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, fVl28 = 0.0897860195 x 10"' 



o g M , " , o I II t 



sin c/., ' 9^9 ^-^4/4^ 2. west of 1. AA = aJa /^-S^ 3^5 -J^^^Y^ 9 



cos ^, ^^^^ <r0^dr sin c^, ^9S^<i^Ji<^jL sin AA --gJTy ^V/6 ^ 



tan ^^ ^^-r^</ ^jzji^o ^^3 ^ .. .^vi^ ^^^>^> if„, AA - ^«g ;?^ ^^^yj^ 



t.n A.. V-^' ^^^^ -$^^^ -^V nn« ^ :. .in ^^ sin (?!>, + COS 0^ COS ^Sj r..« A A -y *-^ f^9V94'f^^ 



M = COS 01 tan 0^ - sin <;6i cos AA /^"-^ <!^ 9SS '/ cot u = M/sin AA ^<^^ ££5^>^ 



N = cos 0, tan 4>,- sin 0, cos AA -f" ' SKST/ c?^^"^ '^ cot v = N/sin AA ^/' <^'^^'^^^^ 9^^ 



sin d = cos 0, sin AA/sin v = cos <?S,sin AA /sin u -/-, /^<^ ^ O'/ST/ „ y^P^/ •^'^ .^»^ f^ ^^ 4_ 



esc d 7^$^f<r.s ^^<fy^ cot d T^9'9^x v^^^fx ^ ^v i-r ^-y./r s-- 



1 + cos d ?V^< 9M 9^9^ 3 1-cos d ^V^^^rV^^:^ .in .. 7^y S'S'S^ o-<^ F/<^ 



(sin 0,^sin A..Y S-^a^9^/e'/ (sin ,^,-sin <h. y r ^J^SfJ-^ ^-^ sin v ;^. ^^^ .rf// X^ 



K^ = (s^n0l4-sin0^^^/n ^rns d^ -y"/ /"^^J^^rj-^^ l^^ ^ (sin rA,- sin rA^WH -ros d^ -^^^ ^ ^sS''^^^^ ^.g'^ -^ 



A-64d^+16d'rotd -tr-^^^^ /^S'99 n = 4a'sind +8d/cscd ^^' <i J^ 9 -^ 9 ^ ^ ^ 



c= -(3od, +8d; m^ d 4F /9^ '-<^ ■ /-^^ ^ >/^ -^^-^ AX yy^./^/^f^^^ ^ 



RY - /9. <r^<p ^(^J^-^L r x^ - ^»< //Jg^ 9^S"9f nxY ^/i^> J*^^ yp^srT'i^ 

 vy- -/-/7. 9f^^r79<^ s==AX^RY^cxvnxY^F.Y- 'f^^/S'/'/ ^^^ 



;)d^=-rfMUVd^.-';Ys;n d^ y.^^v^/y/^sj*^/ ;;dj^ =^rfVi9«>y, -^ ^^^'^^^ ^^/9d 



d^ + sd ^ ^^/^.^ 9^<^y^:5 d + sd^ + sd ^^ ■- y"^^ fji^r^^'^ 



S(Sdf) = a(d^ + ?,A^^ 4V^.^<^9^ 9<i^ S(5dp) = a(d, + 5df + ^dp) <i^^^ ^S^^^^ 



> T = d/sind /-'^^^ ^^^^^ ^ 



2u -^y^ ^/ ^sryro'/ 2v rf j^-^ vf^s9c> 



sin 2u -^ ^r^ ^/f9/ sin 2v 7^/ 9ff 9f9S'<0 



U = (f/2)cosVisin 2u -/> /9f94^)(/^ - "^^ V =(f/2)cosV2 sin 2v ^ / f /-^ f^ )< /^ " > ^^ 



VT -^ A 976 /7Xy<i'~'^ TIT -/> ^^^ 9r j^ •^ - "^ 



;i„ = vT-Ti 7^~^> /r^yxx y^^'-'^ n. = .^n ^w -/-s- /rsr^ y^<^ - "^ 



+180 o . M +180 o 



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



Line No. 5, See Tables 1 and 2. True distance ^ ^-^ /-iJ • ^"^ 7 meters. 



130 



