850 MR HENRY BRIGGS ON 



The paper is divided into six sections, thus : — 

 Section I. The Sum of Vector Errors ; 

 Section II The Average Error due to Imperfect Centring ; 



Section III. The Relative Effects of Errors in Centring and those of Sighting and 

 Reading ; 



Section IV. The Propagation of Errors in Traversing ; 



Section V. The Propagation of Errors in Minor Triangulation ; and 



Section VI. A Summary of Results. 



t 



Notation. 

 The following notation is employed, all errors having the plus-or-minus sign : — 



«,, x 2 . Vector errors. 



It. The sum of two or more vector errors. 



v. The average error, due to sighting and reading, in an angle measured by the 



theodolite ; expressed in radians, unless otherwise stated. 

 n. The average error in a bearing taken with a compass-instrument • expressed in 



radians, unless otherwise stated. 

 r. The displacement in centre due to the imperfect setting of a theodolite over a 



station ; expressed in feet, unless otherwise stated. 

 Traverse angles. 



Average errors affecting traverse angles. 

 The angle which is actually measured (in place of T) when the theodolite is 



displaced in centre by an amount r. 

 The bearings of traverse lines. 



The average errors in the bearings of traverse lines. 

 The lengths of traverse lines, in feet. 

 The average errors in the lengths of traverse lines. 

 The total length of a traverse. 

 A coefficient, equal to I -=- JL. 



Values of k for the chain and steel-band respectively. 

 Triangulation angles. 

 The lengths of the sides of triangles, being respectively opposite A, B, C. . . . 



The base of the scheme is the line c. 

 Average errors in the sides a, b, c, . . . . respectively. 



Average fractional errors in the triangulation lines. 



A check-base of a triangulation scheme. 



The calculated and measured lengths of a check-base respectively. 



The average error in z x and z B respectively. 



The average value of the difference of z A and z B . 



The number of triangles in a triangulation scheme. 



Triangulation stations. 



The distance of a triangulation station, A\ from station 1, the origin of the survey. 



Section J. The Sum of Vector Errors. 



Theorem. — The average error in the position of a point influenced by two or more 

 vector errors is equal to the square root of the sum of the squares of the average 

 magnitudes of the vector errors, and is independent of their relative clinures. 



T, T v T 2 . . 



■ ■ T n . 



1, Tj, < 2 . . . . 



t n . 



S. 





Pv &> P& ■ ■ 



■ ■ &• 



P v P 9 F* ■ 



• • • P'„. 



L, L v L 2 , L 3 



. . . . L 



h n» 2> 3 - • 



■ ■ In- 



w. 





h: 





A-j and fc r 





A,B,C,... 





a, b, c, . . . , 





a v b v c v . . 





a' b ' c' ' ' 





z. 





»Ai 2 B- 





2j, Z 2 - 





»8> 





n. 





1, 2, 3 ... . 



N. 



z». 





