Dr. S. P. Thompson on Photometry. 127 



the thickness of the metal will interfere with the illumination 

 of the screen in directions not absolutely in line with the axis 

 of the aperture. 



Let the screen PQ (fig. 6) be at a distance oc= OX from 



Fig. 6. 



the diaphragm at ; the thickness of the diaphragm being 

 called Sx, and the radius of the circular aperture in it a. It 

 is required to find the illumination at a point P on the screen 

 at a distance PX = ?/ from the point X which is on the axis of 

 the aperture. Let the angle POX be called 6. Then the 

 apparent aperture as viewed from P will be bounded by two 

 portions of ellipses (the front and back edges of the hole 

 viewed in perspective), having each as semi-major axis a, and 

 as semi-minor axis a cos 6. These two ellipses will overlap, 

 their centres being displaced by an amount equal to 8% sin 6. 

 If we represent the ratio of the thickness of the metal to the 

 radius of the aperture as &E/a = tan </>, then we may write the 

 following expression for A, the effective area of the hole, as 

 visible in the direction OP, as follows : — 



A = 2a 2 1 cos 6 . [J _ sin- 1 (tan <j> . tan 0)1 - tan cf> . tan 6 V f^W^ta^l 



Hence, since the real hole has area =aV, the ratio tj of the 

 illumination at P to the central illumination at X will be 



V= - | cos 6. f|- sin" 1 (tan <f>. tan 0)1 - tan 0. tan 6 Vl-tan 2 <£.tan a j . 



