HARMONIC ANALYSIS AND PREDICTION OF TIDES 97 
276. Then, referring to formulas (263) and (264) 
n=365 
>) [ysln cos 24(n—1)a= 
n=1 
a sin 12a, [ sin 12365(a,+a) 
48 ~* gin da, sin 12(a,+a) 
in 12 365 BLS. 
en Tangy 008 U2XB6K(a—a) $11.50, 6} | 421) 
cos {12><364(a,+4@)+11.5a,+ ag} 
and 
n=365 : 
>> [Yeln Sin 24(n—1)a= 
n=1 
1 sin 12a, [= 12X365(a,+a) 
ag “1s sin 12(a,-Fa) 
sin 3d, sin 12(a,+a) 
_ sin 12365 (a,—a@) 
sin 12(a,—a) 
Now let 
sin {12 364(a,+a)+11.5a,+ a,} 
ath (12364 (aa) +11.5ay+ 06} | (422) 
A’ =A, COS a, 
and (423) 
A’ .=—A, sil a, 
then (421) and (422) may be reduced as follows: 
n=365 
> [ysln cos 24(n—1)a 
i 
| ee) 
48 sin 3a; sin 12(a,+qa) 
sin 12365 (a,—a) 
sin 12(a,—a) 
sin 12a, sin 12° X365(@,+¢) = 9 > | et ~ 
sin 3; l ain IGesn) {12X364(a,+ a) +11.5a,} 
sin 12X365(a,—a@) . hoe py, 
sm 12(@,—a) °" (12364(a—«) +11.50,} |A ; (424) 
cos {12 364(a,+a)+11.5a,} 
+ 
cos {12 364(a,—a) +11.54,} |4’, 
1 
+48 
+ 
and 
n=365 
[ysln SIN 24(n—1)a 
n=1 
1 sin 12a, [sin 12365(a,+4a) sin {12 X364(a,+ 4) +11.5a,} 
48 sin 4a, sin 12(a,-+a) 
_ sin 12 365(a,—a) 
sin 12(a,—«a) 
_ 1 sin 12a, [ sin 12X365(a,+4a) 
48 sin 3a, sin 12(a,+a) 
__sin 12X365(a,—a) 
sin 12(a,—a) 
sin {12364(a,—a) + 11.505) |’ 
cos {12 <364(a,+a) +11.5a,} 
cos (12364 (a,—a)-+11.5a,} |4”, (425) 
