TIDES AND CURRENTS IN BOSTON HARBOR 105 



perhaps best done by adding the hourly heights of the tide over a period of a 

 year or more and deriving the mean hourly height. It is to be noted that in 

 such a determination the mean sea level is not freed from the effects of prevailing 

 wind, atmospheric pressure, and other meteorological conditions. 



The plane of mean sea level must be carefully distinguished from the plane 

 of half-tide level or, as it is frequently called, mean-tide level. This latter 

 plane is one determined as the half sum of the high and low waters. It is therefore 

 the plane that lies halfway between the planes of mean low water and mean high 

 water. The plane of half-tide level does not, at most places on the open coast, 

 differ by more than about a tenth of a foot from the plane of mean sea level, and 

 where this difference is known the plane of mean sea level may be determined 

 from that of half-tide level. Like all of the tidal planes, the plane of half-tide 

 level should be determined by observations covering a period of a year or more. 



For many purposes the plane of mean low water is important. This plane 

 at any given place is determined as the average of all the low waters during a 

 period of a year or more. Where the diurnal inequality in the low waters is 

 small, as on the Atlantic coast of the United States, this plane is frequently 

 spoken of as the "low- water plane" or "the plane of low water"; but strictly 

 it should be called the plane of mean low water. 



Where the tides exhibit considerable diurnal inequality in the low waters, 

 as on the Pacific coast of the United States, the lower low waters may fall con- 

 siderably below the plane of mean low water. In such places the plane of mean 

 ower low water is preferable for most purposes. This plane is determined as 

 the average of all the lower low waters over a period of a year or more. Where 

 the tide is frequently diurnal, the single low water of the day is taken as the 

 lower low water. 



The plane of mean high water is determined as the average of all the high 

 waters over a period of a j^ear or more. Where the diurnal inequality in the high 

 waters is small, this plane is frequently spoken of as "the plane of high water" 

 or "the high-water plane." This usage may on occasion lead to confusion, and 

 the denomination of this plane as the plane of mean high water is therefore 

 preferable. 



In localities of considerable diurnal inequality in the high waters the higher 

 high waters frequently rise considerably above the plane of mean high water. 

 A higher plane is therefore of importance for many purposes, and the plane of 

 higher high water is preferred. This plane is determined as the average of all 

 the higher high waters for a period of a year or more. Where the tide is fre- 

 quently diurnal, the single high water of the day is taken as the higher high water. 



The tidal planes described above are the principal ones and the ones most 

 generally used. Other planes, however, are sometimes used. Where a very low 

 plane is desired, the plane of mean spring low water is sometimes used, its name 

 indicating that it is determined as the mean of the low waters occurring at spring 

 tides. Another plane sometimes used, which is of interest because based on 

 harmonic constants, is known as the harmonic tide plane and for any given place 

 is determined as M2 + S2 + K1 + O1 below mean sea level, 



MEAN VALUES 



Since the rise and fall of the tide varies from day to day, chiefly in accordance 

 with the changing positions of sun and moon relative to the earth, any tidal 

 quantities determined directly from a short series of tidal observations must be 

 corrected to a mean value. The principal variations are those connected with 

 the moon's phase, parallax, and declination, the periods of which are approxi- 

 mately 29H days, 273^ days, and 27^ days, respectively. 



In a period of 29 days, therefore, the phase variation will have almost com- 

 pleted a full cycle while the other variations will have gone through a full cycle 

 and but very little more. Hence, for tidal quantities varying largely with the 

 phase variation, tidal observations covering 29 days, or multiples, constitute a 

 satisfactory period for determining these quantities. Such are the lunitidal 

 intervals, the mean range, mean high water, and mean low water. For quantities 

 varying largely with the declination of the moon, as, for example, higher high 

 water and lower low water, 27 days, or multiples, constitute the more satisfactory 

 period. 



As will be seen in the detailed discussion of the tides at Fort Hamilton, the 

 values determined from two different 29-day or 27-day periods may differ very 

 considerably. This is di e to the fact that these periods are not exact synodic 

 perioc's for the different variations, and to the further fact that variations having 

 periods greater than a month are not taken into account. Furthermore, meteoro- 



