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CHAIN SURVEYING

INSTRUMENTS AND METHODS

Surveying is that branch of civil engineering which treats of the principles and methods employed for determining the relative positions of points on the earth's surface. Surveying is divided into three general branches, namely, chain surveying, in which no other measuring instrument is employed than a chain or tape for measuring distances; angular surveying, in which angle-measuring instruments are employed in connection with distance-measuring instruments; and leveling, which treats of the determination of elevations, or vertical distances.

The instruments used most commonly for measuring distances are the engineers' chain, the surveyors' chain, and the steel tape. Marking pins and range poles are used in connection with the chain, especially in measuring long lines.

The engineers' chain is 100 ft. long and is composed of 100 links of steel or iron wire, each two adjacent links being connected by small rings. The length of a link, including a ring at each end, is 1 ft. The engineers' chain is used chiefly in railroad surveying, but it is also used to some extent in other kinds of surveying where the foot is the unit of measurement.

The surveyors' chain, often called Gunter's chain, from the name of its inventor, is the same as the engineers' chain in every respect, except that its length is 66 ft., or 4 rd., instead of 100 ft. Like the engineers' chain, it is divided into 100 links, and consequently the length of each link is .66 ft., or 7.92 in. This chain is mainly used in land surveying, where the acre is the unit of area. It is very convenient for this purpose, as areas expressed in square chains can be expressed in acres by simply moving the decimal point one place to the left, there being 10 sq. ch. in 1 A. It is also well to remember that there are 80 ch. in 1 stat. mi.

The surveyors' chain is used in all United States land surveys, and whenever the word chain occurs in a legal document, it is understood to mean a surveyors' chain, or 66 ft.

Steel tapes are now used extensively in surveying and are largely superseding both the engineers' and the surveyors' chain. They can be obtained in any length from 1 yd. to 1,000 ft. and graduated to order. For city surveying, and for many other purposes, a tape 50 ft. long is generally preferred. For some purposes, tapes 300 or 500 ft. long and even of greater length are used. In some tapes, the handle forms part of the end division or graduation, the length of the tape counting from the outside of the handle. In others, the graduations begin on the inside of the handle, where the tape is attached, and in others the graduations begin on the tape itself, a short distance from the handle. When using a tape, the surveyor should ascertain where the graduations begin, as otherwise he may make serious errors. The tape has sometimes attached to it a handle that contains a spring balance for measuring the pull on the tape, a level bubble to guide in holding the tape so that it will be level, and a thermometer to show the temperature of the tape.

Correction for Erroneous Length of Chain.-The length of a chain or tape is altered by changes in temperature, and by wear and distortion. The variations due to temperature are very small, and need to be considered only in very accurate work. The alterations due to wear and distortion are sometimes considerable.

The length of the chain should be tested often. This is done either by comparing the chain with a chain or tape of standard length, or by stretching it between two points whose exact distance apart is known. It is advisable to have two such points marked permanently on an office floor, smooth pavement, curb, or some other convenient place.

If, after a line has been measured, the length of the chain (or tape) is found to be in error, the true length of the line can be easily determined by means of the following formula: Lo=L+eL,

in which Lo=true length of line;

L = length of line as actually measured;

e error in length of one unit of measure.

If, for instance, the length of a line is measured in feet, and the measurements are made with a 50-ft. tape that is found to be

.1

.1 ft. too long, the error is

or .002 ft. in 1 ft. In this case, 50'

e=.002. If the measurement is recorded in chains, and the chain is found to be .1 li. too long, the error is .1 li., or .001 ch. per chain, and e=.001.

It should be understood that the correction eL expresses the same kind of units as e. If, for instance, e is 1.5 in. per ch., and the length of the line is expressed in chains, its true length is L ch. ± 1.5 L in.

If the chain is too long, the distance measured with it will be recorded as too short, and the correction eL should be added; and if the chain is too short, the distance measured will be recorded as too long, and the correction eL should be subtracted. EXAMPLE.

The length of a line, measured with a 100-ft.
It was afterwards found that
What was the true length of

chain, was found to be 1,048 ft.
the chain was .19 ft. too long.
the line?

SOLUTION.-If the error is .19 ft. in 100 ft., it is roo of .19 =.0019 ft., or, say, .002 ft. per ft. Then, e= .002, L= 1,048, and, therefore, Lo=1,048+.002×1,048 = 1,050 ft., nearly. The error is added, because, the chain being too long, the recorded length of the line was too small.

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Keeping Notes.-The notes of a chain survey are usually

kept in a transit book. The accompanying illustration shows

a sample of notes of a chain survey. The right-hand page is used for sketches and remarks. The line that is being run is commonly represented by the red center line. In case more room is needed for sketching, the line that is being run may be represented by a line drawn on one side of the center line of the page and parallel to it. In sketching, it is better to face in the direction in which the line is being measured and to represent the line as running from the bottom to the top of the page in the notebook.

FIELD PROBLEMS

To Run a Line Over a Hill When the Ends of the Line Are Invisible From Each Other.-The points A and B, Fig. 1, are supposed to be on opposite sides of a hill, and to be invisible from each other. It is desired to run a line between them, or to locate some intermediate points.

Having set two poles at A and B, two flag

FIG. 1

men with poles station themselves at C and D, approximately in line with A and B, and in such positions that the poles at B and D are visible from C, and those at C and A are visible from D. The flagman at C lines in the flagman at D between Cand B, and then the flagman at D lines in that at C between D and A. Then the flagman at C again lines in that at D, and so on, until C is in line between D and A at the same time that D is in line between C and B. The points C and D will then be in line with A and B.

To Erect a Perpendicular to a Line at a Given Point.-Let it be required to erect a perpendicular to the line AB at the point B, Fig. 2. A triangle whose sides are in the proportion of 3, 4, and 5 is a right triangle, the longest side being the hypotenuse; for 5242+32. The following method is based on this principle: Lay off on BA a distance BC of 30 ft. (or li.). Fix one end of the chain at one of the extremities

as C, and the end of the ninetieth link at the other extremity B. Hold the end of the fiftieth link and draw the chain until both parts are taut. The point D where the end of the fiftieth link is held will then be a point in the perpendicular, and the direction of the latter will therefore be BD.

The distance BC may be any other convenient multiple of 3. In general, if BC is denoted by 3 a, BD must be 4 a, and CD must be 5 a. Thus, BC may be made equal to 21 (=3×7) li.; in which case BD must be 4X7-28, and CD must be 5X7 =35, li. As 35+28-63, one end of the chain must be fixed at one of the extremities of BC, the end of the sixty-third link at the other extremity, and the chain pulled from the end of the thirty-fifth link until both parts are taut.

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To Determine the Angle Between Two Lines.-Let AD and AE, Fig. 3, be two lines on the ground. To determine the angle DAE, measure off from A on AD and AE equal distances AB and AC. Measure the distance BC. Then the angle DAE is calculated from the relation

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EXAMPLE. If AB and AC are each 100 ft. and BC is 57.6 ft., what is the value of the angle DAE?

SOLUTION. Substituting the values of BC and AB in the preceding equation,

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whence, DAE = 16° 44′, nearly; and, therefore, DAE= 16° 44′ X2=33° 28'.

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