874 MR HENRY BRIGGS ON 



In this connection lies the chief utility of this portion of the investigation, for it 

 provides a criterion on the accuracy of distance- transmission when the check-base 

 ceases to afford a safe measure of it. 



Section VI. Summary of Results. 



The conclusions reached in the foregoing portions of the paper are here collected in 

 an abridged form under two heads, (A) and (B). Under the first of these heads are 

 placed those results which may be considered as already recognised by surveyors, and 

 under the second are given those which the writer believes to be new. The numbers in 

 brackets call attention to the formulae deduced in the previous sections, from which the 

 various conclusions are derived : — 



(^4) (a) Displacements in centre have a greater influence on short than on long lines ; 

 hence the necessity for closer centring on short lines. (See (7) and the curves, fig. 3, 

 which allow this question to be studied fully.) 



(b) Centring errors in triangulation are generally negligible.* [(7) and p. 857.] 



(c) In compass traversing (loose-needle work) short lines are advisable [(15) and 

 (19)], and in theodolite traversing, long ones [(16) and (20)]. The fact that a superior 

 accuracy may be attainable by a compass instrument than by a theodolite when the 

 traverse lines are very short is admitted by some.t A proof of this is given (p. 861), and 

 it is shown that the length of line for which the accuracy becomes equal for the two 

 kinds of instrument is capable of being roughly calculated. 



(d) The best shape of triangle for triangulation purposes is the equilateral. It is 

 shown [(25) and curves, fig. 5] that theoretically the best shape is an isosceles triangle 

 having an angle of 67° 30' at the apex ; fig. 5 indicates, however, that in this respect 

 there is no appreciable difference between an equilateral triangle and one of this 

 theoretically best shape, and for other reasons stated (p. 865) it is concluded that the 

 equilateral may be considered the most suitable form for practical purposes. 



(e) No angle in a triangulation triangle should be more than 120° or less than 30°. 

 This rule, given in most text-books and forming an article of faith for almost all sur- 

 veyors, is shown to be of value only under certain conditions. It is, however, always on 

 the safe side, and in that respect may be taken as demonstrated. The question is dealt 

 with more fully below. 



(/') The accuracy of a triangulation may be tested by a comparison of the measured 

 and calculated length of the check-base. Such a comparison is usually viewed as the 

 most rigorous test that can be applied on the accuracy of a survey. It is generally 

 assumed that if the difference between the two values for the length of the check-base is, 

 say, - ., ^ () t of that distance, the accuracy of the survey as a whole is expressible by that 



* See Middleton and Chadwick's Treatise on Surveying, 1904, Part I., p. 193, for instance. 



t For example, see " Notes on Railway Surveying," by C. J. Albrecht, Mm, Proc. I.C.E., cliv. p. 262, where a com- 

 pass instrument is advised for running trial lines in country overgrown by forest, or in broken ground. 



