Tides and Tidal Currents in the Proximity of Land 325 



apparent that to a current diagram which is a circle and whose sense of ro- 

 tation is cum sole belongs a circular diagram of forces cum sole, whose phase 

 is 90° "ahead of" the phase of the velocity, here we have s = Sj{a—f). 



It can also be proven that a circular current diagram contra solem 

 u = r cos at, v = r s'mat requires a tidal force contra solem with 



G x = —Rsinat , G v = Rcosat and r n = 



A comparison of the two cases shows that equal tidal forces (R = S) 

 produce very different tidal current velocities, depending on whether they 

 rotate cum sole or contra solem; at 54° N. lat. (southern North Sea) we have 

 for M 2 a-f = 0-229 x 10 -4 and o+f= 2-58 x 10 -4 , so that on the Northern 

 Hemisphere a frictionless tidal current rotating to the right subject to the 

 action of the Coriolis force is eleven times stronger than a current rotating 

 to the left, all other conditions being alike. 



If two of these circular motions are superimposed, we can derive the general 

 case of a force rotating in an ellipse. To a tidal force 



G x = -{R+S)s\nat, G y = (R-S)cosat , (XI.7) 



to which corresponds a diagram of forces which has the form of an ellipse 

 with the semi-axes (R-\-S) and (R—S), belongs a tidal current 



/ & , S \ 



u = — —j. H 7 cos at = A cos at 



\o+f a-f J 



l R S \ . 



v = — — 7 sine? = Bsmat . 



\a+f a-f) 



The current diagram is an ellipse with the semi-axes 



R S 



(XI. 8) 



a+f^a-f 



The discussion of the equations (XI. 7 and 8) leads to very important con- 

 clusions. If R and S are equal, then the cum sole current is definitely pre- 

 ponderant among the frictionless tidal currents, because a—f < a-\-f Further 

 we have 



if S > R: B always negative; with a diagram of forces cum sole, friction- 

 less tidal current always cum sole; 



if S = R: G y = : with alternating force, frictionless tidal current cum sole, 

 axis ratio of the current ellipse/: a; 



if S < R: with a diagram of forces contra solem, frictionless tidal current 

 cum sole, as long as R/S < (<y+f)/(p—f); 



if -= = 4- or--— 7^ = -: force contra solem, frictionless tidal current 



S a— J R + S a 



alternating; 



