M1—Smaller lunar elliptic diurnal constituent. This constituent, with J1, modulates the amplitude of the declinational K1, for the effect of the Moon's elliptical orbit. A slightly slower constituent, designated (M1), with Q1, modulates the amplitude and frequency of the declinational O1, for the same effect. Speed = T – s + h + p = 14.496,693,9° per solar hour.

Speed = 2T – 2s + 2h = 28.984,104,2° per solar hour.

Speed = 3T – 3s + 3h = 43.476,156,3° per solar hour.

Speed of M4 = 2M2 = 4T – 4s + 4h = 57.968,208,4° per solar hour.

Speed of M6 = 3M2 = 6T – 6s + 6h = 86.952,312,7° per solar hour.

Speed of M8 = 4M2 = 8T – 8s + 8h = 115.936,416,9° per solar hour.

Maelstrom—Famous whirlpool off the coast of Norway in the Lofoten Islands between Moskenesoy and Mosken.

magnetic azimuth—Azimuth reckoned from the magnetic north or magnetic south. See magnetic direction.

magnetic declination—Same as variation.

magnetic direction—Direction as indicated by a magnetic compass after correction for deviation but without correction for variation.

marigram—A graphic record of the rise and fall of water level. The record is in the form of a curve in which time is generally represented on the abscissa and the height of the water level on the ordinate. See tide curve.

marine boundary—The mean lower low water line (MLLWL) when used as a boundary. Also, lines used as boundaries seaward of and measured from (or points thereon) the MLLWL. See coastal boundary.

mascaret—French for tidal bore.

mean current hour—Same as current hour.

mean diurnal tide level (MDTL)—A tidal datum. The arithmetic mean of mean higher high water and mean lower low water.

mean high water (MHW)—A tidal datum. The average of all the high water heights observed over the National Tidal Datum Epoch. For stations with shorter series, comparison of simultaneous observations with a control tide station is made in order to derive the equivalent datum of the National Tidal Datum Epoch.

mean high water line (MHWL)— The line on a chart  or map which represents the intersection of the land with the water surface at the elevation of mean high water. See shoreline.

mean higher high water (MHHW)—A tidal datum. The average of the higher high water height of each tidal day observed over the National Tidal Datum Epoch. For stations with shorter series, comparison of simultaneous  observations with a control tide station is made in order to derive the equivalent datum of the National Tidal Datum Epoch.

mean higher high water line (MHHWL)—The line on a chart or map which represents the intersection of the land with the water surface at the elevation of mean higher high water.

mean low water (MLW)—A tidal datum. The average of all the low water heights observed over the National Tidal Datum Epoch. For stations with shorter series, comparison of simultaneous observations with a control tide station is made in order to derive the equivalent datum of the National Tidal Datum Epoch.

mean low water line (MLWL)—The line on a chart or map which represents the intersection of the land with the water surface at the elevation of mean low water.

mean low water springs (MLWS)—A tidal datum. Frequently abbreviated spring low water. The arithmetic mean of the low water heights occurring at the time of spring tides observed over the National Tidal Datum Epoch. It is usually derived by taking an elevation depressed below the half-tide level by an amount equal to one-half the spring range of tide, necessary corrections being applied to reduce the result to a mean value. This datum is used, to a considerable extent, for hydrographic work outside of the United States and is the level of reference for the Pacific approaches to the Panama Canal.

mean lower low water (MLLW)—A tidal datum. The average of the lower low water height of each tidal day observed over the National Tidal Datum Epoch. For stations with shorter series, comparison of simultaneous observations with a control tide station is made in order to derive the equivalent datum of the National Tidal Datum Epoch.

mean lower low water line (MLLWL)—The line on a chart or map which represents the intersection of the land with the water surface at the elevation of mean lower low water.

mean range of tide (Mn)—The difference in height between mean high water and mean low water.

mean rise—The height of mean high water above the elevation of chart datum.

mean rise interval (MRI)—The average interval between the transit of the Moon and the middle of the period of the rise of the tide. It may be computed by adding half the duration of rise to the mean low water interval, subtracting the semidiurnal tidal period of 12.42 hours when greater than this amount. The mean rise interval may be either local or Greenwich according to whether it is referred to the local or Greenwich transit.

mean river level—A tidal datum. The average height of the surface of a tidal river at any point for all stages of the tide observed over the National Tidal Datum Epoch. It is usually determined from hourly height readings. In rivers subject to occasional freshets, the river level may undergo wide variations and, for practical purposes, certain months of the year may be excluded in the determination of the tidal datum. For charting purposes, tidal datums for rivers are usually based on observations during selected periods when the river is at or near a low water stage.  

mean sea level (MSL)—A tidal datum. The arithmetic mean of hourly heights observed over the National Tidal Datum Epoch. Shorter series are specified in the name; e.g., monthly mean sea level and yearly mean sea level.

mean sun—A fictitious sun which is assumed to move in the celestial equator at a uniform speed corresponding to the average angular speed of the real Sun in the ecliptic, the mean sun being alternately in advance and behind the real Sun. It is used as a reference for reckoning mean time, noon of mean local time corresponding to the time of the transit of the mean sun over the local meridian. See equation of time and mean time.

mean tide level (MTL)—A tidal datum. The arithmetic mean of mean high water and mean low water. Same as half-tide level.

mean time—Time based upon the hour angle of the mean sun as distinguished from apparent time which is based upon the position of the real Sun. The difference between apparent and mean time is known as the equation of time.

mean water level (MWL)—A datum. The mean surface elevation as determined by averaging the heights of the water at equal intervals of time, usually hourly. Mean water level is used in areas of little or no range in tide.

mean water level line (MWLL)—The line on a chart or map which represents the intersection of the land with the water surface at the elevation of mean water level.

meteorological tides—Tidal constituents having their origin in the daily or seasonal variations in weather conditions which may occur with some degree of periodicity. The principal meteorological constituents recognized in the tides are Sa, Ssa, and Sl. See storm surge.

Metonic cycle—A period of almost 19 years or 235 lunations. Devised by Meton, an Athenian astronomer who lived in the fifth century B.C., for the purpose of obtaining a period in which new and full Moon would recur on the same day of the year. Taking the Julian year of 365.25 days and the synodical month as 29.530,588 days, we have the l9- ear period of 6,939.75 days as compared with the 235 lunations of 6,939.69 days, a difference of only 0.06 day.

Mf—Lunar fortnightly constituent. This constituent expresses the effect of departure from a sinusoidal declinational motion. Speed = 2s = 1.098,033,1° per solar hour.

midextreme tide—An elevation midway between extreme high water and extreme low water occurring in any locality.

mixed (current)—Type of tidal current characterized by a conspicuous diurnal inequality in the greater and lesser flood strengths and/or greater and lesser ebb strengths. See flood current and ebb current.

mixed (tide)—Type of tide characterized by a conspicuous diurnal inequality in the higher high and lower high waters and/or higher low and lower low waters. See type of tide.

Mm—Lunar monthly constituent. This constituent expresses the effect of irregularities in the Moon's rate of change of distance and speed in orbit.

Speed = s – p = 0.544,374,7° per solar hour.

modified epoch—See kappa prime (6t) and epoch (1).

modified-range ratio method—A tidal datum computation method. Generally used for the East Coast, Gulf Coast, and Caribbean Island stations. Values needed are mean tide level (MTL), mean diurnal tide level (DTL), mean range of tide (MN), and great diurnal range (GT) as determined by comparison with an appropriate control. From those, the following are computed:

MLW = MTL - (0.5*MN)

MHW = MLW + MN

MLLW = DTL - (0.5*GT)

MHHW = MLLW + GT

Monsoon Current (Southwest Monsoon Current) —An Indian Ocean current setting in a generally eastward to southeastward direction off India and Ceylon. It replaces the North Equatorial Current, reversed by wind stress of the south-west monsoons, in August and September.

month—The period of the revolution of the Moon around the Earth. The month is designated as siderial, tropical, anomalistic, nodical, or synodical according to whether the revolution is relative to a fixed star, vernal equinox, perigee, ascending node, or Sun. The calendar month is a rough approximation to the synodical month.

MSf—Lunisolar synodic fortnightly constituent. Speed = 2s – 2h = 1.015,895,8° per solar hour.

multiple tide staff—A succession of tide staffs on a sloping shore so placed that the vertical graduations on the several staffs will form a continuous scale referred to the same datum.