Chta-Shun Yth 
k 
gt gov Sk digas mirage (77) 
which is just the solution of Kelland (1839). 
We shall now proceed to study truly internal waves. 
VII. A GENERAL METHOD OF SOLUTION 
Given a density stratification Pg anda channel cross sec- 
tion, our task is to find the relation between a2 and k* determin- 
ed by (44) and (45), supplemented by (47) if there is a free surface. 
Since o?% appears in the denominator of the third term in (44) and 
as a multiplier of that term, (44) is inconvenient to use as it stands. 
We shall transform it into an equation in v. Differentiating (44) 
with respect to y, andusing (43), we have 
a?" 5 34 Zz “ye 
; 5 ye ak v sik vy) + (9,v'). = oie (78) 
with the accent on pg and on v indicating differentiation with res- 
PECt tole y. - 
The boundary condition (45) has to be written in terms of 
v alone. Since u is given by (34) and v by (43), we can write 
3 EP’) 
Fao ; ( gts 5 ) vdy + £, (x) : (79) 
where fj(x) is an arbitrary function of x. It will be shown later that 
the boundary condition (45) demands that f)(x) be a constant. 
Hence 
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