HAKMOISriG ANALYSIS AND PEEDICTION OF TIDES. 61 



The argument of component S^ is taken as one-half that of the 

 component Sj, and the argument of component Sa is one-half that 

 of the component Ssa. The factor F for the reduction of each of 

 the meteorological components is taken as unity, since the magni- 

 tudes of these components appear to be unaffected by changes in 

 the longitude of the moon's node. 



ANALYSIS AND PREDICTION. 



21. HARMONIC CONSTANTS. 



In the preceding chapter there were found from a consideration 

 of the tidal forces the principal components that may be expected 

 to exist in the tide. Each component is represented by the product 

 of a coefficient, which may include a variable function of /, depending 

 upon the longitude of the moon's node and the cosine of an argument 

 which defines the component and determines its period. The period, 

 being independent of conditions upon the earth's surface, is the same 

 for every locality and gives to each component its identity. 



The coefficients and phases of the components of the true tide do not, 

 however, agree with the corresponding coefficients and phases of the 

 equilibrium tide, but vary in different localities. It is therefore 

 necessary, in order to represent the true tide at any place, to sub- 

 stitute for the coefficients 6f the equilibrium tide the amplitudes of 

 the true components determined from actual observations, and also 

 to find corrections for the phases of the equilibrium components 

 which will make them conform to the true phases. These phase cor- 

 rections are called the epochs of the components and are constants 

 for any locality. 



The amplitudes {H) and the epochs (/c) comprise the harmonic 

 constants which are to be determined by the harmonic analysis of 

 the tidal observations taken at the place for which the results are 

 sought. The principal use of these constants is in the prediction of 

 the tides. 



22. OBSERVATIONS. 



The most satisfactory observational data for the harmonic analy- 

 sis are from the record of an automatic tide gauge, which traces a 

 continuous curve from which the height of the tide above any 

 adopted datum plane may be readily obtained for any hour. This 

 record is usually tabulated to give the height of the tide at each 

 solar hour of the series, the kind of time used being that which is 

 customarily used at the place. Where an automatic tide gauge is 

 not available, hourly heights as observed directly upon a plain tide 

 staff may be used for the analysis. The record should be complete 

 with each hour of the series represented. If a part of the record has 

 been lost, the hiatus may be filled by interpolated values; or if the 

 gap is very extensive, the record may be broken up into shorter 

 series which do not include the defective portion. 



If the hourly heights have not been observed, but a record of the 

 high and low waters is available, an approximate determination of 

 the larger components may be obtained by a special treatment. The 

 results, however, are not nearly as satisfactory as those obtained 

 from the hourly heights. 



