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'' 



1 radian = 206,264.8062 seconds 





^___^Ur^,^^,^ J-'P°^9'^9f(.S'9 ^ Always west of 1. AA = A - A -^/^ • ^ ^ /C- /^ -^ 



^ \\\ ' ^ > >■ . Ill , y 



sin<^ -^S^^ /9y^~V ..r.Krf.^^ --^^? ^r^'P'7^ sinAA ^- /^^^^•^^^ 

 cos Z r"^^^ 0>^.^^5 eosA,^^ -f-' ^9f ^^^^ 9 sin AA^ ^. ^ f^ -^-^^5^^ 



k = sin <^^ cos A<^^ 7^.A?f /3f3^^ K = sin Ac/., cos <^^ — - ^J^^ff^^^"? 



' m ' m ~ iTi 'III / •% y 



H ^cos'A<^^-sinV^ = cosV^-sin^Ac^^ ^' ^ 9/ ^ .r"-f / .? i-L V- ^^T'^V^/'^'^ 



l.^sin^A^^__-.Hsin^AA_^_ -T. ^^ ^ 9.«-.i^ 9S 9Ji- on. d :. 1 -? T T*"^ 9 r.^ ^ ^g'r4.''^ »- 



A^ ^/^^ 9>^^-<^V.^^ s\nA^ ./^^-^^.^V^ T = d/sind + ^^^^=£lZ^.ZV^ 



V=TT4- V7^/ 7<^9<^?^0JZ^ Y^TI-V -t^/./JS 'r<^:iV3JL XY tV. 9/^ ^^^ f ^d) ^ 

 x^ y-^. 9y/ //'/^^^ 9 Y^ ^/.J^a S9asS^ v=e.^ cos d ^-T^. i^^S"^^//^ 



A=4nfiT4-(E/15mi 7^i'<:?^/<5'y 9<^^^9^ n = 8(6 + T^) -r^-S^. ^^r3x5''<^ -^/-3- 



AX y-zy'^. f.^7s-'7<^9S'^ RY « ^^-rr ^.yy Vi^.?9^^ rx- - /5^^. ^^.^^^ yv^.r7 .^— 



nXY 7>^/-^^ .ry-z:^ -^-^ ^/^J^ EY^^^^f^lf^^M^^f =-(f/4) (TX -Wl '^^.^/V'^S^y^^ 



T^K^ -f-A^^j ^9^/ 9sr^ s, = ^ ^;n d (T + ;^j ) ^^^ ^<:^.^> <r:r ^ 



Sf2 = + (f yi28) (AX + BY + CX' + DXY + EY') —-' J^Ca^^JT'^ /^ ~ ^ 



T + gf + gf2 y- /. <^^^?^/C /4 ? S, = a sin d (T + Of +gp) J^cg^.^ £>^^.JXJif ^ 



O t " 



sin (g.+g,) =(Ksin AA)/L — ^^^^/^.^ f S^ g, +g, ^ ^^ -^T^ V3^ "/^f 



sin (a,- g,) =(k sin AA) /(I -T .l T"^- /-T:^— V/AJ' ^ a,- a, X ^/ ^J^ -fJ'. <^ ^l^ 



'/2(gg,+ ga,)=-(f/2)H(T+l) sin (n ,^ a.} -f- 9. 9^>a .^^^^/.Z. X /<i^ ' ^ hn. '/'f. 9^'^f}^/99 )^/a -^ 

 y2(ga, - gg,) = -(f/2)H(T-l) sin (a, - a.) -<:>. ^^^ .<-'/fA.^)(/^"'^^ 8a, -^^.9 99 9fS^r^)(A :)-'^ 



a, v± kz- ^^' ^'^^ ^2 ^i/ ^g^ ^^jO£^ 



5a,^± ^ ^ /. ^f g:^^? gg, _3t ^Lf .^-^^ Z:?^/^ 



= + g, + ggi gj-j = + gj + Sa, 



1° dk. =£^<J^-2, True distance 9^^^ . ^^<^ ' ^^ 



C / // i> • // 



meters 



1 rue Azimuths ^^ _ „ _ ^ , . j^ -> =3 ,— ^/ 



Line No. 13 



138 



