COS d = 1 - 2L, h = sinM = 4L(1 - L), U = 2kV(l - U, 



V = 2KVL, X = U + V, Y = U-V 



T = (d/sin d) = 1 + (1/6) h + (3/40) h' + (5/112) h' + (35/1152) h" + (63/2816) h' + . . , . 



Eo = -2 cos d, A„=-D„Eo= - 4EoT% Do = 41% B„ = - 2D„, Co = T-'/2(Ao + Eo) (137) 



S = a sin d [T - (f/4) (TX - Y) + (f764) (A„X + BoY +CoX^ +DoXY +EoY')] 



sin (aj + a,) = (K sin AA)/L, sin (a^ - a,) = (k sin AA)/(1 - L) 



'AiSa, + 8a,) = - (f/ 2) TH sin (a, + a,) 



'/2(Sa, - Sa,) = - (f/2) TH sin (a, - aj 



ai_2 = Oi + Sa, , a2-i = ^2 "*" ^cij- 

 The azimuth formulas of (137) are obtained by manipulation of expressions given on pages 

 126-128 of THE DISTANCE BETWEEN TWO WIDELY SEPARATED POINTS ON THE SURFACE 

 OF THE EARTH, W. D. Lambert, Journal of the Washington Academy of Sciences, Vol. 32, No. 5, 

 May 15, 1942, [13], Note that in the distance and azimuth formulas of (137), the same quantities 

 H, T, L, k, K are used. 



Figure 22 in an example of the arrangements of equations (137) and computations for 

 comparison with those of Figure 21, page 80. The results are: 



Parametric Latitude 

 Fig. 22 

 8i SP 



622.30 621.08 



True distance 



Geodetic 



: Latitude 



meters 



Fi 

 Sf 



Ig. 21 

 ^ Sf^ 



8,466,621.01 



618.26 



621.11- 



True Azimuths 







109° 57' 17';41 





16': 86 



265° 37' 10': 59 





10 ':71 



16': 68 



11'; 37 



As was to be expected both approximations are adequate within any operational requirements. 

 The coefficients Ao, Bq, C^, Do, Ej of the parametric latitude form. Figure 22, are slightly less 

 complicated than those of the geodetic form. Figure 21. But no conversion to parametric latitudes 

 needs to be made for Figure 21. For purely geodetic computations further investigation needs to 

 be made and it is suggested that computations be made using both forms against the computed 

 lines contained in the revised issues of ACIC Reports 59 and 80, Sept. 1960 and December 1959. Ll2j 



