14 Mr. T. K. Chinmayam on the Flow of 



where r is the distance of the point from the edge 0, <p, <£' 

 are the angles which the diffracted and incident beams 

 respectively make with the direction xO. If we denote the 



angle P'OY (fig. 1) by a, <£= ~-«; f =| , so that the 

 expression (6) becomes 



. \ / - cos I kr — nt-\--r) i + 1 A 



since a, is small so far as our present investigation is 

 concerned. Now r = V ! 0—y + x 2 /2y ; a — x\y approximately. 

 Hence the above expression may be written 



The total disturbance at P' is thus 



f = cos (ky - nt) — \/7cos (Icy -nt + k 2a6 z + 2y6 2 ) 



~- cos( k y + ^ nt + T ) . 



2irx \ J 2y 4 / 



Remembering that 



x = 3ad 2 j2 + 2y 0, # 2 / "2y = 2y6 2 + 3a0 3 , 



we get for the intensity of illumination at any point the 

 expression 



l = l + S-2 v / Scos X , (7) 



where S^+A + ^cos (*rf*+ £), . (8) 



% = ^(2^ 3 + 2^ 2 )+6, ....... (9) 



and tan e= 7= (10) 



2x /7+^ X cos(^ 3 +^ 



7T^ \ 4/ 



Equations (4) and (7) give for the positions of the maxima 

 and minima of illumination 



x=2y6 + 3a6 2 /2, » 



2a6s + 2y6 2 ~m\/2-eX/27r) ' ' * * (11 ^ 



We see that the introduction of the diffraction term has 



