HARMONIC ANALYSIS! AND PREDICTION OF TIDES 67 
199. To obtain value of H,, add above equations 
a=(n—1) 
See —n A, 
a=0 
co (n—1) a=(n—1) 
2s as GOL >) 60520 TE Sion ds de gee +C, >) cosaku 
a=0 
a=(n—1) a=(n—1) | 
Sy sin a w+, > sin 2 qu pert oP +S, >>} snalu 
: a=0 
a= (n— = a=(2—}) 
==) H.+> 0 S00 am >> Sn 25 sin amu (283) 
a 
—1) =(n—1) 
From (273), > cos am u and >) sin am u each equals zero, 
a=0 
since neither k nor J, the maximum values of m exceeds 5 
Therefore 
a=(n—1) 
pp. —ele (284) 
and y 
oe 285 
One 7 a= a ( ) 
200. To obtain the value of any coefficient C, such as C,, multiply 
each equation of (282) by cosa pu. Then 
hy cos O=H) cos 0 
+0, cos 0+C, cos 0+ _______- +0; cos 0 
+S, sin 0+8, sin 0+ _______- +S, sin 0 
h, cos p u=H cos p u 
+C, cos u cos p u+C, cos 2u cos p u+__~--- +C;,, cos k u cos p wu 
+8, sin u cos p u+S, sin 2u cos p u+ -------- +S, sinl wu cos pu 
hz cos 2p u= Hh cos 2p u 
+(C, cos 2u cos 2p u+C; cos 4u cos 2p u+__------ 
+C;, cos 2k u cos 2p wu 
+; sin 2u cos 2p u+S, sin 4u cos 2p u+___----- 
+S; sin 21 u cos 2p u 
Die ve cos (n—1) p u=H, cos (n—1) p 
+C, cos (aon, u cos (n—1) p HG cos (n—1) ucos (n—1) put 
+C;, cos (n—1) k u cos (n—1) p 
+S; sin (n—1) uw cos (n—1) p noted sin 2 (n—1) ucos (n—1) pu+_- 
+S, sin (n—1)lucos (n—1) pu (286) 
Summing the above equations 
a=(n—1) a=(n—1) 
DI cosa — ea Cos a pew 
a=0 a=0 
a=(n—1) a=(n—1) | 
>) cosaucosapu+tS,; >) smaucosapu 
a=o 
(Formula continued next page) 
