The effect of astronomical periods longer than 1 year can be accounted for by 

 regarding An and 0^ as the sum of a mean value and a perturbation with a period on tlie 

 order of 9 to 19 years. Thus, the practical prediction equation may be expressed in the form 



^ys 



it) = ho + 2 iny Ans cos (a„t - Uny - Kns) (2) 



n 



where hjs(t) is the tide at station, s, during year, y, at time, t; Ans and Kns are 

 standardized amplitudes and phases for a particular location; and iny and Vny modify tlie 

 ampUtudes and phases for the particular year. The parameters iny, called the "node 

 factor" and Vny, called the "equilibrium argument," are determined from astronomical 

 theory. Derivations and tabulations of yearly values for the period 1900 to 2000 are given 

 by Schureman (1941). The subscript y indicates that the parameter may change yearly but 

 is independent of location. The combined parameters inyAns and (Vny + ^ns) are 

 determined from the analysis of tide records. A period of 369 days is generally chosen for 

 ajialysis. The theoretically determined f^y and Uny are then ehminated from the 

 empirically derived factors to obtain Ans and Kns- The subscript s indicates tliat tliese 

 parameters depend on the location of the tide station. The subscript n is a summation 

 index. 



After the parameters iny, Ans, On, ^ny and Kns have been determined, equation (2) 

 can be used for tide prediction without additional consideration of the theory of tides. 



The following discussion of the tide generation forces is not essential in understanding 

 the remainder of this report; however, it provides an understanding of tide phenomena, 

 useful in the interpretation of tide records, when no tide predictions are available. 

 Derivations are given only to the extent that they provide insight for physical processes or 

 mathematical techniques. Several references are cited to provide greater detail in the study 

 of tidal theory. Most derivations are based on Schureman (1941). The discussion of 

 shallow-water tides is based on Doodson and Wareburg (1941). 

 1. The Tide Generation Force. 



Every particle of the Earth is subject to the gravitational fields of the Sun and Moon as 

 well as the gravitational field of the Earth. This attractive force is inversely proportional to 

 the square of the distance between the particle and the center of the distant attracting body. 



The universal law of gravitational attraction between any two bodies may be stated as 



G m, m, 



Fg = — ^ (3) 



The gravitational force of the Earth for mass mi , may be obtained from equation (3) by 

 letting Fg equal gmi , d equal the radius of the Earth, a, where g is tlie gravitational 

 acceleration of tlie Earth at the surface, and m2 equals the mass of the Earth, E. Solving 

 the resulting expression for G yields: 



a^e 

 G = -r^ (4) 



26 



