HARMONIC ANALYSIS AND PREDICTION OF TIDES 95 
n=365 
>} sin 24(n—1)b cos 24(n—I1)a 
n=1 
sin 12n(b—a) sin 12(n—1) (b—a) 
eee 
Tee sin 12(b—a) 
La sin 12n(b+a@) sin 12(n—1) (6+) 
? sin 12(6+4a) 
__, sin 4380(6—a) sin 4368(6—@) 
nite ¢ sin 12(6—a) 
, sin 4380(b-++@) sin 4368(6+-a) 
TRe sin 12(6+a) (416) 
273. By substituting in (412) to (416) the numerical values of 
a, 6, ete., from table 2, the corresponding equivalents for these 
expressions are obtained. These, in turn, may be substituted in 
(410), (411), and similar equations for the other unknown quantities 
to obtain the 10 normal equations given below. In preparing these 
equations the symbols a, 6, c, d, and e are taken, respectively, as the 
speeds of constituents Mm, Mf, MSf, Sa, and Ssa. 
n=36 
5 
D>) Yn COS 24(n—1)a 
n=1 
=183.05A’+0.72B’ +0.76C’ +4.88D’ + 4.96 E" 
+2.14A"+4.29B” +5.040” —0.34D”—0.70E” oes 
n=305 \ 
D5 Yn sin 24(n—1)a 
n=1 
=? 14A’—4.15B’ —4.900’ + 3.80)! +3.88 FE" 
r +181.95A”+1.01B”+1.06C” +0.34D” +0.68 E” 
n=365 
>) Yn COS 24(n—1)b 
n=1 
=—(0.72A’+183.17B’ +0.56C’ —1.50D/ — 1.51 EF’ 
—4.15A”+0.88B” +0.92C” —0.09D” —0.18 EF” (417b) 
n=365 - 
24 Yn sin 24(n—1)b 
=4.29A’+0.88B’+0.920’+3.05D’+3.06E’ 
if +1.01A”+181.83B” —0.80C” —0.08D” —0.17 EF” 
n=365 
24 Yn COS 24(n—1)e 
=0.76A’ +0.56B’ +183.19C’ —1.68D’—1.70E” 
Ff —4.90A” +0.92B” +0.97C” —0.11D” — 0.21 FE” (417¢) 
n=365 z 
24 Yn sin 24(n—1)e 
=5.04A’+0.92B’ +0.970’ +3.24D’+3.25E’ 
a +1.06A” —0.80B” + 181.810” —0.10D” — 0.20 h” / 
n=365 
Ss Yn COS 24(n—1)d 
=4.88 A’ —1.50B’ —1.680’ + 182.38D’— 0.24 F’ 
i +3.80A”+3.05B” +3.24C” +0.00D” +0.01 F” (417d) 
n=365 
Ds Yn sin 24(n—1)d 
= —0.34A’—0.09B’ —0.11C’ +0.00D’ +0.00 EF’ 
+0.34A” —0.08B” —0.10C” +182.62D”+0.00 EK” 
