provinces must be obtained from the local authorities and entered on the final plan. In maps or plans on a small scale it is usual to represent roads and railways by double lines and thick lines of any convenient exaggerated breadth, which bears some definite ratio to the actual breadths shown in the original plotting of the details. The principles of theodolite triangulation are illustrated in the reduced plan, Plate V., where they are applied to a district about four miles long and two miles wide, or nearly nine square miles; the base line is about a mile in length. No secondary set of triangles was used, traversing along all the roads and closing on the main stations having been carried out as a preferable. alternative in the secondary part of the survey; the smaller detail was put in with offsets and compass bearings. Traverse Surveys.-The method of traversing has already been explained in Section 1 of this chapter, and its application in surveying of other sorts in the succeeding sections. Short portions of traverse work may be carried out with the theodolite wherever the filling in of detail with precision happens to be necessary in parts of triangulation surveys; but when the greater part of any survey is conducted on the principle of traversing rather than of triangulation, its object of operation is confined to a long strip of country of comparatively small breadth, seldom exceeding a quarter of a mile. Surveys of this description are rarely made for other purposes than those of engineering, and more especially the intended location of long lines of communication, roads, railways, or canals, or of conduits and pipes of water supply or drainage; they may hence be generally treated as engineering surveys, conducted within certain limits of deviation suitable to the proposed works. The main lines of traverse falling generally within these fixed limits of deviation, the traverse stations are fixed either within or close to these limits, as the survey work proceeds, in accordance with general convenience, and the visibility of neighbouring stations, and lateral objects of observation; the number of stations in a traverse should, apart from these considerations, be as few as possible, as this diminishes the number of angular observations, and hence also the amount of error. In large traverse surveys of this description there is seldom any opportunity for closing the polygon of main traverse by returning to its starting point, without necessitating a double amount of work, a serious consideration in extended surveys; and sometimes, also, there is no opportunity of closing on points of known position used in former surveys; hence the need of verifying the work fully by sufficient angular observation on lateral objects, spires, towers, buildings, etc. At each traverse station both the inward and the outward angle are severally observed and recorded, and their sum 360° affords a check against inaccuracy of reading. The true bearing of the starting line of traverse is generally obtained with the help of the compass, although it is better to fix a true meridian and observe from it throughout the survey; the bearings of all the remaining lines of traverse will then not require successive computation. The main traverse may either be plotted by assuming a direction for any starting line, scaling distances, and protracting the inward angles, or by scaling distances and protracting the bearings. Both of these methods, however, being liable to undiscoverable errors or mistakes, the mode of reducing the whole to a single meridian and plotting them by rectangular co-ordinates is to be recommended for accuracy and certainty. The accompanying form for the reduction of a short piece of theodolite-traverse to a series of rectangular co ordinates may be used as an example. The reduction is thus computed. Starting with two sets of data, the distances and the checked inward angles, and one given bearing. Ist. To compute the theodolite limb - bearings throughout, Let P be the given bearing from any preceding station, a be the inward angle at the actual station, F the required limb-bearing to the following station, Then FP+a±180°; using the positive sign when P+a 180°, and the negative sign when P+a7180°. 2nd. To obtain the reduced bearings, or angles formed with the meridian either from North or South. When the theodolite limb-bearing F lies between o° and 90°, the corresponding reduced bearing is F to the NE.; when between 90° and 180°, it is 180°-F to the SE.; when between 180° and 270°, it is F-180° to the SW.; and when between 270° and 360°, it is 360°-F to the NW. 3rd. To obtain the successive co-ordinates for each point from the preceding point. The abscissa along the meridian = distance x cosin reduced bearing. |