ON A CERTAIN CLASS OF FRAUNHOFERS DIFFRACTION-PHENOMENA. 5 



The expression for the intensity becomes 



The diffraction figure arising from the given distribution consists 

 of concentric circles whose radii are proportional to the roots of the 

 equation 



J°( r a)=o. 



The experimental verification of this result was communicated 

 some time ago to the Tokyo Physico-Mathematical Society. 1 



It is remarkable that the same phenomenon can be observed in 

 an indefinitely thin annulus of radius a. From the expression for 

 the intensity of the diffracted light for a circular opening, 



r— ( aJ1 fr fl > )' 



r 



we easily find, for a circular annulus of breadth oa and radius a, 



n 



a = ( aJ°(ya)oa j , 



which shows that the same diffraction pattern will be exhibited by the 

 annulus with the above mentioned distribution. 



III. Suppose the openings are distributed at equal angular 

 intervals along the periphery of a Pascal's limaçon whose equation is 

 of the following form. 



r = a + b cos #. 



Applying formula (B), and writing 



r m — a + b cos (m a—ß) , & = m a — ß, 



we find easily that 



1. Tökyö-Sügaku-But8urigaku-kicai Kiji. 5. p. 75. 1893. 



