148 HYDROGRAPHICAL SURVEYING [chap. v. 



(19) The mean of (17) and (18) gives mercatorial bearing of 

 A B as found through C. 



(20) Apply L D A B to the true bearing of D from A, and 

 obtain the true bearing of B from A. 



(21) Apply Z D B A to the true bearing of D from B, and 

 obtain the true bearing of A from B. 



(22) The mean of (20) and (21) gives mercatorial bearing of 

 A B as found through D. 



(23) Compare the result of (19) and (22), and take the mean. 

 From the astronomical positions of A and B calculate merca- 

 torial bearing and distance A B. 



The mercatorial bearing thus found will almost certainly 

 differ from that found by triangulation in (23) ; but if the angles 

 have been carefully observed and the inaccessible objects C, D 

 are favourably situated, both with respect to each other and 

 to A and B, the result by triangulation should be preferred, and 

 plotting on the line A B, using the angles found in the calcula- 

 tion, the accuracy of the work will be proved by the intersection 

 of the points. Intermediate points may be shot in from the 

 ship's positions. 



The observed astronomical positions should be adjusted to 

 the results by triangulation so far as bearing is concerned. 

 The necessity for so doing in this and in the preceding 

 example is greatest when A and B are nearly north and south of 

 each other. It diminishes as their bearing approaches an east 

 and west direction, on account of the probabiUty of their 

 difference of latitude being less liable to error than their 

 meridian distance. When nearly north and south of each 

 other, it is unnecessary to observe the meridian distance. 



Example XIII. — To find the proper position in which to place 

 the ship in order to obtain the most favourable geometrical condi- 

 tions for fixing a jjoint on shore from two other known stations on 

 the same shore to the right and left, or on each side of it, as the 

 case may be. 



Reference may advantageously be made to Shortland's 

 "Nautical Surveying," p. 188, on which will be found the 

 proof of the following proposition : 



In Fig. 36 A and B are two fixed stations on the coast. It 



