8 ZEJLON, ON TIDAL BOUNDARY-WAVES. 



* (( , = (j sili kx.e iat , 

 we ha ve: 



..',- = d.ia . sin kxe iot 

 dt 



as the vertical component of velocity of that surface, and with sufficient approximation 

 this will give the normal velocity of the boundary. This must be equal to the normal ve- 

 locity of the particles of fluid against the surface; so: 



äia sin kxé at = — (' - j — c. e iai .- ,'"' 

 \dyly~o ox 



or, to the first power of small quantities: 



3) fi.io= — c.k.fj. 



With the approximation used, the pressures on each side of the boundary will be: 



p' 



-91. + () f 



p = 



p 



du 



- g '<» + dt' 



On equating p to p we need only conserve the terms due to the disturbance, i. e. containing 

 any of the quantities a, ii, a', [>'. Tims from: 



ti ii (i ii ' 



9lo(Q-Q) = Q Ti -Q öl 



or 



we obtain: 



4) g t -ik(g — g') = o-(yc( — g'«'). 



Fihally, for the upper free surface, we have the condition left: 

 IV. for y = ti should be: 



V' = o, 



where p in the same manner as before means the part of the pressure caused by the dis- 

 turbance. Denoting the elevation of the free surface by >,/,>, wc find: 



v = I" 

 ..l'"f'\ 







<J\I>< - 



-(# 



11 ',/,' 

 tit 





=//- 



