COMPARISON WITH AN EXISTING EXPANSION 

 On page 8,GIMRADA Research Note No. 11, E. M. Sodano, April 1963 [23] one finds the 

 following formula: 



S 



— = d+f + f') + a[(f+f^) sin<?!,-(fV2)0'csc <^] 



f+f f + f^ . f' X 



sin cos (f) + — (fe^ cot (p \ 



■(^ 



2 2 2 



f^ . 3 \ 



cot d) — — sin (A cos ^(h\ 

 8 ' / 



:os^(^j - a^ (f^/2) sin cos <f) 

 Now the correspondence between the parameters as used in (133) and those of Sodano 



£2 f2 



I sin 4> cos d) — — 



16 2 



— sin cc 



2 



(134) 



m(Sodano) = X/2, a(Sodano) = '4 ( Y + X cos d), ^(Sodano) = d, b^ (Sodano) = a(l - f) (135) 

 (a is equatorial radius, f the flattening). 



If we substitute from (135) into (134) , retaining terms to f^ inclusive, we can write (134) 



— = d - (f/4) (-Xd - Y sin d) 



+ (fVl28) (16d' cot d) X - (I6d' esc d) Y (136) 



+ (2d + sin 2d - 8d'' cot d) X' 

 + (8d^ esc d) XY - (2 sin 2d) Y' 

 Now comparing (132) and (136) find that the equations are identical which gives an 

 independent check of Sodano's inverse formula. 



COMPUTING FORM IN TERMS OF PARAMETRIC LATITUDE 

 Given on the reference ellipsoid the points Pi(0„ X,), ^.^{62,^^; P2 west of Pj, west 



longitudes considered positive. (Geodetic latitudes are converted to parametric by tan 6 = {\-i). 



tan (j) or an equivalent formula). Formulas (133) may be used as follows: 

 With d^ = 'Aid, +6,), Ad^ = ¥2(0, - 6,), AX = A , - A., AA^ = ^ 



let k = sin 9^ cos A9^, K = sin A6^ cos 0^^, 



H = cos'A^^- sin'^^ = cos' 61^ - sin'A(9jj,, 



L = sin'A6l^+Hsin'AA^ = sin'd/2, 1 -L = cos'd/2. 



87 



