112 U. S. COAST AND GEODETIC SURVEY 



Setting y=0.1 and solving for t (this value of t giving half the duration of 

 slack), we get for the duration of slack the following values: For a current 

 with a strength of 1 knot, slack water is 24 minutes; for currents of 2 knots 

 strength, 12 minutes; 3 knots, 8 minutes; 4 knots, 6 minutes; 5 knots, 5 minutes; 

 6 knots, 4 minutes; 8 knots, 3 minutes; 10 knots, 2}/^ minutes. 



HARMONIC CONSTANTS 



The tidal current, like the tide, may be regarded as the resultant of a number 

 of simple harmonic movements, each of the form y — A cos {at + a) : hence, tidal 

 currents may be analyzed in a manner analagous to that used in tides and the 

 harmonic current constants derived. These constants permit the characteristics 

 of the currents to be determined in the same manner as the tidal harmonic con- 

 stants and they may also be used in the prediction of the times of slack and the 

 times and velocities of the strength of current. 



It can easily be shown that in coastal or inland tidal waters the amplitudes of 

 the various current components are related to each other, not as the amplitudes 

 of the corresponding tidal components, but as these latter inultiplied by their 

 respective speeds; that is, in any given harbor, if we denote the various compo- 

 nents of the current by primes and of the tide by double primes, we have 



M'j: S'2: N'2: K'l: 0'i = m2M"2: szS'^: n2N"2: fciK"i: 0iO"i 



where the small italic letters represent, respectively, the angular speed of the 

 corresponding components. This shows at once that the diurnal inequality in 

 the currents should be approximately half that in the tide. 



MEAN VALUES 



In the nonharmonic analysis of current observations it is customary to refer 

 the times of slack and strength of current to the times of high and low water of 

 the tide at some suitable place, generally near by. In this method of analysis 

 the time of current determined is in effect reduced to approximate mean value, 

 since the changes in the tidal current from day to day may be taken to approxi- 

 mate the corresponding changes in the tide; but the velocity of the current as 

 determined from a short series of observations must be reduced to a mean value. 



In the ordinary tidal movement of the progressive or stationary wave types 

 the change in the strength of the current from day to day may be taken approxi- 

 mately the same as the variation in the range of the tide. Hence, the velocity 

 of the current from a short series of observations may be corrected to a mean 

 value by multiplying by a factor equal to the mean range of the tide divided by 

 the range for the period of observations. It is to be noted that in this method of 

 reducing to a mean value any nontidal currents must first be eliminated and the 

 factor applied to the tidal current alone. This may be done by taking the strength 

 of the tidal current as the half sum of the flood and ebb strengths for the period 

 in question. 



In some places the current, while exhibiting the characteristic features of the 

 tidal current, is in reality a hydrauhc current due to differences in head at the 

 ends of a strait connecting two independent tidal bodies of water. East River 

 and Harlem River in New York Harbor and Seymour Narrows in British Colum- 

 bia are examples of such straits, and the currents sweeping through these 

 waterways are not tidal currents in the true sense, but hydraulic currents. 

 The velocities of such currents vary as the square root of the head, and hence 

 in reducing the velocities of such currents to a mean value the factor to be 

 used is'the square root of the factor used for ordinary tidal currents. 



