line mE is then measured through the On; thus proving the triangle PBC, and determing the position of the straight fence DE, which position is further proved by offsets and a crossing at, and south of D, the crooked fences having been taken by offsets in the usual way: thus completing the survey with little more than one third of the lines required by the former method. The student can readily add the field-notes in the latter case. 5. Required the plans and contents of two straight-fenced fields, each having five sides, from the following field notes, ag given by old methods. NOTE. In the two preceding examples, nine lines are required in each case, by the circuitous methods there adopted. Each field, by the improved methods, here laid down, may be surveyed by five lines, or both fields by only one line more than are required by the methods given in the preceding field notes. Precisely the same system of lines may be adopted in the former case, as has been done in the Example 1. The latter case is left to the ingenuity of the student. PROBLEM VIII. WOODS, LAKES, AND SWAMPY GROUNDS. When woods, lakes, and swampy grounds are required to be surveyed, where lines cannot be measured upon them, a system of lines must be adopted for each particular case, so combined by triangulation as to prove their accuracy, among themselves, when laid down on paper. If the wood, or other inaccessible space, (as far as measuring is concerned) be either of, or very near, a triangular shape, the three sides of a triangle will compass it, which may be proved by a tie-line at one of its corners, if the wood or lake will admit one of sufficient length, but, if not, any two of the sides of the triangle may be prolonged for this purpose, offsets, or rather insets, being taken to the boundary of the wood or lake, in the usual way. m 1. Here the three sides of the triangle A B C compass a lake The or large pond, insets being taken therefrom to the margin of the water. accuracy of the work is proved by the tieline pq, or, if this line be thought too short, (as it appar ently is) the sides longed to m and n, till B m, Bn, each equal about one third of AB, and the tie-line mn, being measured, will establish the accuracy of the work, or prove it wrong, as the case may be. 2. The annexed figure shews the survey of a wood, which is C effected by the four main-lines Da AB, BC, CD, D A, the first line being prolonged to p, and stations being left at m, n, and for the tie-lines mn, pq. It scarcely need be added that when the lines A B, AD, B C, are laid down by the help of P the two tie-lines, the line CD will exactly fit in, if all the work has been accurately done. 3. Required the plan and area of a wood from the following field notes, two of the fences of which are straight. NOTE. As a general rule for surveying woods and lakes, the following may be given :-Measure as many lines round the boundary to be surveyed as will compass it, and tie all the angles, except the two last, as in the preceding examples; you will thus obtain a system of lines that will prove among themselves, as the last measured side will just reach from the last station to the first, if the work have been done with accuracy. But the shapes of woods, &c., are so various that it would not be adviseable, in every case, to adhere to this method: much must, therefore, be left to the skill of the surveyor. In the southern counties of England, where coppice wood is sold by the acre for fuel, it is very frequently required to survey a portion of a wood, (the coppice being cut down, and the large timber still standing); in such cases, the lines must be taken within the space to be surveyed, as the adjoining uncut coppice prevents their being taken outside. The lines must, therefore, be ranged among the growing timber, as well as they can; and the tie-lines taken through the most convenient openings left by the trees. Surveys of this kind, it may be proper to add, are best performed with the help of the Prismatic Compass, or the Box Sextant, which are sufficiently accurate for these surveys, which are always of samll extent. TO SURVEY A SMALL ESTATE, DIVIDED INTERNALLY BY A small estate, of a form nearly triangular, is divided into six fields by four straight fences, as shewn on the annexed plan. The survey is commenced at A, by measuring the line AD, taking the offsets, and leaving stations at the crossing of these fences at B and C. The line DE is now measured, also crossing two of the straight fences. From the OE the line E A is measured, leaving stations at the hedgecrossings F and G: thus completing the triangle ADE. Next, the line BG is measured, close to the straight fence B G, and crossing the straight fence a b. Lastly, the line FC is measured, again crossing the straight fences a b and co: a station being left at m, about a chain's distance from o, and one chain measured close by the fence oc to n, and from thence to Om: (the last operation being, in most cases, the most readily performed before the line passes the fence co) thus completing the survey. The position of the straight fence ab is proved to be correct by the crossing of three of the lines of the survey, viz., B G, FC, and DE; the crossings made by these three lines on a b, must be in a right line on the plan, otherwise there has been an error in the field notes. The straight fence oc has only two crossings by the surveying lines FC, DE, its position is, therefore, not duly proved to be correct without the tie-line mn, measured in the manner already stated. This expeditious method of proving the position of a straight fence, crossed by two chain lines (as the fence co), was never adopted till done so by the author, in the parish survey under the Tithe Commissioners, who, in their instructions to surveyors, directed the lengths of all such fences to be measured to establish the accu racy of their positions. Now the measurement of the length of such a straight fence as co, which is nearly perpendicular to the two chain lines that cross it, gives a very imperfect proof of the accuracy of its position, especially if it be a long one. In this latter case the fence co might be a full chain from its true position at one end, and its length, as shown by the plan. would be so near the measured length that the error would not be detected; whereas the tie line mn, shown on the plan, would detect the error at once, by its increased or diminished length. However, when two chain lines cross a straight fence obliquely, the length of the fence, from crossing to crossing, evidently gives a sufficient proof of the accuracy of its position; yet to measure a short tie line, at one of the crossings, is a shorter method of proof, in all cases where the length of the fence is considerable. The method of proof recommended by the Commissioners in question, ought, therefore, never to be adopted, except where one or both of the chain lines cross the straight fence obliquely and at a short distance. It seems hardly necessary to remark that the positions of the straight fences G B, C F are determined by the lines measured close to them. Thus the survey of six fields may be made, and its accuracy proved, by five lines, with the two short tie lines mn, no, which may be regarded as mere offsets. Besides, had the fences G B, C F been crooked, the same lines would have effected the survey by offsets thereon. Moreover, the survey of these six fields, all the internal fences being as shown in the plan, may be accurately effected by four lines, in the following manner. The triangle ADE remaining as the foundation of the survey, let a station, or rather direction point, p be entered in the field notes, in the direction of the straight fence a b, and another similar point at q, in the direction of the straight fence oc; leave also a proper station mark, or pole, at r; on arriving at s in E A, leave another station, in such a position, that a line from s to r will cross all the four straight fences. This last line will prove the fundamental triangle ADE and the positions of the four straight fences, at the same time, without measuring the lines by the fences GB, CF; which can have now three crossings by chain lines, and the other two fences a b, o c have each two crossings by chain lines, and each one direction point, viz: p and q; through which points these fences must respectively pass, after they have been drawn through their crossings on DE, and the other line from s to r, not shown on the plan. This method of determining the position of straight fences, though theoretically elegant, cannot always be easily |