HARMONIC ANALYSIS AND PREDICTION OF TIDES 45 
latitude factors common to the terms combined, we have the following 
formulas in which numerical values from table 1 have been sub- 
stituted for constant quantities. 
term A= (1/2+3/4e?) sin 27 cos (T+h—90° —r) 
= 0.5023 sin 2/7 cos (T+h—90°—1) (216): 
term By.=(1/2+3/4e?)S’ sin 2 w cos (7-+h—90°) 
—0.1681 cos (T-+h—90°) (217) 
term Ay= (1/2+3/4e?) sin’J cos (27+2h—2y7) 
=0.5023 sin’J cos (27'-+2h—2p) (218) 
term B= (1/2+3/4e?)S’ sin? w cos (2T+2h) 
=0.0365 cos (T+2h) (219) 
- 133. Taking first the diurnal terms, let A represent the lunar co- 
efficient 0.5023 sin 2/ and let B represent the solar coefficient 0.1681. 
We then have 
An=A COS (T+h—90°— vp) 
=A cos vy cos (T+h—90°)+A sin » sin (7'-+h—90°) (220) 
By,=B cos (T+h—90°) (221) 
K,=(A cos v+ B) cos (7 +h—90°) +A sin v sin (T+ h—90°) 
=(A’?+2AB cos y+ B’)” cos | 7+h—90°—tan? 2 SOP, 
Bree a (222) 
in which 
C,= (A?+2AB cos EB)? 
= (0.2523 sin? 27+0.1689 sin 2/ cos »-+0.0283)2 (223) 
Yate a PBS Spey SRT (224) 
Values of v’ for each degree of N, which is the longitude of the 
moon’s node, are included in table 6. 
134. The obliquity factor for K, will be taken to include the entire 
coefficient (A?+2AB cosv+ B’)? and its mean value will be taken as 
the mean of the product (A?+2AB cos v +B’)? cos v’. 
From (224) we may obtain 
cos v’=(A cos v+ B)/(A?+2AB cos v+ B?)? (225) 
Then for mean value of coefficient of K, 
[(A?+2AB cos v+ B?)? cos v’|}p>=[A cos v+ B]) 
=[0.5023 sin 27 cos v+0.1681],>=0.5305 (226) 
the numerical mean for sin 2I cos y being obtained from formula (68). 
For the node factor of K, divide the coefficient of (222) by its mean 
value and obtain 
f (K,) = (0.2523 sin? 27-+0.1689 sin 27 cos v+-0.0283)?/0.5305 
= (0.8965 sin? 27+0.6001 sin 27 cos v+0.1006)? (227) 
