502 J. RHEINBERG ON RESOLUTIONS OBTAINED WITH DARK-GROUND 



Abbe Theory takes full cognisance of refraction as it deals with 

 the subject on the broad principles of wave-motions, which 

 include refraction and reflection as well as diffraction. On a 

 later occasion he stated that the observational facts contradicted 

 the suggestion that refraction accounted for the light scattered 

 by diatoms, glass rulings, etc., but that diffraction, on the other 

 hand, would fully account for appearances. He mentioned too 

 that Abbe had described, thirty years ago, experiments to show 

 that refraction could not explain the behaviour of microscopical 

 objects. It could, however, alter the relative brightness of the 

 diffraction spectra. 



Lastly Mr. Stokes, on the strength of the resolutions obtained, 

 claimed not only that they showed the Abbe Theory to be wrong, 

 but that dark-ground illumination afforded a crucial experiment 

 between the Airy and Abbe Theories, because under this illumi- 

 nation we could cause the points of the object to act as if they 

 were self-luminous, whilst under ordinary illumination contiguous 

 detail of the object would transmit light to tlie objective which 

 w'as in permanent phase relation because it had a common origin. 

 The Airy Theory, which predicted under suitable circumstances 

 higher resolving power, was based on the former conditions, the 

 Abbe Theory was based on the latter ; hence the possibility of 

 the crucial test. He contended that the results being in excess 

 of the limits, we ought to turn to the older Airy Theory for 

 guidance. 



Mr. Conrady, in conclusion, considered the resolutions given by 

 Mr. Stokes in very fair correspondence with his own limits, and 

 laid emphasis on the difficulty of critically testing any theory. 

 He pointed out how the number of lines per inch of a grating, the 

 actual space ruled, any slight irregularities in the ruling as 

 questions affecting the wave length of the light employed, make 

 it extremely difficult to be sure one is working under the given 

 conditions of a theory. 



Although, much to my regret, I was unable to be present 

 during the above discussions, and have therefore largely drawn 

 upon the reports in the English Mechanic, I trust the short resume 

 given will be found impartial and correct. 



Let us briefly see now where the above claims hold good, and 

 wdiere they are fallacious or give rise to misconceptions. 



