854 MR HENRY BRIGGS ON 



average sighting error over an exceptionally short line, say one 15 feet in length, is 

 greater than for one of average length, say 200 feet ; yet, on the other hand, there 

 would not seem to be any sensible difference in accuracy of sighting as between 

 lines, say, 200 and 400 feet long. Moreover, atmospheric unsteadiness and haze, 

 which interfere to a greater extent with long lines, tend to nullify the increase 

 in precision resulting from the finer definition of an object sighted at the ex- 

 tremity of a long draft, and will indeed outweigh it under certain atmospheric 

 conditions. It would therefore be incorrect to assume that sighting errors shrink 

 as the lines increase in length, and we shall approximate closely to the truth if we 

 take this class of error as having a constant average value for all lines except the 

 very shortest. 



Let the average value of the combined errors of sighting, reading, etc., be 

 zhv radians. 



Average Error in Traverse Angles. 



Leaving exceptionally short lines out of consideration, the error, t, in a traverse 

 angle, T, is thus compounded of a constant component, v, and a variable component, 

 namely the error due to imperfect centring. 



Combining these, we have : 



-VWSW-'-Sr 1 )} ■••■(») 



The values of v and r vary greatly with different observers and instruments. 

 To a surveyor it is not of the first importance to obtain results in which general 

 average values of these quantities are assumed ; in order to make fullest use of 

 equation (7) — or, indeed, of any relation in this paper, — it is necessary that he 

 should determine, as nearly as possible, his own average errors using his own 

 instruments. 



Experience in triangulation will be the best guide as to the magnitude of the sighting- 

 and-reading error, i>, — for a triangulation line (as will shortly be shown) is almost always 

 so long that the angular effect of a small centring displacement is negligible ; hence, in 

 measuring a triangulation angle, the second term on the right-hand side of (7) disappears, 

 leaving v as the error in angle. 



If, after considerable experience in minor triangulation, using, say, a reliable 5- 

 inch transit theodolite, and employing three reiterations on each " face " in measuring 

 the angles, it were found that the average error of summation of the three angles of a 

 triangle was 12 seconds, the average error in each angle could be taken as 12 4- v3, or 

 7 seconds. Now, in traversing it is not usual, or necessary, to employ the " reitera- 

 tion " method of measuring angles, a traverse angle being more generally determined 

 by averaging a single face-left and a single face-right observation ; therefore, having 

 assumed three reiterations were used in triangulation, the value of v for a traverse 



