298 Theory of the Tides 



longitudinal oscillations which are identical in all longitudes and for which 

 <r 2 > 4co 2 , i.e. the period is smaller than 12 h, he obtains results which do 

 not show any essential difference with those obtained by Laplace and Hough. 

 With a 2 < 4oj 2 , i.e. for periods larger than 12 h, Solberg expects results 

 differing widely therefrom. A second part of the research in connection here- 

 with is still lacking. Proudman (1942, p. 261) has recently broached the 

 question of the validity of the Laplacian theory and, comparing its results 

 with those of a more accurate theory, discussed thoroughly their discrepancies. 

 He has been able to show that the cellular oscillations with the semi-diurnal 

 components can only be of any importance in the vicinity of the poles, whereas 

 the long period components acquire importance only in the vicinity of the 

 equator. Diurnal cellular oscillations are only possible if their horizontal 

 wave length is of the same order of magnitude as the water depth. This, 

 however, is not the case for the actual oceans. Generally speaking, the 

 necessary improvements made to the solution of the simpler Laplacian theory 

 seem to be only very slight for the ocean as a whole. 



