Internal Waves tn Channels of Vartable Depth 
where 
Z 4 - 
c = toe? ‘ (87) 
Substituting (85) and (86) into (78), and extracting the terms of 
zeroth order in k, we have (P', assumed never to vanish) 
! Bas t Xr ! = 
2 98P 0%20 gp 0 0 Yoo + bg oa) Dix, (88) 
which gives v2qg in terms of voo. 
If terms of zero order in k in (81) are taken, that equa- 
tion becomes, with n, and ng given by (84), 
d 1 =e = 
a= [ of? 9% 20 dy ES iG) Po go 0 
0 
This equation is valid for all y. Hence we can differentiate it with 
respect to y and obtain 
! s ee = 
05 Yaar ee (f'f Pas do) os (90) 
1419 
