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XXVI. On the Intensity at the Focal Point of a Telescope, when 

 the Object-glass is covered by a Diaphragm pierced ivith 

 Circular Apertures. By James Walker, M.A., Demon- 

 strator at the Clarendon Laboratory, Oxford*. 



THE proposal recently made, to reduce the intensity of 

 the image of a star by means of screens placed before 

 the object-glass of a telescope, renders it of importance to 

 determine the theoretical value of the intensity in such cases. 

 In its general form the problem is one of considerable com- 

 plexity ; but when the apertures in the screen are circles, the 

 intensity at the focal point itself can be expressed in a form 

 from which its value can be calculated to any required degree 

 of accuracy. 



Taking the centre of the screen as origin, let the equation 

 of one of the apertures be 



P 2 -2apcosd + a' 2 -r* = 0, (1) 



where r is the radius of the circle, and a the distance of its 

 centre from the origin ; then, if we denote the aberration by 

 /9p 4 , the amplitude of the displacement at the focal point may 

 be represented by a sum of terms of the form 



/^sin-l r/a r*p 2 

 *) -sin-1 rja J p, 



pdpdO, .... (2) 



where i—s/ — \, and p h p 2 are the roots of (1) y and the 

 intensity at this point is obtained by multiplying this sum by 

 the expression obtained from it by changing the sign of i. 

 Expanding e ll3pi in a series, we at once obtain 



and since 



p = 2n+l 14^4-2 



2p-l 



x (r 2 — a 2 sin 2 0) 2 ; 

 the general term of the integral (2) is 



* Communicated by the Author. 



