858 MR HENRY BRIGGS ON 



(l) Errors of Bearing. 



(a) In Simple Compass Traverses. — When some form of compass instrument, 

 such as the miner's dial or the prismatic compass, is used as the means of measuring 

 bearings, and the needle is read to obtain them, the magnetic bearing of any line is 

 ascertained independently of that of any other. A further simplification results from 

 the absence of centring error, since, in this simplest of all traversing methods, the 

 instrument is set, not at every station, but at alternate stations. It therefore follows 

 that if zhu be the average error made in obtaining the bearing of a line, the bearing of 

 all lines of the traverse can be considered as being affected alike by this average deviation 

 u. One exception to this statement, however, needs to be noted, and this is, that in a 

 traverse in which some of the lines are exceptionally short, the average error in bearing 

 of the very short lines is likely to be greater than that of ordinary sights. 



(b) In Theodolite Traverses. — In ordinary theodolite traverses, where the instrument 

 is set at every station, and in which angles are measured, the precision attained in the 

 bearing of any line is dependent on that of the preceding line ; hence, on the average, 

 the error in the bearing of the nth line is greater than that of any of the lines behind 

 it, being indeed, compounded of the errors in all the lines preceding it. 



Consider the case of a theodolite traverse of n lines, of which the first has a known 



bearing, fi v In practice /3 1 is determined in a variety of ways ; it may be a true bearing 



or a magnetic, or an arbitrary one. Only when the first line of the traverse is used as 



"false meridian" will the initial bearing — in this case zero — be affected by no error. 



in all other cases it will be influenced by an error of greater or lesser magnitude. 



Although sometimes difficult to assess, this initial error is always easy to apply, since 



it will swing the survey as a whole, about the first point as pivot, either to the one side 



or to the other. Hence, if we term x x the average amount by which the end-point of 



the traverse is swung by the initial error in /3 1; and x 2 the average error in position of 



the same point due to imperfections in the survey itself, then, no matter what may be 



the relative clinures of these components, their sum, It, can be obtained by relation (l), 



thus — 



R = ± sjxi + xi ..... (8) 



At present we are concerned with the second of these components ; its magnitude 

 is independent of that of the first ; hence in determining x 2 we may assume x 1 as non- 

 existent ; in other words, we may proceed with the investigation on the assumption 

 that /?] is without error, remembering that (8) permits of the initial error in bearing 

 being taken into account after x 2 has been evaluated. 



Let Lj, L 2 . . . . L n represent the lengths of the lines of the traverse under con- 

 sideration ; T lt T 2 . . . . T n _!, the traverse angles ; t v t 2 . . . . t n _ i} the average errors 

 by which these angles are respectively affected ; also let /8 1? fi 2 . . . . fi n be the bearings 

 of the lines, and fi\, fi'. 2 . . . . f n the average errors in those bearings, fi\ being taken 

 as zero. 



