454 Mr. L. N. Gr. Filon on certain Diffraction Fringes 



of the source be less than ^y, then throughout the integration 



27rk 



~rr~ (.9 + v ) i s ^ ess than t/G numerically. 



But 



77 9 /36 



■i J 



and differs but little from unity. 



"We may therefore in this case write 



. 2 2irk 



sm *_ (3+t)) ^ 



*<*+•>) 



V 6X 



throughout the range of integration. 

 If now the limits be v 1 and v 2 we have 



i_-«?^( W .<-S E a) 4 , 



4AW 



™ \ TT (ll ~ i3) + sm bx sin bx J 



' "4 T^ + 2 sin — \i ^ cos yj \ K J \ 



ira \_ bX hX bX J 



Let 2c = length of chord through the point perpendicular to 

 the direction of the slits, then 



2c = v 1 — v 2 , 



and let v = coordinate of the mid-point of this chord. Then 



T 8A 2 M 2 Chirac . kirac krcaiq + v ) 1 



I= ^r l^r + sm i?r cos — * r- 



The fringes therefore disappear when 

 Azirac 



Their visibility is 



. 4:7rac 1 4*7rac 



