Chapter II 

 HARMONIC ANALYSIS OF THE TIDES 



Paragraphs 



Harmonic components defined 49-50 



Combination of components 51-59 



Astro nomical periods '. 60-63 



Speeds of tidal coinponents 64-76 



Computation of hourly component heights 77-90 



Computation of amplitude and initial phase 91-96 



Augmenting factors 97-98 



Elimination 100 



Long period components 101 



Mean values and epochs defined 102-103 



Equations of equilibrium tides 104-1 1 1 



Equilibrium argument. 112-114 



Equilibrium components 115-116 



Computation of epochs 117-122 



Mean values 1 23-1 28 



Mean values of coefficients 129 



Inference of constants 130-131 



Summary of methods 132-133 



Representative constants 134 



Prediction of tides 135-138 



49. Harmonic components of the tide. — It is reasonable to assume, 

 and will later be shown, that, except as affected by irregular meteoro- 

 logical disturbances, the tide curve at any station is the resultant of 

 a limited number of sinusoidal (cosine or sine) curves, whose periods 

 are determined by the periods of the tide-producing forces. This 

 relation is expressed by the equation: 



y=Ho-i-Ai cos (ai^+aO+^aCOs (^2^+ 0:2) +^3 cos (asti-aa)^ • ■ ' (27) 



in which y is the height, at the time t, of the tide above an arbitrarily 

 chosen datum, Hq is the height of mean sea level above this datum, 

 and the subsequent terms in the form A cos (at-\-a) are the component 

 tides. Of each component the coefficient A is the amplitude or 

 semirange, a is the speed, the angle at-\-a is the phase at the time t, and 

 a (alpha) is the initial phase. Placing: 



a=3607T orar=360° (28) 



it follows that at increases from zero to 360° as t increases from zero 

 to T; and again as t increases from T to 2T, and so on. Tis therefore 

 the period in which the component goes through its cycle of fluctua- 

 192750—40 3 (27) 



