119. A great number of similar problems might be proposed. The solution of them does not, however, properly belong to surveying. The laying out of the ground, and the tracing of lines, after the figure and area have been determined, are the only parts which appertain to a practical treatise. The manner of tracing lines having been already explained, it seems unnecessary to add the numerous examples often given under this head of the subject.

CHAPTER IV.

Of the Surveying Compass:—Of Surveying with the Compass.— Of the Plane-Table.

120. Before considering the principles involved in the method of surveying now to be explained, it will be necessary to describe the instrument principally used in the field, and which is called

THE CIRCUMFERENTER, OR SURVEYOR'S COMPASS.

Pl. 2, Fig. 2. This instrument consists of a compass-box DCE, a magnetic needle, a brass plate AB, from twelve to fourteen inches long, two plain sights, AF and BG, one of which is more fully shown in Fig. 3; and a stand, which is sometimes a tripod, and sometimes a single staff pointed with iron at the lower end, so that it may be placed firmly in the ground.

The open sights, AF and BG, are placed at right angles to the plate AB, and fastened to it firmly by the screws a and b. In each sight there is a large and small aperture or slit; the larger aperture being above the smaller in one of the sights, and below it in the other. A hair or thread of silk is drawn vertically through the middle of the large aperture, as shown in Fig. 3.

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 freely around the point of support, will settle to a state of rest: the direction which it then indicates, is called the magnetic meridian.

In the interior of the compass-box, there is a graduated circle divided to degrees, and sometimes to half degrees: the degrees are numbered from the extremities of the diameter NS, both ways to 90°.

The length of the magnetic needle is a little less than the diameter of the graduated circle, so that the needle can move freely around its centre, within the circle, and its positions be noted on the graduated arc.

The compass-box is turned about its centre, without moving the plate AB, by means of the milled screw L: it is fastened to the plate AB, by the screw P.

In using the compass, it is important to ascertain the exact angle which may be included between the magnetic meridian and the direction that may be given to the line drawn through the eye and the sights AF and BG.

To effect this, a small arc HI is described on the bar AB, having its centre at the centre of the compass-box. This arc is divided to degrees, and sometimes to the parts of a degree. A vernier is also used, which is permanently attached to the compass-box.

When the 0 point of this vernier coincides with the o point of the graduated arc HI, the line of the compass-box marked NS, has the same horizontal direction as the line along which the sights are directed.

Now, supposing the 0 of the vernier to coincide with the 0 of the arc HI, if the end of the needle does not stand at one of the lines of division of the graduated circle, let the whole degrees be read. Then, turn the compass-box by means of the screw L, until the needle points exactly to the line which marked the whole degrees: the space passed over by the 0 of the vernier, shows the minutes that are to be added.

OF SURVEYING WITH THE COMPASS.

121. The line about which the earth revolves is called its axis; and the two points in which the axis meets the surface

122. A meridian is a line traced on the surface of the earth, which would, if sufficiently produced in both directions, pass through the poles. Hence, all the meridian lines intersect each other at the two poles.

The poles, however, are so distant from each other, that no sensible error will arise in supposing the meridians to be parallel; and since, in all the surveys made with the compass, the surface of the ground is regarded as a horizontal plane, the meridians are represented by horizontal and parallel lines.

123. When the compass is placed on its stand, and the needle is allowed to settle to a state of rest, the direction it assumes has been named the magnetic meridian. Although this line is different from the true meridian, yet in the surveys made with the compass, we shall take for the meridian that line which is determined by the direction of the magnetic needle.

124. If the right hand be turned towards the point where the sun rises, the direction pointed by the farthest end of the needle is called north; the direction shown by the nearest end is called south, and the line thus indicated is called a north and south line, as well as a meridian.

125. A line perpendicular to the meridian is called an east and west line: the east point being on the right hand, and the west on the left.

126. A line traced or measured on the ground, is called a course; and the angle which this line makes with the meri dian 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.

W

D

N

When the course, like AB, falls between the north and east points, the bearing is read, north 46° east, and is written, N 46° E.

When the course, like AC, falls between the north and west points, the bearing is read, north 30° west, and is written, N 30° W.

When the course, like AF, falls between the south and east points, the bearing is read, south 70° cast, and is written, S 70° E. When the course, like AD, W falls between the south and west points, the bearing is read, south 70° west, and is written, S 70°

W.

D

N

B

E

A

F

S

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

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

128. 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 of the points is north or south of the other. Thus, in running the course from A to B, AC is the difference of latitude, north.

129. 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,

N

H

C

B

G

W

A

E

S

according 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. 130. It will be found convenient, in explaining the rules for surveying with the compass, to attribute to the latitudes and departures the algebraic signs, + and ; which are read plus and minus.

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-.

131. The meridian distance of a point is the perpendicular let fall on the meridian, from which the distance is estimated. This meridian is called the assumed meridian. Thus, if the distance be estimated from NS, BC will be the meridian distance of the point B.

132. The meridian distance of a line, is the distance of the middle point of that line from an assumed meridian: 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 tine 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.

133. When a piece of ground is to be surveyed, we begin at some prominent corner of the field, and go entirely around the land, measuring the lengths of the bounding lines with the chain, and taking their bearings with the compass. It is not material whether the ground be kept on the right hand or on the left, and all the rules deduced for one of the cases, are equally applicable to the other. To preserve, however, an uniformity in the language of the rules, we shall suppose the land to be always kept on the right hand of the surveyor.