KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 47. N:C) 4. 46 



plified or not, will immediately serve to satisfy the conditions 1 Ii of ]>. 11. Kor ili<- 

 pressure-condition at the common boundary, it is easily seen that, but for the terms 



dep . dö) 

 i ' and : > 

 ox ox 



and for small quantities of the second order, just the same conditions as for the case of an 

 infinite tidal wave-length will be obtained, only with that difference that c is to bereplaced 

 by c cos K x. 



Since to the tidal wave in itself corresponds a definite vertical displacement of the 

 boundary, this for the fulfilment of the pressure-condition as a whole will have to be added 

 to >]. Forming the modified differential equations we may verify that: 



But for quantities of the second order of smallness the solution of the fixed-ridge 'problem 

 is obtained by replacing in the displacement %, corresponding to the oscillating ridge, 



x by x + -sin a t . cos Kx, 



and adding to the result the vertical displacement of the boundary proper to the tide 

 when not disturbed by the ridge. 



This statement, of course, also implies that the wave-length of the boundary- 

 waves should be small compared to that of the original tide. 



