CHAP. IV.] RESULTS OBTAINED ASTRONOMICALLY 115 

 " mean true bearing " of this common side ; using this, the 

 triangulation is reworked, giving 



N. , E. 



Mercatorial bearing A B= 50° 06' 00" — 



^ S. W. 



Probable error = half the difference of the bearings = 1' 30". 



feet subtended x 34 



r 30" = 



100 



.*. Feet subtended = 265 feet. 



With distance 265, and bearing 50°, from Traverse table 

 diff. lat. = 1-7" and diff. long. = 2-3", which is the probable error 

 of mercatorial bearing A B expressed in terms of diff. lat. and 

 diff. long. 



Whence, from (a) and (b), maximum probable error in the 

 triangulation, due to errors of both distance and bearing, ex- 

 pressed in terms of diff. lat. and diff. long. 



= Diff. lat. (3-1" + 1-7")= ±4-8". 

 and Diff. long. (4-1" + 2-3") = ± 6-4". 



A B (from astronomical observation) = N. 50° 00' 00" E. 100-00'. 

 A B (from triangulation) =N.,50 06 00 E. 99-80. 



Difference = 6' 00" 0-20'. 



B AB' = 6'0", BC = 0-20'. 



B' C X 34 



6'0"- . 



100 



Whence — 



B'C = 1,059 feet, BC =1,212 feet. 



CBB' = 41°, BB' = 1, 610 feet. 



8—2 



