239 



Looking upstream, as is customary in regarding channels whicli lead 

 in from the sea, the rotation of the earth therefore tilts the water 

 surface upward to the right at high water, and upward to the left at 

 low water; with the consequence that the tidal range on the right 

 (ascending) bank is greater than that on the left bank by 4coy2 sin X/g. 

 Since w=0. 0000729, and the value of g is not far from 32.16, this 

 increase in range becomes, when z is expressed in statute miles and v 

 in feet per second, 0.05 vz sin X. If z is expressed in nautical miles of 

 6,080.2 feet, and v in knots, the difference in range is 2.92^2 sin \/g, or 

 0.09 vz sin X. 



459. The observed differences in the tidal ranges on the two banks 

 of a wide estuary conform fairly well with this form.ula. Thus at the 

 entrance to Delaware Bay the distance between the two shores is 10 

 nautical miles, and the average current at high and low water is 

 about 1 knot. The entrance is at latitude 38°20, whose sine is 0.62. 

 The difference in range between the two shores from the formula is 

 0.56 feet while the observed difference is 0.6 foot. At the head of the 

 bay the width is 4 nautical miles, the current is 1.3 knots, and the 

 latitude 39°23, giving a calculated difference of 0.3 foot, while the 

 actual range on the right, ascending, bank is 0.2 foot greater than on 

 the left. A similar concordance with the formula is observed in other 

 tidal waters. 



13- 18 gl O 3 6 S 18 tty IS ff\ 34 



Oct. II OclJ2 



standard Time -hours 



Figure SI.— Tide curve of Delaware Kiver at Philadelphia October 11-12, 1924. 



460. Overtides and overcurrents in an estuary. — As is to be expected, 

 the tide advances more rapidly up an estuary, or any long closed 

 tidal channel, at high water, when the depth in the channel is the 

 greatest, than it does at low water when the depth is the least. The 

 further a tidal station is up an estuary, the earlier is the time of high 

 water with respect to the time of low water. The time interval from 

 low water to high water, or the "duration of the rise," steadily be- 

 comes less as the distance of the station from the entrance increases, 

 and the time interval from high water to low water, or the ''duration 

 of the fall" becomes greater. The tide curve takes the typical saw- 

 tooth form exemplified by the tides on the Delaware at Philadelphia, 

 shown in figure 8 1 . 



