288 PROFESSOR AIRY, ON THE DIFFRACTION OF 



part of the third bright ring corresponds to w = 11,63, or *= — — , and 

 that its intensity is about ^— - of that of the center. 



The rapid decrease of light in the successive rings will sufficiently 

 explain the visibility of two or three rings with a very bright star 

 and the non-visibility of rings with a faint star. The difference of 

 the diameters of the central spots (or spurious disks) of different stars 

 (which has presented a difficulty to writers on Optics) is also fully 

 explained. Thus the radius of the spurious disk of a faint star, where 

 light of less than half the intensity of the central light makes no 



1 17 



impression on the eye, is determined by making /* = 1,616, or s=— — : 



whereas the radius of the spurious disk of a bright star, where light 

 of — the intensity of the central light is sensible, is determined by 



1 97 

 making n = 2,73, or * = — — . 



The general agreement of these results with observation is very 

 satisfactory. It is not easy to obtain measures of the rings; since 

 when a is made small enough to render them very distinct as to form 

 and separation, the intensity of their light (which varies as a^) is so 

 feeble that they will not bear sufficient illumination for the use of 

 a micrometer. Fraunhofer however obtained measures agreeing pretty 

 well (as to proportion of diameters, &c.) with the results above. 



For verification of the numbers it would probably be best to use 

 an elliptic aperture. By an investigation of exactly the same kind as 

 that above it will be found that the rings will then be ellipses exactly 

 similar to the ellipse of the aperture, but in a transverse position ; that 

 the major axes of the rings for the elliptic aperture will be the same 

 as the diameters of the rings for a circular aperture whose diameter 

 — minor axis of ellipse of aperture, but that the intensity will be 

 greater in the proportion of the squares of the axes. I have not yet 

 had an opportunity of examining this in practice. 



