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1st. By dividing it by 160, when it is in square rods (Art. 85).

2d. By dividing it by 4840, when it is in square yards (Art. 87).

3d. By dividing it by 43560, when it is in square feet (Art. 87.)

BOOK III.

COMPASS SURVEYING.

SECTION I.

DEFINITIONS.

97. The Axis of the earth is the immovable diameter about which it revolves; and the poles are the points in which the axis meets the surface.

98. Any plane passing through the axis of the earth is called a meridian plane; and its intersection with the surface is called a meridian line, or simply a meridian.

99. All the meridians converge towards the poles, but they vary so little from parallelism, within the narrow limits of surveys made with the compass, that they may, without sensible error, be regarded as parallel straight lines.

100. If a magnetic needle be suspended freely, and allowed to settle to a state of rest, a vertical plane passed through its axis is called the plane of the magnetic meridian; and its intersection with the surface of the earth is called the magnetic meridian, or sometimes, a North and South line. A line perpendicular to a North and South line, is called an East and West line.

101. A line traced, or measured on the ground, is called a Course; and the angle which this line makes with the magnetic

meridian, passing through the point of beginning, is called the Bearing.

Thus, if we start from the point

A, and measure in the direction AB, the line AB is the course, and the angle NAB is the bearing.

When the course, like AB, falls between the north and east points, aud makes an angle of 46° with the meridian, the bearing is read, north 46° east, and is written, N. 46° E.

W

E

D

FIG. 56.

When the course, like AC, falls between the north and west points, and makes with the meridian an angle of 30°, the bearing is read, north 30° west, and is written, N. 30° W.

When the course, like AD, falls between the south and west points, and makes an angle with the meridian of 70°, the bearing is read, south 70° west, and is written, S. 70° W.

When the course, like AF, falls between the south and east points, and makes with the meridian an angle of 70°, the bearing is read, south 70° east, and is written, S. 70° E.

A course which runs due north, or due south, is designated by the letter N, or S; and one which runs due east, or due west, by the letter E, or W.

102. If, after having passed over a course, the bearing is taken to the back station, this bearing is called the back sight, or reverse bearing.

103. The perpendicular distance between the east and west lines, drawn through the extremities of a course is called the northing or southing, according as the course is run towards the north or south. This distance is also called the difference of latitude, or simply the latitude, because it shows the distance which one end of the course is north or south of the other.

Thus, in running the course from A to B, AC is the difference of latitude, north.

104. The perpendicular distance between the meridians passing through the extremities of a course, is called the departure of that course, and is east or west, according

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as the course lies on the east or west side of the meridian passing through the point of beginning.

Thus, in running the course AB, CB is the departure, east.

105. It is found convenient, in explaining the rules for surveying with the compass, to attribute to the latitudes and departures the algebraic signs, + and −.

We shall, therefore, consider every northing as affected with the sign+, and every southing as affected with the sign We shall also consider every easting as affected with the sign +, and every westing as affected with the sign.

106. The meridian distance of a point is its perpendicular distance from any assumed meridian. Thus, if the distance be estimated from the meridian NS, BC will be the meridian distance of the point B.

107. The meridian distance of a line, is the meridian distance of its middle point, and is east or west, according as this point lies on the east or west side of the assumed meridian. Thus, FG drawn through the middle point of AB, is the meridian distance of the line AB.

The sign will always be given to the meridian distance of a point or line, when it lies on the east of the assumed meridian, and the sign, when it lies on the west.

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108. The Surveyor's Compass consists of a compass-box, DCE; a magnetic needle; a brass plate, AB, from twelve to fourteen inches long; two plane sights, AF and BG; two spirit

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levels placed at right angles to each other; a brass head, K, to fit the compass to a stand, which is sometimes a tripod and sometimes a single staff, called Jacob-staff, pointed with iron at the lower end so that it may be placed firmly in the ground.

109. The compass-box DCE is circular, and generally about six inches in diameter. At the centre is a small pin, on which the magnetic needle is poised. This needle, if allowed to turn

ly around the point of support, will settle to a state of rest;

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