316 



The Harmonic Analysis of Tidal Observations 



the harmonic analysis of the tides show that the tide, in a given locality, 

 can be considered as a combination of a great number of constituent tides 

 with constant amplitude and constant phase. These constants have been 

 computed by harmonic analysis from good tidal records for coastal localities 

 for the most important components, and they are characteristic and valid 

 for the tide in a locality without any changes for a long period of time. 

 Nothing prevents then the computation of any component tide for a given 

 day of the year, and the sum of all these partial tides then gives the tidal 

 process of the whole day under consideration, i.e. for each hour the expected 

 height of the water above chart datum. If Z is the height of the mean sea 

 level above chart datum, the height of the water H (above chart datum) at 

 the time / is given by H = Z + ^,cost/,-. A i is the amplitude of the partial 

 tide i and U t = a t t + T { +P { in which a t is the frequency of the partial tide, 

 T f is the angle which the tide i has reached in the locality, on the day con- 

 cerned at h (T t increases every day by 24a { ) and P t is the phase of the tide, 

 i.e. the negative x number of the component tide (corrected for the local 

 time); P, + 7i- is the total angle of the tide in the locality on the day under 



12 

 Time, 



20 



24 



Fig. 127. Computation of the tide of Pola for 6 January 1909 (Full moon close to the winter 

 solstice, very low water). computed, observed tides. 



consideration at h . If A-, and P t are given as constants by the harmonic 

 analysis, then H can be computed for any day, as a function of time, especially 

 since T { can be easily determined and tabulated for every day of a year. 

 These computations for a great number of days are very extensive (see 

 tide-prediction machines), when many constituents are considered, but they 



