BLUE-VIOLET LIGHT IN TIIK SOLAR CORONA ON AUGUST 30, 1905. 333 

 where p designates the radius of the opening, the angular distance of CP at the 



o_ 



centre of the object-glass, \ the wave-length, r = sin 0, u = rp, and J, (u) BESHEL'H 



A, 



function of order 1. Let there be thirteen holes arranged as defined above and the 

 distance between each two be equal to a, and let a diagonal of the hexagon and the 

 ar-axis enclose angle <, then the state of oscillation at P is given by 



sin a UW- J, (n)\ 1 + 2 cos (ra cos <) + 2 cos (ra cos( + </>)) + 2 cos (ra cos(^ -<j>\\ 

 I it \_ \ w // w // 



+ 2coB(ra^/3siji<f>) + 2coe(ra^/3co6\^ + ^U + 2 cos ( ray/3 cos fe -<f>\] I. 



The intensity at P is the square of the coefficient of sin a. The position of point P 

 is determined with reference to C by its linear distance =/sin (/= focal-length) 

 and its position-angle <^> counted from a line parallel to one of the diagonals of the 

 hexagon of the screen. For same values of the intensity is the same for <f> and it 

 is periodical with reference to <f>, with a period of ir/3. Hence the intensity can be 

 developed into a cosine-series progressing by multiples of 6$. 



To find the quantity Q of light falling on a ring round C limited by radii , and ,, 

 I multiply the intensity by the element ^ f ^0 of the area in the focal plane and 

 integrate from < = to 2n- and from , to The integration with reference to <f> 

 can be carried out. The result is, if u be introduced instead of , 



u , a 

 ' 



Q.,, = V 



+ Jfc 1 (f\)' (irp>) 1 2 P { J> ("))" du [8 J (u') + 5 J (2') + 2 J (3u') 



u, U 



+ 6J ( ysV) + J (2 v/3V) + 4J, 



J designates BESSEL'S function of order zero. I transform the second integral. 

 The values of J and J, are with sufficient accuracy for values of u larger than v, 



- 4= (*+?) ( J >(^)) S = ~ - C 1 - 81 " 2j: -)- 



if \/x 



The terms in [ ] have, for the first screen, respectively the periods 70, 35, 23, 

 40, 20, 26, and owing to these short periodic terms the quantity to be integrated 

 changes sign at small intervals of . To a given value of u it say, = nir, a limit u, 

 near (n+\)jr can be found whicli makes the second integral zero. I have 

 convinced myself by mechanical quadrature that this deduction is correct even for 

 u, = 0, w, = TT, ..., K! = STT, Uy = 4ir. For our purpose it is unnecessary to take the 

 second part into account. Therefore, if all the light falling on the ring be considered 



