Tides and Tidal Currents in the Proximity of Land 



351 



given by t] = >h + ^2 an d H.W. occurs when dr\\dt = 0. Letting t H denote 

 the local time for H.W. this equation gives 



at H = tan _1 (— tanxA-tanh//.v) . (XI. 26) 



This function gives the time of H.W. at any position along the channel for 

 any chosen coefficient of damping. 



Equation (XI. 26) can be used to find the relative height of H.W. at any 

 point — the ratio of height of H.W. at the point under consideration to the 



-80° -100° 



TIME OF HIGH WATER 



Fig. 144. Relations between the ratio of height of high water at any point to the height 



of high water at the barrier r\\r\^, the time angle of high water ot H , the phase difference of 



a primary wave at that point relative to the barrier xx, and the coefficient of damping /z. 



Reflection occurs where ?;/t? =1-0 and atfj = 0. 



height at the reflecting barrier — along the channel. Restricting rj and r) to 

 the elevations at H.W. the ratio rj/rj can be written 



vho = |/{K cos h2/^.v+cos2%x)} 



(XI.27) 



This function relates the height of H.W. at any position along the channel 

 to the height at the barrier for any chosen coefficient of damping. Redfield 

 derives in the same way the time of slack water or maximum current at any 

 point. Letting t s denote the local time of slack water, at s is given by 



