DISTANCE COMPUTING FORM — ANDOYER-LAMBERT 



TYPE APPROXIMATION WITH SECOND ORDER TERMS 



(No conversion to parametric latitudes) 



Clarke Spheroid 1866, a = 6,378,206.4 meters 



f/2 = 0.00169503765, f/4 = 0.000847518825, f7l28 = 0.0897860195 x 10"' 



O 1 II O I II 



sincA. •/. ^■// ^^"^^3 2. west of 1. AA^aJa. V^^ /<^ . ^ ^ G 



cos ch^ ^^ '^^O Ji r ^C "P sin 0, ^'^VJ^ 9f7^/ sin AA 7^> ^^/ -^/^JX. 

 tan ^, 7-, i<r^ ^^9 9^/ cos <^, ^^^^^j^^i^f^os AA 7^. 5^5^^ 93/3/^ 



tan ^. "^'f-^y ^ 9"7 ^ S rc^^ d = sin 0, sin c^^ + cos <^i cos 02 cos A A " ^ ^^^'^ '9^<fS ^ 



M = cos 0^ tan 9S2 - sin 0, cos AA — ' ^'^^ S'ft^ <g ^ cot u = M/sin AA — - 9ff Ff^^ / 



N = cos 0, tan 0,- sin <^, cos AA r. ^^ ;><g^ F^ cot v = N/sin AA ^ /- ^^O^f <^i^^ 



sin d = cos 0,sinAA/sin v = cos (^S^sin AA/sin n ^. «i^^-i=^ 6J12-S'/ ^ y^'j/ V<^ i/^,^ /C 



CSC d ^'/^^^^^s-'/s-r cot d 't^'fj^^j^S'// V v^ ^-^j- ><^- ^99 



1 + COS d ^/> 9999^:^^^^ l-cos d ^> ^'^^ ^f^7 sin u y-^^y/ ^»r^^^ 



(sin 0, + .inW^A W.<^ji^«g^/^^i (sin.^,-sin^,) ^ V. CJ^/f^JJ//'" -^,^ ^ ^^ V^^ ^^^9^^ 



K, = (sin 0, + sin (^2)7(1 + cos d) '^'f-JS'/V9<i.^3 K^ = (sin 0,- sin 4>^f/{\-cos d) ^. ry^J*^ f.^-^'/ 



A =- 64d^ + 1 6d f cot d 7^ ^.^fO^S<r^ 9f n = 48 's in d +8d; esc d -/- - ^^^^ '^^9^9^ 

 C= -(30d, +8d^^ Pn^d.F/9^ -^ ^<^^-/-J'/^</<^>i AX V-X/^-^ /^^^^^ 



^y -^.s/3'9Jf^t-S' cx^ ^/-^^y^^^y^s- nxY ^' -^^ ^ / ^ $^a F^/ 



FY^ T".^'^^^ /^J' ^,ry/ S = AX+RY+CX^ + DXY + EY^ "- V^f^^r/^"^^ 



^dj^-rf/d^m^-w.;n^^ ~-<^>^^»^>/X/^'^ ;;^j'^4-(fVi9«^y, ~^?.^^^9f )( y^> -^ 

 ,^^,,^ .^yJL ^/S-f^ff^ ,^.,A^.,,^ ^^-^^ ^^^^ ^-^-^ ^<^ 



S(Sdf) = a(d^ + Sdf)^Lf^fl^^3^:!_^ S(§dp) = a(d, + Sdf + 5dp).ZS._^^^^^:^„ 



., T . d/.;n d /- ^^^^ ^J'^r^a 



2u ^^/ ^/ ^J'. <^S-i. 2v ^^ ° V<< ^^^^^^ 



sin 2u — - 9'9'f 9S^^9 sin 2v ^' '9 f' 9 $^9^/^ 



U = (f/2) cos^<^, sin 2u - 9'999^-i^<^'!r^/<f'''^ =(f/2) cos^a sin 2v T 9- 9^^^^//^//^ '^ 



VT 7^ 9' 9&''9 y VS'X Z^?-'^ ~~ tit ^9- 7 97 'i^ ci^/^ Y /^^ " ^ 



;;., = VT - TI 7^^ ^^// 7^'/'/ 6^ ^, ^ _TTT + V -^. g^^^ .^^ >/V<^ ^ ^ 



/ 



1^ ^^ Vd.' y/<^ ^^''VV ~:F^ y/^ '/99 



+180 o , ,1 +180 o . 



= a^^ = 180°- u + Su a,_, = a^^ = 180° + v + 5v 



Line No. 1, See Tables 1 and 2. True di-^tanrp » y ^Crv * *r XCJ meters. 



126 



