Tides of the Oceans 



501 



tides in the Atlantic thus become a mixture of independent and co-oscillating 

 tides, in which the latter predominate. We find that the average height of 

 both waves are in a ratio of 2:3. 



The diurnal tides of the Atlantic Ocean could also be explained by this 

 theory. The procedure is the same. We can compute theoretically the am- 

 plitude and phase for the centre axis. However, for the diurnal tides we have 

 the added difficulty that the current observations have been made in different 

 seasons, and this diurnal tide is very severely subjected to the semi-annual 

 periodical variation. But, fundamentally it seems also possible to explain the 

 picture of the diurnal tides. 



Cross -sections 



Fig. 207. Phase of the semi-diurnal tidal current for the centre axis of the Atlantic and 

 results of the current measurements (+). 



Proudman (1944) has made a new attempt to explain theoretically the 

 tides of the Atlantic. It is mathematically correct that for every area of an 

 ocean the tides and tidal currents are fully defined when one knows, for 

 the chosen boundaries of this area, the tidal ranges or the tidal currents, and 

 if the boundary conditions are fulfilled for the shores. Proudman selects as 

 boundaries of the area of the Atlantic Ocean under consideration the parallel 

 of latitude 45° N. and 35° S., and considers the tides of this area as a super- 

 position of a number of oscillations which are possible in an ocean in the 

 form of a canal and which fulfils the boundary conditions. He assumes for 

 these oscillations that there is no friction and he neglects any friction along 

 the coasts. Possible oscillations which Proudman considers are: 



(1) The independent tide caused by the meridional and zonal tide generat- 

 ing force. 



(2) Two waves of the Kelvin type (p. 206), one coming from the north, 

 the other from the south into the area. 



(3) Two Poincare waves, one coming from the north, the other one from 

 the south, taking only the two simplest from the infinite series of these 

 waves (p. 208). We can compute for all these waves the relative tidal ranges 

 and phases, as well as the tidal currents for the entire area under consider- 

 ation, and taking the morphological configuration fully in account. The 

 superposition of these four waves must agree with the observations made 

 at four coastal localities after deducting the forced tide. This will determine 

 the four free constants necessary to transform the relative values into ab- 



