For the Clarke 1866 spheroid of reference we have from the above formulas: 

 ^4, (seconds) = (f, - d = 699':2540 sin 2^, - 0':5936 sin 40 + 0'10004 sin 60, (55) 



A0 (seconds) = - = 699':2520 sin 26 + l':7769 sin 40 + 0':0064 sin 66, (56) 



A0O (seconds) = - <;6„= 349':0318 sin 2(9 + 1'14796 sin 4(9 + O'lOOei sin 66, (57) 



h (meters) = 10,788.3852 - 10,811.2646 cos 20 + 22.9147 cos 40 - 0.0350 cos 60. (58) 



For the Clarke 1866 spheroid, the maximum value of A0 was found to be 11' 39"255 at 

 = 45° 02' 55 '1106. 



The value of A0o, at this maximum of A0 , was found to be 5 ' 49'1037. Finally (58) was 

 checked at = 0, 90° and = 45° 02 ' 55':i06, At = 90°, the check was within 0.0005 meter; 

 at = 0, it was within 0.0003 meter; at = 45° 02' 55'1106, it was within 0.001 meter. 

 The following latitude formulae are from G & G.S. Special Publication No. 67, [5], 

 Where 0o, 0, 6 are shown in figure 1. 



00 - = 700':4385 sin 20o - l':i893 sin 40o + 0':0027 sin 60o (59) 



00 - = 700';4385 sin 20 + l';i893 sin 40 + 0';0027 sin 60 (60) 



00 - = 350'2202 sin 20o - 0'12973 sin 40o + 0'10003 sin 60o (61) 



00 - = 350':2202 sin 26 + 0':2973 sin 40 + 0'10003 sin 66 (62) 



- = 350'12202 sin 26 - 0':2973 sin 40 + 0';0003 sin 60 (63) 



6-4; = 350':2202 sin 20 + 0"2973 sin 40 + 0':0003 sin 60 (64) 



The above are the series expansions for the expressions given as equation (1) page 12, 

 that is 



tan = ^1 - e^ tan = (1 - e^) tan 0o. (65) 



REFERENCES 



[1] Geodesy, Hosmer, Second Edition, John Wiley & Sons, 1930, page 181. 



[2] Army Map Service TM No. 67, Latitude Functions, Hayford Spheroid (International) 1944; 

 AMS TM5-241-18, Latitude Functions, Clarke 1866 Spheroid, December 1960. 



[3] Course in Higher Analysis, Whittaker and Watson, 1962 Edition, page 133, Cambridge 

 University Press. 



[4] Peters, J. Eight-place Tables of Trigonometric Functions, Berlin 1939; Edward Brothers, Inc., 

 Photo-Lithoprint Reproductions, Ann Arbor, Michigan, 1943. 



[5] Latitude Development Connected With Geodesy and Cartography, U.S.C. & G.S. Special 

 Publication No. 67, G.P.O., 1921. 



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