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 I ir O I II 



0^ j/6f ^<^ ^^,^g?.g 9_ T^^y*^//?^^^ X, x/^ ^^ <^<^- '^• ^^ 



si'n .h, -r, P^^ ^^ 9-/^ 2. west of 1. AA = A._-A. 7 y^ ^^ . //-^ 



COS rA, ?^. ^<^r ^V^i^r 3i„ ^^ ^^_^fiL^?%ysin AA ~r ^' Z^^- ^^^i^^S^ 



tan ^, y. F^<^ ^f^^/ cos 0, T^l^^^j^y^^os AA ^«^> ^^^ ^^ »^^/ , 



tan 0, -/"^ /If/^ \P 9'f<i. :S J.OS d = sin 0^ sin c?!,^ + cos c^^zos ^^ cos A A ^ ^- >^^^ <:?.S"gg ?$-^ 



M = cos ./.^ tan ^Sj - sin vSj cos AA -^-/^^ y-J? f 9 ^ cot u = M/sin AA - - .^^^ ^ Pf'/ C 



N = cos 0j tan <^,- sin 0, cos AA Y"' y^S^^^S^ f ^ot v = N/sin AA -^/> ^P^SC^^^ a 

 sin d = cos ^. sin AA/sin v = cos <?!>,sin AA /sin u ^' ^-^^^ ^'j^'f^^ u Xi*<:g> X^^ ^f<S/ <^ 



CSC d ^^> 94^^ ^i^S i^^</ cot d -r^.^g'S y^c'C^ f V V^ J-J- Y^.J^V C 

 1 + c..A -tAf9^^'^^c:'^ ^_^^^ J 7^, ^^'^/f^f9C sin u 7^> ^^^.J- ^^'^ r^ 



(sin .A, -. ..in ^,^ V/ r/f^J^S-^, S (^-„ ^ _ ,j„ ^j 2 ^ J^. ^^yf^<^//^ -^„ ^ -y^, ^^4- r^S^S 



Ki = (sin 0, + sin <^,)V(1 + cos H^ -^ 9/3 J^^ 7^^ K, = (sin ^S.-sin <?!,,)V(l-cos d) -^. ^'^-^ /^^^ ff 



y =1^^ +K 7-yr Y/^JS<iJ'^S' Y = K^ -K, TV V//^<£f^ ^f XY -^^ s-r /f <:><:> <^<^^ 



A - fi4d^ + 1 6d ^ rot d ^^^' ^//-Tt^ /^-3 C n = 48 sin d +8d/ esc djT^^LJ^^^^ZZ^ZZZZ 

 R = -9n -/•/- /^X-^>r^^.?/' F - ^n sin 9d :^^- ^9^ ^ySYiP .;n 9H •T^^^'^^^'^^'^ 



c= -(30d^ +8d; not d 4 E /9^ - j^-^-// 9S/y^^ AX -ty^.^9/c3(, ^c.^ 



RY -.r: "79^^ a ^ -^<^>r" px^ -/-j^- <^f<^^f9<i'S'S-' nxY ^ ^- >^<=^-^ ^ -^^^ .s^-^/ 

 ,rY2 ■/-/. ^^ ^7 «<r-/^ ^ s=AX4RY^ry^+DXY+EY^ --^' ^<i'^.:i.yJ^9^F' 

 ^dj^-rf/dUXd^.--^Y.;n d^ -/> 9f^<^S^//a -^ ;;dj^ = 4-(fVi9R^S --^ -9^/^ / /^ - ^ 



d^ + ;;d -?^.^^<^/.ri^ ;^^c^ d^ + Sdf + ;^d^^ -y^,/^C M^f^^? 



S(sdf) = a(d^ + ;idj) ra'/^ ^^^- ^ ^^ s(sdp) = a(d, + sdf + ;^dp) /^^^<^^' ^^'"^ 



T = d/sin d /.^^-a. <^^^YS3 



sin 2u -' ^^<^ /f<:>S3 sin 2v ^. 5^^^ ffS^^ 



U = (f/2)cos=0isin 2n -r^J^-f'i'^-f/A?-'^ V =(f/2)cosV2 sin 2v T*"^- 9y^f^> ^ /^ ~ "^ ^ 



VT r- ^- 97^c:2.<i,4--'Xy^ - •• ut ^ j^. y^^^^^"^ X y^ ~ "^ 



su = VT - Ti 7-//^^ ^•^-^>j'^ X' A^ - Y g^ ^ _UT ^ V ^ //: 3^rv/^f x" /^ - ^ 



- u 



-z-?^ /^ ^v: ^/^ ,v y-4^V ^-^^ y^'^Y<^ 



+180 o , ,1 +180 o ^ 



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



Line No. 7, See Tables 1 and 2. True distance_»^ Z^ ufi^' 7- • /■ /^ f meters. 



132 



