308 



H. XAGAOKA. 



and by the wnve leno-th of light employed in tlie oh^^ervntion. In 

 addition to this, there is the equation of condition 



ii/2 + «2 _ 2 az -=0 



expressing the faet that tlie aperture lies on a cylinder of radius a. 



In actual calculation, it is more convenient to use polar co- 

 ordinates. In the right circular section of the cylinder, assume polar 

 co-ordinates with the pole on the axis, and take 



y — a sin /? , z = a {1— cos ß), 



Then da = a dx da. 



Thus fß^'-""y-^'"'\h = ae'^'jdx e'Y^//.'"('" "■" ^ ^ " '-'' ^^■ 



where 2/> denotes the hreachli of the slit. 

 The integral 



idx e = 



Ü 



2 sin Ih 



I 

 It thus remains to find the integral 



taken between proper limits. 



Introduce an auxihary angle â', such that 



a m — 5 si)i (Y , a n = c cos />' 



where c = a ^ni- + n'. 



