904 U. S. COAST AND GEODETIC SURVEY 
> yn sin 24(n—1)a 
=A’ > cos 24(n—1)a sin 24(n—1)a+A” 2 sin? 24(n—1)a 
+B’ > cos 24(n—1)6 sin 24(n—1)a+B” = sin 24(n—1)b sin 24(n—1)a 
+0’ > cos 24(n—1)e sin 24(n—1)a+C” 2 sin 24(n—1)e sin 24(n—1)a 
+D’ > cos 24(n—1)d sin 24(n—1)a+ D” & sin 24(n—1)d sin 24(n—1)a 
+ E’ > cos 24(n—l1)e sin 24(n—1)a+ E” © sin 24(n—1)e sin 24(n—I1)a 
(411) 
the limits of n being the same as before. 
Normal equations of forms similar to (410) and (411) are easily 
obtained for the other unknown quantities. 
272. By changing the notation of formulas (265) to (267) the fol- 
lowing relations may be derived: 
365 sin 24na cos 24(n—1)a 
2 1 
bs cos? 24 (n—1)a=4n+4 COAG 
i 60a cos 8736a 
ze fr rinse 87 ; 
Ween: sin 24a 412) 
1 sin 24na cos 24(n—1)a 
sin 24a 
sin 8760a cos 8736a 
Mi Got 2a SERS BON Cae Cen ONe 
Se sin 244 (413) 
oh sin? 24(n—1l)a=3n— 
Sone 24(n—1)b cos 24(n—l)a 
n=1 
1 sin 12n(b— a) cos 12(n—1)(b—a) 
=s sin 12(b—a) 
es 12n(b+a) cos 12(n—1)(b+a) 
u sin 12(6-+a) 
__ ,sin 4380(b—a) cos 4368(b—a) 
2 sin 12(b—a) 
as sin 4380 (6+) cos 4368(b-+-a) 
a sin 12(6-++a) 
(414) 
n=36 
Sain 24(n—1)b sin 24(n—1)a 
nmi! 
sin 12n(b—a) cos 12(n—1)(b—a) 
sin 12(6—a) 
, sin 12n(6-+a) cos 12(n—1)(b+a) 
Te sin 12(6+a) 
__, Sin 4380(6—a) cos 4368(6—a) 
im sin 12(6—a) 
2 a 4380 (b +4) cos 4368 (b+ a) 
sin 12(6+a) (415) 
1 
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