(255) The Field-notes of a field, in which offsets occur, may be most easily recorded by the Third Method; as in Fig. 176.

When the Field-notes are recorded by the Fourth Method, the offsets may be kept in a separate Table; in which the 1st column will contain the stations from which the measurements are made, the 2d column the distances at which they occur, the 3d

* In the “Third Method," the bearings should be written obliquely upward, as directed in Art, (249), but are not so printed here, from typographical diffi. culties.

column the lengths of the offsets, and the 4th column the side of the line, "Right," or "Left," on which they lie.

For calculation, four more columns may be added to the table, containing the intervals between the offsets; the sums of the adjoining pairs; and the products of the numbers in the two preceding columns, separated into Right and Left, one being additive to the field, and the other subtractive.

(256) Tests of accuracy. 1st. The check of intersections described in Art. (246), may be employed to great advantage, when some conspicuous object near the centre of the farm can be seen from most of its corners.

2nd. When the survey is platted, if the last course meets the starting point, it proves the work, and the survey is then said to "close."

3d. Diagonal lines, running from corner to corner of the farm, like the "Proof-lines" in Chain Surveying, may be measured and their bearings taken. When these are laid down on the plat, their meeting the points to which they had been measured, proves the work.

4th. The only certain and precise test is, however, that by "Latitudes and Departures." This is fully explained in Chapter V, of this Part.

(257) A very fallacious test is recommended by several writers on this subject. It is a well-known proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two; since the figure can be divided into that number of triangles. Hence this common rule. "Calculate [by the last paragraph of Art. (243)] the interior angles of the field or farm surveyed; add them together, and if their sum equals twice as many right angles as the figure has sides less two, the angles have been correctly measured." This rule is not applicable to a compass survey; for, in Fig. 167, page 144, the interior angle BCD will contain the same number of degrees (in that case 160°) whether the bearings of the sides have been noted correctly, as being the

angles which they make with NS-or incorrectly, as being the angles which they make with N'S'. This rule would therefore prove the work in either case.

(258) Method of Radiation. A field may be surveyed from one station, either within it or without it, by taking the bearings and the distances from that point to each of the corners of the field. These corners are then "determined," by the 3d method, Art. (7). This modification of that method, we named, in Art. (220), the Method of Radiation. All our preceding surveys with the compass have been by the Method of Progression.

The compass may be set at one corner of the field, or at a point in one of its sides, and the same method of Radiation employed. This method is seldom used however, since, unlike the method of Progression, its operations are not checks upon each other.

(259) Method of Intersection. A field may also be surveyed by measuring a base line, either within it or without it, setting the compass at each end of the base line, and taking, from each end, the bearings of each corner of the field; which will then be fixed and determined, by the 4th method, Art. (8). This mode of sur veying is the Method of Intersections, noticed in Art. (220). It will be fully treated of in Part V, under the title of Triangular Surveying

(260) Running out old lines. The original surveys of lands in the older States of the American Union, were exceedingly deficient in precision. This arose from two principal causes; the small value of land at the period of these surveys, and the want of skill in the surveyors. The effect at the present day is frequent dissatisfaction and litigation. Lots sometimes contain more acres than they were sold for, and sometimes less. Lines which are straight in the deed, and on the map, are found to be crooked on the ground. The recorded surveys of two adjoining farms often make one overlap the other, or leave a gore between them. The most difficult and delicate duty of the land-surveyor, is to run out these old boundary lines. In such cases, his first business is to find

monuments, stones, marked trees, stumps, or any other old "corners," or landmarks. These are his starting points. The owners whose lands join at these corners should agree on them. Old fences must generally be accepted by right of possession; though such questions belong rather to the lawyer than to the surveyor.* His business is to mark out on the ground the lines given in the deed. When the bounds are given by compass-bearings, the surveyor must be reminded that these bearings are very far from being the same now as originally, having been changing every year. The method of determining this important change, and of making the proper allowance, will be found in Chapter VIII, of this Part.

(261) Town Surveying. Begin at the meeting of two or more of the principal streets, through which you can have the longest prospects. Having fixed the instrument at that point, and taken the bearings of all the streets issuing from it, measure all these lines with the chain, taking offsets to all the corners of streets, lanes, bendings, or windings; and to all remarkable objects, as churches, markets, public buildings, &c. Then remove the instrument to the next street, take its bearings, and measure along the street as before, taking offsets as you go along, with the offset-staff. Proceed in this manner from street to street, measuring the distances and offsets as you proceed.

Fig. 177.

* "In the description of land conveyed, the rule is, that known and fixed monuments control courses and distances. So, the certainty of metes and bounds will include and pass all the lands within them, though they vary from the given quantity expressed in the deed. In New-York, to remove, deface or alter landmarks maliciously, is an indictable offence."-Kent's Commentaries, IV, 515.

Thus, in the figure, fix the instrument at A, and measure lines in the direction of all the streets meeting there, noting their bearings; then measure AB, noting the streets at X, X. At the second station, B, take the bearings of all the streets which meet there; and measure from B to C, noting the places and the bearings of all the cross-streets as you pass them. Proceed in like manner from C to D, and from D to A, "closing" there, as in a farm survey. Having thus surveyed all the principal streets in a particular neighborhood, proceed then to survey the smaller intermediate streets, and last of all, the lanes, alleys, courts, yards, and every other place which it may be thought proper to represent in the plan. The several cross-streets answer as good check lines, to prove the accuracy of the work. In this manner you continue till you take in all the town or city.

(262) Obstacles in Compass Surveying. The various obstacles which may be met with in Compass Surveying, such as woods, water, houses, &c., can be overcome much more easily than in Chain Surveying. But as some of the best methods for effecting this involve principles which have not yet been fully developed, it will be better to postpone giving any of them, till they can be all treated of together; which will be done in Part VII.