255 



by the procedure set forth in paragraph 239, from the amphtudes and 

 phases, referred to a common origin of time, of the corresponding 

 components of the tides at stations at the two entrances. The tabu- 

 lated epoch of each of the tidal components is the difference between 

 the phases of the ecpiilibrium and actual tidal components at the 

 station. To transform these epochs to a common origin of time, they 

 may be converted into Greenwich epochs, by adding the longitude 

 of the station multiplied by the subscript of the component (paragraph 

 120). After the harmonic constants of the head have been deter- 

 mined, the predicted heights and times of the two daily maximum 

 heads in the strait may be run off on a tide-predicting machine. The 

 relation between the square of the strength of the current at a selected 

 station in the strait and the corresponding head, and the lag of the 

 current with respect to the head, are both determined from the 

 averages of an adec[uate number of current measurements at the 

 station. From these relations, the predicted times and heights of the 

 heads are readily converted into predicted times and strengths of 

 the current. By applying suitable scales to the tide-predicting ma- 

 chine, the times and strengths of the currents may be read off directly. 



499. Harmonic analysis of rotary currents. — Data on the rotary off- 

 shore currents are provided principally by hourly measurements of 

 the current directions and velocities at the lightships operated by the 

 Lighthouse Service of the United States. The south-north and west- 

 east components of the observed currents are analyzed, and their 

 harmonic constants in each direction determined. It is not difficult 

 to show that the current curve of the resultant of each of the harmonic 

 components, produced by combining its coordinate components in 

 the two directions, is an ellipse. The resultant currents of the com- 

 ponent are a maximum and a minimum in the direction of the major 

 and minor axes of the ellipse. The azimuths of these maximum and 

 minimum currents are determined from the coordinate amplitudes 

 and epochs of the component, by a formula whose derivation and 

 application need not be repeated here, and the harmonic constants 

 of the component in these directions determined. The direction of 

 the maximum and minimum velocities of the resultant of all of the 

 components nearly coincides with the axes of the principal lunar 

 semidiurnal component, Mg. By transforming all of the components 

 to these axes, the strengths and times of the current in these directions 

 may be predicted. 



500. Computation of average times oj reversing currents. — The succes- 

 sive times of slack water and of the strengths of the current at a station 

 ordinarily are taken off a plot of the hourly or half-hourly current 

 measurements. The respective intervals after the precedmg pre- 

 dicted high or low water at an established reference tidal station in 

 the vicinity, or the intervals after the times of slack and strength at 



