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 C II _ O I II 



0^ ^g^ ^^ ^.^.^^^ 2. T^/'/*^//?^^ A^ y^ ^^ (P^^.^^a M/ 



sin rA, i^.^C^ fJ'/^ir 2. west of 1. AA^A^-A^ aV ^V yJ.9f 9 



cos ^, -r. ff^ J?V'r'/^ sin <^, -^.^^:? ^/^^/ sin AA ^^ ^-^^ i^U^i^ 



tan rA, ^^4-^^ ^<^3/^ cos 0, -A- <^^^ ^"^^^^K os AA y"-^.?^ ^^^ ^^ 



tan r^^^ 'f'f-^y ^^^70^ P„g (] ^ sin 0^ sin c;^^ + cos 0i cos 0^ cos A A ^-^ ^^/^ J?a^// 



M = cos 0, tan <?!.j - sin 0. cos AA '^- ^^^ <^^^S^9 ^ot u = M/sin AA '^'^^'^ f-^'jAST f 



N = cos <^, tan <^,- sin <^, cos AA — '^■^^ ^^^ (^ cot v = N/sin AA — ' ^^/ -?^ .^«^ sf 



sin d = cos (jij sin AA/sin v = cos <;62sin AA/sin n -/--^SO >/.jJ? ^ 7 u ^ d) ^Z <^y--3-3y 



CSC d -// ^s-'^^j-^/^ cot d y-/^^f ci^.y'/C ^ fa ^^ ^/-^sT 



1 + rnsd -r/. 7^9J^r^// i-cos d 'f-^'Pc^ 9//f9 sin u -^^^46 c^^J?^/ 



(sin rA. + sin 0^^^ y/ ^.?^^ j >>^/ (sin rA^-sin ^,) ^>^>^?.^ ^^^ f ^ sin V T^- ^5^^ 9ff/f 



Ki = (sin<;6, + sin9i>,)V(l + cos d) 7"^ ^/^ , P /^. fr .:>U. K3 = (sin <^,-sin 0,)y(l-cos d) -^^//^ S^^^^'-^ 



A = fi4d^ + 1 6d ^' cot d y^.<X /y3 /6 ^ J*/ n - 48 sin d +8dj.' esc d -T 3 7. ^'^ ^ VJ^^9 



c= -(30d, +8d^ nnt ^ 4 E /9^ - »<^- -ra^^ ^f^- A y ^4<r. ^^^^^?/ <// 



FY' y/^' 7.5^- ^Ji'^^t^ s=Ay+RY + ry^+nxY + EY' ^j** j^-rj ^r-.^^r'-^ 



;)d^^-rfMUVd^.-qYs;n H^ ■r.a^>a-^/i-99^^ ;tdj^ = +rfVi9«^y. -A- d>aao^^S^// 



d^ + Sd ^ '/-'i'S'C 9y9f^</ H^ + Sd^ + Sd j^ y. :Py^ >^4-2?c^ ^-T- 



S(Sdf) = a(dr + ;idj) y/*^^ ^i^j". x^V s(Sdf.) = a(d^ + sdf + ;^dp) ^. f^^, 9f^'. ^^^ „. 



^ T = d/smd //^^/-^^9S'<7^ ^ / 



2u /^<^ ^^ y-^' Z'S'^ 2v yf^> 'ff ys.<r/c 



sin 2u y-//^^" ^3^99 sin 2v ^^ J^- ^3 f<^ 9 



U = (f/2)cos'<?S^sin 9,1 . <g^//>^ ^v^'^g?-^^ V =(f/2)cosV2 si" 2v -°?. ^-^/^^X/^ ~ 



;;„ ^ VT - TI a^/ /^^}Saji<i 9 ;^v ^ _TTT + V - ^ ^^/J^^ 9JjS^JL ^ V^ 



+ Su - 3 ^7. ^<^ ^ + ;iv — ^ ^o>^6 f 



- u ^ z,^ ^/ ^7' 3S 9 + V -^9^ ^</ ^/'^sSi ^ 



+180 o . " / +180 o . 



a.-2 = fluv = 180°- u + Su a,_, = a^^ = 180° + v + Sv 



Line No. 9, See Tables 1 and 2. True distance ^ /-^ ^ f/T' -=^ 9 / dieters. 



134 



