Lord Rayleigh' , s Investigations in Optics. 263 



material confusion, unless indeed the components are of very- 

 unequal magnitude. 



The diminution of star-disks with increasing aperture was 

 observed by W. Herschel ; and in 1823 Frauenhofer formu- 

 lated the law of inverse proportionality. In investigations 

 extending over a long series of years, the advantage of a large 

 aperture in separating the components of close double stars 

 was fully examined by Dawes*. In a few instances it hap- 

 pened that a small companion was obscured by the first bright 

 luminous ring in the image of a powerful neighbour. A di- 

 minution of aperture had then the effect of bringing the smaller 

 star into a more favourable position for detection ; but in 

 general the advantage of increased aperture was very appa- 

 rent even when attended by considerable aberration. 



The resolving-power of telescopes was investigated also by 

 Foucaultf , who employed a scale of equal bright and dark 

 alternate parts : it was found to be proportional to the aper- 

 ture and independent of the focal length. In telescopes of the 

 best construction the performance is not sensibly prejudiced 

 by outstanding aberration, and the-limit imposed by the finite- 

 ness of the waves of light is practically reached. VerdetJ has 

 compared Foucault's results with theory, and has drawn the 

 conclusion that the radius of the visible part of the image of 

 a luminous point was nearly equal to the half of the radius of 

 the first dark ring. 



Near the margin of the theoretical central disk the illumi- 

 nation is relatively very small, and consequently the observed 

 diameter of a star-disk is sensibly less than that indicated in 

 equation (1), how much less depending in some measure upon 

 the brightness of the star. That bright stars give larger disks 

 than faint stars is well known to practical observers. 



With a high power, say 100 for each inch of aperture, the 

 sharpness of an image given by a telescope is necessarily de- 

 teriorated, the apparent breadth of a point of light being at 

 least 8^- minutes. In this case the effective aperture of the 

 eye is Tj ^j inch. In his paper on the limit of microscopic 

 vision§, Helmholtz has shown that the aperture of the eye 

 cannot be much contracted without impairing definition — from 

 which it follows that the limit of the resolving-power of tele- 

 scopes is attained with a very moderate magnification, pro- 

 bably about 20 for each inch in the aperture of the object-glass 

 or mirror. 



* Mem. Astron. Soc. vol. xxxv. 

 t Ann. de VObserv. de Paris, t. v. 1858. 

 X Lecons a" Opaque Physique, t. i. p. 309. 

 § Pog-g. Ann, Jubelband 1874, 

 T2 



