306 The Harmonic Analysis of Tidal Observations 



it can, therefore, be said that high water occurs within a constant time interval 

 from the transit of a certain star through the meridian. Without considering 

 the O x tide, the x-number of K x will give in local time the high water on 

 21 June; on each following day it occurs 4 min earlier, for each month 2 h 

 earlier, so that (always in a rough approximation) with such tides the high 

 water will occur at each hour of the day in the course of a year. For instance, 

 if high water occurs on 21 June at 2 p.m., it can be expected on 21 December 

 at 2 a.m. The O x tide causes a periodical increase and decrease in the am- 

 plitude of K x , as does the S 2 tide for the M 2 tide. The contrast between 

 spring tides and neap tides occurs with the diurnal tides every 13-66 days, 

 whereas they do occur every 14-765 days for the semi-diurnal tides. The 

 relative speed is here x K -x = 15041°-13-943° = 1098°/h, or 26-3528° per 

 day. The spring tides occur every 360:26-353° = 13-66 days, which is 26-74 

 times during the course of a year. For the semi-diurnal tides, such spring 

 tides occur only 24-74 times in a year. The difference x K — x Q which corresponds 

 to the "age of the tide" gives the delay of the spring tide. x K — x : 26-3528° 

 = (x K — x o )0038 is the lag in days after the greatest declination of the 

 moon. 



A further complication, in the case of diurnal tides, is caused by the P x 

 tide, whose high water occurs 4 min later each day; hence, its relative motion 

 against the K x tide is 8 min/day, 4 h/month. K x and P x have the same phase 

 at the time of the summer solstice; at that time, both tides reinforce each 

 other. The same is the case for the winter solstice, where the difference in 

 phase is 6 x 4 = 24 h. At the equinoxes (March and September), the dif- 

 ference in phase is 12 h; the two components counteract each other. The P x 

 tide causes the diurnal tides to have a maximum not at the equinoxes but 

 at the solstices. This is a remarkable feature of this type of tide, distinguishing 

 it from the semi-diurnal tides. 



In order to classify the tides of a locality, P, van der Stok (1897) has 



adopted three principal types of tides based on the ratio of the sum of the 



amplitudes of the diurnal components K x + O x to the sum of the amplitudes 



of the semi-diurnal components M 2 + S 2 . This ratio increases when the diurnal 



inequality of the tides increases. It attains a maximum when there is only 



K 4- O 

 one high water a day. Therefore F = — is designated as the "Form- 

 Ma +£2 



zahl" of the tides. Courtier (1938) (see also Dietrich, 1944, p. 69, 

 who increased the number from 3 to 4) has given the following classifi- 

 cation. 



F: 0—0-25 semi-diurnal type; two high waters and two low waters daily 

 of approximately the same height. The interval between the transit of the 

 moon and high water at a locality is nearly constant. The mean range at 

 spring tide is 2{M 2 + S 2 ). 



