868 MR HENRY BRIGGS ON 



greater part of them will run from one triangulation station to the next. Hence — to 

 use a criterion of negligibility already employed (p. 856) — if the distance between two 

 triangulation stations is known with an average error equal to or less than one-third of 

 that accruing in a traverse connecting them, the closing error of the traverse can be 

 assessed without there being need to take the triangulation error into account. For 

 example, if the maximum accuracy in one of these traverses is likely to be 1 in 4000, a 

 suitable accuracy for a triangulation line would be 1 in 12,000. Should it then be 

 found, on completion of the triangulation, that the two values for the check-base agree 

 to within one-twelve- thousandth of its length, it could safely be concluded that the 

 required degree of precision has been attained. 



When the actual fractional error in a check-base has been determined it is probable 

 that the fractional error in all preceding lines will be less than that amowit. 



From considerations such as those just discussed a surveyor decides on the degree of 

 accuracy he requires in the lengths of the triangulation lines, and the verification base 

 allows him to tell if that precision has been reached. 



One of the most important and most difficult questions in triangulation arises before 

 the survey commences and after it has been decided what precision is required, and is, 

 How carefully must the base and angles be measured in order that there may be a fair 

 chance of this degree of accuracy being achieved ? 



A very satisfactory answer to this question can be obtained by the aid of relation 

 (27), which, when the triangles are approximately equilateral, reduces to the following 

 form — 



?-V{^C 4 )'} <*> 



By substituting what we may roughly term the "accuracy ratio" (1 in 12,000, 1 in 

 10,000, or whatever it may be) for — in this equation, suitable values for v and — may 



be ascertained. Theoretically the most equitable arrangement is for — to equal v I — ; 



but this condition cannot always be satisfied. Circumstances may be such that it is 



c c 



easier to attain a low value of v than a low value of ~> in which case — may profitably 



be allowed to assume a higher, and v a correspondingly lower, value than those the 

 strictly equitable arrangement would give ; — for it must be borne in mind that the 

 necessary degree of precision is best secured when the expenditure of labour is a minimum. 

 In this connection it is possible that the following table, calculated from (30) will be 

 useful as a guide. The table is computed on the assumption that an accuracy of 1 in 

 12,000 is desired in the check-base — a sufficiently high degree of precision for most 



minor triangulations — and it gives suitable values of v and — for different numbers of 



roughly equilateral triangles : — 



