64 On Practical Geodesy. 



Were we to use the simpler formula — 



then, obviously, we have — 



log z, = 3-7040792, and .-. z, = 1°, 24', 19"-1687 

 which is C'-OOll too small. 

 To find D^ and w, we have — 



tan i (D, + cu) = ^»«|(^;;--0 . eot i A,. 

 ' cos J {I" + z,) 



tan i P, - o,) = '^ijSI^^j • cot i A, 



cot J A,, = 10-3881059553 

 cos i (^" — z,) = 9-9544060605 



20-3425120158 

 cos J (r + 2 J 9-9490947477 



.-. tan J (D, + (o) = 10-3934172681 



cot J A,, = 10-3881059553 

 sin i (Z" — z,) = 9-6386781718 



20-0267841271 

 sin J (r + 2,,) = 9-6600485181 



.-. tan J (D, — to) = 10-3667356090 



.-. 1 (D, + co) = 67°, 59', 3r"4286 



... J (D, — o) = 66°, 44',, 31"-4287 



.-. D, = 134°, 44', 02'-8573 



to = 1°, 15', 00"-0001 



This case in which the given latitude is less than the 

 sought latitude, is made known to us by the given azimuth 

 A,, being less than the computed angle D,. 



To find U,— 



sin s, = 8-3896105836 sin I" = 99023486165 

 sin A, = 9-8456996715 sin A, = 9-8456996715 



18-2353102551 19-7480482880 



sin to = 8-3387529285 sin D, = 9-8514909614 



sinL'= 9-8965573266 .-. sin L' = 9-8965573266 

 .-. L' = 52°, 00'. 15"-3097 



