CHAP, v.] USE OF THE SHIP FOR TRIANGULATION 145 



Repeat the operation three or more times as a check, and 

 test each of the triangles A D E, B D E when the observers 

 return to the ship. True bearings of C are obtained from 

 A and B. 



Assume B C= 10,000 units. 



(1) In A BCD, find CD. 



(2) In A B C E, find C E, E B. 



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



(4) In A A C D, find C A. 



Compare values of C A as found in (3) and (4) as a check. 



(5) In A A E B, given E A, E B, A E B, find Z « B A E, 

 ABE, and A B. 



(6) Knowing true bearing of C from A, apply Z « C A E 

 and B A E, and obtain true bearing of B from A. 



(7) Knowing true bearing of C from B, apply Z ^ C B E and 

 ABE, and obtain true bearing of A from B. 



(8) The mean of (6) and (7) is mercatorial bearing of A B, 

 as found through E. 



(9) Apply convergencies to true bearings of C from A and B 

 respectively, and find the reversed true bearings. 



Z A C B = difference of these reversed true bearings. 



(10) In A ACB, given CA, CB, Z A C B, find Z« CAB, 

 C B A, and A B. 



(11) To the true bearing of C from A, apply Z CAB, and 

 obtain true bearing of B from A. 



(12) To the true bearing of C from B, apply Z C B A, and 

 obtain true bearing of A from B. 



(13) The mean of (11) and (12) is mercatorial bearing of A B, 

 as found through C. 



(14) Compare results of (8) and (13), and adopt the mean. 



(15) Compare the values of A B as found in (5) and (10). 



(16) Calculate mercatorial bearing and distance A B from the 

 observed astronomical positions. 



The mercatorial bearing thus found will almost certainly 

 differ from that found by triangulation in (14) ; but if the 

 angles have been carefully observed, the result by triangulation 

 should be preferred. Plotting on the line A B, using the angles 

 found in the calculation, the accuracy of the work will be 

 proved by the intersection of the points. This could not be 



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