On the Limits of Resolving Power. By E. M. Nelson. 525 



stars being known, the angle was found. The bright ring No. 4 

 was measured by a microscope with a screw micrometer. With 

 reference to Nos. 6 and 7, the telescope would doubtless divide 

 a 2" • 85 star, indicating a 4" • 5 limit, and an unsuccessful search 

 was made for one upon which to experiment. Late measure- 

 ments of e x and e 2 Lyra? were kindly supplied by Mr. Lewis, of 

 Greenwich. No. 13 was very difficult to measure, and the value 



9. 



10. 



11. 

 12. 

 13. 



14. 

 15. 



Radius, first dark ring for circular aper-) 



ture (Airy theory) . . . . J 



Radius, first dark ring for circular aper-l 



ture, as measured . . . . / 



Radius, first bright ring for circular aper-l 



ture (Airy theory) . . . . f 



Radius, first bright ring for circular aper-l 



ture, as measured . . . . I 



Dawes' empirical limit = theoretical fori 



a square aperture = Abbe's table (at> 



the end of the Journal) . . .1 



«, Lyrse, when easily separated J circular \ 

 « 2 Lyrse, not separated . . I 1-575 i n / 



Artificial double stars at 300 yds. distance,! 

 circular aperture . . . . . J 



Rayleigh's experiments with gratings andl 



rectangular aperture, greatest distance \ 



196 in. Mean value . . . . ) 



Author's experiments with gratings andi 



circular aperture at 90 to 700 yards. > 



Mean value . . . . . ) 

 Rayleigh's theoretical limit for dark bar i 



on bright ground . . . . f 



Mean value for dark bar, measured by) 



circular aperture at 300 yards . . / 



Mean value for dark bar, measured by a I 



microscope . . . . . I 



Maximum number of lines resolved by) 



Mr. A. A. C. Merlin . . . . / 



Value adopted in Table of "Working 



Limits " . 



Telescope* 1 Microscopef 



c\ j 2N.A. k 



% 



1-2197 

 0-8266 

 1-63 

 1-1597 



1-0000 



1-053 



0-7884 



0-9957 

 1-0923 



1-0649 



555 

 765 



42 



282 



555 



796 

 591 



535 

 975 



85 



569 

 913 

 691 

 988 

 921 



74,300 



110,000 



55,600 



78,100 



90,574 



86,000 

 115,000 



91,000 

 82,900 



85,100 



725,000 



216,000 



244,000 



82,700 



69,672 



* Angular subtense of interval separated by 1 in. of aperture. 

 t Number of lines resolved by an objective of N.A. 1*0 with white light and 

 full cone. -. 1' 



here given is probably a little too small. It is important to 

 microscopists, because it forms the basis for the correction for anti- 

 point in micrometrical measurements.! 



J Should any one wish to experiment further in this direction, the following 

 formulae will be useful : To find the value of c from an angle, multiply the number 

 of seconds by 0-21956 ; to reduce c to an angle, multiply c by 4-5546 ; to find the 

 value of c from the number of lines resolved, divide 90574 by the number of lines, 

 and conversely to find the number of lines resolved from c, divide 90574 by c. 



