**IMPORTANT DEFINITIONS:**

**The Magnetic ****North (****MN)**

Our Earth has a magnetic axis inclined to the line of longitude, which divides the earth into two equal parts. This magnetic axis is the property that influences the needle of a compass. When a compass needle is allowed to swing freely and settle, it points to the northern pole of this axis, and the direction so indicated is referred to as the Magnetic North. The magnetic North therefore is the direction of the pole of the earth’s magnetic axis from any point on the earth’s surface as indicated by the freely suspended needle of a compass. It is important to note that the Magnetic North forms the basis for all angular measurements with surveying instruments. Without it, surveying with the theodolite and compass would not be possible.

**True North (TN)**

The direction indicating the pole of the earth’s geographic axis in the Northern Hemisphere All other lines referenced to this are referred to as true north bearings. (See Fig.2.1) The figure below shows the Magnetic North (MN), the True North (TN), the True South, (TS) and the Magnetic South (MS).

**The Azimuth**

The Azimuth is the smallest bearing to a point measured Eastward or Westward from a particular reference North. Azimuths may be measured either with reference to the Magnetic North or to the True North and referred to as Magnetic North and True North Azimuths respectively. The azimuth begins from °0 or 360° representing North and runs through 90° East, 180° South, 270° West and back to 360°North.

**BEARINGS**

The mathematical analysis of survey data begins with the reduction of the bearings obtained from the analysis above, to quadrantal bearings.(See Fig. 3.1 below)

The next thing to do is to resolve the measured ground distances to their Horizontal and vertical components. We do this by finding the sine and cosine of each quadrantal bearing and multiplying by the measured distance on the ground. The sine of the bearing, multiplied by the distance gives the horizontal X axis value or Easting Component often referred to as the DEPARTURE while the cosine of the bearing multiplied by the measured distance gives the Vertical Y axis value or Northing Component often designated as the LATITUDE.

One very important characteristic to note about quadrantal bearings is that, they are measured relative to the N and S and NOT to the E and W cardinal points. Quadrantal bearings always have a preceding N or S followed by E or W depending on the quadrant in which the bearing falls. (N=north, S=South, E=East and W=West) (See Fig. 3.1) The primary objective of reducing whole circle bearings to quadrantal bearings is to reduce the bearings to values between 0 and 90 degrees. This facilitates the calculation of sines and cosines which, when multiplied by the distances measured will produce DEPARTURES and LATITUDES respectively.

**Angles of the first Quadrant:**

Angles equal to or less than 90 degrees retain their values and is placed in the first quadrant. 90-degree angles are referred to as Due East. For example a bearing of 75 degrees is referred to asN 75o E in quadrantal terms. A bearing of 90 o is referred to as DUE EAST.

**Angles of the second Quadrant:**

Bearings greater than 90o, but less than 180o, are usually subtracted from 180o. The resulting angle is then measured from the South cardinal point. South falls into the second quadrant. 180-degree bearings are referred to as Due South. For example, a bearing of 170o reduced to quadrantal bearings will be (180 o-170o) = S 10o E. A bearing of 180 o is referred to as DUE SOUTH.

**Angles of the third Quadrant:**

Bearings greater than 180o, have 180o subtracted from them to produce quadrantal bearings of the third quadrant. The resulting bearings are measured from the south cardinal point and written as S “bearing” W. For example, a whole compass bearing of 196o would be (196o -180o) = S 16o W in quadrantal terms. A bearing of 270 o is referred to as DUE WEST.

**Angles of the fourth Quadrant:**** **

Angles greater than 270 o fall into the fourth quadrant. To obtain quadrantal

bearings of the fourth quadrant, such bearings are subtracted from 360o. For example, a whole compass bearing of 288owould be (360 o -288o) = N 72o W. A bearing of 0 o or 360 o is referred to as DUE NORTH.

**Local Attraction**

This is a term denoting any local influence that causes the magnetic needle to be deflected away from the magnetic meridian for that locality. This causes wrong measurements to be obtained. Measuring both the forward and the back bearing helps to detect local attraction. Some sources of local attraction are: permanently fixed objects of iron, steel and magnetite in the ground. Local attraction includes iron and steel articles about the person. High-tension lines are known to influence the needle of the compass and should be avoided where possible. Generally, the difference between the forward bearing (FB) and the Back Bearing (BB) is equal to 180o.

**The Forward Bearing and Back Bearing**

When the bearing of a line is stated in a direction from an original point to a terminal point, it is known as a forward bearing. The back bearing is opposite in direction, to the forward bearing.

If the difference between the forward bearing and the back bearing is exactly 180°, then, the two stations are free from local attraction. As an example, consider a survey line along stations A, B and C. If the forward bearing from A to B is 95°and the back bearing to A from B is 275, the difference between the two bearings is exactly 180° and there will be no reason to suspect any local attraction at stations B and A. If from stationB the bearing to station C is 240 (Forward Bearing) and the back-bearing from station C to B is 61, the difference between the two bearings will be 179°. Since it is already known that there is no local attraction at stations A and B, then there is good reason to suspect local attraction at station C. To confirm this suspicion a forward bearing is taken to station A from station C, and a back-bearing taken from A to C. Since A is known to have no local attraction, if the difference between the two bearings is not exactly 180°, then the presence of local attraction at station C is confirmed.

**Magnetic Declination/Variation (MD or MV)**

This is the angle the magnetic axis makes with the earth’s geographic axis.(angle q in Figure 12). It is often synonymously referred to as the Magnetic Variation because its value does vary from one point on the earth’s surface to the other. The Isogonic chart of Ghana shows this variability across the entire country as at 1958. The magnetic axis oscillates between West and East, over an angle of about 22°. In other words, its maximum deviation from the true North is 11°. In Ghana, it is presently inclined to the west of True North, and is decreasing at the rate of 6.5 minutes of arc per annum (6.5′). Consequently, the magnetic declination of a particular area is usually subtracted from all magnetic bearings recorded in the field before plotting is done, to reduce the bearings to values that relate to the true north. It is usually very important to critically examine the forest reserve boundary schedule to see whether the bearings refer to the true North or to the magnetic North.

Where the bearings refer to the true North, the magnetic declination of the area in that particular year must be added to each bearing before using the schedule in the field. If however, the schedule is with reference to the Magnetic North, then the use of an ISOGONIC CHART becomes relevant.

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