44 On Practical Geodesy. 



Then to find 8,„ l^^, and A^^, we have — 



8, = (j-^^) ' '^"^ ^" ^'"^ * ^^" + ^') ' (^" - ^') 

 ^^^ = 90° — (L" + S,) 

 A,, — D/; = sin D,, • tan J 0, • S,, 

 1^° This case, in which the given latitude l^ is greater 

 than the sought latitude l^^, is made known to us by the 

 given azimuth A^ being greater than the computed angle D^^. 

 And as we must have (see formulae 21) the sought azimuth 

 A^^ also greater than the angle D^^ it is evident' that by put- 

 ting ^ to represent the excess, we have — 



shewing that the formulse given in the "Account of the 

 Principal Triangulation of Great Britain and Ireland " (see 

 pages 247, 249, 676 of that work) are erroneous in every 

 case in which the given latitude is greater than the sought 

 latitude. 



(Case '2nd.) 

 Given ?^^, A^^, s ; to find to, l^, and A^. 

 To find 0^^, D^, (0, U, we have — 

 _ s 



K.,, • sm 1" 



tan i (D, + ») = "ZlZ.Z'i ■ "»' * ^" 



COS ^ (6 + ^//) 



or, g.^ ^, ^ sin I" ' sin A, 



sin D, 

 To find B„ l^, and A^, we have — 



S, = (1^2) • sin L'- sin 1 (I" + LO • (I" ~ L') 



l^ = 90° — (L' — S,) 

 r>, — A^ = sin T>, ' tan f ^,, • 8, 



