The compass ring is graduated to half a degree but the readings can be well estimated to 15 minutes, which means that the error of reading should not exceed 7½ minutes. But due to magnetic changes and variation of declination etc., the readings can seldom be relied upon to less than 10 minutes, therefore, the permissible error per bearing should never exceed this amount. Thus the angular error of closure should not exceed 10√N, where N is the number of stations or sides of the traverse.
The angular error of 10 minutes corresponds to lateral deviation of 1 in 344.
Closing Error and Its Graphical Adjustment:
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While plotting a closed traverse, the starting and the ending points seldom coincide, and this discrepancy by which the ending point fails to meet with the starting one is called the closing error or error of closure. The error occurs due to wrong measurement of lengths and bearings of lines in the field and due to faulty plotting.
When the closing error exceeds the permissible limit, the fieldwork, should invariably by repeated.
But when the error is found to be within the permissible value, the traverse may be adjusted graphically by one of the following two methods:
First Method:
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This method is the graphical application of Bowditch’s rule.
In this method, the correction is applied to the lengths as well us to the bearings of the lines in proportion to their lengths Therefore, this method is also known as proportionate method. Here each station is shifted proportionately according to the length and direction of the closing error. This method is used when the angular and linear measurements are equally precise.
It is explained as follows:
For example, AB’C’D’E’A’ [fig. 5.28 (a)] is a traverse as plotted from the bearings and lengths of the lines, where AA’ is the amount of closing error which is to be adjusted.
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To adjust it, draw a line AA’ (Fig. 5.28 b) equal in length to the perimeter of the traverse to any convenient scale and set off along it the distances AB’, B’C’, C’D’, D’E’ and E’A’ equal to the lengths of the sides of the traverse. The scale need not be the same as that of the plan but is usually kept much smaller, At A’, draw a line A’ a parallel and equal to the closing error A’A. Join Aa and from B’, C’, D’ and E’ draw lines B’b, C’c, D’d and E’e parallel to A’ A meeting the line Aa at b, c, d and e respectively.
The intercepts B’b, C’c, D’d and E’e give distances through which the stations B’, C’, D’ and E’ are to be shifted. In this case, it will be noticed, that the stations will have to be shifted downwards. To do this, draw lines parallel to the closing error at each of the stations B’, C, D’, E’ and set off along them the respective intercepts on the proper side. Joining the points having shifted positions is obtained an adjusted traverse ABCDEA.
When only the magnitude of correction to be applied at each station is required, draw A’a perpendicular to A A’ and equal in length to the closing error [fig. 5.28 (c)]. Then the intercepts B’b, C’c, D’d and E’e represent the corrections at B’, C, D’ and E’ in magnitude only but not in direction.
Second Method:
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In this method, the correction is applied only to the lengths of the sides of the traverse without changing their bearings. This method is suitable when the angular measurements are more precise than the linear measurements.
It is explained as follows:
Let A’BC’D’E’A’ ‘Fig. 5 .29 be a traverse as plotted from the bearings and lengths of the lines, where A’A” is the amount of closing error which is to be adjusted. To do this , produce AA” to meet any side of the traverse. In the figure, Å, A’ produced meets the produced line D’E’ at O .From this point O, draw lines to all the angular points as shown. Bisect the length of the closing error at A. From A, themed-point of A’A” draw AB parallel to A’B’ to meet OB’ at B. Also from A, draw AE parallel to A”E’ to meet OE at E. Similarly, from B and C draw lines BC ad CD parallel to B’C” and CD’ to meet OC and OD’ at C and D respectively. Then ABCDIZA in an adjusted traverse.
