mentioned above results are 

 obtained much below Conrady's limits, although we know that if 

 the object is refracting light in the case of the last three examples 

 given it will also be doing so in the first two examples. 



We may, I think, attribute this deficiency in resolution in the 

 first two cases, where the illuminating cone is excessive compared 

 with that of the objective cone, in great part to the same causes 

 which bring about a loss of detail " by flooding out " in the case 

 of ordinary transmitted illumination when we use an illuminating 

 cone larger than the objective will stand. I do not enter into 



