HAHMONIC AiSTALYSIS AjSTD PREDICTION OF TIDES. 97 



Effect of T, on S, 



'2 



Acceleration = tan ^ .n c^^o^ , n v (383) 



17.0281 + cos (/i — pi) 



Kesultant amplitude = 0.343 V8.5318 + cos(7i-pi) (384) 



The above formulas give the accelerations and resulting amplitudes 

 for any individual high water. For the correction of the constants 

 derived from a series covering 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 d* To take account of the longitude of 



the moon's node, the factor of reduction from section 12 should be 

 introduced. If the mean coefficients are indicated by the subscript 

 o, formulas (376) and (378) may be written 



Acceleration = tan~^ 



j{A)A,a , , . (385) 



^/TB)57&"'°'^ 



Resultant amphtude = -J 1 + ( /(zixT "^ ^ /^zIt ^^^ "^ ^^^^^ 



In the cases under consideration the ratio :FrD\ will not differ 



greatly from unity, the ratio -77V ^^dll be rather large compared with 



cos (j), 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 (385) . 



A 1 i- /(■^) XI sin 



Acceleration = 77^^ tan ^~. /'qq7\ 



f{A) A^a , , (387; 



^^^ + cos<?S 



Also because -j^ in these cases is small compared with unity, the 

 following may be taken as the approximate equivalent of (386) : 



Resulting amplitude = 1 +{[2") V ^ + (xT + 2 ^ cos - 1I (388) 



To allow for the effects of the longitude of the moon's node, the 

 tabular value of the acceleration should, therefore, be multiplied by 



the ratio -Tv-TY and the amount by which the resultant amplitude 



differs from unity by the same factor. In the particular cases under 

 consideration the factor/, for components P^, 83, and Tj, is unity for 



each. Therefore, for the effect of P, on K,, the ratio -tv^tv = ^ttt^^-t 



= F(Ki) , and for the effect of Kj upon 83, this ratio is /(Kj) . For the 

 effect of T2 upon 83 the ratio is unity. 



