Wednesday 29 August 2018

ORIENTATION OF PLANE TABLE




ORIENTATION

The method of setting up plane table at each of the successive stations parallel to the position it occupied at the starting station is known as orientation.
  Orientation must be done when the plane table is set up at more than one station. As already started, plane tabling is base on principle of parallelism. So, the relative position of the objects on the map will be accurate only if the orientation is proper. But orientation is not done, then the map will not represent the actual position of the objects.
  Orientation may be done by magnetic needle and back-sighting.

Orientation by magnetic needle: This method is suitable when the local attraction is not suspected in the area.

Procedure [a] Suppose A and B are two stations. The plane table is set up at station A and levelled by sprit level. The centring is done by U-fork and plumb bob so that the point a is just over station A. Then the tough compass or circular box compass is placed on the right-hand top corner of the sheet in such a way that the needle is coincides with ‘0-0’ mark. After this a line representing the north line is drawn through the edge of the compass box. The table is then clamped.

[b]. With the alidade touching the point a, the ranging rod at B is bisected and a ray is drawn. The distance AB is measured and plotted to any suitable scale.    

[c]. The table is shifted and centred over B, so that the point b is just over B. The table is levelled. Now the trough compass is placed exactly along the north line drawn previously. The table is then turn clockwise or anticlockwise until the needle coincides exactly with the 0-0 mark of the compass.
  While turning the table, care should be taken not to disturb the centring. In case it is, it should be adjusted immediately.

[d]. When centring and leveling are perfect and the needle is exactly at 0-0, the orientation is said to be perfect (Fig. 8)




Orientation by back-sighting: This method is accurate and is always preferred.

Procedure [a] Suppose A and B are two stations. The plane table is set up at station A and levelled by sprit level. The centring is done by U-fork and plumb bob so that the point a is just over station A. Then the tough compass or circular box compass is placed on the right-hand top corner of the sheet in such a way that the needle is coincides with ‘0-0’ mark. After this a line representing the north line is drawn through the edge of the compass box. The table is then clamped.

[b]. With the alidade touching the point a, the ranging rod at B is bisected and a ray is drawn. The distance AB is measured and plotted to any suitable scale.    

[c]. The table is shifted and centred over B, so that the point b is just over B. The table is levelled. Now the alidade is placed along the line ba, and the ranging rod at A is bisected by turning the table clockwise or anticlockwise. At this time the centring may be disturbed and should be adjusted immediately if required. When the centring, leveling and bisection of the ranging rod a A are perfected, then the orientation is said to be perfect (Fig. 9).




(Next post on “METHOD OF TABLING”)


Sunday 26 August 2018

PLANE TABLE SURVEYING





PLANE TABLE SURVEYING

PRINCIPLE AND ACCESSORISES OF PLANE TABLE.

PRINCIPLE

  The principle of plane tabling is parallelism, meaning that the rays down from stations to subjects on the paper are parallel to the lines from the stations to the objects on the ground. The relative positions of the objects on the ground are represented by their plotted positions on the paper and lie on the respective rays.
  The table is always placed at each of the successive stations parallel to the position is occupied at the starting station. Plane tabling is graphical method of surveying. Here, the field work and plotting are done simultaneously, and such survey does not involve the used oh field book.
  Plane table survey is suitable for filling interior details when traversing is done by theodolite. Sometimes traversing by plane table may also be done. But this survey is recommended for the work where grate accuracy is not required. As the fitting and fixing arrangement of this instrument is not perfect, most accurate work can not be expected.  

ACCESSORISES OF PLANE TABLE.

1). Plane table: The plane table is a drawing board of size by 750 mm x 600 mm made of well-seasoned wood like teak, pine, etc. the top surface of the table is well leveled. The bottom surface consists of a threaded circular plate for fixing the table on the tripod stand by a wing nut.
  The plane table is meant for fixing drawing sheet over it. The positions of the objects are located on this sheet by drawing rays and plotting to any suitable scale (Fig. 1).
  



2). The alidade: There are two types of alidade – plain and telescopic.

a). Plain alidade. The plain alidade consists of a metal or wooden ruler of length about 50 cm. one of its edges is beveled and is known as the fiducial edge. It consists of two vanes at both ends which is hinged with the ruler. One is the known as the ‘object vane’ and carries a horse hair; the other is called ‘sight vane’ and is provided with a narrow slit (Fig. 2).  
  

Fig. 2 

b). Telescope alidade. The telescope alidade consists of a telescope meant for inclined sight or sighting distant objects clearly. This alidade has no vanes at the ends but is provided fiducial edge.
  The function of the alidade is to sight objects. The rays should be drawn along the fiducial edge (Fig. 3).


Fig. 3 

3). The sprit level: The sprit level is a small metal tube containing a small bubble of sprit. The bubble is visible on the top along a graduated glass tube.
  The sprit level is meant for leveling the plane table (Fig. 4).


Fig. 4 

4). The compass: There are two types of alidade – (a) the tough compass and (b) the circular box compass.

a). The Touch Compass. The tough compass is a rectangular box made of non-magnetic metal containing a magnetic needle pivoted at the centre. This compass consists a ‘0’ mark at both ends to locate the N-S direction (Fig. 5).


Fig. 5

b). The Circular Box Compass. It carries a pivoted magnetic needle at the centre. The circular box fitted on a square base plate (Fig. 6).
  Sometimes two bubble tubes are fixed at right angles to each other on the base plate.
  The compass is meant for making the north direction of the map.


Fig. 6

5). U-fork or plumbing fork with plumb bob: The U-fork is a metal strip bent in the shape of ‘U’ having equal arm lengths. The top arm is pointed, and bottom arm carries a hook for suspending a plumb bob (Fig. 7).
  This is meant for centering the table over a station.


Fig. 7 

(Next post on “ORIENTATION OF PLANE TABLE”)


Tuesday 21 August 2018

CHECK ON CLOSED AND OPEN TRAVERSE FOR COMPASS SURVEYING




CHECK ON CLOSED AND OPEN TRAVERSE

CHECK ON CLOSED TRAVERS

1). Check on angular measurements.

a). The sum of measured interior angles should be equal to (2n-4) x 90⁰ where  n is the number of sides of the traverse.
b). The sum of measured exterior angles should be equal to (2n+4) x 90⁰.
c). The algebraic sum of the deflection angles should be equal to 360⁰.

Right hand deflections are considered positive and left-hand deflection negative.

2). Check on linear measurements.

a). A line should be once each of two different days (along opposite direction). Both measurement should tally.
b). Linear measurements should also be taken by stadia method. The measurements by chaining or by other method should tally.


CHECK ON OPEN TRAVERS

In open traverse, the measurements can not be checked directly. But some field measurements can be taken to check the accuracy of the work. The methods are discussed below.

a). Taking cut-off lines. Cut-off lines are taken between some intermediate stations of the open traverse. Suppose ABCDEFG represents an open traverse. Let AD and DG be the cut-off lines. The length and the magnetic of the cut-off lines are measured accurately. After plotting the traverse, the distances and bearings are noted from the map. These distances and bearings should tally with the actual records obtained from the field (Fig. 12)


b). Taking an auxiliary point. Suppose ABCDEF an open traverse. A permanent point P is selected on the side of it. The magnetic bearings of this point are taken from traverse stations A, B, C, D, etc. If the survey carried out accurately and so is the plotting, all the measured bearings of P when plotted should meet at the point P. The permanent point P is known as the ‘auxiliary point (Fig. 13)



(Next Post on “PLANE TABLE SURVEYING”.)


Monday 20 August 2018

KERALA IS FACING ITS WORST FLOOD IN 100 YEARS. MORE THAN 300 PEOPLE HAVE LOST THEIR LIVES AND MORE THAN 2 LAKH PEOPLE HAVE BEEN DISPLACED.
TOTAL DAMAGE IS OVER 19,500,00,00,000 INR.

IT IS IMPORTANT THAT COMMON PEOPLE LIKE US HELP!
YOU CAN DONATE DIRECTLY TO THE CHIF MINISTER'S DISTRESS RELIF FOUND (CMDRF) THROUGH THE BANK ACCOUNT (GIVEN BELOW). WHATEVER AMOUNT POSSIBLE :

LINK
https://donation.cmdrf.kerala.gov.in/

THANK YOU 🙏

Sunday 19 August 2018

METHODS OF TRAVERSING BY COMPASS




METHODS OF TRAVERSING

Traverse survey may be conducted by the following methods:

1). Chain traversing (by chain angles)
2). Compass traversing (by free needle)
3). Theodolite traversing (by fast needle) and
4). Plane table traversing (by plane table)

1). Chain traversing: Chain traversing is mainly conducted when it is nor possible to adopt triangulation. In this method the angles between adjacent sides are fixed by chain angles. The entire survey is conducted by chain and tape only and no angular measurements are taken. When it is not possible to form triangles, as, for example, in a pond, chain traversing is conducted, as shown in Fig. 11.a and 11.b.
  The formation of chain angles is explained below.


First method- Suppose a chain angle is to be formed to fixed direction of sides AB and AD. Tie stations T₁ and T₂ are fixed on lines AB and Ad. The distances AT₁, AT₂ and T₁T₂ are measured. Then the angle T₁AT₂ is said to be chain angle. So, the chain angle is fixed by the tie line T₁T₂ (Fig. 11.a).
    
Second method- Sometimes the chain angle is fixed by chord. Suppose the angles between lines AB and AC is to be fixed. Taking A as the centre and a radius equal to 15 metre, an arc intersecting the lines AB and AC at points P and Q, respectively, is drawn. The chord PQ is measured and bisected at R (Fig. 11.b).

Let Angle PAR = θ

Then Angle BAC = 2θ

Here, AP = AQ = 15 m

In triangle PAR,

Sinθ = PR/AP = 2PR/2AP = PQ/30

Θ = Sinˉ¹ PQ/30

  The angle θ can be calculated from the above equation, and the chain angle BAC can be determined accordingly.

2). Compass traversing: In this method, fore and back bearings of the traverse legs are measured by prismatic compass and the sides of the traverse by chain or tape. Then the observed bearings are verified and necessary corrections for local attractions are applied. In this method, closing error may occur when the traverse is plotted. This error is adjusted graphically by using ‘Bowdithc’s rule’ (which is describe in future post).

3). Theodolite traversing: In such traversing, the horizontal angles between the traverse legs are measured by theodolite. The lengths of the legs are measured by chain, or tape, or employing the stadia method or by digital instrument. The magnetic bearing of starting leg is measured by theodolite. Then the magnetic bearings of other sides are calculated. The independent coordinates of all traverse stations are then found out. This method is very accurate.

4). Plane table traversing: In this method, a plane table is set at every traverse stations in the clockwise or anticlockwise direction, and the circuit is finally closed. During traversing the sides of the traverse plotted according to any suitable scale. At the end of the work, any closing error which may occur is adjusted graphically.

(Next Post on “CHECK ON CLOSED AND OPEN TRAVERSE”.)



Friday 17 August 2018

PRINCIPLE OF COMPASS SURVEYING




PRINCIPLE OF COMPASS SURVEYING

  The principle of compass surveying is traversing, which involves a series of connected lines. The magnetic bearings of the lines are measured by surveyor compass and the distances od the lines are measured by chain or tape. Such survey does not require the formation of a network of triangles.
  Interior details are located by taking offsets from main survey lines. Sometime subsidiary lines may be taken for locating these details.
  Compass surveying is recommended when:

a). A large area to be surveyed,
b). The course of a river or coast line to be surveyed and
c). The area is crowded with many details and triangulation is not possible.

  Compass surveying is not recommended for areas where local attraction is suspected due to the presence magnetic substances like steel structure, iron ore deposit, electric cable conveying current, and so on.
 
TRAVERSING

  As already started in the last section, surveying which involves a series of connected lines is known as traversing. The sides of the traverse are known as ‘traverse legs’.
  In traversing, the lengths of the lines are measured by chain or tape and the directions are fixed by compass or theodolite or by forming angles with chain and tape.
 A traverse may be two types- closed and open.

Closed traverse: When a series of connected lines forms a closed circuit, i.e. when the finishing point coincides with starting point of a survey, it is called a ‘closed traverse’. Here ABCDEA represents a closed traverse (Fig. 9). Closed traverse is suitable for survey of ponds, forests, estates, etc.



Open traverse: When a sequence of connected lines extends along a general direction and dose not return to the starting point, it is known as ‘open traverse’ or ‘unclosed traverse’ Here ABCDE represents an open traverse (Fig. 10).




(Next Post on “METHODS OF TRAVERSING”.)


Wednesday 15 August 2018

THE EARTH'S MAGNETISM. —Dip of the Needle




Magnetic Declination: The horizontal angle between magnetic meridian and true meridian is known as ‘magnetic declination’.

  When north end of the magnetic needle is pointed towards the west side of the true meridian the term ‘Declination West’ (θ W) (Fig. 7.a).

  When north end of the magnetic needle is pointed towards the east side of the true meridian the term ‘Declination East’ (θ E) (Fig. 7.b).



Isogonic and agonic lines:
  The lines passing through zero declination is said to be the ‘aogonic’ line (Fig. 8).




Variation of Magnetic Declination: The magnetic declination at a place is not constant. It varies due to the following reasons:

a). Secular Variation: The magnetic meridian behaves like a pendulum with respect to the true meridian. After every 100 years or so; it swings from one direction to the opposite direction, and hence the declination varies. This variation is known as ‘secular variation’.

b). Annual Variation: The magnetic declination varies due to the rotation of the earth, with its axis inclined, in an elliptical path around the sun during the year. This variation is known as ‘annual variation’. The amount of variation is about 1 to 2 minutes.

c). Diurnal Variation: The magnetic declination varies due to the rotation of the earth, with its own axis in 24 hours. This variation is known as ‘diurnal variation’. The amount of variation is found to be about 3 to 12 minutes.

d). Irregular Variation: The magnetic declination is found to vary suddenly due to some natural causes, such as earthquake, volcanic eruptions and so on. This variation is known as ‘irregular variation’.

Dip of the magnetic needle: If a needle perfect balanced before magnetisations, it does not remain balanced position after it is magnetised. This is due to magnetic influence of earth. The needle is found to be inclined toward the pole. This inclination of the needle with the horizontal is known as ‘dip of the magnetic needle’.
  It is found that the north end of the needle is deflected downwards in the northern hemisphere and that its south end deflected downwards in the southern hemisphere. The needle is just horizontal at the equator. To balance dip of the needle, a rider (brass or silver coil) it provided along with it. The rider is placed over the needle at a suitable position to make it horizontal.

Local attraction: A magnetic needle indicates the north direction when freely suspended or pivoted. But the needle comes near some magnetic substances, such as iron ore, steel structure, electric cable conveying current: etc. it is found to be deflected from its true direction, and dose not show the actual north. This disturbing influence of magnetic substance is known as the ‘local attraction.    
  To detect the present of local attraction, the fore and back bearing of a line should be taken. If the difference fore and back bearings of the line is exactly 180⁰, then there is no local attraction.
  To compensate of local attraction, the amount of error found out and is equally distributed between fore and back bearings of the line.
  For example, consider a case when

Observed FB of line AB = 70⁰30’
Observed BB of line AB = 230⁰0’

Calculated BB of line AB = 70⁰30’ + 180⁰ = 250⁰30’
Corrected BB of line AB = ½ (230⁰0’+250⁰30’) =240⁰15’
Hence Corrected FB of line AB = 240⁰15’ -180⁰ = 60⁰15’

Method of application of correction

a). First method: The interion angles of a traverse are calculated from the observed bearings. Then an angular check is applied. The sum of interion angles should be equal to (2n-4) x 90⁰ (n being the number of sides of the traverse. If it is not so, total error equally distributed among all the angles of the traverse.
  Then starting from the unaffected line, the bearings of lines may be corrected by using the corrected interior angles. This method is very laborious and is not generally employed.

b). Second method: In this method interior angles are not calculated. From the given table, the unaffected line is first detected. Then, commencing from the unaffected line, the bearings of the other affected lines are connected by finding the amount of correction at each station.
  This is an easy method, and one which is generally employed.
  If the all lines of a traverse are found to be affected by local attraction, the line with minimum error is identified. The FB and BB of this line are adjusted by distributing the error equally. Then, starting from the this adjusted line, the fore and back bearings of other lines are corrected.
  

(Next Post on “PRINCIPLE OF COMPASS SURVEYING”.)


Tuesday 14 August 2018

COMPASS TRAVERSING




COMPASS TRAVERSING

TYPES OF COMPASS
  There are two types of compass:
1). Prismatic compass and
2). Surveyor’s compass.

PRISMATIC COMPASS. – In this compass, the readings are taken with the help of a prism. The following are essential parts of this compass.

(a). Compass Box. The compass box is a circular metallic box (the metal should be non-magnetic) of diameter 8 to 10 cm. A pivot with a sharp point is provided at the centre of the box.

(b). Magnetic Needle and Graduated Ring. The magnetic needle is made of a broad, magnetised iron bar. The bar is pointed at both end. The magnetic needle is attached to a graduated aluminium ring.
  The ring is graduated from 0⁰ to 360⁰ clockwise, and the graduations begin from the south end of the needle. Thus 0⁰ is marked at the south end, 90⁰ at the west, 180⁰ at the north and 270⁰ at the east. The degrees are again subdivided into half degree. The figures are written upside down. The arrangement of the needle and ring contains a agate cap pivoted at central pivot point. A rider of brass or silver coil is provided with the needle to counterbalance its dip.

(c). Sight Vane and Prism. The sight vane and the reflecting prism are fixed diametrically opposite to the box. The sight vane is hinged with the metal box and consist of a horsehair at the centre. The prism consists of a sighting slit at the top and two small circular holes, one at the bottom of the prism and other at the side of the observer’s eye.

(d). Dark Glasses. Two dark glasses are provided with the prism. The red glass is meant for sighting illuminous objects at night and blue glass for reducing the stain on the observer’s eye in bright daylight.

(e). Adjustable Mirror. A is provided with the sight vane. The mirror can be lowered or raised and can also be inclined. If any object is too low or too high with respect to the line of sight, the mirror can be adjusted to observe it through reflection.

(f). Brake Pin. A brake pin is provided just at the base of sight vane. If presses gently, it stops the oscillations of the ring.

(g). Lifting Pin. A lifting pin is provided just at the below the sight vane. When the sight vane is folded, it presses lifting pin. The lifting pin then lifts the magnetic needle out of the pivot to prevent damage to the pivot head.

(h). Glass Cover. A glass cover is provided on the top of the box to protect the aluminium ring from (Fig. 1).



Fig. 1

THE SURVEYOR'S COMPASS. —The surveyor's compass is an instrument for determining the direction of a line with reference to the direction of a magnetic needle. The needle is balanced at its centre on a pivot so that it swings freely in a horizontal plane. The pivot is at the centre of a horizontal circle which is graduated to degrees and half-degrees and numbered from two opposite zero points each way to 90°. The zero points are marked with the letters N and S, and the 90° points are marked E and W. The circle is covered with a glass plate to protect the needle and the graduations, the part enclosed being known as the compass-box. A screw is provided for raising the needle from the pivot by means of a lever. The needle should always be raised when the compass is lifted or carried, to prevent dulling the pivot-point; a dull pivot-point is a fruitful source of error. Both the circle and the pivot are secured to a brass frame, on which are two vertical sights so placed that the plane through them also passes through the two zero points of the circle. This frame rests on a tripod
and is fastened to it by means of a ball-and-socket joint. On the frame are two spirit levels at right angles to each other, which afford a means of levelling the instrument. This ball-and-socket joint is connected with the frame by means of a spindle which allows the compass-head to be revolved in a horizontal plane, and to be clamped in any position.

True Meridian: The line passing through the geographical north pole, geographical south pole and any point surface of the earth, is known as the ‘true meridian’ or ‘geographical meridian’ (Fig. 2). The true meridian at a station is constant. The true meridian passing through different points of the earth’s surface are not parallel but converge towards the pole. But for surveys in small area, the true meridian passing through different points are assumed parallel.    



Magnetic Meridian: The magnetic needle possesses the property of pointing in a fixed direction, namely, the Magnetic Meridian (Fig. 2).
 The horizontal angle between the direction of this meridian and of any other
line may be determined by means of the graduated circle, and this angle is called the Magnetic Bearing of the line (Fig. 2), or simply its Bearing. By means of two such bearings the angle between two lines may be obtained. Bearings are reckoned from 0° to 90°, the 0° being either at the N or the S point and the 90° either at the E or the W point. The quadrant in which a bearing
falls is designated by the letters N.E., S.E., S.W., or N.W. For example, if a line makes an angle of 20° with the meridian and is in the southeast quadrant its bearing is written S 20° E.
Sometimes the bearing is reckoned in a similar manner from the geographical meridian, when it is called the true bearing (Fig. 2). In general, this will not be the same as the magnetic bearing. True bearings are often called azimuths and are commonly reckoned from the south point right-handed (clockwise) to 360°; i.e., a line running due West has an azimuth of 90°, a line due North an azimuth of 180°. Sometimes, however, the azimuth is reckoned from the north as in the case of the azimuth of the Pole-star.

Arbitrary Meridian: Sometimes for the survey of a small area, a convenient direction is assumed as a meridian, known as the ‘arbitrary meridian’. Sometimes the starting line of a survey is taken as the ‘arbitrary meridian’. The angle between arbitrary meridian and a line is known as the ‘arbitrary bearing’ of the line.

Grid Meridian: Sometime, for preparing a map assume several lines are parallel to those on adjoining sheets, although they are numbered differently. The vertical lines are not true north and south lines unless on one particular line which corresponds with a meridian that is roughly the central meridian of the country. The whole network forms what is called a grid and the northward direction of the vertical lines is called grid north. Grid bearings are bearings referred to the direction of grid north as given by the vertical lines. At any point the difference between the directions of true north and grid north is a small angle called the convergence, and this varies according to the position of the point east or west of the central meridian, being greater in magnitude the farther away the point is from this meridian.

Designation of magnetic bearing: Magnetic bearings are designated by two systems:
b). Quadrantal bearing (QB)



Whole-circle bearing (WCB): The bearing of an object is the angle between some fixed direction and the direction of the object. Thus, in (Fig. 3), if is the position of the observer
and OP the fixed direction from which bearings are reckoned, the
bearing of the point A is the (Fig. 3) angle POA.
  Usually bearings are reckoned clockwise from through 90⁰, 180⁰ and 270⁰ to 360⁰ from the fixed direction, so that in fig. 3 the angles marked α, β and θ are the bearings from to A, B and C respectively. Bearings reckoned in this way are called whole-circle bearings.

Quadrantal bearing (QB): The magnetic bearing of a line measured clockwise or counter clockwise from the North pole or South pole (whichever is nearer the line) towards the East or West is known as the ‘quadrantal bearing’ (Fig. 4).  



Reduced bearing (RB): In computing, and in work with the magnetic compass, it is often convenient to use what are called reduced bearings. A reduced bearing is the angle between the main vertical line marking the direction to which bearings are referred and the given line, measured 0⁰ from to 90⁰ the shortest way, east or west and north or south of the point, to that line. Thus, in fig. 5, in which the circle is divided into four quadrants
numbered I, II, III and IV, the reduced bearings of the lines OA,
OB, OC and OD are indicated by the Greek letters α, β, y and δ, and
are all reckoned the shortest way, east or west, from the line SN. If
the bearings are given on the whole-circle system, it can easily be seen
from the figure that we have the following rules for obtaining reduced
bearings:




    If the whole-circle bearing lies in the first quadrant, i.e. between and 90⁰, the reduced bearing is the same as the whole-circle bearing.

   If the whole-circle bearing lies in the second quadrant, i.e. between 90⁰ and 180⁰, the reduced bearing is 180⁰ minus whole-circle bearing.

   If the whole-circle bearing lies in the third quadrant, i.e. between 180⁰ and 270⁰, the reduced bearing is whole-circle bearing minus 180⁰.

  If the whole-circle bearing lies in the fourth quadrant, i.e. between 270⁰ and 360⁰, the reduced bearing is 360⁰ minus whole-circle bearing.

It should be noted that a reduced bearing never exceeds 90⁰ in value, and, when bearings are derived and expressed in the first place as whole-circle bearings, and reduced bearings are used only as a convenience in computing, a reduced bearing need take no account of the quadrant in which the line lies. If, however, it is desired to specify the quadrant in which a reduced bearing lies, this is done by putting the letter N or S before the figures giving the actual bearing, according as to whether the latter is
measured from the direction of north or south, and then inserting
after the figures the letters E or W to show whether the bearing lies east or west of the north and south line. Thus, the bearings a, j8, y and S in fig. 5 would be written as NαE, SβE, SyW and NδW respectively. Magnetic compasses are often graduated on the quadrantal system, with the letters, N, E, S and W marked on the card or rim, and accordingly magnetic bearings are commonly booked and expressed in terms of reduced bearings, with the proper distinguishing letters before and after them to specify the quadrant.
The rules given above are so simple that it is hardly worth while attempting to memorize them, as any given case can easily be worked out from first principles. As practice is gained, the computation becomes almost automatic without conscious effort. The importance of reduced bearings in computing lies in the fact that most mathematical tables only tabulate the values of the trigonometrical functions and their logarithms in terms of angles lying between and 90⁰. Accordingly, when whole-circle bearings are used, it is usually necessary to convert them into reduced bearings before entering the tables.

Fore bearing and Back bearing: In fig. 6, AB, is the reference direction from which bearings are reckoned. Then the bearing of the line AB is the angle marked a. At B draw BE' parallel to AB. At B bearings are reckoned clockwise from BE', and the bearing of the line BA is the angle marked α',
which, it will easily be seen, is 180⁰+α. If the direction AB is taken
as the forward direction of the line and the bearing in that direction
as the forward or fore bearing, the bearing in the back or reverse direction BA differs from the forward bearing by 180⁰, and is known as the back or reverse bearing of the line as viewed from station A. It will thus
be seen that the back bearing of AB at station A is the forward bearing
of BA at station B. By drawing diagrams for each case, the student can verify the following rules: 



 If fore bearing is in quadrants I or II, back bearing = fore bearing + 180.

If fore bearing is in quadrants III or IV, back bearing = fore bearing - 180.

These rules also follow from the rules for working out bearings from angles, because, since BA is the direction of AB turned clockwise through 180⁰, the bearing of BA can be obtained by adding the angle of reversal (180⁰) to the bearing of AB.

EXAMPLE

Fore Bearing  
     67⁰        131⁰     216⁰     348⁰        12⁰   +180⁰     +180⁰    -180⁰     -180⁰    +180⁰
   247⁰        311⁰      36⁰       151⁰      192⁰
Back Bearing……..     

(Next Post on “THE EARTH'S MAGNETISM. —Dip of the Needle”.)


ESTIMATING

  ESTIMATING   What is an Estimate?       Before starting any work for it’s execution the owner or client or builder or contractor shoul...