42 



ANGULAR SURVEYING 



smallest fractional part of the main scale that can be read by 

 means of the vernier is called the least reading of the vernier. 

 If the least reading of the vernier is denoted by r, the smallest 

 subdivision of the main scale by s, and the vernier is divided 

 into n equal parts, then s 



n 



For example, if the smallest division of a level rod is .01 ft., 

 and the vernier is divided into 10 equal parts, then the least 

 w reading of the vernier is r = . 01 -=-10 = .001 ft. 



In order to give this reading, the total length 

 of the vernier must be (n l)s. In the exam- 

 ple just given the total length of the vernier 

 must be (10-1) X .01 = .09 ft. Such a rod and 

 vernier are illustrated in Fig. 3. 



To measure the length of a line, as Coo, 

 Fig. 3, with a scale having a vernier, place 

 the zero of the scale at the beginning of the 

 line, as at C, and slide the vernier, as MN, 

 up the scale until its zero coincides with the 

 end of the line. In the example under con- 

 sideration the position would be that of M'N'. 

 Then the subdivision of the scale immediately 

 preceding the end of the line will give the 

 reading of the scale, in this case .34 ft. To 

 this must be added the reading of the ver- 

 nier. This is determined by the number of 

 the division mark of the vernier that coin- 

 cides with a division mark of the scale. In 

 this case, this number is 8; the reading of the 

 FIG. 3 vernier is therefore 8X. 001 = .008. Hence, the 



length of Coo is .348 ft. 



Transit Verniers. Transit verniers are constructed on the 

 same principle as those used for measuring lines. If the 

 smallest division of a horizontal circle of a transit is $ = 30' 

 and the vernier is divided into 30 parts, the least reading of 

 the vernier will be 30' -7-30=1', and the vernier must cover 

 on the circle a length equal to iX(30-l) = 14 30'. 



Fig. 4 shows part of the horizontal circle of a transit AB 

 with the doublt verniers M N and MN'. The vernier MN is 



