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ON RESOLUTIONS OBTAINED WITH DARK-GROUND 

 ILLUMINATION AND THEIR RELATION TO THE 

 ABBE THEORY. 



By Julius Kheinberg, F.R.M.S. 



(^Read October 22nd, 1912.) 



The nature of the Image and the resolving power which is 

 obtained with Dark-ground Illumination being a matter of con- 

 siderable interest, I venture to make a few remarks on the 

 interesting controversies which have taken place at the Quekett 

 Meetings on the subject this year, since the discussions have, I 

 am afraid, left the subject in an unsatisfactory state, which might 

 give rise to misunderstandings and false impressions in the minds 

 of many. 



The course and main points of the controversy, shortly stated, 

 have been as follows : 



Mr. A. E. Conrady demonstrated, basing himself on the Abbe 

 Theory, that full resolving power of an objective was only obtain- 

 able when the dark-ground illuminator had at least three times 

 the numerical aperture of the objective in other cases he stated 

 it to be equal to one-fourth of the N.A. of the objective plus one- 

 fourth the N.A. of the condenser. 



Mr. W. B. Stokes urged that the latter proposition was not 

 correct, that refraction by the object had not been sufficiently 

 taken account of, and that higher resolutions were obtainable. 

 In support of this he gave details of dark-ground resolutions 

 obtained by Mr. E. M. Nelson, chiefly, I believe, on diatoms, and 

 in a later paper gave a table of resolutions* obtained by Mr. 

 Nelson with a Grayson ruling (which he had himself had the 

 opportunity of seeing), which in a couple of instances showed 

 resolutions 20 per cent, to 25 per cent, in excess of Mr. Conrady 's 

 limits. From which he inferred that the Abbe Theory was wrong 

 as regards dark-ground illumination. 



To Mr. Stokes's objections Mr. Conrady pointed out that the 



* See p. 499 of current number of the JOURNAL Q.M.C., and p. o04of this 

 paper. 



