AN INVESTIGATION INTO THE EFFECTS OF ERRORS IN SURVEYING. 869 



Number of Triangles 



Average Error in 



Average Error 



Suggested Mode of 



in the Scheme. 



Angle in Sees. 



in Base. 



Measuring Angles. 



n. 



v. 



c 1 -^-c. 





1 



12 



1 : 14,500 



Single F.L. and F.R. 



observation. 



3 



8-5 



1:17,000 



2 reiterations on each 

 face. 



5 * 

 5 1 



8-5 



1 : 28,000 



Ditto. 



or 7 



1 : 18,000 



3 reiterations on each 









face. 



7 



7 



1 : 25,500 



Ditto. 



9 



6 



1 : 23,500 



4 reiterations. 



The mode of measuring the angles entered in the last column refers to the use of a 

 reliable modern 5 -inch transit theodolite, with two verniers to the horizontal limb 

 each reading to 20" of arc. Dogmatism would be very out of place in dealing with the 

 mode of measurement best to employ to attain a certain average error in angle, 

 surveyor's methods and instruments differing as they do ; the methods named in column 

 4 of the table merely express the writer's individual experience with instruments of the 

 above-named kind. 



It could be urged that this process of determining suitable values for v and — is 



faulty in one important respect, namely, that if the values stated in the table were used 

 they would only ensure that the average error in the check-base would be 1 in 12,000, 

 and not that the actual error would be less than that ratio. In other words, it would 

 seem as though we had only secured roughly an even chance * of the actual error being 

 below 1 in 12,000. In answer to this very logical objection, attention is called to the 



fact that the values for - in the third column have purposely been kept considerably 



below those which will actually be obtained if the base is over 500 feet long, and if it 

 is measured with a standardised steel tape by an approved method. While few will 

 be willing to go so far as one writer on surveying, who states that the difference between 

 successive measurements of a base should not exceed 1--- 160,000 of the length, it is 

 pretty widely admitted that, when the temperature correction is applied, the standard 

 tension given, and the slope determined, an accuracy of 1 in 50,000 can be secured.t 



To show that the latter ratio is by no means excessive, and also to illustrate the 

 method of ascertaining the accuracy of a base measurement, the following example is 

 given. Attention is called to the fact that the discrepancies between the readings are, 

 if anything, greater than those one usually expects in practice : — 



Example. — After applying the necessary corrections, the results of six measurements 

 of the length of a base were obtained as : 1014-52, 1014*59, 1014-63, 1014*50, 1014-60, 



* More exactly, a chance of about 9 to 7, owing to the average error being equal to T18 of the probable error, 

 t Compare with J. B. Johnson's Theory and Practice of Surveying (Wiley, New York). 



