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signals from the leveler. For ordinary work, the type first mentioned is preferred by engineers, the target rod being used where very accurate work is required.

It is very important that the rod should be held truly vertical when sighted at. Different devices are employed for this purpose, and for work requiring great accuracy, such as bridge foundations, a rod level that fits closely to the angle of the rod and carries two small spirit levels is used to plumb it accurately. For ordinary work, however, this is not required. The leveler can plumb the rod across the line of sight by observing whether it coincides with the vertical cross-hair of the instrument, and he can obtain good results by making the rodman slowly tip the rod backwards and forwards in the direction of the line of sight and then taking the shortest reading.

FIELD WORK IN LEVELING

Example in Direct Leveling.-The principles of direct leveling are illustrated in the accompanying illustration.

Let A be the starting point, which has a known elevation of 20 ft. The instrument is set at B, leveled up and sighted to a rod held at A. The target being set, the reading, 8.42 ft., called a backsight, is the distance that the point where the line of sight cuts the rod is above the point A, and is to be added to the elevation of the point A; 20.00+8.42=28.42 is called the height of instrument and is designated by H. I. The instrument being turned in the opposite direction, a point C is chosen, which must be below the line of sight. This point is called a turning point, and is designated by the abbreviation T. P. Drive a peg at C, or take for a turning point a rock or some other permanent object upon which the rod is held. The first reading on a turning point is a foresight, and is to be subtracted from the height of instrument at B to find the elevation of the point C. Let the rod reading be 1.20 ft. Then, 28.42-1.20 27.22 ft., is the elevation of the point C. The leveler carries the instrument to D, which should be of such a height above C that, when leveled up, the line of sight will cut the rod near the top. The backsight to C gives a reading of 11.56 ft., which, added to 27.22 ft., the elevation of C, gives 38.78 ft., the height of instrument at D. The

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rodman then goes to E, a point where a foresight reading is 1.35, which, subtracted from 38.78, the

H. I. at D, gives 37.43 ft., the elevation of E. The level is then set

up at F, being careful that line of sight shall clear the hill at L. The backsight, 6.15 ft., added to 37.43 ft., the elevation of E, gives 43.58 ft., the H. I. at F. The rod held at Ggives a foresight of 10.90 ft., which, subtracted from 43.58 ft., the H. I. at F, gives 32.68 ft., the elevation at G. Again moving the level to H, the backsight to G of 4.39 ft. added to 32.68 ft., the elevation of G, gives 37.07 ft., the H. I. at H. Holding the rod at K, a foresight of 5.94, subtracted from 37.07, gives 31.13, the elevation of the point K. The elevation of the starting point A is 20.00 ft., the elevation of the point K is found by direct leveling to be 31.13 ft., and the difference in the elevations of A and K is 31.13 -20.00 11.13 ft.; that is, the point K is 11.13 ft. higher than the point A.

At each setting of the level, foresight readings can be taken on a number

of points, before taking a foresight on a turning point, preparatory moving the level to

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to

a new position. The elevation of any

point will be equal to the H. I. minus the foresight reading.

A turning point is a point where the rod is held for a foresight, and after the level has been moved to a new position, for a backsight. The backsights are (+) readings, and are to be added; the foresights are (−) readings, and are to be subtracted. A point for a foresight having been determined, the rodman drives a peg firmly in the ground and holds the rod upon it. After the instrument is moved, set up, and a backsight taken, the peg is pulled up and carried in the pocket until another turning point is called for.

Balancing Backsights and Foresights.-The most valuable and reliable safeguard against errors in leveling is obtained by equal backsights and foresights on turning points. They should usually be equal in pairs; that is, each pair of sights on turning points, one backsight and one foresight, should be of approximately equal lengths. Should any inequality of length occur in one pair of sights, it should be balanced up in the next pair, or as soon as possible. For example, should the foresight in one pair of sights be longer than the backsight, then in the next pair of sights the backsight should be made correspondingly longer than the foresight. The sights should be balanced as perfectly as possible between bench marks. It is not necessary to measure the lengths of the sights accurately; they can be determined closely enough by counting steps in walking. A man of ordinary stature, when walking naturally, will average about 40 steps in each 100 ft. of distance, usually a somewhat less number on smooth and level ground, and a greater number where the ground is rough or sloping, either ascending or descending.

Keeping Level Notes.-Many forms on which to keep level notes are used. The distinguishing feature of one of the best, which is here shown, is a single column for all rod readings. The backsights being additive and the foresights subtractive readings, they are distinguished from other rod readings by the signs + and

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Checking Level Notes.-A well-known method of checking level notes provides for checking the elevations of turning points and heights of instrument only, which is sufficient, as

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all other elevations are deduced from them. The method depends on the fact that all backsights are additive (+) quantities, and all foresights are subtractive (-) quantities. The accompanying level notes are checked as follows: The elevation of the bench mark at station 0 is 100.00 ft., to which all backsights, or + readings, are to be added and from this sum all foresights, or readings, are to be subtracted. The sum of the backsights, with elevation of bench mark at Sta. O, is 122.59. Sum of foresights on turning points is 24.27, and difference is 98.32 ft., the elevation of the last turning point. When a page of level notes is filled, the notes should be checked and a check-mark placed at the last height of instrument or elevation checked. When the work of staking out or crosssectioning is being done, the levels should be checked at each bench mark on the line. After each day's work, the leveler must check on the nearest bench mark.

Profiles. A profile represents a longitudinal section of the line of survey. In it all abrupt changes in elevation are clearly outlined. Vertical and horizontal measurements are usually represented to different scales, to render irregularities of surface more distinct through exaggeration. For railroad work, profiles are commonly made to the following scales: horizontal, 400 ft. 1 in.; vertical, 20 ft. = 1 in.

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A section of profile paper is shown in the accompanying diagram. Every fifth horizontal line and every tenth vertical

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