Prom (229) 

 Therefore 



58 V. S. COAST AND GEODETIC SURVEY. 



For the mean value of the variable part the coefficient of (228) we 

 have 



[iA,^ + B^' + 2A,B^ cos vY^ cos v% (232) 



,_ A^ cos v + B^ /'oQQ^ 



cos V - (^^2^js,^-^2A,B, cos vY ^ ^ 



[(A^^ + 5^2 + 2A,B^ cos vY cos v% 



= [^1 cos v + Bi]o 



= [A sin 2/ cos v + B sin 2w]o (234) 



Substituting (159) in (234), 



mean value of variable part of coefficient of K^ 



= A sin 2C0 [1 - 3/2 sir^ i]-}-B sin 2co = 0.2655 (235) 



Kef erring to (228) and (235), 



j^.r^ A sin 2co [1-3/2 sin^ i]+B sin 2a, 



oi ^1 [A' sin2 27+52 gin2 3^0 + 2AB sin 2/ sin 2co cos vf ^^'^'^^ 



From the spherical triangle ,^T^ in Figure 6 it may be shown 



that 



cos -i — cos CO cos 7 /^„»\ 



cos v = '. -. — f (237) 



sm CO sm I ' 



From which it follows that 



2 (cos i — cos CO cos 7)2 — sin^ co sin^ 7 /r.oo\ 



cos 2v = r— ^^^^ (238) 



sm^ CO sm^ / 



Substituting (237) and the numerical values of the constants from 

 Table 2 in (236) we obtain 



Fof K, = [0.1009 + 3.0073 cos 7+0.8093 cos^ 7-3.5793 cos" 7]-^ (239) 



For the mean value of the variable part of the coefficient of (230) , 

 referring to (231) and (156), we have 



\_{Ai + Bi-\-2A^ B^ cos 2oY cos 2ij'\ 



= [j.2 COS^ y + ^jjo 



= \A sin^ 7 COS 2o-\-B sin^ wjo 



= ^ sin^ w (1 - 3/2 sin^ '^) + 5 sin^ w = 0.0576 (240) 



Eef erring to (230), (239), and (240), and to Table 2, 



A sin^ 6j (1-3/2 sin^ i) +5 sin^ oj 



Fof K, = i 



'2 \A? sm* 7+52 sin'' w + 2 ^B sin2 7 sin2 oj cos2 u]i 

 = [51.0453 - 63.9167 cos 7- 5.8300 cos2 1 + 19.0186 cos* 7]-i (241) 



