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From the table of azimuths, take the azimuth corresponding to the year and nearest latitude. If the observed elongation were east, the true meridian lies on the west of the line which has been found, and makes with it an angle equal to the azimuth. If the elongation were west, the true meridian lies on the east of the line: and, in either case, laying off the azimuth angle with the theodolite, gives the true meridian.
180. To find the true meridion with the compass.
1. Drive two posts firmly into the ground, in a line nearly east and west'; the uppermost ends, when driven firmly, being about three feet above the surface, and the posts about four feet apart: then lay a plank, or piece of timber three or four inches in width, and smooth on the upper side, upon the posts, and let it be pinned or nailed, to hold it firmly.
2. Prepare a piece of board four or five inches square, and smooth on the under side. Let one of the compass-sights be placed at right-angles to the upper surface of the board, and let a nail be driven through the board, so that it can be tacked to the timber resting on the posts.
3. At about twelve feet from the stakes, and in the direction of the pole-star, let a plumb be suspended from the top of an inclined stake or pole The top of the pole should be of such a height that the pole-star will appear about six inches below it ; and the plumb should be swung in a vessel of water to prevent it from vibrating.
This being done, about twenty minutes before the time of elongation, place the compass-sight, which is fixed in the piece of wood, on the horizontal timber, and slide it east or west, until the aperture of the compass-sight, the plumb line, and the star are brought into the same range. Then if the star depart from the plumb line, move the compass-sight, east or west, along the timber, as the case may be, until the star shall attain its greatest elongation, when it will continue behind the plumb-line for several minutes ; and will then recede from it in the direction contrary to its motion before it became stationary. Let the compass-sight be now fastened to the
the plumb line illuminated: this may be done by an assistant holding a small candle near it.
Let now a staff, with a candle or lamp upon it, be placed at a distance of thirty or forty rods from the plumb line, and in the same direction with it and the compass-sight. The line so determined, makes, with the true meridian, an angle equal to the azimuth of the pole star ; and, from this line, the variation of the needle is readily determined, even without tracing the true meridian on the ground.
Place the compass upon this line, turn the sights in the direction of it, and note the angle shown by the needle. Now, if the elongation, at the time of observation, were west, and the north end of the needle lies on the west side of the line, the azimuth, plus the angle shown by the needle, is the true variation. But should the north end of the needle be found on the east side of the line, the elongation being west, the difference between the azimuth and the angle would show the variation : and reciprocally when the elongation is east.
Escample 1.-Elongation west, azimuth 2° 04
Variation Example 2.-Elongation west, azimuth North end of the needle on the east, angle
1° 59 4° 50
2° 51' east.
Variation Example 3.-Elongation east, azimuth North end of the needle on the west, angle
Variation Example 4.-Elongation east, azimuth North end of the needle on the east, angle
OF SURVEYING IN GENERAL.
181. We propose to explain in this chapter the manner of surveying a piece of land, for the determination both of its area and bounding lines. We shall use for this purpose the theodolite, the compass, the plain table, and the cross; and the instruments for plotting will also be used in delineating the survey on paper.
182. Plate 7 is the map of a piece of land to be surveyed. Looking upon it, the part on the right is bounded by a river, the upper side by a wood and cultivated land, the left-hand side by a fence and creek, and the lower part by a row of buildings.
183. The theodolite, being far the best of the surveying instruments, is to be used for determining the positions of the prominent points, or objects, and the more extended lines; after these are fixed, the shorter lines are to be traced with the compass, and auxiliary perpendiculars erected with the cross; then, the plain table is to be taken in hand, and the places of objects that are near each other, are to be determined by it.
184. Walk once or twice over the land, observe its general contour, the most prominent points for stations, and the best line that can be selected for a base. The base line should, in general, be as long as possible, though it would be useless to measure one of greater length than the average of the lines to be computed; it should, if convenient, be measured on the most level part of the land, and should always be so chosen, that the important points can be seen from its extremities.
Art. 82, and erect station staves, with flags on them, at the points to be determined. Suppose, in the present example, that we have measured the base line AB, and found it equal to 97 rods, and erected station staves at the points A, B, E, C, and D, which, for the sake of presenting a full example, we will name, Frog's point, Williams's corner, Day's house, Wood's barn, and Four corners, respectively.
We are now on the field with the theodolite. We remove the staff at A, place, by means of a plumb, the axis of the theodolite, over the station, and bring the 0 of the vernier, which is under the eye-glass of the telescope, to coincide with the 0 of the limb. Loosen the clamp screw and turn the body of the instrument until the telescope comes nearly on the base line; then tighten the clamp screw, and, by means of the tangent screw, bring the intersection of the hairs of the telescope to coincide with the bottom of the station staff at B. Then direct the lower telescope to the same point: sight from A to the stations C and E, (the only remaining ones that can be seen from A,) by turning the vernier plate, and without moving the limb, and read both the verniers. Enter in the notebook the degrees and minutes read at the vernier under the eye-glass, and in a separate column, the minutes shown by the other vernier; in a third column is to be entered the degrees read, and a mean between the minutes for the direction.
Take up the theodolite, replace the station staff, go to the other extremity B, of the base line, and place the instrument so that the line marked 0 and 180 shall coincide with the base BA, the O point being towards A ; clamp the limb and sight to the stations E, C, and D, and read the angles as before.
Let the instrument be now removed to C. Place the 0 of the vernier under the eye-glass, to the angle that differs by 180° from the one which shows the direction from A to C, or from B to C, which latter arc is found in the column D. Then, without moving the vernier plate on the limb, direct the telescope to that extremity of the base from which the direction used was taken, when the line of the limb, marked 0 and 180,
note the directions as before,
The following is the manner of entering the field notes.
Let the instrument be now placed, after the same manner, Then sight to all the other stations which can be seen, and intersects them, as to make the angles on the same side equal.
Williams's Corner, Station B.