88 



TJ. S. COAST AND GEODETIC SUEVEY. 



Formula (333) represents the mean value of the B ordinate for a 

 particular day of the page record. The average value for the 7 days 

 may be "written 



n=-3 \ ^ / 



= \ F,F,B [cos Q>t + ^) cos (-3 ^) -sin {U + 0) sin (-3 ^) 



+ COS (6^ + /3) cos (-2 ^) -sin (&p + /3) sin (-2 ^) 



+ COS (6^ + ^) cos (-1 ^) -sin {U^^) sin(-l ^) 



+ cos {U + /3) cos - sin {U + /3) sin 



+ COS {W + « COS (?«^) -sin (U + ») sin (?55^) 



4- COS 



(6. + « cos (2 ^^) -sin (ii + « sin (2 ?«5^) 

 (fe + « cos (3 ^-55*P) -sin (6( + ^) sin (3 ??^)] 

 =+F.F,Sri + 2cos 555^ + 2 cos2?52^ + 2cos3?55^1cos(fe + |S) 



+ COS 



=^ F,F,5 



-^ i^,i^25 



. ^ 3606?? 3 3606p 



sm 2 ^ COS TT ^ 



a 2 g 



. , 360&?? 



cos(6/ + /3) 



" . 1260&P' 

 sin 



sm 



1806ff 



cos (&i + /3). 



(334) 



Replacing the equivalents of F^ and Fj in (334), the average value 

 of the B ordinate as obtained by the secondary summations may be 

 written 



/ . 1260&P 



/24a . 15&p\/24 . 15pi\ / ^^^ a 



Vx^^^^^JW'''' 2 ;l , ,^ 180&P 



Bcos{U + ^) (335) 



/ sm 



Since the true ordinate of component B at any time t is equal to 

 B cos (U + ^), the reciprocal of the bracketed coefficient will be the 

 augmenting factor necessary to reduce the B ordinate as obtained 

 from the summations to their true values. 



