366 Tides in the Mediterranean and Adjacent Seas 



although for a long time it was regarded as the best presentation of the North 

 Sea tides. The rejection of WhewelPs chart was principally based upon the 

 opinion first expressed that the co-tidal lines are similar to the crest-line of 

 the tide wave. This erroneous view was retracted later on by himself and 

 corrected in so far as these co-tidal lines connect only the geometrical lo- 

 calities, where high water occurs simultaneously. This difference has been 

 well described by Thorade (1924, p. 27) and Schumacher (1924, p. 35). 



The conception that several systems of waves coming from different di- 

 rections were responsible for the tides of the North Sea was prevalent during 

 the second period. Borgen (1898, p. 414) considered for the first time the 

 observations on tidal currents, but arrived at the same conclusion that all 

 essential tidal phenomena could be explained by two systems of progressive 

 waves. A similar opinion was expressed by Krummel (1911, p. 350). He 

 however, considers as a given feature an amphidromy in the Hoofden, which 

 had already been proven hydrodynamically by Harris (1904). Krummel tries 

 to explain the tidal picture by several progressive waves that are influenced 

 by the bottom configuration and interfere with the direct waves. The co-tidal 

 lines are very much curved and this curvature was based upon the supposition 

 that the tide will be earlier in deep water than in shallow water, as the rate 

 of travel of a progressive wave increases with the square root of the depth. 

 It is obvious that no satisfactory results can be obtained by such purely 

 qualitative discussions. 



During the third period, research is based on the hydrodynamical theory 

 of the tides. The great width of ihe North Sea does not permit a more exact 

 direct application of the methods described in the previous chapters, which 

 apply mainly to narrow, channel-like adjacent seas. However in a first ap- 

 proximation, we can consider the North Sea z$> a wide channel, open against 

 the open ocean at its northern end and which receives from this side strong 

 impulses to co-oscillate with the external tide. The opening at the southern 

 end is not of great importance. The tidal energy entering the North Sea 

 through the Strait of Dover is small, and as Kelvin (1891, p. 201) pointed 

 out already in 1878, its influence does not go beyond the island of Texel. 

 One can consider, as far as the tides are concerned, the region south of 

 53° N. lat. as belonging to the English Channel. 



If we consider the North Sea as a bay open on one end, the character 

 of its semi-diurnal co-oscillating tide is defined by the value of v. The average 

 depth of a great number of west-east cross-section show in rough approxi- 

 mation that the depth increases linearly from the south towards the north. 

 The period of the free oscillation of such a basin gives v = 1-47 and the 

 co-oscillating tide with the external tide in the north has, according to Defant 

 (1923, p. 57), two nodal lines, one located not far from the northern opening, 

 the other one a little less than one-third of the total length from the inner end. 

 As the phase at the northern end is approximately 95 h, the centre section 



