120 U. S. COAST AND GEODETIC SUEVEY. 



and Gulf coasts of the United States, including Porto Rico and the 

 Atlantic coast of the Panama Canal Zone, this datum is mean low 

 water. For the Pacific coast of the United States, Alaska, Hawaii, 

 and the Philippines, the datum is in general mean lower low water. 

 For the rest of the world, the datum is in general mean low water 

 springs, although there are many localities where somewhat lower 

 planes are used. After the datum for any particular place has been 

 adopted its relation to the mean water level may be readily obtained 

 from simple nonharmonic reductions of the tides as observed in the 

 locality. The value of Hq thus determined is a constant that is 

 available for future predictions at the stations. 



The amplitude H and the epoch k for each component tide to be 

 included in the predictions are the harmonic constants determined by 

 the analysis discussed in the preceding chapters. Each place will 

 have its own set of harmonic constants, and when once determined 

 will be available for all times, except as they may be slightly modified 

 by a more accurate determination from a better series of observations, 

 or by changes in the physical conditions at the locality such as may 

 occur from dredging, by the depositing of sediment, or by other 

 causes. 



The factor /is the reciprocal of factor F, discussed in section 12. 

 It is introduced in order to reduce the mean amplitude to the true 

 amplitude depending upon the longitude of the moon's node. The 

 factor / for any single component, therefore, passes through a cycle 

 of values. The change being slow, it is customary to take the value 

 as of the middle of the year for which the predictions are being 

 made and assume this as a constant for the entire year. The error 

 resulting from this assumption is practically negligible. Each com- 

 ponent has its own set of values for /, but these values are the same 

 for all localities and have been compiled for convenient use in Table 

 14 for the middle of each year from 1850 to 1999. 



The quantity a represents the angular speed of any component 

 per unit of time. In the application of formulas (465) and (466) to 

 the prediction of tides this is usually given in degrees per mean solar 

 hour, the unit of t being taken as the mean solar hour. The values 

 of the speeds of the different components have been calculated from 

 astronomical data by formulas derived from the development of the 

 equilibrium theory which has already been discussed. These speeds 

 have been compiled in Table 3 and are essentially constant for all 

 times and places. The quantity (Fo + w), which was discussed in 

 section 10, is the value of the equilibrium argument of a component 

 at the initial instant from which the value of t is reckoned; that is, 

 when t equals zero. In the prediction of tides this initial epoch is 

 usually taken at the midnight beginning the year for which the pre- 

 dictions are to be made. In strictness the V, or uniformily varying 

 portion of the argument alone, refers to the initial epoch, while the u, 

 or slow variation due to changes in the longitude of the moon's node, 

 is taken as of the middle of the period of prediction and assumed to 

 have this value as a constant for the entire period. The quantity 

 {Vo + u) is different for each component and is also different for each 

 initial epoch and for different longitudes on the earth. In Table 15 

 there have been compiled the values of this quantity for the begin- 

 ning of each year from 1850 to 2000 for the longitude of Greenwich. 



