On the Limits of Resolving Power. By E. M. Nelson. 523 



4" "56 

 Dean of Hereford, was - — , this being the theoretical limit for 



a ° 



a telescope with a square aperture, and this is the limit which 

 practical astronomers still use.* 



The star known as e x Lyree was examined, and widely sepa- 

 rated, by a telescope of 1 * 575 in. aperture ; the mean distance of 

 the components, as lately determined by three different observers, 

 is 3" • 045. The value of c in this instance is therefore 1 ■ 053, or 



4". 796 

 in angular measure it is , a result not differing greatly from 



that used by Dawes. The same telescope refused to separate the 



components of e 2 Lyrse, which are 2" ■ 28 apart. Here the value of 



3" • 591 

 c is • 7884, and the angle is . The true telescopic limit lies, 



therefore, between these two results, and probably nearer the first. 



Lord Eayleigh, experimenting with a rectangular aperture and 

 a grating, obtained 1 ■ 0923 for the value of c ; the greatest distance 

 the grating was removed from the telescope was 196 in. 



The author's experiments with circular apertures and gratings, 

 at distances varying from 90 to 700 yards, gave for c the slightly 

 smaller value of 1 ■ 0649. Lastly, we have Eayleigh's theoretical 

 limit for the visibility of a dark bar upon a light ground, which 

 gives c a value of * 125 ; its value as practically measured appears 

 to be 0-42. 



The theoretical value of c for the length of the radius of 

 the first bright ring is 1 • 63 ; its value, however, as practically 

 determined in a microscope, is 1 ■ 16, or 29 p.c. less. It will be 

 remembered that the difference between the theoretical and practical 

 measurements of the radius of the first dark ring with a telescope 

 amounted to 32 p.c, and now we have a very similar difference 

 between theory and practice in a measurement by a microscope. 



The theoretical length of the radius of the first dark ring in a 



c A, f 

 microscope may be determined from the telescope formula - 



by writing for the diameter of the telescope objective, a, its micro- 

 scopical equivalent, viz. 2 N.A. /, where N.A. stands, as usual, for 

 the Numerical Aperture. The quantity / must now be restored to 

 the formula, because the microscopical limit deals with linear 

 measurements, and not with angular quantities. So the standard 



formula for the telescope, — — . becomes n . T . . 

 r a 2 N.A 



As we shall be dealing with a resolving limit expressed in 



" lines to the inch," the reciprocal of this quantity will be re- 



* The Dean used a slightly larger wave-length ; this makes the quantity 4"* 56 

 instead of 4" - 55, as above. 



2 M 2 



