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AE being the true level line, EC is the correction for curvature, which is therefore equal to the square of the distance divided by the earth's diameter. Taking the earth's diameter as 7,916 miles, the correction for 1 mile would be

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The correction for 10 chains is in. The correction is proportional to the square of the distance and the effect of curvature is to make distant points appear lower than they really are. The effect of curvature and also of refraction is eliminated by placing the instrument midway between the two points the difference of whose levels is required.

Fig. 131.-The A Level.


Fig. 130. Correction for Curvature.

Refraction.-Rays of light coming through the atmosphere are refracted or curved downwards. The effect is to make objects appear higher than they really are. The error due to refraction is thus in a contrary direction to that due to curvature, and its amount is on an average about of the error due to curvature. It, however, varies with the state of the atmosphere, and is somewhat uncertain. See also pages 185, 370.

Other Instruments: Plumb Line Levels.-The A level is shown in Fig. 131. It is so made that when the plumb line

Fig. 132.-Plumb Line Level.

is adjusted to the mark on the cross-piece, the feet of the level are at the same height, and a line joining them is horizontal.

Another form of the plumb-line level is shown in Fig. 132. In this the cross-piece is at right angles to the plumb line, and is therefore horizontal when the plumb line coincides with its mark. These forms are not convenient for producing a line. For this purpose the last form is inverted. By sighting along the crosspiece we get a level line when the vertical piece is plumbed with the plumb line.

Reflecting Levels. These instruments are made on the principle that a ray of light which strikes a reflecting plane at right angles is reflected back in the same direction. When the eye is reflected in a plain mirror the line joining the eye and its



Fig. 133.
Reflecting Level.


Fig. 134.
Reflecting Level.

image is perpendicular to the mirror, and if the mirror is vertical this line is horizontal, and may therefore be used for finding points at the same level as the eye. The first form (Fig. 133) is a rhomb of lead about 2 in. in the side and 1 in. thick. On one side, the shaded part of Fig. 133, is a mirror. The right hand part of the rhomb is cut off as shown in the figure, and a wire AB is stretched across it. To use the instrument, hold it up by the string D, with the mirror opposite the eye, so that the eye is seen bisected in the mirror by the wire AB. Then look through the opening at B and any point in line with the eye and wire will be on the same level with them. The instrument is made to hang vertical by means of the weight shown. Fig. 134 shows this instrument as made by Stanley. The second form is a hollow

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brass cylinder with an opening at the top as in Fig. 135. Inside is a small mirror, and this mirror is made to hang vertical by means of a weight within the cylinder. The instrument is used similarly to the first already described, the lower edge of the opening serving the same purpose as the wire in the first instrument. The third form is a small steel cylinder (Fig. 136), about 5 in. long and in. diameter, highly polished, and hung from the centre of one end by a fine thread. To use it, it is

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held by the thread with one hand, and with the other hand a card is held between the eye and the instrument, the upper edge of the card as seen reflected in the cylinder being used in the same way as the wire in the first form of the instrument.

Boning Rods.-These are used by foremen for working to levels given to them by the engineers on pegs. For instance, in Fig. 137, suppose the pegs at A and B are driven in to a certain

level. Then by placing a boning rod on each of these pegs and sighting forward to a third boning rod held at c, when the boning rods are truly in line the foot of the third boning rod will be at the


Fig. 137. Boning Rods.

same level as the pegs at A and B, or if the pegs at A and B are driven in to a certain gradient, the foot of the boning rod at c will be on this gradient. The boning rods must of course be all exactly the same height.

Practical Hints, Obstacles and Difficulties. Always if possible set up the level midway between the back-sight and foresight points. Any error of adjustment of the instrument is thereby eliminated, as also errors due to curvature and refraction. For instance, if the instrument is out of adjustment, and the reading on the back sight is 0.10 too small, the reading on the fore sight will also be 0.10 too small, if the level be midway. The difference of the readings will, however, be correct, as they are both in error the same amount; the correct difference of level is therefore determined.

Change Points. In soft ground, where there are no solid stones to hold the staff on for the change points, as for instance in pasture land, &c., it is a good plan to make the staff-holder carry a chaining. Staff arrow which he drives into the ground up to the head. The staff is then held on the chaining arrow as in Fig. 138.

Figs. 139 and 140 show foot plates specially made for the same purpose. These are driven into the ground and the staff is held on the knob.

Fig. 138. Change Point.

Steep Slopes.-In ascending or descending a hill the instrument will be set up so that the collimation line strikes as near the top of the staff as possible in the back sights and near the bottom in the fore sights. The

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sights will thus be of unequal length, and if the instrument is out of adjustment errors will be introduced. To avoid this, set up on one side of the line along which the levels are being taken. When the slope is very steep, the greatest distance up the hill at which the collimation line will strike the staff may be so little that the staff cannot be read. In that case also the level must be set up to one side of the line along which the levels are being taken.

Levelling Across a Hill. It will save time to set up the level on one side and sight over as shown in Fig. 141, in place of

Fig. 140.
Foot Plate.



Fig. 139.-Foot Plate.

Fig. 141.—Levelling over a Hill.

setting up on the top of the hill; this also applies to levelling across a hollow.

When the Staff is too low or too high. In levelling over a line of pegs already driven in, when the staff is too low, direct the chainman to raise it until it can be read, and then measure from the bottom of the staff to the top of the peg and add the measurement to the staff reading. If the staff is a little too high, measure from the top of the peg to where the line of sight cuts it, and book the measurement with a contrary sign, i.e., if a back sight minus and if a fore sight plus.

When the Staff is too near to read the Divisions.— When no figure is visible, direct the chainman to raise the staff slowly until a figure comes in sight, and then lower it again. If

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