112 HYDROGRAPHICAL SURVEYING [ciiAr. iv. 



If no clieck base has been measured, we can still form a good 

 idea of the probable error of — 



(1) The measured base in " feet per mile." 



(2) The sides of the various triangles, if, as should be the 

 case in a properly arranged triangulation, we can occasionally 

 calculate the individual side of a triangle through two or more 

 different lots of triangles, getting two or more results from 

 the same side, and adopting the mean, and so obtaining a 

 probable error in terms of " feet per mile." 



Then (1) + (2) =" probable error" of the distance A B ex- 

 pressed in "feet per mile"; and :(l) + (2); x length of A B in 

 miles = probable error of A B in feet. 



Knowdng the bearing of A B, find the diff. lat. and diff. 

 long, corresponding to this probable error, in seconds, as 

 before. 



This is the " probable error " of the length of A B (by 

 triangulation) expressed in terms of diff. lat. and. diff. long. 



(b) Error in bearing can be estimated if true bearings have 

 been observed at or near both A and B. 



Let the true bearing observed at or near A, say, be worked 

 through the triangulation until it can be compared with the 

 true bearing observed at or near B by means of a common 

 side. 



The mean of the two will be the " Mean True Bearing " of 

 that particular side, and should be adopted. 



From this mean true bearing calculate the mercatorial 

 bearing of A B (by triangulation). 



Half the difference of the aforesaid true bearings will be the 

 probable error of the mercatorial bearing of A B (by triangula- 

 tion) expressed in arc. 



Calculate the number of feet subtended by this angle at the 



distance A B in a direction at right angles to A B by the 



formula — 



... , feet subtended x 34 



Angle m seconds = , , 



distance in miles 



and thence the corresponding diff. lat. and diff. long, in 

 seconds. 



The " maximum probable error " in the triangulation wiU 

 thus be the probable error due to distance as found in (a) + the 



