V. SYNTHETIC METHOD
28. On the Method and Notation
The general nature of the synthetic method has been already explained; we now propose to develop the expressions for the tide from the result as expressed in the harmonic notation. It should be desired to make a comparison of the results of tidal observation as expressed in the synthetic method with those of the harmonic method, or the converse, or to compute a tide-table from the harmonic constants by reference to the moons transits and from the declinations and parallaxes of sun and moon, the analytical expressions of the following sections are necessary.
In chapter iv. the mean semi-range and angle of retardation or lag of any one of the tides have been denoted by H and κ. We shall here, however, require to introduce several of the Hs and κ's into the same expression, and they must therefore be distinguished from one another. This may in general be conveniently done by writing as a subscript letter the initial of the corresponding tide; for example Hm, κm will be taken to denote the H and κ of the principal lunar tide M2. This notation does not suit the K2 and K1 tides, and we shall therefore write H″, κ″ for the semi-diurnal K2, and H′, κ′ for the diurnal K1 tide. These two tides proceed according to sidereal time and arise from the sun and moon jointly, and a synthesis of the two parts of each is effected in the harmonic method, although that synthesis is not explained in chapter iv. The ratio of the solar to the lunar part of the total K2 tide is ·46407; hence ·683 H″ is the lunar portion of the total K2. There will be no occasion to separate the two portions of K1, and we shall retain the synthesis which is effected in the harmonic method.
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