128 . COAST AND GEODETIC SURVEY 
Along the Gulf of Mexico coast this difference is from a foot to 1% feet. Along the 
Pacific coast the difference is about 2% feet along California and Oregon and from 4 to 
5 feet along Washington. These differences are obviously only approximate, and 
along a given stretch of coast will vary with the hydrographic features of the coastal 
body of water. 
Datum Planes From Harmonic Constants 
The harmonic constants comprise the simple constitutent tides which are derived 
’ from the harmonic analysis of the tide observations. The basis of the harmonic 
analysis lies in the conception of the tide as the sum of a number of simple tides, each 
of which has a definite period that is determined by some motion of the moon or sun 
relative to the earth. The most complete list of harmonic constants for the world is 
the ‘‘List of Harmonic Constants’ which is being published in loose-leaf form by the 
International Hydrographic Bureau, Monaco. In 1942 the Coast and Geodetic 
Survey issued Publications TH-1 and TH-—2, listing the eight principal constants, 
TH-1 giving the constants for the Atlantic Ocean, including the Arctic and Antarctic 
regions, and TH-2 giving the constants for the Pacific and Indian Oceans. 
Formulas have been developed by Harris,! by means of which the various datum 
planes may be derived through the harmonic constants. ‘These formulas are somewhat 
involved if it is desired to derive the datum planes accurately, but for approximate 
determinations the formulas may be simplified considerably. 
As examples, it may be noted that the plane of mean high water for tides of the 
mixed and semidaily types is given approximately by the formula HTL+1.1Mz2, in which 
HTL is half-tide level and M, is the principal lunar semidiurnal constituent. In 
the same way mean low water is given approximately by HTL—1.1M,. To test the 
degree of approximation of these formulas we may derive the plane of mean high 
water for Boston, Mass., and for Seattle, Wash. 
The value of M; for Boston is 4.44 feet and for Seattle 3.50 feet. From the approxi- 
mate formula above, mean high water at Boston is derived as 4.88 feet above half-tide 
level and at Seattle as 3.85 feet above half-tide level. These values compare with 
primary determinations of 4.72 feet at Boston and 3.83 feet at Seattle. The simple 
formula therefore gives mean high water above half-tide level correct within 0.1 or 0.2 
foot. 
An approximate value for the datum of lower low water on the Pacific coast of 
the United States is given by the formula MLUW—0.6(K,+0,), in which MLW is 
mean low water and K, and O,, respectively, the principal lunisolar diurnal and principal . 
lunar diurnal constituents. Since mean lower low water is given by subtracting the 
mean low-water diurnal inequality from mean low water, the formula amounts to taking 
MDL as equal to 0.6 (K,+0;), which is obviously but a rough approximation. Thus 
if we derive the values of 0.6 (K,+O,) for San Francisco and Seattle, we get 1.17 feet 
for San Francisco and 2.53 feet for Seattle which compare with primary values of 1.14 
and 2.84 respectively. 
The datum of higher high water on the Pacific coast is given approximately by 
MHW-+0.3(K,+0,), in which MHW is mean high water and K, and O, as above. 
It is to be emphasized, however, that the simple formulas given above for the planes 
1R. A. Harris. Manual of Tides, Pt. III (Washington, D. C., 1895). 
