On a Table of Numerical Apertures. By J. W. Stephenson. 8tl 



point taken had been, as nearly as may be, midway between E and 

 r, i. e. = 0'508 fji, the numerical aperture would itselfhoNe been 

 the true measure of resolving power, being exactly equal to the 

 number of hundred-thousands of lines in an inch ; tlius giving 

 100,000 lines as the maximum of a dry lens, 133,000 as that of 

 a water-immersion, and 152.000 as the ideal maximum of a homo- 

 geneous-immersion objective with crown-glass covers. 



As the resolution by the same objective is affected by the 

 intensity of the illuminating beam, by the colour of the object, and 

 other circumstances, it is not possible to assign an absolute measure 

 — using the line D (= 0'5889yu-), for instance, in the computation, 

 the resolving power would be found to be 10^ per cent, less than 

 the tabular results: on the contrary, if the line F (= 0* 4861 /a) 

 were selected, the resolving power would be 8 • 4 per cent, greater, 

 or taking the line = 0-40/^ (near Hi), as probably sufficient for 

 photographic resolution, the maximum number of lines which could 

 be delineated by a dry lens would be 127,000, by a water immer- 

 sion 168,910, or, by a homogeneous immersion objective (under 

 present conditions) 193,040, although, if flint-glass covers with 

 suitable homogeneous fluid were adopted, the ultimate limit might, 

 on this hypothesis, be extended to, say, 200,000; and on the as- 

 sumption that the space between each of these lines was equal to 

 the lines themselves, it follows that the width of each line would 

 be ^^)^^o„Q of an inch, but it by no means hence follows that this 

 would be the ultimate photographic limit for a single line. 



(03^ There is no loss of aperture on objects mounted in balsam, 

 or any more highly refractive medium (as was formerly supposed 

 by many, myself included), under either of the systems, in fact 

 the full resolving power (with transmitted light) can be attained 

 only if the object is mounted in a medium whose refractive index 

 is equal to, or greater than, the numerical aperture of the objec- 

 tive, so that if ever homogeneous objectives are constructed for 

 flint-glass covers, some more highly refractive medium than balsam 

 must be used for mounting the objects, such as bisulphide of 

 carbon or oil of cassia. 



