Tides and Tidal Currents in the Proximity of Land 



331 



(3) % = the angle of orientation which the major axis of the ellipse forms 

 with the positive axis; it is positive, when the maximum velocity (cor- 

 responding to the maximum wave height) is to the left of the + x-axis. 



(4) The angle r (in time r/a) which gives the phase difference expressed 

 in degrees between the time of the maximum velocity and the time 

 of maximum wave height. 



2JMP+NQ) 



{M 2 -Q 2 ) + {N 2 -P 2 Y 



2(MP+NQ) 



(XI. 14) 



Fig. 135. 



All these quantities can be computed in a simple way with (XL 24) from 

 the values M, N, P, Q, as shown by Werenskiold (1916, p. 360) 



2V = j/| ^\V{(M+Qf + (N-Pf}+\{(M-Qf + (N+Pf}\ , 



2aV = |/| jW{(M+Qr + (N-Py}-V{(M-Qf + (N+Pf}} 



tan 2% 



tan2T = (M 2 -Q 2 )-(N 2 -P 2 ) 



Table 37 contains two cases computed according to the equations (XI. 23) ; 

 both are for the M 2 tide (a = 1 -4052 x 10 -4 ). In both cases the current diagram 

 is an ellipse cum sole, with the greatest velocities at the surface. The minimum 

 velocity decreases more rapidly with depth than the maximum velocity. This 

 causes the ellipse to become narrower in approaching the bottom. The 

 maximum velocity occurs before the high water, the difference increases with 

 depth. The conditions in cases of friction can be represented schematically 

 in Fig. 136, according to Figs. 130 and 131. A discussion of the equation 

 (XI. 23) by Fjeldstad gives the same conclusions and results as found by 

 Thorade and Sverdrup in a different way. 



Sverdrup and Fjeldstad deal also with the case which is important for 

 the polar regions, when a sea is covered by a layer of ice (pack-ice) which 

 dampens the movement of the water through friction. In that case the boundary 



