The Harmonic Analysis of Tidal Observations 317 



offer the great advantage of permitting the comparison of the predicted tide 

 with the actual tide, and are, therefore, very instructive. These comparisons 

 make it further possible to examine thoroughly the influence of air pressure 

 and wind on the sea level in a harbour with strong tides. Figure 127 gives 

 such a comparison for Pola, on 6 January, 1909; it shows a tidal curve at 

 full moon with calm weather and a very strongly developed first low water. 

 One can see how well the prediction corresponds to the tidal process, although 

 only seven partial tides were used for the prediction (Kesslitz, 1900). 



The practical use of the harmonic method has only been carried through 

 in recent times, although there is no doubt that it is the most accurate method. 

 Especially for localities where the amplitudes of the diurnal tides are large 

 it is far superior to all other methods. Of course, it presupposes the know- 

 ledge of the harmonic constants. However, with time the number of coastal 

 localities for which these constants are known increases rapidly. The German 

 tide tables of 1939 contain the harmonic constants of about 1800 localities 

 for as many as ten tides, the Admiralty tide tables (1938) has these constants 

 for 2650 reference localities; besides for 3500 subordinate stations the con- 

 stants for M 2 , S 2 , Ki and O x have been derived from the reference stations 

 by means of differences (Admiralty tide tables, part IT, London, 1938), 



A practical procedure of predicting the height of the tide in a locality at any arbitrary time 

 has been given by the German Tide tables starting in 1940. The following 10 components are used: 



To the usual 7 main components (4 semi-diurnal and 3 diurnal), they have added the so-called 

 shallow-water tides fi 2 = 2MS 2 , M 4 and MS 4 . They are of some importance in regions of very 

 shallow water, as is often found off harbours. The M 4 , as an overtide or harmonic of M 2 , causes 

 an asymmetry of the semi-diurnal tidal curve, and combined with MS A also a slight variation of 

 spring and neap time. An example will illustrate the computation. (Table 35). The first and the 

 second lines contain the tidal constants for the indicated components for a locality. They can be 

 taken from the list of harmonic constants. 7} is listed under "speed" at under the hour angle which 

 can be found, for all days of the year and all hours of the days, in the tide tables. The sum of the 

 last three lines gives the angle U, which is to be reduced by entire multiples of 360, for the computa- 

 tion of cos U. The values of A cos U, which can also be taken directly from tables, are in the vertical 

 column at left. Their sum together with Z gives the height of the tide H at the hour in question. 



If the other partial tides are neglected, there will be an error which will seldom be important 

 enough to interfere with navigation, if the constants are not known for the other components, 

 or if a lesser accuracy is sufficient, these constants must be left out in the forms. The error then 

 is at the most equal to the sum of the amplitudes of the neglected tides. 



(d) Tide-predicting Machines 



The computations for the tide tables for a complete year would represent 

 a most laborious and expensive work, if it were accurately done every year 

 for a great number of harbours. In each coastal locality there are yearly 



