572 PKOCEEDINGS OF THE SOCIETY. 



areas to have a common diameter of ¥ ^Vir in., and the dark dividing 

 lines a diameter of one-tenth of that magnitude I should not be far 

 from the mark. Now suppose an object identical in form with Tri- 

 ceratium Favus but reduced in scale to one-tenth of the above specified 

 dimensions. We should then have a number of luminous areas sepa- 

 rated by distances not exceeding say one-eighth of a wave-length of 

 light. "Would such a structure be resolved in the image formed by a 

 perfectly corrected objective ? That is a question of vital importance 

 to the future of Microscope manufacture, for if the physical nature of 

 light makes it impossible for those dividing lines to be rendered visible 

 in a magnified image we are already very near the final limit of per- 

 fection in the objective. But if that delicate tracery is theoretically 

 visible there is still a large area to be conquered by the makers of 

 optical instruments. 



Now on this point Lord Rayleigh's results, if I understand them 

 aright, are conclusive. If these boundary lines are to be considered 

 as dark bars on a bright field, they may by suitable illumination be 

 rendered visible and would still be visible, in theory, if their diameters 

 were further reduced to less than one-millionth of an inch. 



But this depends upon the area of the bright discs. Are they or 

 are they not large enough to constitute a bright ground, or must they 

 be treated as component parts of a compound structure ? 



On this point it is not easy to deduce an answer from the paper now 

 under consideration, for although its main results are made perfectly 

 clear the mathematical argument is not fully intelligible without Lord 

 Rayleigh's earlier paper, which is to be reprinted in the number of the 

 Journal in which the present paper will appear, but to which I have not 

 present access. 



But if I mistake not it will be found that the grating limit applies 

 only when the dark and bright areas have approximately equal diameters, 

 and that any great discrepancy such as is here postulated of 10 to 1 — 

 and in fact a discrepancy very much less than that — will bring the case 

 to be considered under the single bar limit and not under the grating 

 limit. It thus appears that the instance which I have put, although it 

 goes much beyond the limit of resolving power, as this is commonly 

 stated by microscopists, is very far from the theoretical limit established 

 by Lord Rayleigh's recent investigation of the subject." 



