Spherical Formulae (see Figure 16) 



cos d = sin cji^ sin 02 + cos <;6i cos <ji ^ cos A A 

 sin A = (cos 02 sin AX)/sin d, sin B = (cos 0isin AA)/sin d 

 cot A = (cos 01 tan 02- sin 0i cos AA)/sin AA 

 cot B = (cos 02 tan 0, — sin 02 cos AA)/sin AA 

 sin d = (cos 0i sin AA)/sin B = (cos 02 sin AA)/sin A. 

 The Andoyer-Lambert correction [13] for distance is: 



(73) 



f 

 Sd = -_ 



4 



d + 3 sin d d - 3 sin d 



(sin 01 - sin 02) + (sin 0i + sin 02)^ 



1 - cos d 1 +COS d 



where d is spherical distance from (73) and s = a(d + Sd), f is the flattening, f = (a - b)/a, 

 where a, b are the semiaxes of the reference ellipsoid (a is the radius of the auxiliary sphere). 



Now (73) and (74) are essentially the same as used for several years in Loran computations 

 except for the conversion to parametric latitudes which is not required with these formulas. 

 The only difference in the appearance of the formulas is in the terra 3 sin d in (74) which is 

 simply sin d in the formulae for parametric latitude, [l4]. 



The corrections to the spherical angles A and B as given by (73) to get geodesic azimuths 

 are, [13]: 



f r d 



sin d 



d 



(74) 



8k 



SB 



cos^02 sin 2B — cos ^0, sin 2A 



sin d J 



[cos ^02 sin 2B - cos ^0i sin 2A 

 sin d J 



(75) 



the geodetic azimuths being then 

 180°- A + §A, a 



180 + B + SB. 



AB - """ -->.-, "g^ 

 The formulae as given by (73), (74), (75) were arranged in computing forms to make the 

 check computations of the ACIC chosen lines. Note that the azimuths as given in the ACIC 

 publications differ by 180° from the usual geodetic azimuths and the forward and back azimuths 

 are interchanged from the conventions used in the check computations. The lines chosen are 

 shown in TABLE 1, the comparisons are given in TABLES 2 and 3, while the actual computations 

 are in Appendix 2. 



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