then added to the final measurement to obtain thefigure that is to be divided by the total numberof repetitions. In this example,The mean angle then isEnter this in the column headed “Mean Angle.”The following computation shows that youshould use the same method to obtain the meanclosing angle.In the example shown above, the sum of themean angle (82°44´40´´) and the mean closing angle(277°15´20´´) equals 360°00´00´´. This reflectsperfect closure. In actual practice, perfect angleclosure would be unlikely.RUNNING A DISTANCE (LINE)It is often necessary to extend a straight linemarked by two points on the ground. One of themethods discussed below may be used dependingon whether or not there are obstacles in the lineahead, and, if so, whether the obstacles are smallor large.Double Centering or Double ReversingThis method is used to prolong or extend aline. Suppose you are extending line AB, shownin figure 13-16. You set up the transit at B,backsight on A, plunge the telescope to sightahead, and set the marker at C´. With thetelescope still inverted, you again sight back onA; but this time do it by rotating the telescopethrough 180°. You then replunge the telescopeand mark the point C´´. Mark the point C halfwaybetween C´ and C´´. This is the point on the lineFigure 13-17.-Bypassing a small obstacle by the angle off-set method.AB you need to extend. If the instrument is inperfect adjustment (which seldom happens),points C´ and C´´ will coincide with point C. Forfurther extension, the instrument is moved to Cand the procedure repeated to obtain D.Bypassing an Object by Angle OffsetThis method is applied when a tree or othersmall obstacle is in the line of sight between twopoints. The transit or theodolite is set up at pointB (fig. 13-17) as far from the obstacle aspractical. Point C is set off the line near theobstacle and where the line BC will clear theobstacle. At B, measure the deflection angle a.Move the instrument to C, and lay off thedeflection angle 2a. Measure the distance BC, andlay off the distance CD equal to BC. Move theinstrument to D, and lay off the deflectionangle a. Mark the point E. Then, line DE is theprolongation of the line AB.Bypassing an Object byPerpendicular OffsetThis method is used when a large obstruction,such as a building, is in the line of sight betweentwo points. The solution establishes a line parallelto the original line at a distance clear from theobstacle, as shown in figure 13-18. The instrumentFigure 13-18.-Bypassing a large obstacledicular offset method.13-15by the perpen-Figure 13-16.-Double centering.
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