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be used. Some of those put down are also invisible, occurring in the evening, before it is dark, or after daylight in the morning. In such case, if it be necessary to determine the meridian at that particular season of the year, let 5 h. and 59 min. be added to, or subtracted from, the time of greatest eastern or western elongation, and the observation be made at night, when the star is on the meridian.

The following table exhibits the angle which the meridian plane makes with the vertical plane passing through the polestar, when at its greatest eastern or western elongation: such angle is called the azimuth. The mean angle only is put down, being calculated for the first of July of each year.

Lat. 320
Lat. 34° Lat. 36°
Azimuth Azimuth Azimuth


1° 50' 1° 52' 1° 56'

1° 58' 2° 22° 6' 2° 10′

1837 | | 1° 50' 1° 52' 1° 55' 1° 58' 2° 2' 2° 52° 10'


1° 50' 1° 52' 1° 55' 1° 58' 20 120 5′ 29 1839 1° 49' 1° 52′ 1° 54′ 1° 57′ 2° 1′ 2° 41′ 2° 9′ 1840 | 1° 49′ | 1° 51′ | 1° 54′ │1° 574′ | 2° 03/20


1° 48' 1° 51′ 1° 53' 1° 57′ 2° 0′


1° 59'

2o 21' 2° 7'

1° 48' 1° 50' 1° 53' 1o 561′ 1o 591′ 1° 47′ | 1° 50′ 1° 52′ | 1° 56′ 1844 1° 47′ 1° 49′ 1° 52′ 1° 49' 1° 52'1° 55' 1° 58' 2° 2' 1° 55′ 1° 58′ 2° 2′ |: 1845 1° 46′ 1° 49′ 1° 51′ | 1° 55′ 1° 58' 2° 12° 6' 1846 1° 46′ 1° 48' 1° 51′ 1° 54′ 1° 57' 20 1o 543′ │1o 573′ | 2°


2o 61


1′ │2° 51′ The use of the above tables, in finding the true meridian, will soon appear.

To find the true meridian with the theodolite.

157. Take a board, of about one foot square, paste white paper upon it, and perforate it through the centre; the diameter of the hole being somewhat larger than the diameter of



Lat. 38° Lat. 40o
Azimuth Azimuth

Lat. 42o


Lat. 44°


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3′ 2o 71′ 3'

to a vertical staff, as to slide up and down freely and let a small piece of board, about three inches square, be nailed to the lower edge of it, for the purpose of holding a candle.

About twenty-five minutes before the time of the greatest eastern or western elongation of the pole-star, as shown by the tables of elongations, let the theodolite be placed at a convenient point and levelled. Let the board be placed about one foot in front of the theodolite, a lamp or candle placed on the shelf at its lower edge; and let the board be slipped up or down, until the pole-star can be seen through the hole. The light reflected from the paper will show the cross hairs in the telescope of the theodolite.

Then, let the vertical spider's line be brought exactly upon the pole-star, and, if it is an eastern elongation that is to be observed, and the star has not yet reached the most easterly point, it will move from the line towards the east, and the reverse when the elongation is west.

At the time the star attains its greatest elongation, it will appear to coincide with the vertical spider's line for some time, and then leave it, in the direction contrary to its former motion.

As the star moves towards the point of greatest elongation, the telescope must be continually directed to it, by means of the tangent-screw of the vernier plate; and when the star has attained its greatest elongation, great care should be taken that the instrument be not afterwards moved.

Now, if it be not convenient to leave the instrument in its place until daylight, let a staff, with a candle or small lamp upon its upper extremity, be arranged at thirty or forty yards from the theodolite, and in the same vertical plane with the axis of the telescope. This is easily effected, by revolving the vertical limb about its horizontal axis without moving the vernier plate, and aligning the staff to coincide with the vertical hair. Then mark the point directly under the theodolite; the line passing through this point and the staff, makes an angle with the true meridian equal to the azimuth of the pole-star.

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

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

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

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

2° 04'

4o 06'

6o 10' west.

1° 59'

4o 50'

2o 51' east.

2° 05'

8o 30'

6o 25' west.

1° 57'

8° 40'

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.


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, 180°, and from the point I to the point L, 180°. In some plain-tables, however, they are numbered from 0 to 360o.

There are, generally, diagonal scales of equal parts cut on

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