149 



diurnal inequality may be ascertained by extending the cubature 

 through two semidiurnal tidal cycles; i. e., through a period of 25 

 hours. If the difference between spring and neap tides is large, a 

 cubature might be made of a representative tide of each kind. If the 

 tides are of the mixed or diurnal types, a cubature of a representative 

 tropic tide and of a representative equatorial tide would be necessary 

 to determine the characteristic currents produced by each. 



304. Average tide curves. — A cubature based on average tide curves 

 gives a better general picture of the discharges and currents in a tidal 

 channel than one based on the tides during a single day. Cubatures 

 prepared fro.m average tide curves before and after a major change has 

 been made in a channel afford a conclusive determination of the effect 

 of the change upon the tidal discharge and currents. Average curves 

 of tides of the semidiurnal type .may be prepared by averaging the 

 tidal heights, taken from the graphic record of an automatic tide gage, 

 at hourly or half -hourly intervals for the 12 hours beginning with the 

 time of each lunar transit. The observations should extend over a 

 period of 15 or 29 days, or a .multiple of the latter. A consideration 

 of the principles of harmonic analysis, explained in chapter II, indi- 

 cates that an average curve so prepared is substantially that of the Mo 

 component of the tide and its overtides. 



Average curves of spring and neap tides .may similarly be prepared 

 by averaging the recorded tidal heights at hourly or half-hourly inter- 

 vals after the lunar transit immediately preceding the times of spring 

 and neap tides respectively; and average -curves of tropic or equatorial 

 tides by averaging the heights at the sa.me intervals for a period of 25 

 hours after the lunar transits next preceding the times of such tides. 

 Obviously, a long continuous record of the tides at each of the stations 

 .must be available to prepare good averages of tides which occur but 

 twice a month. 



305. Composite curves of mean tidal fluctuations. — The range of an 

 average curve of all semidiurnal tides, prepared by the process out- 

 lined in the preceding paragraph, is less than the actual mean tidal 

 range during the period. For the mean cubatures of the Delaware 

 River made by the United States Engineer Office at Philadelphia, tide 

 curves were prepared by computing, by the ordinary methods, the ele- 

 vations and lunitidal intervals of mean low and liigh water, and con- 

 necting them with a composite curve derived from 10 recorded tide 

 curves whose range, duration of rise and fall, and half-tide level were 

 nearly the same as the range, duration of rise and fall and half- tide 

 level of the mean tide. The composite curve is prepared by adjust- 

 ing, proportionally, the duration and height of the rise and of the 

 fall of each of the recorded tides to the mean duration and mean rise 

 and fall, and averaging the results. For this purpose the periods 

 from low water to liigh water and from liigh water to low water on 



