PROCEEDINGS OF THE SOCIETY. 12 7 



is entirely clue to the small influence near the optical axis of the disturb- 

 ing factors which eventually, beyond a certain limited field, assume such 

 proportions as to destroy all semblance of definition, no matter how 

 rigorously the sine condition may be fulfilled, and the sine condition has 

 nothing whatever to do with a flat field, which is, as a matter of fact, 

 impossible of attainment in Microscope objectives of considerable N.A., 

 as the essential Petzval condition cannot possibly be fulfilled in these. 



Helmholtz next comes hi for his share of "criticism." 



This most careful and philosophical physicist is accused of precipi- 

 tation, and the suggestion — of course utterly unfounded — is made against 

 him that he has left half his work undone. And the now well-known 

 postscript to his paper,* which is really devoted to a very flattering 

 reference to Professor Abbe's theories, is cited in proof, although it 

 begins with the statement that Helmholtz's paper had been completely- 

 worked out and made ready for the printer when he became acquainted 

 with Abbe's researches. 



On pages 16 and 17 of Mr. Gordon's paper an attempt is made to 

 prove that Lord Rayleigh supported at least some of the novel notions. 

 More particularly, Lord Eayleigh's statement as to the resolution of 

 two very close lines under a certain kind of oblique illumination is cited. 

 Here Mr. Gordon overlooks that the illumination called for is that there 

 must be a difference of phase of \ A between the light reaching the two 

 lines from the distant source. Evidently this condition can only be 

 realised when the two lines are at least \ A apart, in which case it calls 

 for grazing incidence ; this case of abnormal resolution, imperfect 

 though it is, and restricted, moreover, to an isolated pair of lines — 

 rather a rare object — therefore breaks down at the very point where it 

 might occasionally be of value, i.e. at the universally accepted limit of 

 resolution ; and Lord Rayleigh himself is evidently aware of this, for he 

 has often since that demonstration expressed his faith in the approximate 

 correctness of the accepted limit of resolution. The visibility of single 

 bright or black lines or dots is a matter apart altogether, as Lord Rayleigh 

 invariably points out ; it is a question of contrast rather than of resolu- 

 tion, and such small black or white dots or lines cease to be visible 

 wherever a number of them are clustered together at distances within 

 the accepted limit of resolution. 



It is difficult to see how science is to profit by these absolutely un- 

 founded attacks on its foremost exponents, and by these strange mis- 

 interpretations of their writings. It seems to me that Mr. Gordon's 

 views will result in misleading a large majority of microscopists who are 

 not sufficiently acquainted with optics and mathematics to be able to 

 detect the weak points by their own unaided scrutiny. And it is to 

 such microscopists that I suggest that they should put to themselves the 

 following question : — If the accepted limits of resolution be false, and if 

 Mr. Gordon should have really discovered means of evading them, why 

 does he not convince us by the simple and straightforward process < if 



* A translation of this postscript will be found in the report of the discussion on 

 Mr. Gorduii's second paper in Part 2 of the Journal of the It. M.S. for 1903. 



