GllDKD WAVE PR(1P.\0.\TIO\ 'rilliorcil (i V KO.M A(;\ KTK ' MKDIA. Ill 1 1 7!^ 



shaded regions are regions of like sign, and nil those carry solution 

 curves (dotted hues), by the same reasoning as was employed in Part I, 

 Section 4.11. Two branches of the TE]\I limit mode exist; in the area 

 bounded by (0,4) r , 0^ , (Ob')t and in the area Ob, /i , (Ob')t ■ The branch 

 in the first region begins at o- = Anth Xi,X2 given by 



XiVl - Xi^ tan aVl - Xr = XaVl - Xo^ tan a\/l - Xj^, 



Xi + X2 = p 



and ends at the intersection of (0,i)t , 0^ with a = 1 — p and /3^ = 

 (since X2 = on (0^)t). The branch in the region Ob , h , {Ob')t begins 

 with /32 = 00 , 0- = 1 and proceeds towards a = ^ ^^"^ = 1 . 



The region bounded by 7i , {Oa)t , h contains an infinity of solution 

 curves, the incipient modes. The n ^ of these begins at o- = 1, Xi = 1, 

 the intersection of /„ and Ic (the line Ic is also the transform of X2 = — «= , 



Oav I.^. A 



ObV^(0'b)t 



(Oa)t 



(Ob)t 





 •A2 A,' 



Fig. (S - Zero ;iii(l infinity contour.s of L(Xi , <x) and L(7'(^i). <^) i'l t^ie first 

 quadrant of the X - cr plane. Cross-hatched regions are excluded l)y the Polder 

 relation; shaded areas are regions of unlike sign of the two functions. Dotted 

 curves are solution curves. 



