150 



each of the recorded curves are divided into, say, 10 equal intervals, 

 the recorded rise or fall during each interval is multiplied by the 

 ratio of the total mean rise or fall to the total recorded rise or fall, and 

 the results added successively to the computed elevation of low water. 

 The tides at the proportional intervals are then averaged, and plotted 

 at the corresponding mean intervals. The tides at semihourly inter- 

 vals after a lunar transit then may be taken off the plotted curve. 

 The result is a tide whose high water and low water are at the times 

 and elevations of mean high and low water, and whose semihourly 

 rates of rise or fall are the composite of those of the selected tides. 

 This composite tide curve has a total period, from high water to high 

 water, or from low water to low water, of half of a mean lunar day, 

 12.42 mean solar hours. 



306. Similar composite curves of spring or neap tides could be pre- 

 pared by adjusting a number of tides near the time of spring or neap 

 tides to the computed times and elevations of mean low and mean 

 high water of spring tides ; and composite curves of tides of the mixed 

 type by similarly adjusting suitable recorded tides to the times and 

 elevations of mean lower low, liigher low, lower high, and higher high 

 waters. It may be observed that the sum of the durations of the rise 

 and fall of spring and neap tides differs slightly from the mean lunar 

 half day or day. 



307. Computations. — Designating the successive tidal stations along 

 the channel, beginning at or near the head of tide, as station 0, station 

 I, station 2 • • • station A^", let: 



Vo} 2/i> 2/2, • • • Vn be the heights of the tide at these stations at 



the time t, this time usually being on the hour and half hour. 

 At, the time interval used in the computations, usually /2 hour, 



or 1,800 seconds. 

 Vo' , Vi , 2/2' •• ■ Vn , the tidal heights at the time t-\-M. 

 Ui, U2, Us ' ■ • ?7„, the mean area of the water surface between 



stations and 1, 1 and 2, etc., during the time interval 



between t and ^ + A^. 

 At/i, Ay2, Ays • • • Ay^, the mean rise in the water surface 



between the successive stations during the same interval. 

 AFi, Ay2, AF3 • • • AVn, the algebraic increase in the volume 



of water between the successive tidal stations during the 



same interval. 

 Then evidently 



AVr=U,Ay„ AV2=U2Ay.2, • • ', AV,= U,Ayn 



If the stations are sufficiently close together, the mean rise in the 

 water surface between any two stations during the time interval At 

 may be taken as the increase in the mean elevation of the tides at 

 the two stations during that period so that: 



