On Practical Geodesy. 



tan (45° - j l^) ^ cos |( A3, + A,3 + 0^3 J 

 tan (45° - J l^) cos i (A3, + A,3 -CO3 J 



cosi(A,, + A54— ^45) 



33 



(-b) 



tan (45° — 1 ^,,_,) _ cos 1 ( 

 tan (45° — | 



cos j- ( 



In) 



cos J ( 



) COS J ( 



) 



And therefore we have — 



L 1_^ =r the product of the dexters of these equations, 



tan(4o°— 1Z„) ^ 2 ^ ' 



an equation from which we can at once express the latitude 

 of the 71^^ station in terms of the latitude of the 1'* station 

 and the azimuths and differences of longitudes. 



Should the to-^ station be coincident with the 1'* station, 

 we must have the dexter of (129) equal to unity. This fact 

 will be found to be of importance in case any even number 

 of stations form the vertices of a closed geodesic polygon. 

 For instance, if there be four mutually visible stations such 

 as B, C, D, E— 



c c„ *c 



B 



E B 



E B 



then numbering the stations in the orders indicated in the 

 above diagrams, we have — 



cos|(A^,+A,,+<^i,) . cosi(A3, + A,3+a>3 4) 

 cos i(Ai 2+^3^—0)^ J cos^(A3,+A,3— CU3J 



(A.3+A 



32+^23) . cosj (A,^+A^, + (u ,J 

 cos 4 (A,^+A^,— (u^J 



cos 4(^2 3+^3 2— ^23) 

 corresponding to the stations taken in each of the three 

 indicated orders. And in the case of any such even number 

 n of stations (the first and last of which are coincident) it is 

 obvious that if all the azimuths be known, and that all the 

 differences of longitude with the exception of any two 

 which are consecutive be known, then we can easily (by 

 solving a quadratic equation) express the tangent of either 

 of these two differences of longitude in terms of the known 

 azimuths and differences of longitude. 



