18 



Transactions of the Society. 



have in place of the two antipoints postulated by Helmholtz two 



luminous areas having each a transverse diameter at least = . 



° sin u 



these areas may be clearly distinguishable, even though their 



X 

 adjacent edjres are separated by a distance •< 



J ° l J 2 sin u 



The problem of resolving power which thus emerges, when the 

 case is considered of two small luminous areas uf finite dimen- 

 sions, having each a diameter of not less than measured away 

 ' ° sin u J 



from the bounding edge, engaged the attention of Lord Eayleigh in 

 1903, and one particular case of it was treated in a paper which he 



communicated to this Society, 

 being the last of the paper.s 

 enumerated at the head of this 

 article. Lord Eayleigh assumes 

 two such areas separated by a 

 dark bar, and calculates by the 

 method of his former paper 

 what in that case would be the 

 minimum breadth of such a 

 dark bar, which would visibly 

 separate the field into two 

 luminous areas. 



XL The result varies ac- 

 cording to the reciprocal phase 

 relation of the adjacent lumi- 

 nous edges. If these have a 

 constant phase difference A (</>) 

 = ^ X the bar will be a visible 

 boundary, however narrow. 

 But if the phase difference 

 A (</>) = 0, that is to say, if the same wave-front extends beneath 

 the bar and illuminates both the separated areas — the worst case 

 — then the bar must have a minimum breadth = fe X. If, on 

 the other hand, there is no phase relation, and therefore no 

 regular interference, the bar will still be visible, although it has 

 a breadth no greater than ^ X. Here, at last, we begin to get 

 into touch with fact. The conditions which Lord Eayleigh stipu- 

 lates for in this paper are such conditions as may possibly arise in 

 practice. Luminous areas and dark bars of the small but finite 

 dimensions named are objects which the microscopist is actually 

 concerned at times to see, whereas a luminous point — the word 

 " point " being used in a mathematical sense — is a figment of the 

 scientific imagination and a single antipoint is what no man has 

 seen or ever will see. 



Fig. 10. 



