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measured are of considerable length, as from 30 to 40 chains, it will be neces sary to take the tie-lines at least 10 chains from the angles, across which they are measured; for a small error, in laying down the plan with short tie-lines, will cause the main lines to deviate considerably from their true position when prolonged. However, it sometimes happens that long tie-lines cannot be obtained in consequence of obstructions. In such cases the tie-line must be carefully measured to even one-fourth of a link; the distance of each tie-line from its angle and the tie-line itself must then be all multiplied by 4, thus throwing fractions out of the question, and with the three lines, thus increased, the triangle determining the position of an angle of the trapezium, may be accurately constructed. The proof-line and its distances from its angle must be similarly treated, that the accuracy of the work may be fully established.
2. Required the plan and area of a straight-sided field from the following dimensions.
When the figure has been laid down, the diagonal AC will be found = 1962, and the perpendiculars thereon from B and D respectively = 632 and 514 links. Whence the area is 11a. Or. 5 p.
3. Draw the plans, and find the contents of two enclosures, from the following field-notes, both by calculation from the offsets and by casting.
NOTE. In each of the two following examples, it will be seen that there are two straight sides, and two that require offsets: also, in the former example, one of the crooked sides is crossed by the chain-line, thus producing insets, the content corresponding to which must be subtracted, as in former cases.
FIELDS HAVING MORE THAN FOUR SIDES.
Various methods will suggest themselves to the surveyor for taking lines to lay down a field that requires more than four main lines to take its boundary. The method of dividing such
fields into trapeziums and triangles is, in most cases, circuitous, and displays little skill on the part of the surveyor, especially where all the sides are crooked, and where a plan is required. A few methods of surveying fields of this kind will, therefore, be presented to direct the student; although their variety of shape is so endless, that no general rule can be given for laying out lines on the ground, that shall give an incontestably accurate plan. To tie every angle in succession, though true in principle, is by no means a safe method, especially where there are a great number of angles to be tied, as an error in one of the tie-lines will derange the whole of the work, without affording the means of detecting where the error lies.
NOTE. The following examples of surveys of this kind occurred in part of the author's extensive practice, as a surveyor of parishes, under the TitheCommissions. The student is recommended to sketch the following specimens on a large scale, and find their contents by the usual methods.
1. Here a field of five sides is surveyed by the same number of lines, viz. AB, BC, CD, Dm, and An, the last two intersecting in E. These lines evidently constitute a decisive proof among themselves, and all of them are available in taking the boundary.
In surveying this field (poles or natural marks being supposed to be fixed at A, B, C, D, and E) commence close to the river's edge, in the line AB prolonged backwards, enter the offsets and the station A in the field-book. On arriving at Om, in the direction ED, enter its distance, and so on to B, measuring the line to the fence; from B proceed to C, in like manner, measuring beyond the station to the fence. The place of then is to be noted, on arriving in the direction EA, while measuring CD. Dm is next measured, the place of the OE being noted. Lastly, go from m to E, and measure An, entering the place of the OE a second time, all the offsets being supposed to be taken during the operation.
Construction of the plan. Select the distances Am, AE, and Em from the field-book, and with them construct the triangle Am E, prolong the sides to their entire lengths, up to the boundaries, and fix the places of the stations B, n, and D.
Now, if the measured length of Dn just fit between D and n, the work is right with respect to the triangles A Em, EDn. Lastly, prolong Dn to the OC, and, if the distance from thence to the B be the same as shewn by the field-book, the whole of the work is right. But, if the distance Dn do not agree, the work must be examined from the beginning; if only the distance BC fail, then only that distance and the portions m B, Cn need be examined.
NOTE. It may here be proper to add that, if a straight fence had passed at or near the stations m and n, excluding the portion of the field towards B and C, these stations would have determined the position of that fence, thus completing the survey of a five-sided field with only the four lines Am, mD, Dn, n A, which may be measured consecutively.
2. The annexed figure Am DnBCE is a seven-sided field, or rather resolveable into a seven-sided field for the purposes of
surveying, one of the sides CE is straight, and the fence AmDnB too much bent to be taken by one line, crossing and recrossing it, with offsets taken to the right and left. The lines here required are only five, viz. AB, BC, CD, DE, and EA, which may be mea
sured consecutively, the stations m and n in AB, being carefully noted in the field-book, give at once the means of laying down the plan, and proving its accuracy. The student will at
once perceive that the triangle mn D should be first laid down, and its sides Dm, Dn, prolonged to the stations C and E, from whence the lines CE, EA, must respectively reach the points B and C to confirm the accuracy of the work. This done, the offsets on the several lines may be laid off, through which the bent fences are to be drawn, the side, CE, being straight, is determined by joining the stations C and E, which are assumed to be therein, or, what means the same thing, by the edge of its ditch or drain.
NOTE. It ought here to be remarked, that by the ordinary method of surveying, this field would require nine lines to effect its survey, viz., for the trapezium ABCE, its four sides and two diagonals or tie-lines, thus making six lines; and for the triangle Dmn, at least three other lines, (its tie-line included) thus making in all nine lines, or nearly twice the number required by the method here given.
3. The following figure comprises two fields, by the side of a river; each field, for the purposes of surveying, may be con
sidered a five-sided field.
The five lines AB, BC, Cm, nE, and EA, are found amply sufficient to accomplish an accurate
survey, in consequence of the three fences, terminating at the river being straight, their positions are determined by the intersections of the surveying lines, the middle fence by three intersections, and the two end fences by two intersections and one offset each, thus proving the accuracy of their positions. The two main triangles of the survey, viz. An E, m BC, mutually prove one another by the intersection at the station D.
It will be unnecessary to explain the method of laying down the figure, as that will be obvious from what has been done before. It may, however, be proper to remind the student that the largest triangles ought to be laid down first, and the accuracy of the plan will be shewn by the agreement of the OD with the proper intersection of the lines Cm, En.
NOTE. By the common place method, used by the generality of surveyors, the two fields, in the last example, are made to require no less than 12 lines instead of 5, as here shewn, viz., one in the same position as the A B, one near the three bends in the river and two close by the right and left straight fences; thus forming a trapezium, which, with two diagonals, or tie-lines, requires 6 lines in the usual way: the two triangles, abutting from the side of the trapezium next the river, requiring, as sides and tie-lines, three lines each, that is, 6 lines more for the purpose of taking the bends of the river; thus making 12 lines in all, as already stated.
4. Required the plan and the area of a field, having six sides, from the following field-notes, taken from an old, though still much practised, method. The first figure shews the lines according to the old, the second according to the improved method.