780 



[chap. 23 



exact solutions of these problems considerable mathematical difficulties im- 

 mediately arise. The results are interesting in so far as they make clear the 

 influence of the geometry and of the depth upon the development of the tides. 

 A comparison of theoretical solutions with the observed oceanic tides is in- 

 appropriate because of the considerable deviations between the shape of the 

 models compared with the existing oceans. 



Fig. 11. Co-tidal and co-range 

 lines of Ki constituent in 

 an ocean bounded by 

 meridians 180° apart. 

 (After Doodson, 1935, 

 Fig. 3.) 



ooooo o 



Fig. 12. Co-tidal and co-range 

 lines of K2 constituents 

 in an ocean, mean depth 

 2.75 miles, bounded by 

 meridians 180° apart. 

 (After Doodson, 1938. 

 Fig. 21.) 



Fig. 13. Semi-diurnal tide K2 in a quartre of an ocean 60° wide, bounded at 62.2"N and S. 

 (After Rossiter, 1958a, Fig. 5.) 



Important progress was made by Proudman and Doodson (1927), who 

 treated the oceans bounded by meridians on the non-rotating and on the 

 rotating earth. Doodson made calculations from a great number of models and 

 found out that the positions of the co-tidal and co-range lines depend very 

 much on depth. In Fig. 11 the diurnal constituent Ki and in Fig. 12 the semi- 

 diurnal constituent K2 are shown for an ocean which covers a hemisphere. 



