Tides and Tided Currents in the Proximity of Land 341 



and constant cross-section (corresponding to the mean depth of the basin). 

 Then one proceeds with the computation according to (XI. 17) until the last 

 cross-section (opening). One obtains here a definite value for //, which, if 

 it were correct, would be zero. If this is not the case, one adds to the com- 

 puted distribution of amplitude another one, corresponding to a co-oscillating 

 tide, which at the last cross-section (opening) gives an amplitude — ?/. The 

 total sum of the two satisfies the differential equations of the independent 

 tide and also the boundary condition at the opening. In this way, one can 

 compute the independent tide nearly as rapidly as the co-oscillating tide. 



A condition for these methods is that the tide-generating force in the 

 considered region of the ocean is synchronous everywhere along the "Talweg". 

 If this is not the case, for instance, for long and curved canals, one must 

 divide the tide-generating force into two periodic components with prescribed 

 phase, and make the computation for each component separately. Such 

 a division is always possible. The results added again with their respective 

 phases will give the longitudinal oscillation of the ocean basin, whereby all 

 orographic factors are taken into consideration. 

 (b) Effects of the Rotation of the Earth 



As regards the influence of the Coriolis force on standing waves of the in- 

 dependent tide and the co-oscillating tide in adjacent and boundary seas, see par- 

 ticularly the explanations given in Chapter VI, 5th para. (p. 204), which can also 

 be applied in this instance. To consider in first approximation the Coriolis 

 force, it is sufficient to compute the horizontal tidal currents of both kinds of 

 tides from the corresponding values of I and, as explained en pp. 143, 154, to 

 determine the transverse oscillations caused by the deflecting force of the earth's 

 rotation. The superposition of the longitudinal oscillation and the transverse 

 oscillations transforms the nodal lines into amphidromies, which rotate contra 

 solem. The alternating tidal currents change into rotary currents and their 

 vector diagrams are ellipses, in this case there is not a complete equilibrium 

 between the transversal gradient and the Coriolis force (same as for the 

 Kelvin waves). 



Taylor has given an accurate solution of the kind of co-oscillation which 

 can be expected of a rectangular bay of uniform depth with the external 

 tide before its opening into the open ocean. The result is explained on p. 210. 

 At some distance from the inner end, the co-oscillating tide has the simple 

 form of the superposition of the incoming and the reflected Kelvin wave 

 with alternating currents. In the part of the bay closest to the end, however, 

 there appear transverse oscillations which make it possible that the boundary 

 condition £ = at the closed end is fulfilled. Figures 91 and 92 show 

 the distribution of the co-tidal lines and co-range lines and the current dia- 

 grams of the tidal currents for a bay whose length is twice its width. The 

 case discussed corresponds approximately to the North Sea 53° N. lat., width 

 465 km, depth 74 m. The northern amphidromy shows the superposition of 



