151 



Al\=L^[(2/'o + ?/'i)/2-(2/o+2/i)/2], 



AVo= U,[(y\-hy'.^/2-{y,-^y,)/2], etc. (185) 



The total increase in the volume of water in the tidal prism from 

 the head of tide to any station, A^, is then: 



2AF=AFi + AFo+ • • •, AVn (186) 



This summation obviously should include the increase in volume in 

 any long tidal tributary above station A^ which is separately cubatured. 



Taking the origin of distances at the entrance to the channel, the 

 tidal discharge and the velocity at a given station are positive during 

 the tidal flood currents, when the total volume of tide water between 

 the station and the head of tide is increasing, and negative during the 

 ebb, when tliis volume is decreasing. 



The mean tidal discharge, Qt, at station N, during the time interval 

 A^, is then: 



Q,=^AV/At (187) 



The fresh water discharge, Qf, at the station is similarly the sum of 

 the fresh-water discharges entering the channel above that station. 

 This discharge may be regarded as constant during the period of cuba- 

 ture. Since it is an outward discharge, it is intrinsically negative. 

 The total discharge. Q, is then 



Q = Q-Qf (188) 



Designating the mean area of the cross section at station A^ during 

 the interval At as A', the mean velocity during this interval is : 



v^Q/X (189) 



308. The mean areas Ui, U2, etc., of the water surface between the 

 tidal stations during the successive intervals may be derived by tak- 

 ing off with a planimeter, from a map of the waterway, the areas at 

 successive stages of the tide, and constructing a diagram from which 

 the area at any elevation may be read. Ordinarily, it is sufficient to 

 take off from the map the areas at high and low water and to join 

 them on the diagram with a straight line. The area at each semi- 

 hourly interval is read from the diagram at the mean elevation of 

 the mean of the tides at the ends of the section. 



The areas between the stations should include any tidal tributaries 

 which enter the section, and should extend to the head of tide in these 

 tributaries, unless tidal volumes in the tributary are cubatured from 

 stations thereon. They should include also the effective storage area 

 in any tidal marshes adjacent to the channel. 



