ILLUMINATION AND THEIR RELATION TO THE SPECTRUM THEORY. 499 



detail resolvable with dark-ground by spectral interference is 

 considerably less than with a wide axial cone. For example, 

 let 



N.A. of objective = I'O, 

 ,, illuminator = 1-35. 

 X = 5,080 tenth metres, .-. k = 50,000 per inch. 

 .-. N = (1-35 4 1-0) 25,000 



= 58,750 intervals per inch. 



A wide axial cone would be expected to resolve 75,000 or more 

 with an objective of 1*0 N.A. and this light. 



The Airy theory, in which resolution of details is considered 

 as solely due to the contraction of the diffraction patterns or 

 antipoints representing points in the object, would give with 

 suitable objects a higher resolving power to objectives than 

 follows this application of the Abbe theory, and it is this which 

 makes a crucial test possible. If objectives will give better 

 results than the Abbe theory will allow, then we are justified 

 in turning to the older theory for guidance. 



The first experiment which I made was with an old objective 

 of 0-85 N.A. and a dark-ground illuminator of 1*35 N.A. This 

 resolved a diatom known as Navicula rhomhoides from Cherry- 

 field, U.S.A., believed to have rows of perforations 60,000 to 

 the inch. This result justified me in putting the matter of dark- 

 ground resolutions into the hands of Mr. E. M. Nelson, whose 

 unrivalled skill, experience and equipment have made him a 

 referee in such matters. Through his kindness I have details 

 of a great number of experiments, and I have been privileged 

 to see many of the most important repeated by him. It will 

 sufiice, however, if I give a few of the results obtained with 

 a Grayson ruling by the light of an oil lamp. 



cja. 



68 

 71 

 68 

 75 

 70 



* This was originally given as 37 instead of 32. I am indebted to 

 Mr. J. Rheinbergr for the correction. 



