288 Theory of the Tides 



given by the equilibrium theory for the central meridian. The amplitude 

 for Ki is given in a ratio to the amplitude of the equilibrium theory. For 

 the semi-diurnal tide K 2 , on the contrary, the maximum amplitude has been 

 taken equal to one and the lines 0-8, 0-6, 0-4, 0-2 have been drawn "solid". 

 For each case, the amplitude can be computed relative to the maximum value 

 of the equilibrium theory H with the aid of a coefficient. Only a quadrant 

 of the entire ocean has been described, as there is always symmetry to the 

 equator and to the central meridian. 



It is shown that, for the diurnal tide K x , there is resonance for the depths 

 of 26,510 ft (8080 m) and 9449 ft (2880 m). Figure 121 illustrates the tide 

 for the cases ft = 0, 20 and 30 63, which corresponds to the depths oo, 

 14,520 ft (4420 m), and 9449 ft (2880 m). ft = gives the equilibrium tide. 

 Tide ranges at zero occur at the equator and at the pole, and the tide wave 

 travels from east to west in the shape of co-tidal lines converging towards 

 the pole. Decreasing depth influences especially the tide at the pole. Whereas 

 here the amplitude was previously zero, it now reaches there the maximum, 

 and the co-tidal lines do not converge any longer towards the pole; at the 

 boundary meridian there is a constant variation of the phase from the equator 

 to the pole. The changes in the tidal picture beyond the first resonance depth 

 are not great, but a point where the amplitude is zero, namely, an amphidromy, 

 can be spotted in the central meridian. This form then appears clearly with 

 the second resonance depth of 9449 ft (2880 m); this amphidromy governs 

 the entire picture of the ocean, while, in a most characteristic way, the large 

 amplitudes remain in the vicinity of the pole. In the equatorial section of 

 the ocean, the variations in phase are only slight, with very small amplitudes. 

 With further decreasing depth, the central amphidromy splits up apparently 

 in two parts; one lies in the western, the other one in the eastern quadrant, 

 but the amplitudes are very small. Large amplitudes only occur in the polar 

 regions where the whole phenomenon of the diurnal tide is concentrated. 



Figure 122 shows three cases of the semi-diurnal tide K 2 . The first case 

 applies again for ft = and gives the equilibrium tide. We notice a star- 

 shaped distribution of the co-tidal lines around the pole with a regular 

 propagation of the tide from east to west with maximum amplitudes at the 

 equator. If the depth becomes smaller, the amphidromic distribution of the 

 co-tidal lines moves suothward (northern hemisphere) on the central meridian 

 and at ft = 2 (depth 44-3 km) a well-developed amphidromy appears at 

 approximately 52°. With further decreasing depth this amphidromy splits 

 in two; with ft = 6 (depth 14-8 km) each quadrant is governed by an am- 

 phidromy with a positive direction of rotation (counter-clockwise). The 

 picture becomes more and more complicated with further decreasing depth, 

 so that with ft = 18 (depth 4-92 km) each hemisphere has already 3 amphi- 

 dromies (two in the positive, one in the negative sense of rotation), as shown 

 by the centre, picture in Fig. 122. With a depth of 14,500 ft (4430 m) 



