12 H. NAGAOKA. 



we get the following values of the differential coefficients at the point 

 of intersection: — 



d x ' cy 



where r m is the m-tli root of J 1 (ar)=o, and equal to V x 2 n + if m , and 

 x n = — — -= — jr. Thus, the principal axes are proportional to 



-tnd 



y «n« o ( »-. - ^^- *) y <n« o ( 



r m + — tttt- 



Taking the distance between the centres of the circular apertures 

 as equal to 1.72 times the radius, and tracing the curves about the 

 points of intersection of the bands, we find a great resemblance 

 between the diffraction figure actually observed by Fraunhofer 1 and 

 that deduced by calculation, which otherwise gives only straight lines 

 and rings. 2 



There are, besides, many instances in which the introduction ot 

 the curve of equal intensity enables us to find a likeness between the 

 observed and the calculated result, especially in those problems which 

 are easily solvable by the application of Bridge's theorem. 



The present problem can be reduced to one in geometry. Con- 

 sidering intensity / as z coordinate, construct a surface 



and cut it by a plane 



Z = Ô I . 



1. Fraunhofer, ' Werke,' München. 



2. Schwerd, 'Beugnngserscheinungen,' Mannheim, 1835. 



