CITY SURVEYING 137 



Measure of Precision. It is customary to express precision 

 in terms of the probable error: when it is said that a line has 

 been measured with a precision of ^fa, it is usually meant that 

 the probable error derived from the series of measurements 

 is not numerically greater than -^faf of the determined length 

 of the line. Thus, in the preceding example the precision was 

 .0031 -r- 501.064 = TBiWr. 



Precision Required. In important cities, a precision of 1 in 

 50,000 should be obtained in land-surveying measurements; 

 that is, the mean of two measurements of a given line should 

 have a probable error of not more than Sft ft 00 of the length of the 

 line. This will generally be accomplished if the two measure- 

 ments differ by not more than 50 3 00 , or, say, ygthnr' f the length 

 of the line. This result is not very difficult to secure if the 

 proper methods and instruments are used. In villages and 

 small towns, a precision of T fc\ nr is ordinarily sufficient, but it is 

 so easy to secure a better precision than this that no two meas- 

 urements of the same line should differ by more than T^,, of 

 its length, giving a precision of the mean of the two measure- 

 ments of about ssfonf. 



Precision in Angular Measurements. In order that the 

 direction of a line may be determined so that a distant end 

 shall not depart from its true position by more than ^fonr 

 of the length of the line, the angle on which the direction 

 depends must be measured to about the nearest 4 sec. A 

 transit reading to 30 sec. will permit an approximation .to this 

 result if the mean of three readings of the angle is used. An 

 instrument reading to 20 sec. will ordinarily, by a triple meas- 

 urement, permit a little closer result than the required one, 

 and one reading to 10 sec. may give the requisite precision 

 with a single measurement, though at least two measurements 

 should be made for a check on the accuracy of the work. 



Ordinarily, the position of a point can be more precisely 

 determined by linear than by angular measurement, and, 

 therefore, the former method of determination is in general 

 to be preferred. 



Adjustment of Measured Angles of a Triangle. It is fre- 

 quently necessary, in precise plane surveying, as in locating 

 bridge piers, making topographical surveys of cities, etc., to 



