The Harmonic Analysis of Tidal Observations 305 



(see also Miyahara, and Niimi, 1939). For the complete analysis of 

 observations extending over one year, see also, the papers written by Harris 

 (1897) and Schureman (1924) and those of Sterneck (1923, p. 39). 



The procedure is somewhat different for deriving the harmonic constants 

 of the long-period tides. It starts with the daily sums of the hourly heights, 

 which are freed from the influence of the short-period components by simple 

 reduction factors. For the rest, one proceeds according to the same principles 

 as previously; only the execution is simpler and clearer. For more detail- 

 ed information we refer to the papers of Darwin and Hessen (1920, 

 p. 441). 



2. Characteristics of the Tides as Shown by their Harmonic Constants 



The amplitudes and kappa numbers of the harmonic analysis are par- 

 ticularly well suited to define more clearly a number of properties of the 

 tides. As stated already, each component or partial tide varies as to its 

 importance. A few determine the essential features of the tidal process. The 

 7 most important component tides are: M 2 , S 2 , N 2 , K 2 and K 1 ,0 1 ,P 1 and, 

 among these, the two largest semi-diurnal and diurnal tides M 2 , S 2 and K lt O x 

 respectively, stand out as the most important ones. The rvalue of M 2 gives, 

 for semi-diurnal tides, the approximate time of occurrence of the high water 

 after the transit of the moon through the meridian (high water lunitidal 

 interval, establishment). At full and new moon the sun and the moon pass 

 through the meridian simultaneously at noon; however, the two components 

 have a lag which are given by the ^-values x M and x s . The difference of the 

 angular velocities or speeds of 30°- 28 -984° = 1 016°/h or 24-384° in a day 

 which makes the M 2 tide lag daily by 84 h = 50 min behind the S 2 tide. 

 At the syzygies both waves have the same phase and their amplitudes are 

 to be added M 2 + S 2 ; the time of this spring tide is determined by the K-value 

 of the ,S 2 -tide which is * s /30 hours in civil time. The interval between the 

 spring tide and full moon and new moon is given by x s — x M \ (x s — « Af )/24-384 

 = 004(* s — y. M ) is then the quantity which is called the "age of the tide". 

 The difference between the amplitudes M» — S 2 gives the amplitude of the 

 neap tides. The effect of a small diurnal tide on a large semi-diurnal tide 

 is to increase the heights of alternate high water and decrease the heights 

 of the intermediate high waters with similar effects in the heights of low water. 

 Similarly, alternate high waters may be accelerated in time and the inter- 

 mediate high waters may be retarded with similar effects in the times of low 

 water. These effects are referred to as the "diurnal inequality". The diurnal 

 inequality, therefore, is mainly governed by the amplitude of S 2 . 



For the diurnal tides the phase of the K x tide, together with the phase 

 of the O x tide, determines the time of high water. This high water does not 

 show any relationship any more with the transit of the moon through the 

 meridian. The phase of the principal tide K x conforms to sidereal time and 



20 



