= / sin g \ 2 /l 3 2 c \ _ I sin 2a \ (l 3 2 c \ 

 q \R cos i|i/ \C 3<J> 2 / \R 2 cos ^/\C difidtft/ 



/ cos a \ 2 /l_ 3 2 c \ + / 2 cos a tan jA A dc\ 

 + ^ R^ j \C 3* 2 / V " \ AC dw/ 



/ cos q tan j>\ / tan j; sec jA /3q\ 



i dc = i_ [• / co^ax /i 3C\ + /i sex] 



C ds R [ \cos <Jj/ \C 3<j>/ \C 3<Jj/J 



I d£ = !_ [. /sin_qN/l 3CN + qs /I BC \1 (75) 



C dw R^ [ \cos ifi/VC 3<}>/ \C 3^ /J 



where 



R = the radius of the Earth 



e 



<f> = longitude of the point on the surface the wave ray is passing 

 through 



i|) = latitude of the point 



C = celerity of the wave 



s = a measure of distance in the direction the wave is traveling 



a = the angle between the wave ray and a line of equal latitude 



3 = a ray separation term 



Using the spherical coordinate system shown in Figure 9, Hwang and 

 Divoky (1975) give the linear long-wave equations as 



3U g 3ll r; 



iT = "F^ +f C V C76) 



e 



and 



3v g 3n ^ 



— = : - f u f771 



3t R sin 3d) e *■"■> 



49 



