The Harmonic Analysis of Tidal Observations 315 



meridian at 11 min after noon, viz. 1211 p.m. The curve gives a lunitidal 

 interval of 8 h 4 min the correction for the lunar parallax was 2 min so 

 that the high water will occur at 2017 h. The table gives for the height of 

 the high water 6-89 ft (210 cm), the correction was 5 cm so that the corrected 

 height of the high water will be 2 m 15 cm. 



Not many tide tables of this kind are being used, although they would 

 be very practical. 

 (b) Method of the Reference Stations 



Instead of computing extensive tables for the time and height of the high 

 and low waters for all coastal localities, which may be very numerous and 

 for which detailed tidal observations are generally not available, this is only 

 done for a certain number of selected harbours. The tide tables contain only 

 detailed predictions of all high water and low water times and heights for 

 such "reference localities'". If synchronous observations of the tide are 

 available over a certain period of time for two localities lying in the same 

 tidal area, the average tidal differences in time and height between these 

 localities can be ascertained, and it will be seen that these differences remain 

 somewhat constant. The tidal curve at the subordinate station is similar to 

 that at the reference station, i.e. the differences in time and the difference 

 between the high and low waters are almost constant between the two stations. 

 One station can serve as a reference for a great number of more or less neigh- 

 bouring coastal localities, and the tidal difference of a certain locality is the 

 difference in time between the establishment of the subordinate station as 

 compared with the establishment of the reference station corrected by the 

 difference in longitude expressed in time. 



The computation of the tides for the subordinate station is then simply 

 made by adding the tidal difference to the tidal values of the reference station 

 valid for that particular day, which can be found in the tables computed in 

 advance. In practice the tables will give all high waters, low waters and times. 

 Then there is a table for each subordinate station giving the difference in 

 amplitude and in time for the high waters and low waters between the sub- 

 ordinate and reference station. Furthermore, there is a table giving the cor- 

 rections for amplitude and time to be applied to spring and neap tides. This 

 method is particularly suited for tides which are of the semi-diurnal and 

 diurnal type, and less suited for the mixed type, where errors up to several 

 hours occur; the errors in height are correspondingly large, 

 (c) The Harmonic Method 



The common tide table gives generally only the height of the tide at the 

 time of high and low water and complicated computations are necessary to 

 determine with some accuracy this height for other hours. In view of the 

 increasing need for accurate knowledge of the water depth, they are in- 

 sufficient to solve correctly a great number of problems. The harmonic method 

 of computing the tides eliminates this deficiency. The dynamic theory and 



