AN OBJECT-GLASS WITH CIRCULAR APERTURE. . 287 



In the use of tins table n must be taken = — -.-^. If instead of 



using the linear distance h to define the point of the field at which 

 we wish to ascertain the illumination, we use the number of seconds *, 



then A = /. *.sin 1", and n must be taken = — as sin 1". If \ be taken 



for mean rays = 0,000022 inch, n must be taken = 1,3846 x as, a being 

 expressed in inches. From this expression, and from the numbers of 

 the table, we draw the following inferences. 



1. The image of a star will not be a point but a bright circle 

 surrounded by a series of bright rings. The angular diameters of these 

 (or the value of s corresponding to a given value of n) will depend 

 on nothing but the aperture of the telescope, and will be inversely as 

 the aperture. 



2. The intensity of the light being expressed (on the principles 

 of the undulatory theory) by the square of the coefficient of 



sin-^ivt-f- A), 



and the intensity at the center of the circle being taken as the standard, 

 it appears that the central spot has lost half its light when « = l,6l6, 



I 17 

 or s = — — ; that there is total privation of light, or a black ring, when 



2 76 

 n = 3,832, or * = — — ; that the brightest part of the first bright ring 

 a 



Q WQ -I 



corresponds to w = 5,12, or * = — — , and that its intensity is about — of 



a Oi 



5 16 

 that at the center; that there is a black ring when n = 7,14, or s= -- — ; 



a 



that the brightest part of the second bright ring corresponds to ra = 8,43, 



or * = — — , and that its intensity is about — r of that of the center ; 



7 32 

 that there is a black ring when w =10,17, or *= — — ; that the brightest 



