Internal Waves tn Channels of Vartable Depth 
If the inertial effect of density variation is neglected, (63) becomes 
Zz 
p + dA @ - k@ = 0. (65) 
The boundary conditions at the sides are, in accordance with (45) 
and (62) and with u and v given by (34) and (43) , 
for the two sides given by (45), respectively. 
The solutions for symmetric modes have the form 
¢= A coshax coshyy cosk(z-ctt+e) , (67) 
provided 
2 2 (2 Zz 
Gh ON oN Sate J) die : (68) 
The € in (67) is an arbitrary constant. Since the channel is sym- 
metric and (67) is symmetric with respect to x, it is necessary to 
consider only the boundary. 
y = mx (62a) 
where 
g if 66 
ears ee a 
Substituting (67) into (66a) andusing (62a), we obtain 
1413 
