KUNGL. SV. VET. AKADEMIENS HANDLINGAR. HAND 47. NIO 4. 41 



with (p and \p functions of time, in order to study, as a preparation, the case of an infinite 

 tidal wave-length, the following conditions are at once satisfied: 



. d<D< dO' . , 



1 . - = ä — = for y = h, 



o [i an 



a 00 do' 



2. r- = -. tor « = 17, 

 dn dn J ' 



3. -— = fory = — h + y cos kx, putting 



y = — a sinh kh + 8 cosh kh. 



Then there is left only the pressure-condition for the common boundary. Retaining 

 only terms due to the presence of the ridge, we have for y = i\\ 



Tt 



c a sin at . 8 . coth kW sin kx — c coth kh 1 ~ sin k x — -r- . cos kx] 



\dt dt i 



dt 



and 



ldO'\ s 



— ca sinat . a sin kx + c coth kh l-r^sin kx =- cos kx) , 



\dt dt I 



ldO\ 2 - 



u' 2 = I -t— I = + 2c 2 (cos 2 at . Sk coth kh' cos kx + k cos at . coth kh' (fp cos kx + if'sm kx 



u 2 = irr I = — 2 c 2 (cos 2 a t .ak . eoskx + k cos at . coth kh{fp cos kx + ip sin &#). 



Forming then the pressure-condition: 



we obtain the following system of equations: 



q (o — Q')(p = — c -=- . a + c 2 cos 2 a t . k (aS + <■)) + kc 2 cos at .a .(p 

 g(Q — Q')yj= + c. J. .a — ca sin a t . (a 8 + 0) + kc 2 cos at. a . xp- 



Cl t 



Here, for shortness: 



a = q coth kh + o' coth kh' 

 = _ ZlQ 



sinh kh 

 a (i + Q = ua -f /?^' coth fcA'. 



Now for y =ri the general surface-condition gives us: 



dij d(D di; dO 



(I t dx d x y ' 

 K Sv. Vet. Akad. Handl. Band 47. N:o 4. 



