114 



HYDROGRAPHICAL SURVEYING [chap. iv. 



Examples. 



(l) By Astronomical Ohservatioyi. 



Let A (by observation) 26° 57' 51-6" N. . . 

 Let B (by observation) 28° 02' 08-4" N. . . 



Maximum probable error of diff. lat. 



Mercatorial distance A B (by observation) 1° 25' 54" 

 Maximum probable error of diff. long. 



Mercatorial bearing and distance A B — - 50° 00 00 — 

 ^ S. W. 



±0 

 + 1 



±5 

 = 5 



6" 



0" 

 0" 



10000' 



(2) By Triangulation. 



(a) A B calculated from base measured near A= 99-88'. 

 A B calculated from base measured near B = 99-72'. 



Mean value of A B = 99-80'. 

 Probable error in A B ± 0-08'. 



Or suppose no check base has been measured : 

 (i.) Probable error in the measured base owing to irregu- 

 larities of ground, etc., is estimated at 1 foot per mile. 



(ii.) Mean probable error in length of any side is estimated 

 from the results obtained whilst working out the triangulation 

 to be 3-82 feet per mile. 

 Thus: 



(i.) + (ii.)= 1+3-8= 4-8 feet per mile. 

 4-8 X A B - 4-8 X 100 = 480 feet - 0-08'. 

 Or probable error in A B = ± 0-08'. 



With 0-08' distance, and bearing 50° — 



Probable error of A B expressed in terms of diff. lat. = ± 3- 1". 

 Probable error of A B expressed in terms of diff. long. == ± 4- 1". 



(6) The true bearing, as observed at or near A, when worked 

 through the triangulation and compared with the true bearing 

 observed at or near B, by means of a common side, is found 

 to differ 3' 00". 



The mean of these two true bearings is now adopted as the 



