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CHAPTER IV.

CHAIN SURVEYING.

SECTION I.

DEFINITIONS.

200. Definition. LAND SURVEYING is the art of measuring the dimensions of a tract of land, so as to furnish data for calculating the content and determining the area.

201. The position of the angular points of a tract may be determined either by measuring the lines of the survey, the diagonals, offsets, &c., or by linear measures in connection with angular distances. These different methods of fixing the points give rise to different modes of surveying,--the first of which, as it is performed principally by the chain, may be called chain surveying.

202. Advantages. As the chain, or some substitute, such as a tape-line or a cord, is readily procured by every one, surveying by this method may be performed where the more expensive instruments cannot readily be procured. To every farmer it may be important to know the content of a particular field, or of several fields, that he may divide them properly, or that he may know the value of crops which he is about to buy or to sell; or for various other purposes that need not be mentioned. He should, therefore, not be under the necessity of calling in a professional man to do for him what he himself, with a pair of carriage lines, can do, if not as well, yet fully well enough for all practical purposes.

In order that this very simple method may be fully understood, we shall treat of it somewhat at length. It must not be inferred from this that it is recommended in preference to the other methods to be explained hereafter, but only as a substitute to be used, when, from the circumstances of the case, these are inapplicable or inconvenient.

203. Area Horizontal. It must be remembered that, in land surveying, it is the horizontal area that is required, and not the actual surface of the ground. Every measurement must, therefore, be made horizontally, as explained in Art. 149, et seq., and, where angles are taken, they must be horizontal angles.

As the method of chaining has been fully explained in the articles above referred to, it will be unnecessary to repeat the directions here. There are, however, certain preliminary operations to be performed, which will form the subject of the next section.

SECTION II.

FIELD OPERATIONS.

A. TO RANGE OUT LINES, AND TO INTERPOLATE POINTS.

204. Ranging out Lines. THIS requires three persons, each of whom should be provided with a rod some ten or twelve feet long, one end being pointed with iron, that it may be thrust in the ground. He should also have a plumb-line, that he may set his rod upright. The first,

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whom we shall call A, takes his station at the point of beginning. Looking in the direction of the line, he places B in the proper direction, signalling him to the right or left as may be required. When the position is determined, B sets his rod firmly in the ground. C then goes forward, and looking back, by ranging with the rods of B and A, he puts his rod in line. A then comes forward, and, going ahead of C, puts himself in line, by ranging with C and B. They thus continue, the hindmost always coming forward, until the other end of the line is reached. At the point at which each rod was erected a stake should be driven for future reference.

Lines may be prolonged in the same manner to any extent that may be desired.

If the operation is carefully done, the rods being set plumb, the line will vary very slightly, if at all, from a straight line, even when extended several miles.

205. To interpolate points in a line. The men in chaining should keep themselves exactly in line. This may readily be done by a careful follower, when the end of the line can be seen. If, however, one end is not visible from the other, and from every point in the line, there will be nothing by which the follower can range his leader, unless there are staves set up for that purpose, at points along the line. The fixing of such points is called interpolation.

206. On level ground. If, for any purpose, such points were needed in a line on level open ground, a person, stationing himself at one end, can signal another into the proper position. As many points as are wanted can thus be determined.

207. Over a hill. If a hill intervenes, from the top of which both points may be seen, let two persons, provided with rods, put themselves as near in line as possible. Then, by alternately signalling to each other, their proper

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places can be found. Thus, let XY (Fig. 79) be the Fig. 79. line to be interpolated. A will take his station in the supposed position of the line, and signal B until he ranges with X. B then places A in line with Y at C; A again signals B to D, in line with X; and so they proceed till they are both in the line XY.

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208. If an assistant is not at hand, or if but one point can be found from which both ends of the line can be seen, one person can put himself in line by having a rule with a sight at each end; wires, set upright, will do very well: lay this on some support, and then go to each end in turn, sighting to the end of the line; he can thus determine whether it is the proper position, and alter it until he finds himself rightly placed.

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209. By a Random Line. When the ends cannot be seen from each other, nor from any intermediate point, it is necessary to run a random line. This is done as directed in Art. 204, following a course as near that of the line to be interpolated as possible.

When the foremost person has come opposite the end of the line, measure the whole length, noting the distance to each stake, (the stakes, for convenience, being set as nearly as possible at equal distances ;) also measure the distance by which the end of the line is missed, then say:—

As the whole distance is to the distance to any stake, so is the whole deviation to the correction for that stake. Measure the distance thus determined, in the proper di rection, and set the stake, or a stone, accordingly.

Thus, let AB (Fig. 80) be the line to be interpolated. Run the random line AC, setting stakes at D, E, F, &c. Measure CB and the distance from A to D, E, F, and C.

Suppose AC measures 27.56 chains, AD 10 chains, AE 15 chains, AF 20 chains, and BC= 1.57 chains.

Then, 27.56: 10: 1.57 .57, the correction for D.
Similarly, Ee=.85, and Ff = 1.14 chains.

Set off Dd, Ee, and Ff, the calculated distances; set stakes at d, e, and f, and range out the line

anew.

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Instead of working out each proportion, it is more concise to divide the deviation by the number of chains in the measured length: this will give the correction for one chain. This correction, being multiplied by the distance to each stake, will give the correction for that stake.

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10 x .057 =

=

.057, the correction for 1 chain.

.57, the correction for D;

15 x .057 .85, the correction for E;

20.0571.14, the correction for F.

210. Across a valley. When the line runs across a valley, let two points A and B be determined on opposite sides of the valley, from which the intervening ground can be seen. Then let one person take his station at A, and, holding a plumb-line over the stake, let him sight to B: he can then direct his assistant into the proper position, and thus fix as many points as are desirable.

NOTE.-These operations are all done more accurately and rapidly by means of the transit or theodolite.

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