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line from A to D, and consider it as the first closing line, and let fall a perpendicular on DE.

REMARK III. When the point from which the division line is to be drawn, falls between the extremities of a course, dividing the course into two parts, consider one of the parts as an entire course, and the other as forming a new course, having the same bearing. The manner of making the caloulation will then be the same as before.

Method of Surveying the Public Lands.

151. In the year 1802, the following method of surveying the public lands, was adopted by Colonel Jared Mansfield, then surveyor-general of the North-Western Territory.

152. The country to be surveyed is first divided by parallel meridians, six miles distant from each other; and then again, by a system of east and west lines, also six miles from each other. The whole country is thus divided into equal squares, which are called townships. Hence, each township is a square, six miles on a side, and contains 36 square miles.

The townships which lie along the same meridian, are called a range, and are numbered, to distinguish them from each other.

Each township is divided into equal squares, by meridians one mile apart, and by east and west lines at the same distance from each other. Hence, each township is divided into 36 square miles, each one of which is called a section. The sections of a township are numbered from 1 to 36, and each contains 640 acres.

To describe a section accurately, we say, section number 5, in township number 4, in range 3d, west of a known meridian, the one, for example, drawn through the mouth of the Great Miami river. This description fixes precisely the place of the section. Go to the 3d range of townships, west of the known meridian, find township number 4 in this range, and lastly, section number 5 of that township. The corners of the sections should be marked by permanent corner-posts, or by lines blazed on trees.

The sections are divided into half sections, quarter sections, and even into eighths of sections. The following table shows the content of a township, and its subdivisions.

1 township=36 sections=23040 acres.

1 section=640 acres.

section=320 acres.

section=160 acres.

section= 80 acres.

The principal meridians, and the principal east and west lines, have been established by astronomical observation, and the lines of subdivision run with the compass.

VARIATION OF THE NEEDLE.

153. The line indicated by the magnetic needle, when allowed to move freely about the point of support, and settle to a state of rest, has been called the magnetic méridian. This, in general, is a different line from the true meridian, which always passes through the poles of the earth, when sufficiently produced in both directions.

154. The angle which the magnetic meridian makes with the true meridian, at any place on the surface of the earth, is called the variation of the needle at that place, and is east or west, according as the north end of the needle lies on the east or west side of the true meridian.

155. The variation is different at different places, and even at the same place it does not remain constant for any length of time. The variation is ascertained by comparing the magnetic, with the true meridian.

156. The best practical method of determining the true meridian of a place, is by observing the north star. If this star were precisely at the point in which the axis of the earth,

produced, pierces the heavens, then, the intersection of the vertical plane passing through it and the place, with the surface of the earth, would be the true meridian. But, the star being at a distance from the pole, equal to 1° 34' nearly, it performs a revolution about the pole in a circle, the polar distance of which is 1° 34': the time of revolution is 23 h. and 56 min.

To the eye of an observer, this star is continually in motion, and is due north but twice in 23 h. 56 min.; and is then said to be on the meridian. Now, when it departs from the meridian, it apparently moves east or west, for 5 h. and 59 min., and then returns to the meridian again. When at its greatest distance from the meridian, east or west, it is said to be at its greatest eastern or western elongation.

The following tables show the times of its greatest eastern and western elongations.

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The eastern elongations are put down from the first of April to the first of October; and the western, from the first of October to the first of April; the time is computed from 12 at noon. The western elongations in the first case, and

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.

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1837 1° 50' 1° 52' 1° 55' 1° 58' 20 2' 20 512° 10'

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1° 57' 2° 01' 2° 4'
2004/2

1° 49′ │1° 51′ 1° 54′ 1° 57.

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1840 1841 1° 48' 1° 51′ 1° 53' 1° 57' 2° 0' 2° 32° 8'

1842

1843

1° 56' 1° 59' 2° 3′

20 7

21 2° 7

2

1° 48' 1° 50' 1° 53' 1° 47' 1° 50' 1° 52' 1° 56′ 1° 59' 1844 1° 47'1° 49' 1° 52' 1° 55′ 1° 5812° 2′ 2° 61

1845 1° 46' 1° 49′ 1° 51'1° 55′ 1o 58' 2o

112° 6'

1846 1° 46′ 1° 48′ | 1° 51′ │1° 54′| 1° 57′| 2° 1′

2

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 the telescope of the theodolite. Let this board be so fixed

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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

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