PREDICTION OF TIDES 
HARMONIC METHOD 
341. The methods for the prediction of the tides may be classified 
as harmonic and nonharmonic. By the harmonic method the ele- 
mentary constituent tides, represented by harmonic constants, are 
combined into a composite tide. By the nonharmonic method the 
predictions are made by applying to the times of the moon’s transits 
and to the mean height of the tide systems of differences to take 
account of average conditions and various inequalities due to changes 
in the phase of the moon and in the declination and parallax of the 
moon and sun. Without the use of a predicting machine the har- 
monic method would involve too much labor to be of practical service, 
but with such a machine the harmonic method has many advantages 
over the nonharmonic systems and is now used exclusively by the 
Coast and Geodetic Survey in making predictions for the standard 
ports of this country. 
342. The height of the tide at any time may be represented har- 
monically by the formula 
h=H,4+2 f H cos [at+ (V.+u) —«] (451) 
h=height of tide at any time t. . 
H,=mean height of water level above datum used for pre- 
diction. 
H=mean amplitude of any constituent A. 
f=tactor for reducing mean amplitude H to year of pre- 
diction. 
a=speed of constituent A. 
t=time reckoned from some initial epoch such as beginning 
of year of predictions. 
(V,+u)=value of equilibrium argument of constituent A when 
in which 
k=epoch of constituent A. 
In the above formula all quantities except h and ¢t may be con- 
sidered as constants for any particular year and place, and when these 
constants are known the value of h, or the predicted height of the 
tide, may be computed for any value of ¢, or time. By comparing 
successive values of h the heights of the high and low waters, together 
with the times of their occurrence, may be approximately determined. 
The harmonic method of predicting tides, therefore, consists essen- 
tially of the application of the above formula. 
343. The exact value of ¢ for the times of high and low waters will 
be roots of the first derivative of formula (451) equated to zero, 
which may be written— 
Ga af H sin [at+ (V.+u)—«]=0 (452) 
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