368 Tides in the Mediterranean and Adjacent Seas 



It is possible to explain the distribution of the co-tidal lines by using 

 Taylor's theory on oscillations in a rectangular basin, open at one end. It can 

 be shown that the two amphidromies and the changes in the tidal currents 

 during a full tidal period are caused by the superposition of an incoming 

 Kelvin wave and its reflection on the southern end. Fundamentally, the 

 North Sea tides can be considered as tides co-oscillating with the external 

 tide at its wide northern opening. 



Defant (1923, p. 177) and Proudman and Doodson (1924, p. 185) pub- 

 lished almost simultaneously their theories in which they attempted to derive 

 the distribution of the vertical tide over the entire area of the North Sea from 

 the numerous observations on tidal currents. Defant used as basis the charts 

 of the tidal currents published by the Deutsche Seewarte (1905) and, by 

 means of the equation of continuity, derives the periodic variations of the 

 vertical displacements of the sea level during the tide; Proudman and Doodson, 

 on the contrary, start out from the equations of motion and, with the aid Of 

 reliable current measurements taken on profiles across the North Sea, they 

 compute the variations of the vertical displacements of the sea surface. 

 Defant's and Proudman-Doodsorfs distribution of the co-tidal and co- 

 range lines are very similar and correspond to the distribution found by 

 Sterneck. Figure 153 gives an example of Proudman and Doodson's map. 

 Both tidal presentations were based on the relation between the vertical tides 

 and the tidal currents and are, therefore, not a result of a theory. 



Another set of co-tidal lines was given by Merz (1923, p. 30; 1921, p. 393), 

 based on coastal data and the numerous tide curves obtained at sea. It con- 

 tains only the amphidromy in the southern part of the North Sea; the northern 

 amphidromy is lacking and is replaced by a dense crowding of co-tidal lines. 

 Sterneck (1925, p. 147) has proven that, according to recent Norwegian 

 observations, the tide wave progresses southward along the Norwegian coast, 

 which is incompatible with a rotary tide. The apparent lack of this second 

 amphidromy must perhaps be attributed to the effect of friction. The Kelvin 

 wave penetrating from the north is not totally reflected on the shallow coast 

 of Germany, a large part of its energy is lost because of the small depths 

 off the southern coast and complicated configuration (islands, sand banks 

 and wadden). The reflected wave, although still sufficient to cause the forma- 

 tion of the amphidromy in the Deutsche Bucht, is perhaps too weak to pro- 

 duce a second one at a greater distance. It should also be considered that 

 part of the incoming tidal energy makes its way through the Kattegat, is 

 used up for the greater part in the Belt and then in the Baltic, and does not 

 return any more into the North Sea. The superposition with the incoming 

 wave gives only a narrow and dense crowding of co-tidal lines and in the 

 wide area of the North Sea the impression of a progressive wave travelling 

 southward. Figure 154 gives the best and most recent picture of the tides of 

 the North Sea taken from the German Tide Tables. There is no doubt that 



