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.

To find the true meridian with the compass.

158. 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 board, to which the compass-sight is fastened, on the horizontal plank, 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 horizontal plank. During this observation it will be necessary to have the plumb-line lighted: this may be done by an assistant holding a candle near it.

Let now a staff, with a candle or lamp upon it, be placed at a distance of thirty or forty yards from the plumb-line, and in the same direction with it and the compass-sight. The

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 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 the reverse when the elongation is east.

1. Elongation west, azimuth. North end of the needle on the west, angle

2° 04'

4o 06'

2. Elongation west, azimuth North end of the needle on the east, angle

3. Elongation east, azimuth North end of the needle on the west, angle

4. Elongation east, azimuth

1° 59'

4o 50'

2° 05'

8o 30'

8° 40'

North end of the needle on the east, angle

Variation 10° 37' east.

REMARK I. The variation at West Point, in September, 1835, was 6° 32' west.

REMARK II. The variation of the needle should always be noted on every survey made with the compass, and then if the land be surveyed at a future time, the old lines can always be re-run.

159. It has been found by observation, that heat and cold sensibly affect the magnetic needle, and that the same needle will, at the same place, indicate different lines at different hours of the day.

If the magnetic meridian be observed early in the morning, and again at different hours of the day, it will be found that the needle will continue to recede from the meridian as the

ture, when it will begin to return, and at evening will make the same line as in the morning. This change is called the diurnal variation, and varies, during the summer season, from one-fourth to one-fifth of a degree..

OF THE PLAIN-TABLE.

160. Pl. 3, Fig. 1. The plain-table consists of two parts; a rectangular board CDBA, and a tripod EHG, to which it is firmly secured.

Directly under the rectangular board are four milled screws which pass through sockets inserted in a horizontal brass plate these screws are worked against a second horizontal plate, for the purpose of levelling the table; the table having a ball and socket motion, similar to the limb of the theodolite. For the purpose of levelling the table, a small detached spirit-level is used. This level being placed over the centre, and also over two of the levelling screws, the screws are turned contrary ways until the level is horizontal; after which, it is placed over the other two screws, and made horizontal in the

same manner.

Between the upper horizontal plate and the table, there is a clamp-screw, similar to the clamp-screw of the theodolite, which being loosened, the table can be turned freely about its axis. There is, also, a small tangent-screw, by which the smaller motions of the table are regulated, after the clampscrew is made fast. Neither of these screws can be seen in the figure.

The upper side of the table is bordered by four brass plates, about one inch in width, and the centre of the table is marked by a small pin, F. About this centre, and tangent to the sides of the table, conceive a circle to be described. Suppose the circumference of the circle to be divided into degrees and parts of a degree, and radii to be drawn through the centre and the points of division. The points in which these radii intersect the outer edge of the brass border, are marked by lines on the brass plates, and the degrees are numbered in the direction from left to right, from the point L to the point I, 180o, and from the point I to the point L, 180o. In some plain-tables, however, they are numbered from 0 to 360°. There are, generally, diagonal scales of equal parts cut on

the plates DLC and AIB, the use of which will be explained hereafter.

Near the two other edges of the table, two small grooves are made, into which the plates of brass DB and CA are fitted, and these plates are drawn to their places by means of milled screws which pass through the table from the under side, and screw firmly into the plates. The heads of two of the screws, Q and S, are seen in the figure, as also one of the plates and its two screws in Fig. 3. The object of these plates is to confine a sheet of paper on the table. By loosening the screws, and pressing them upwards, the plates are raised above the surface of the table; the edges of the paper can then be placed under them: then, by turning the screws back again, the plates are drawn down and the paper held tightly. Fig. 1 represents the table with the paper partly put upon it one edge of the paper has been placed under the plate DB, and the screws S and Q, tightened. The paper, before being put on, should be moistened, in order to expand it; and then, after it has been dried, it will fit closely to the table.

A ruler, AB (Fig. 2), with open vertical sights, is used with the plain-table. This ruler has a fiducial edge, which is in the same vertical plane with the hairs of the sights. A ruler with a telescope, and a vertical limb, similar to the vertical limb of the theodolite, is sometimes used with the plain-table. A compass, also, is often attached to the table, to show the bearings of the lines.

The plain-table is used for two distinct objects.

1st. For the measurement of horizontal angles.

2dly. For the determination of the shorter lines of a survey, both in extent and position.

To measure a horizontal angle.

161. Place, by means of a plumb, the centre of the table directly over the angular point: then level the table; after which, place the fiducial edge of the ruler against the small pin at the centre: direct the sights to one of the objects, and note the degrees on the brass plate; then turn the ruler and sights to the other object, and note the degrees as before. If the ruler has not passed over the 0 point, the difference of

taken from 180°, and the remainder added to the smaller, gives the required angle.

Of the determination of lines in extent and position.

162. Having placed a paper on the table, examine the objects and lines which are to be determined, and measure a base line in such a direction, if possible, that all the objects can be seen from its extremities. Then place the plain-table with its centre, nearly, though not accurately, over one extremity of the base; make it truly horizontal, and turn it until the larger part of the paper lies on the same side of the base with the objects.

Then, tighten the clamp-screw, and mark with a pin the point of the paper directly over the station, which point is determined most accurately by suspending a plumb from the lower side of the table. Press the pin firmly on this point, bring the fiducial edge of the ruler against it, and sight to the other extremity of the base line, and mark with the pin or pencil, the direction of the line on the paper. Sight in like manner to every other object, and draw on the paper the corresponding lines, numbering them from the base line, 1, 2, 3, 4, &c.

Then, with a pair of dividers, take from the scale a certain number of equal parts to represent the base, and lay off the distance on the base line from the place of the pin. Take up the table, carry it to the other extremity of the base, and place the point of the paper corresponding to that extremity, directly over it. Place the fiducial edge of the ruler on the base line, and turn the table, by means of the tangent-screw, until the sights are directed to the first station. If, however, in bringing the table to this position, the corresponding point of the paper has been moved from over the extremity of the base line, move the legs of the tripod until it is brought back to its place. Let the table be then levelled, after which, place the ruler again on the base line, and bring the table to its proper position by the tangent-screw, and continue the adjustment until the extremity of the base line on the paper is directly over the station, and in the same vertical plane with the base line on the ground. Then direct the sights to all the objects sighted to from the other station, and mark the