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 1 II , , O I II 



^. /O ^<^ ^^- ^^c> ^ 7^^y*^/yp <^^ \l /f^ ^'^ -^"^ ' <^<^ <P 



J^^^^ y^^jfjX^ yVS^O 2. west of 1. AA^aJa, ^ ^^ ^>>V^ 



cos <h, -r.^^9^ ^^fSf9 sin <^, -T" /^S^yS/f sin AA -T. ^^^V J'^S'S^^ 



tan ^, y.^3^ y^S-f-S-f cos <i>, -r-^ 9f^r^^^<s^ .c.^ AA -r-ff^ V5S^^^ 



tan 0; y"' ^'^^ S'^^ fy cos d = sin 0^ sin 0^ + cos (^^ cos 02 cos A A " ^^ ^^^ //^^ 9 



M = cos 0, tan 4>^ - sin c^, cos A A — ^'if^V <^^9^ ^f>^ S cot u = M/sin AA " - 9^j^ ^^.2'^^ 

 N = cos <;i, tan 0,- sin <?!,, cos AA ^' ^'^•^ ^i^j^ F^'^6^ cot v = N/sin AA ^> /yC'<i'^ S-j/J^J S 

 sin d = cos 0, sin AA/sin v = cos <;6jsin AA /sin u -/> ^ ^'^ ^j^^ ''^'^^ xx X-^/ -:r^ ^-^ ^^ "^ 



esc .\ -^/S'/fx 6d f4 cot d v-/>3^. /W<^ r<srj2.'i'^ V </■/ »<i^ ^9.^9 ^ 



1 + rosd -^/.ff"? //S^^ 9" 1-cos d V-x^^>gr^/<f/ sin u -^. y/.^ 0->^'''^/C5 



(sin ^, + ^in rA.^^ yy/r^ ^.f.y 9^ (sin rA,-sin ,^,,1 ^ T^.^g'^J^ 7^^^^^/ sin V 7^-, 9^ ^ ^ ff -^ / 



K, = (si^0, + sin<?!,,)^/(l + COS A\ r:/:>fOy^7J/9jf9 k-^ = (sin rA,-sin rA.'lVn-cos d) ^^ 96 4 ^^S j/^ , ^ 



x=K,.K, y/'^J'd ¥9sZaA Y=K,-K.^ ^'f9^y//aV9^ xy 9^f 3<9rsr9 ^ 



Y^ 7^/. ^9^^fA 9</ Y ' 'A ^^/^>^^ ^ ^ d 'i>9S''93^/9/ ^ ^ -^,^^^-^^^-3 9^ f 



A = 64d^ + 16d ^ cot d Z^^^:^.^^L_^^^^^ D = 48'sin d + 8d; esc d j:l^:<i_£^:f_£^^^^^ 

 R = -9n - /> V99'S'/^<i<^ . ^n sin 9^ y-^< ^V/ ^^^^^ sin 9d -^^ /^/ ^ ^'P^/ 



c= -(30d, +8d^ ... d ^E/91 -^^^ /C3 ^^9^-9 AX v-<^ ^^93^^/ ^ <ry 



RY -^ ^. Wf^^y^^'7 cx' -^'SJd /^^o^9 nxY -^?^ e^-'9ff<r<^S'''^ 9 

 FY^ /o' '/f^f^S'<^-3r^ y=Ax^RY4-rx^ + nxY + EY^ v-v^.i^sf/ ^^9^ JiS9 



;idj^-rfMUYd^,-qY.indi — ^^^w'jtr^-j'^^j^ ;;Hj^ = +(fVi9.8)s ^ ^' oJ/<sr9 )< /^ - ^ 



d .^A -^^^'94-^9V ^^9 A ^^A^.^A^ ^^^C^<r ^f<i^ /-/^ 



s[sdp = a(d^ . ^A,) VM 99/^ 99J s(sdf.) = a(d, . sdf . gdf.) ^^■^, ^^^- -^•^<^ , 

 2u <^^^ ^^ ,r/,99^ 2v ^9 -^9 <f^'^^-x 



sin 2u —^'99^ J^^^ST^ sin 2v ^' 9 9 f 9 9 f'9<r' 



U = (f/2)cosVisin 2ii «- - C<^/^Od^ <S'^// V =(f/2) cos'(j>. sin 2v V"- ^^^/^'/^ ^f ?// 



Su = VT - T1 y^ Jo^'Ji^X, ^-^ V/ ~ sv = -UT + V -7^ .^^sj>-?6-^^ 9 S" 3^:1. 

 + Su 7^// y^^.-^^f ^ Sv V,^^ y^^<^9/ 



- u -- /<i^y^ <^^ --^^ ^^^ + , ^ y/^ ^r V9^9C 



+180 o . " . +180 o I " //^ 



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



Line No. 4, See Tables 1 and 2. True distance 



129 



y/^. ^^.r. /<^4 



