136 HYDROGRAPHICAL SURVEYING L^hap. v. 



Let the observed angle B G P = A. 



Let the observed true bearing of B from W, Z B W n = K. 



Let the observed angle B W P = F. 



Let the difference of the reversed true bearings of B from O 



and G (convergence being applied to the direct 



bearings), Z GBO-B. 

 Let the difference of the reversed true bearings of B from 



O and . W (convergence being applied to the direct 



bearings), Z OBW = C. 

 Let the difference of the reversed true bearings of P from 



O and G (convergence being applied to the direct 



bearings), Z GPO = D. 

 Let the difference of the reversed true bearings of P from 



O and W (convergence being applied to the direct 



bearings), Z OPW = E. 

 Let the unknown angle B G == 

 Let the unknown angle B W = 



G = G ?/i . sec m G W =- W w . sec nW 



= a . sec <^ — G = 6 , sec H - 



(1) 



GO a . sec 4> — G a . cos H — 

 W O ~ 6 . sec H^ " 6 . cos ^^Qf' 

 GO sin D WO sin F 



OP sin <^- A OP sin 0+r 



GO sin D . sin 0+F 

 (2) .-. ^-^ = 



(3) 



WO sin E . sin <^-A 



G O sin B W _ sin C 



O B ~ sin <^ B sin 0* 



GO sin B . sin 

 W O ein C . sin ^ 



a . cos H — sin B . sin 



From (1) and (3) .-. 



6 . cos ^ — G sin C . sin 

 a . (cos H . cos + sin H . sin B) _ sin B . sin 



h . (cos (f) . cos G + sin </) . sin G) sin C . sin 9 



