2G8 



Lord Rayleigh's Investigations in Optics. 



The third and sixth columns show the intensity in various 

 directions relatively to the intensity in the principal direction 

 (■m = 0); and the curve ABCD (fig. 2) exhibits the same 

 results to the eye. A comparison with Table I. shows that a 

 considerable advantage has been gained, the relative illumina- 

 tion at B being reduced from -4053 to -3205. On the other 

 hand, the augmented brightness of the first lateral band 

 (towards C) may be unfavourable • to good definition. The 

 second bright lateral band (towards D) is nearly obliterated. 

 The curve E'BEF represents the resultant illumination due 

 to a double line whose components are of the same strength, 

 and at the same angular interval as before. The relatively 

 much more decided drop at B indicates a considerable im- 

 provement in resolving-power, at least on a double line of this 

 degree of closeness. 



The increased importance of the first lateral band is a ne- 

 cessary consequence of the stoppage of the central rays ; for 

 in this direction the resultant has a phase opposite to that of 

 the rays stopped. The defect maybe avoided in great measure 

 by blocking out rays somewhat removed from the centre on 

 the two sides, and allowing the central rays themselves to pass. 

 As an example, I have taken the case in which the two parts 

 stopped have each a width of one eighth of the whole aperture, 

 with centres situated at the points of trisection (fig. 3). 



Fiff. 3. 



The function / suitable to this case is readily proved to be 



f=u~ l ( sin u— 2 sin ~ cosk). . . . (5) 



The values of/and/ 2 -f-/ 2 are given in Table III.; and the 

 intensity-curve ABCD is shown in fig. 4. 



Table III. 



u. 



/• 



/ 2 +/*o 2 . 



u. 



f. 



/ 2 +/o 2 - 







+ •75 



10000 



frr 



-•2122 



•0801 



T 71 " 



•6594 



•7727 



i* 



- -0689 



•0084 



In 



•4215 



•3158 



2tt 



+ •1125 



•0225 



l* 



+ •1259 



•0282 



I 71 " 



•2189 



•0852 



71 



-•1218 



•0204 



3n 



•1960 



•0684 



i* 



•2422 



•1043 









The depression at B is even greater than in fig. 2, while the 



