sin 



CSC 



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 t 11 



J -/• ^c ^<:> ix^, <i?.g*y a/ 2. / <s f- /*y/ y^ os ^^ /F" c70 ^<^^<^'^ <^ ^ 



sin </., -^> ^^<^ ^Ji<^9X. 2. west of 1. AA =. A,-A . V«^ VJi- g^-?>s3'f^ ^ 



cos ,/,^ -y^^ ^y/ ^.^^ Jg^.r' sin t/,, ^. ^^^^^^<£ A sjn AA T*"^ ^^ >^ <^^^ "^ ^ 



tan ^, -rV.^yji. ^f^S^ COS c^, V. jV:2-OPO/'/ ^^g ^^ ^. ^.gs-j'^s' ^^ ^ 



tan >/.; -^ -^^ ■7y<^'i^^'P''i^::^ ^„^ d = sin 0, sin (?S, + cos cf,,coscf}^ cos A A 7*^ ^^/V^ »^^->f 



M = cos <^, tan <^, - sin 0, cos AA — - 0<^/ '^ ^ "^ ^ 9 ^ cot u = M/sin AA - .a^/'CVS^^d, 



N = cos <^^ tan ^,- sin <j!>j cos AA -^> ^^^ ^ ;g^^-J'-i ^^t ^ ^ N/si„ ^;^ y-/, <i>C^<^ 3 "f f^ V 



d = cos ^,sinAA/sin v = cos (/..sin AA /sin „ /-- ^^^Z 9/<f30 „ ^^ ^4^ yf-i'-j Z^ 



d -Ti^. <^/<^ -4 9 f-T^ cot d -^-f'ff^ 9V99^ V V^ <r'^ ^^ ^/^ ^ 



1 + cos d 7>-A 94f6'~^^^<S'^ 1-cos d 7-. ^^/ -^^^•^J^sT 'sin u ^. ^^^ ^'^ S^f^ 



(sin ^.^sin ruy ^^^^fy'^^^'^ u^. ^,-sin ^, v 9^3fj^C^^f)(/r /,r. V 7-. ;=^^<^^^<r3'^ 



K. = (sin 9!,^ + sin (?S.)V(1 + COS d)?^/^^^^^:^ K, = (sin <^,-sin 0,)V(l-cos d) ^-^-^ 9 ^/S'S^^^ 

 A = 64dj. + 16d^cot d -y'.^g?. ^-f^ ^/^ ^ ^ D = 48 sin d +8d/ esc d -/-/i^.^ ^.^Z "^y.^ XJ^— 



R^-9n -^7. 9^.UJ^-^^ F.-.^n .;n 9d ^/^^ i^di/9^^9^ .;„ ?d '^- -Z^^. 



C= -(30d^ +8d; cot d+E/2)^^^._Z^^^^ AX ^-^;?^ ^JV ^-T-^J? ^ 



RY -^-y> 9f^^r^-^f vx^ ^^9,J9/fSy^ ^ nxY ^ ^y"- ^'^f/^<^ ^^ 



FY ^ -.^ 4^^"- ^ ■^•/^ ^ ^^<^ V=.Ay^RY4-ry^^DyY + FY^ ■>^JJ' ^-^f'^/^f'9 



;id^--/f/A^rY^^-QV.;n A^ -^.^c^a^JS-jr/s^ ;;dj' = 4-(fVi28^S ^^- /^^^^^/X^^ ~^ 



d^ + sd ^ -7^ - Jr^ ^y^zr^f H^ + sd^ + 5d I -^' c^^^^f/<^f<r' 



S(Sdf) = a(d^ + ;;dj) / <i^>'fjJ/Sr. ^a^9 S(Sdf2) = a(d^ + Sdf + gd^a) /.^'^^^^ f- ^^ ^ 



T ^ d/sin d ^ ^/^<iJ4-^^V ^ 

 2u //^<:^ y-g .:i'^.^'-^^ 2v ^$^ oT^ J'^. <^'^<^ 



sin 2u - - O^S ^ 9^ ">/ sin 2v 7^. ^^9 9* ^ f ^ ^ 



U = (f/2) cos^<^. sin 9n -S'^'^^ 9i/^>SX/a -\ =(f/2) cos^. sin 2v ^X ffJ^/^J^-y/^) ^^ 



VT -A.^> ooSiT^da X /^ -^^ T1T -J^ <o 94- ^g'^^ ^/<^ -^ 



^. ^ VT - T1 -T^^^ > ^^^ 9i^ffX /^ ~ '^ ?.. = -TIT + V 7*/: 9ff rJj^-^X/^ - ; 



+ 5u 



*//^3f^ + gv :t: ^A^^f^ 



+180 o . " ^ y 



= 180°- u + 5u a,_, = av„ = 1^0° + v + Sv 



Line No. 8, See Tables 1 and 2. True distance <^ ■^'^^-^-^7. t:^ 



133 



