286 



Theory of the Tides 



The corresponding critical depths for the solar semi-diurnal tide are about 

 28,182 and 7375 ft (8894 and 2248 m). For the depths between these two 

 values the tide is inverted. 



Hough has also computed the lunar semi-diurnal tides for which a/2a) = 

 = 0-96350. The ratios for the same four depths have been entered in Table 29. 

 One can see that the critical depths are now somewhat displaced; they lie 

 near 26,050 and 6450 ft (7938 and 1965 m). However, for the mean ocean 

 depths existing on the earth all semi-diurnal tides are always inversed. 

 (<:) Tides in Bounded Ocean Basins 



Goldsborough (1913, p. 31, discussion by Doodson, 1928, p. 541) has 

 given a solution for a polar basin of uniform depth bounded by one or two 

 parallels of latitude. The difficulties, in this case as in all similar cases, are 

 in the fulfilment of the boundary conditions (transverse velocity zero at the 

 limiting parallel of latitude). Table 31 gives the amplitude of the tide for 



Table 31. Component tides in a polar basin limited at 60° latitude 

 (Ratio of the amplitudes to the amplitudes given by the equilibrium theory) 



a polar basin limited at 60° latitude. Similar conditions are to be found for 

 a limit of (p = 75° 30'. The long-period tides are unimportant and the semi- 

 diurnal tides are practically equal to those of the equilibrium theory. The 

 diurnal tides vary considerably with the size of the basin and the depth and 

 are as a rule large, whereas in a uniform ocean covering the globe they are 

 negligible. This will show very clearly the great influence of limitation. The 

 large ratios for a small depth indicate an intensification of the diurnal tides 

 in the polar waters, which actually occurs in the observed tides. The diurnal 

 tides are quite prominent, as the semi-diurnal tides are weak. Goldsborough 

 found that the greatest critical depth for a resonance of the semi-diurnal tides 

 is about 160 m when the basin is limited at 60° latitude, and about 12 m when 

 the boundary is at 75 1°. The smallness of these depths against the real ones 

 excludes completely stronger semi-diurnal tides. Goldsborough (1914, p. 207; 



