244 Mr J. Sang on a Systematic Method of 



miter remaining the same, or when the figure becomes a circle. 

 From these reasons the surveyor has unlimited scope for adapt- 

 ing his lines to the offsets. And, indeed, to this object is his 

 chief attention to be directed, as he never requires to measure 

 lines on which offsets are not to be raised. There are, how- 

 ever, a few easily obtained circumstances desirable in the ar- 

 rangement of the lines. I shall point them out, and the mode 

 of ordering the field operations when it differs from the usual 

 4 practice. 



The most convenient zero for the bearings, at least in a large 

 survey, is the north line. If the theodolite be placed at the 

 commencement of a surveying-line, so that when the telescope 

 points north the vernier indicates zero, the indication of the 

 vernier, when the telescope points along the surveying line will 

 give its bearing; and when the theodolite is removed to the other 

 end of the surveying line, and so placed that the vernier indi- 

 cates when the telescope is again directed along the line, the 

 former bearing plus or minus 180, it will be situated, with re- 

 gard to the north, as it was at first, or the telescope will again 

 point north when the vernier indicates zero. When the theo- 

 dolite is in this second position it is said to be set back to the 

 line, and it is ready to measure any other bearing as it did the 

 first. If we measure in this manner a series of bearings until 

 we arrive at a point whose bearing is already measured from 

 the first station, we will be able to examine the accuracy of the 

 work, for the counter-bearing should be equal to the other plus 

 or minus 180. When a bearing is thus twice measured, it is 

 said to be a closing bearing. An error in the measurement of 

 the angles is thus known, at each close, from the simple inspec- 

 tion of the field-book. Since there is some difficulty in placing 

 the theodolite exactly over the hole made by the signal stave, 

 there may be a small error in the second measured bearing, in- 

 dependent of the perfection of the angular instrument. On 

 the third bearing there is a risk of greater error, and so on. 

 This circumstance demands that none of the surveying-lines 

 be very short, and that there be as many closing bearings as 

 possible ; or, what is the same thing, that from each station the 

 bearings of all the other stations within sight be observed. This 

 risk of error is not greater than that from want of centering in 



