14 U. S. COAST AND GEODETIC SURVEY 



rent with a strength of about a third of a laiot in a northwest and 

 southeast direction. Furthermore, the diagram shows that the cur- 

 rent actually observed consisted of a tidal current which was masked 

 by a nontidal current of greater velocity. In fact the diagram per- 

 mits the evaluation of this nontidal current. For this must clearly 

 be given by the line joining the point P with the center of the current 

 ellipse, and this is found to have a length of about half a knot and a 

 direction of S. 60° W. This nontidal current was brought about by 

 the northeasterly wind during the 5-day period in question. 



About 6 months later, throughout the 7-day period July 14-20, 

 1920, the current at Frymg Pan Shoals Lightship was found to set 

 easterly with velocities rangmg from a little less than half a knot to 

 more than a knot. On plottmg the observations, as the left-hand 

 diagram of figure 7 shows, the rotary character of the tidal current 

 comes to light at once. During this 7-day period the wind was blow- 

 ing steadily from the southwest with a velocity averaging approxi- 

 mately 30 miles per hour. This brought about a wmd-driven cur- 

 rent setting a little north of east with a velocity somewhat greater 

 than half a knot, and this completely masked the tidal current. 



HARMONIC CONSTANTS 



The reversing 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, reversing tidal currents may be ana- 

 lyzed in a manner analogous to that used in tides and the harmonic 

 current constants derived. These constants permit the characteris- 

 tics of the currents to be determined in the same manner as the tidal 

 harmonic constants, and thej^ 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 inland tidal waters, like rivers and 

 bays, the amplitudes of the various current constituents are related 

 to each other, not as the amplitudes of the corresponding tidal con- 

 stituents, but as these latter multiplied by their respective speeds; 

 that is, in any given harbor, if wo denote the various constituents of 

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



M\: S\: N'2. K\: 0\=mM"2. sS"2. n^'N'\: kyK'\: o,0'\ 



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

 of the corresponding constituents. This shows at once that the 

 diurnal inequality in the currents should be approximately half that 

 in the tide. 



Rotary currents may likewise be anah^zed harmonically, but in 

 this case it is necessary to resolve the hourly velocity and direction 

 of the current into two components, one in the north-and-south direc- 

 tion and the other in the east-and-west direction. Each set of hourly 

 tabulations is then treated independently and analyzed in the usual 

 manner. When the two sets of harmonic constants have been derived 

 the like-named constants of the north-and-south and east-and-west 

 directions may be combined into a single resultant, which will be an 

 ellipse. 



