12 U. S. COAST AND GEODETIC SURVEY 



Survey and also for 9 years of observations by the navy-yard authori- 

 ties are given in Table 2. These heights are referred as near as prac- 

 ticable to the zero of the original tide scale, which was 30 feet below 

 bench mark 1 on the coping of the dry dock. In Table 3 these heights 

 are referred to the sea-level datum which is defined on page 41. The 

 mean high water from the entire series is 4.81 feet above the sea-level 

 datum and mean low water 4.93 feet below this datum. When cor- 

 rected for the longitude of the moon's node these values become 

 4.80 feet and 4.91 feet, respectively. 



The spring and neap high and low waters depending upon the phase 

 of the moon, the perigean and apogean high and low waters depending 

 upon the parallax of the moon, the tropic high and low waters de- 

 pending upon the declination of the moon, the diurnal high and low 

 waters depending upon the daily height inequalities, and the extreme 

 high and low waters depending upon a combination of astronomical 

 and meteorological conditions are included in Table 27. These planes 

 were derived from the corresponding tidal ranges and inequalities. 



Mean range of tide. — The mean range of tide is the difference in 

 height between the mean of all high waters and the mean of all low 

 waters. From theoretical considerations, the range of tide is least 

 when the longitude of the moon's node is zero and the inclination 

 of the moon's orbit to the Equator is at a maximum and greatest 

 when the longitude of the moon's node is 180° and the inclination of 

 its orbit to the Equator a minimum. This inequality has a period 

 of approximately 19 years, and in order to reduce the range as deter- 

 mined from a single year of observations to a mean value a correction 

 factor is necessary. The mean of the corrected ranges for the navy 

 yard for 39 years is 9.71 feet. The mean range for each individual 

 year as directly obtained and also as corrected for the longitude 

 of the moon's node will be found in Table 4. The corrected ranges 

 have also been arranged in groups, the first three groups containing 

 10 years each and the last group 9 years. The averages for these 

 are (1847-1856) 9.83 feet, (1857-1866) 9.77 feet, (1867-1876) 9.66 

 feet, and (1902-1911) 9.57 feet. It will be noted that the range 

 consistently diminishes but not by a uniform amount, the difference 

 between the third and last group being only 0.09 foot, although 

 there is a gap of 25 years between these two groups. Changes 

 in the mean range of tide in harbors due to various changes in the 

 configuration of the shore line and bottom are not unusual. 



Ranges depending upon pliase and parallax of the moon. — The spring 

 range of tide is the average maximum semidiurnal range near the 

 times of new and full moon; the neap range of tide is the average 

 minimum semidiurnal range near the times of the quadratures of 

 the moon; the perigean range of tide is the average maximum semi- 

 diurnal range when the moon is near its perigee; and the apogean 

 range is the average of the minimum semidiurnal range when the 

 moon is near its apogee. 



Near the times of new and full moon the forces of the sun and 

 moon conspire to increase the range of tide, and near the quadra- 

 tures their forces are opposed to each other, causing a diminution 

 in the range. The nearness of the moon when it is in perigee 

 tends to give an increased range, while its greater distance when 

 in apogee tends to diminish the range. The spring and neap ranges 

 of tide at the navy yard, as derived from a phase reduction of the 



