134 HYDROGRAPHICAL SURVEYING [chap. v. 



The necessary angles and true bearings having been obtained 

 at the different stations : 



(1) From astronomical positions of A and B calculate mer- 

 catorial bearing and distance A B [see (1) in Example I.]. 



(2) Assume A E= 10,000 units. 



(3) In A A E C, find E C. 



(4) In A E F C, find E F. 



(5) In A A F E, given A E, E F, and L F E A, find L « 

 A F E, E A F, and A F. 



(6) Knowing the observed angles C A E, D A E, D F E ; 



(7) .-. from (5) and (6) we have Z « C A F, D A F, D F A. 



(8) In A A D F, given Z « D A F, D F A, and A F, find 

 DF. 



(9) In A F B D, given Z « D F B, D B F, and D F, find F B. 



(10) In A A F B, given Z A F B, A F, and F B, find Z « 

 FAB, FBA. 



(11) From (7) and (10) given Z« C A F, F A B, we have 

 Z CAB. 



(12) Given the observed Z CBFand Z FBA [from (10)], 

 we have Z C B A. 



We have now sufficient data with which to plot on the 

 distance A B, as found in (1). 



If A and B lie in a meridional direction, a meridian distance 

 between them is unnecessary, and the distance A B will be 

 obtained from their observed diff. lat. and mercatorial bearing 

 found in the triangulation. This applies to all examples. 



Example III. — One, inaccessible object visible from both 

 astronomical positions, invisible from each other ; and an inter- 

 mediate station visible from them, and from which the inaccessible 

 object is also visible. 



With a single intermediate station it is obvious that the work 

 is much simplified, and the chances of error will be correspond- 

 ingly diminished. 



In Fig. 26, A and B are two astronomical positions at the 

 extremes of a survey, and invisible from each other. 



C is a conspicuous inaccessible sharp peak, visible from 

 A and B, and also from the intermediate station D, which is 

 also visible from A and B. 



