92 



month. If the observations extend over a year, no sensible error is 

 introduced by taking all of the low or high waters for the 365 or 366 

 days. 



170. Use. — Mean low water datum is the most readily determined 

 of the several low water planes, and adequately serves as a plane of 

 reference for navigation charts and for the designation of channel 

 depths when the tidal range is moderate. It is the official reference 

 plane for navigation charts and for federally improved channels on 

 the Atlantic and Gulf coasts of the United States. Obviously low 

 water of the varying tides is as often as not below this datum. At 

 Eastport, Maine, where the mean tidal range is 18.2 feet, the normal 

 tide occasionally falls 3 feet or more below mean low water datum; 

 but at most of the other stations on the Atlantic coast of the United 

 States, where the tidal range is much less, such minus tides (except 

 those due to storms) do not often exceed 1 or 2 feet, and ordinarily 

 are less. 



171. Correction for longitude of the moon's node. — Because of the 

 variation in the amplitudes of the tidal components with the chang- 

 ing inclination of the moon's orbit to the Equator (par. 102), the 

 several tidal ranges and high and low water datums go through a 

 small variation in a period of 19 years. The mean range derived 

 from observations extending over a month or a year may be reduced 

 to its true mean value by applying a reduction factor, conventionally 

 designated as F{Mn). The corrected mean low water datum is 

 then found by subtracting one-half of the corrected mean range from 

 half tide level; and the corrected mean high water datum by the 

 corresponding addition. These corrections are called the corrections 

 for the longitude of the moon's node, since this longitude determines 

 the inclination of the moon's orbit. 



172. The numerical values of the reduction factor i^(Mn) are 

 derived by deducing an expression for the mean range, Mn, in terms 

 of the amplitudes of the tidal components, and applying to these 

 amplitudes the reduction factors derived in paragraphs 124-126, 

 determined by the inclination, /, of the moon's orbit during the 

 period of the observations. To simplify the correction, the ampli- 

 tudes of the semidiurnal components are assumed to be proportional 

 to the mean values of the coefficients of their equilibrium components^ 

 given in table IV, paragraph 129; and the amplitudes of the diurnal 

 components also proportional to the mean values of the correspond- 

 ing coefficients. The relation between the amplitudes of the diurnal 

 and semidiurnal components is established by the ratio, (Ki4-Oi)/M2,^ 

 of these actual components at the station, as determined by harmonic 

 analysis, or inferred from available data. The derivation of these 

 factors is explained at length in appendix II. 



