Tide-Predicting Machine No . 2 was the first tide-predicting machine to incorporate both a paper graph of the tides the approach used by earlier British machines and dials and scales that showed the tide height and corresponding date and time used by Tide-Predicting Machine No . 1.
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For each term i = 1, \ ldots, n, A _ i is the amplitude of the term s contribution to tide height above mean sea level, \ omega _ i determines the frequency of the term, t is the time, and \ phi _ i is the relative phase of the term.
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At each place of interest, the tide heights are therefore measured for a period of time sufficiently long ( usually more than a year in the case of a new port not previously studied ) to enable the response at each significant tide-generating frequency to be distinguished by analysis, and to extract the tidal constants for a sufficient number of the strongest known components of the astronomical tidal forces to enable practical tide prediction.
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