500 W. B. STOKES, DARK-GROUND ILLUMINATION. 



rrom this table one may note : 



(1) That column (e) shows that resolution with dark-ground 

 is a function of the N.A. of the objective. 



(2) That the last two results are well above the limit demanded 

 by Abbe's spectrum theory. 



If it be objected that resolution was effected by the shorter 

 waves of the light used and not by the mean, I reply that the 

 shortest useful wave-length would not give a theoretical result 

 as high as that obtained in practice. The last three results were 

 checked and repeated with a Wratten G screen, which is not 

 intended to pass waves shorter than 5,100, and actually did not 

 pass any shorter than 5,200. Supposing that this screen did 

 pass waves as short as 5,080 the theoretical limit for the last 

 objective would be 



(1-30 + 0-86) 25,000 = 54,000 lines per inch, 



which is still considerably below the result actually obtained. 



If one is justified in adopting the mean wave-length (say 

 5,700) for calculation, then the last column agrees fairly well 

 with the usual formula for the separation of two self-luminous 

 lines, viz., 



S - Q'61 ^ 



N.A. 



This agreement I believe to be more apparent than real. The 

 sensible width of the lines on the ruling, and the uncertainty 

 as to what resolution by contraction of antipoints really means^ 

 render exact agreement highly improbable. 



It is not the mathematical computation of resolving limits 

 which has prompted the publication of these results. It is the 

 question of mode of resolution which I believe to be important. 

 With the aid of mathematical physicists we may yet solve the 

 problems which all microscopical images present, and to those 

 solutions a study of dark-ground images cannot fail to be of the 

 utmost use. 



Joarn. Quekett Microscopical Club, Ser. 2, Vol. XL, No. 71, November I91i 



