All-101 ^8 



where we have set Ar- = A^ = B r- = B^ =0 since the contributions 



5 3 5 3 



of the terms with those coefficients do not tend to zero as 

 ^ — > CO , 



When (37) and (38) are used to get a relationship be- 

 tween the A. and the B., then the final form for V-j_i^ near x = 

 is found to be 



V = a cos T sin nsy e" M (i Z-I^+ c^)cos(l^^-^) 



lb L 3 2' ^ 2 



+ (^ - ^ ^ + CO sin(Vll.) 



''^^-^ ^ + C ) sin(Vll.)|e'"^/' (^2) 

 3 V/3 ^ 2 J 



where C^ and C. are arbitrary functions of y and 1 and must be 

 23 



found by applying the boundary conditions to the complete solu- 

 tiont 



In a similar manner, if we make the following two sub- 

 stitutions for the right (eastern) boundary 



(x - r) = e 



-1/3 rieh-1/3 

 V, = a cos T sin nsy e e Lv^ + 1.. -1 , 



* 

 we find that h = 1/3 and 



V^, = a cos T sin nsy e [ -Q + AT(y5T)]e^ . 



lb -^ 3 i ' (fy.^^ 



We have used the fact that V., — >0 as ri — > - co . (As stated in 



lb ' 



the appendix, t\ -^- od v/hen the boundary on the right is under 

 consideration, since the boundary layer solutions must become 



* The same remark applies to the value of h as previously made 

 for the value of k« 



