Tides of the Oceans 497 



east, except at 30° N., where the ocean reaches its greatest width. The same 

 applies for the K x tide. The free period of the Atlantic Ocean in its merid- 

 ional axis from about 40° S. lat. up to Iceland is 37-7 h, so that for the M 2 tide 

 v = 304 and for the K x tide v = 1-58. Consequently, the co-oscillating tides for 

 these components will have three and two nodes respectively. If we superpose 

 these two oscillating systems in zonal and meridional direction we obtain 

 a picture of the tides which resembles very closely the co-tidal lines derived 

 from the observations. 



Conditions are similar in the Indian Ocean. Zonal oceans bounded at 10° 

 and 30° S. give for the M 2 tide two nodes, and for the K x tide one node; the co- 

 oscillating tide for which 7} = 20 h would -have two nodes for the M 2 tide and 

 one node for the K x tide. This is mainly what the co-tidal maps show. 



In the Pacific Ocean, which widens from the north towards the equator, 

 the number of nodal lines increases. For zonal oscillations we have in 40° 

 and 30° N. two nodes for the semi-diurnal tides, from 20° N. to the equator 

 there are three nodes. Omitting the Tasman Sea and the Coral Sea, there 

 are two nodes in the South Pacific. A meridional co-oscillating tide should 

 have two nodes. The number of amphidromies actually existing corresponds 

 approximately to the points of intersection of these oscillating systems. These 

 considerations are acceptable for the Atlantic and the Indian Ocean, but they 

 seem too risky for an ocean which has the expansion of the Pacific. All that 

 can be said is that the canal theory supports reasonably well the number 

 of amphidromies and nodal lines respectively of the empirically derived 

 oscillating system. 



The tides of the Atlantic Ocean have been subjected to a more thorough 

 theoretical treatment. Whewell (1833) expressed the opinion when his first 

 map of co-tidal lines was published, that the tide wave of the Atlantic Ocean 

 did not develop in this ocean itself, but penetrated from the south-east. 

 We should observe in the Atlantic Ocean only the effect of a wave which 

 had developed already in the Pacific Ocean or in the Antarctic belt. Later, 

 Warburg (1922, p. 12) has pointed out that a tidal wave, as required by 

 the theory, can only develop in a belt girding the whole earth and that the 

 tides in the Atlantic Ocean could originate only in this belt. 



This conception concerning the origin of the tides in the Atlantic was 

 already contradicted by Airy (1842), who emphasized that the Atlantic Ocean 

 is sufficiently vast to develop its own tides. Whewell noted later that the 

 Atlantic tides were to be considered as standing oscillations with a nodal line 

 extending from Brazil to Guinea. Ferrel (1874, p. 239) has even expressed 

 the opinion that a barrier between South Africa and South America would not 

 alter the tidal wave of the Atlantic Ocean. Harris (1904, part IV B, p. 366) 

 explained the co-tidal lines in the Atlantic Ocean by interferences of two 

 oscillations developed in the ocean itself. Darwin (1910) has taken the 

 position that the wave entering from the south should be of more importance 



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