HARMONIC ANALYSIS AND PREDICTION OF TIDES 83. 
B Aa 
A Bb % 
ESTE CTO feb One Kees ee eae a De See ata eee ee 0. 38086 3. 03904 —2h+v! 18)": 
TeECt Of KeKOntS ot) eee Pee ere els | SE ee ee, ee 0. 27213 3. 66469 | 2h—2p’ 
eC Gio OMS ob eto aa ae hs oe See eee ane 0. 05881 | 17. 02813 —h+p1. 
Substituting the above in (356) and (358) we have 
Effect of P,; on K, 
sin (2h—p’) 
3.0390—cos (2h—v’) 
Resultant amplitude=0.813-/1.6767—cos (2h—v’) (360) 
Effect of K, on 8, 
Acceleration=tan7! (359) 
sin (2h—2v”) 
3.6647-+ cos (2h—2v”) 
Resultant amplitude =0.738/1.9734+cos (2h—2v”) (362) 
Effect of T, on S, 
Acceleration= tan! (361) 
_ Ss (ep) 
17.0281-++ cos (h—/) 
Resultant amplitude=0.343-/8.5318-+cos (h—p;) (364) 
Acceleration=tan“! (363) 
242. The above formulas give the accelerations and resulting 
amplitudes for any individual high water. For the correction of the 
constants derived from a series covermg many high waters it is 
necessary to take averages covering the period of observations. 
Tables 21 to 26 give such average values for different lengths of series, 
the argument in each case referring to the beginning of the series. 
In the preceding formulas the mean values of the coefficients were 
taken to obtain the ratios a To take account of the longitude of 
the moon’s node, the node factor should be introduced. If the mean 
coefficients are indicated by the subscript 0, formulas (356) and (358) 
may be written 
Acceleration=tan— ae (365) 
FB)Bb te? 
Resultant amplitude=/1+( 1 + (Fey +: } Ly) HB Be cosy A, © oo) (366): 
243. In the cases under consideration the ratio Te will not differ 
greatly from unity, the ratio a will be rather large compared with 
cos ¢, which can never exceed unity, and the acceleration itself is 
relatively small. Because of these conditions the following may be 
taken as the approximate equivalent of (365): 
