72 



134. Principal tidal components at representative stations. — ^The 

 harmonic components of the tide have been determined at a large 

 number of tidal stations throughout the world. The amplitudes, in 

 feet, and the epochs, in degrees, of the five principal components at 

 stations used in the ensuing chapters to illustrate the characteristics 

 of the tide and the determination of tidal datums, are abstracted as 

 follows from the extensive data given in Special Publication, No. 98, 

 United States Coast and Geodetic Survey (1924). 



Table V. — Principal tidal components 



HARMONIC PREDICTION OF THE TIDES 



135. The chief use made of the harmonic constants is in the predic- 

 tion of the heights and times of high and low waters at a tidal station. 



The height of the tide at any time during a particular year is given 

 by the equation: 



^=i^o+/jicos (ji^+T'o+^-Ji°)+/KiCos (ki^+Fo+u-Ki°)+ • • • 

 +/K2C0S (k2/+Fo+^'-K2°)+ • • • (96) 



in which Hq is the height of the mean sea level above any standard 

 reference plane, 



Ji, Ki, K2, etc. are the mean values of the amplitudes of the 



several tidal components, 

 / is the mean value during the year (taken as the value at the 



middle of the year) of the factor to reduce the mean value of 



the amplitude to its value for the year (par. 124), 

 t is the time in hours after the beginning of the year, 

 ji, ki, k2, etc., are the speeds of the several components, 

 Vo is the value of V for the component at the beginning of the 



year, 

 u is the value of u for the component at the middle of the year, 

 Ji°, Ki°, K2°, etc, are the epochs of the components. 



