124 U. § COAST AND GEODETIC SURVEY 
Although formula (452) cannot, in general, be solved by rigorous 
methods, it may be mechanically solved by a tide-predicting machine 
of the type used in the office of the Coast and Geodetic Survey. 
344. The constant H, of formula (451) is the depression of the 
adopted datum below the mean level of the water at the place of predic- 
tion. For places on the open coast the mean water levelisindentical 
with mean sea level, but in the upper portions of tidal rivers that have 
an appreciable slope the mean water level may be somewhat higher 
than the mean sea level. The datum for the predictions may be more 
or less arbitrarily chosen but it is customary to use the low-water plane 
that has been adopted as the reference for the soundings on the 
hydrographic charts of the locality. For all places on the Atlantic 
and Gulf coasts of the United States, including Puerto 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 H, thus determined is a constant that is 
available for future predictions at the stations. 
345. The amplitude H and the epoch « for each constituent tide to be 
included in the predictions are the harmonic constants determined by 
the analysis discussed in the preceding work. 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. 
346. The node factor f (par. 77) is introduced in order to reduce the 
mean amplitude to the true amplitude depending upon the longitude 
of the moon’s node. The factor f for any single constituent, therefore, 
passes through a cycle of values. The change being slow, it is cus- 
tomary 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 negli- 
gible. Each constituent has its own set of values for f, 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. 
347. The quantity a represents the angular speed of any constituent 
| per unit of time. In the application of formulas (451) and (452) to 
the prediction of tides this is usually given in degrees per mean solar 
hour, the unit of ¢ being taken as the mean solar hour. The values 
of the speeds of the different constituents have been calculated from 
astronomical data by formulas derived from the development of the 
tide-producing force which has already been discussed. ‘These speeds 
have been compiled in table 2 and are essentially constant for all 
times and places. The quantity (Vo+w) is the value of the equilib- 
rium argument of a constituent at the initial instant from which the 
value of ¢ is reckoned; that is, when ¢ equals zero. In the prediction 
