Internal Waves tn Channels of Vartable Depth 
together with the boundary conditions. Now (123) is just the equation 
for potential flow with uniformly distributed sources of strength C 
If (8) is satisfied (with f now identified with f,,5), andif d, is 
the height of the mth interface, 
b) 
! = 
| fleudide =" A eCica 
0 
(124) 
ee 
th 
N 
a 
Qu 
Q 
ra 
ii 
> 
@) 
ob 
> 
ine) 
O! 
NM 
ra 
ies) 
¥ 
Q 
as, 
Qu 
] 
I 
> 
5 
Q 
3 
by virtue of continuity. In (124) b,, is the width of the mth inter- 
face, and A, the cross-sectional area of the mth layer. (See 
Figure 1), Integrating (11) across b,,, layer by layer, we have 
2 
er eet Pg eet TER eae 
2 
hoe 2 AOC 
Bee foo Nag ee ee) a of) +» = (125) 
REPRE Pao : 
ane c. As > Ge 
“9 n ata rE 20s Tr) tn 
mee 
There are n unknowns oe » not all of which are zero. Hence we 
obtain a determinant which must vanish, Its vanishing gives n values 
for cg . The last of the equations in (125) corresponds toa free 
surface. If the upper surface’is rigid, it is to be replaced by & since 
*Now a rigid flat upper surface is not excluded. 
1429 
