334 PROFESSOR L. BECKER ON THE DISTRIBUTION OF 



together the distribution is almost exactly the same as if all the light had passed 

 through only one of the openings ; and in accordance with the above, if the ring be 

 divided into 12 parts by 6 diameters, beginning at < = 0, each segment contains a 

 twelfth of the light falling on the whole ring. 



The quantity of light falling on such a twelfth of a zone between u = mr and 

 (+I)TT is given by 



Q n = CtVlV/., where /, = 2 f" " 



JIMT 



U 



i designates the intensity outside the object-glaas. 



I next consider the light Q falling on unit area at a point C of the image of a 

 luminous area. Draw circles, radii mr, round C, and divide each ring by 6 diameters 

 into 12 equal parts. Project from centre of object-glass this system of circles and 

 lines on the luminous area. Let the intensity i n m of the source be constant within an 

 area of the source corresponding to part m of ring n ; then, if there were x units in 

 one of these parts, each unit would send Q B (for i = i n m ) divided by x to unit at C, 

 i.e. the x units send Q B to unit at C. The total quantity of light falling on unit at 

 C is therefore given by 



Q = 



or 



Q = 

 where 



At = i 



i 



because 2 f n = 1. Parts 1 and 7, 2 and 8, &c., lie diametrically opposite with 



* 



reference to C. Hence the quantity of light at C is not changed by diffraction if the 

 source be everywhere equally intense, or if the intensity uniformly increase along the 

 lines drawn through C. In the case of the corona the second condition is very nearly 

 satisfied in the neighbourhood of a point, and thus the most luminous diffraction 

 rings hardly affect the quantity of light at C, there being almost as much light lost 

 as gained. 



Let At be known for each of the four screens (i.e. p), and at each distance h. 

 Equal blackness was observed on two photographs exposed equally long with screens 

 a and 6, at two points h a and h h ; hence Q a = Q 6 , and 



h 

 or 



, b see 5 (r)]. 



