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]]>**It is generally found in two patterns:**

(i) Open cross- staff and

(ii) French cross-staff, the first one being in common use.

**(i) ****Open Cross-Staff:**

The simplest form of cross-staff is the open wooden cross-staff shown in fig. 3.7. It consists of a round or square piece of wood about 4 cm thick and varying form 15 cm to 30 cm in diameter or side mounted on an iron shod wooden staff about 2.5 cm diameter and 1.5 m long. The disc is provided with two saw cuts about 1 cm deep at right angles to each other, giving two lines of sight.

The modified form of the open cross-staff is the metal arm cross-staff (Fig. 3.8) in which the wooden head is replaced by four metal arms with vertical slits for sighting through at right angles to each other.

**(ii) ****French Cross-Staff (Fig. 3.9.): **

It consists of an octagonal brass tube with slits on all the eight sides. It has an alternate vertical sighting slit and an opposite vertical window with a vertical fine wire or horse hair on each of the four sides. These are used for setting out right angles. On the other sides are vertical slits, which are at 45° to those mentioned above for setting out angles of 45°. The sights are about 8 cm apart.

It carries a sockets at the base so that it may be mounted on the pointed staff when in use. The sights being too close, it is not as accurate as the open cross-staff.

**Using the Cross-Staff:**

For setting out a right angle at given point on a chain line, it is held vertically over the given point and turned until one of the saw cuts or (the pair of sights) is ranged along the chain line. Then the line of sights through the other saw cut or the pair of sights) is at right angles to the chain line and a ranging rod can be fixed in this direction at a convenient position.

To find the foot of the perpendicular from an object on a chain line, the cross staff is held vertically at an approximate position of the required object and turned until one of the saw cuts or (the pair of sights) is ranged along the chain line.

If on looking through the other saw cut or (the pair of sights) is seen the object from which the foot of the perpendicular is to be drawn, then the point where the cross-staff is held is the correct position of the foot of the perpendicular from the given object. If not, the cross- staff is moved forward or backward along the chain line until the line of sight through the saw cut or (the pair of sights) at right angles to the chain line bisects the given object.

**Testing a Cross-Staff (Refer fig. 3.10): **

Direct one of the saw cuts or (the pair of sights) say ab along the chain line XY and fix a ranging rod at R in the direction of the other saw cut or (the pair of sights) say ‘cd’. Now move the cross-staff horizontally through 90° so that the saw cut or (the pair of sights) ‘cd’ is along XY. If the instrument is correct, the other saw cut or (the pair of sights) ‘ba’ will point towards the ranging rod R, otherwise not, and then it should be rejected.

The cross-staff is a nonadjustable instrument and is not capable of high accuracy. However out of the above two types, the open one being light and strong is more commonly used.

It is more accurate than the cross-staff and is used for setting out accurately the long offsets. It is a small compact hand instrument based upon the principle of reflection.

**There are two forms of the optical square: **

(i) Round or cylindrical and

(ii) Wedge shaped commonly known as Indian optical square.

**(i) Round or Cylindrical Optical Square (fig 3.11):**

It is a round brass box about 5 cm in diameter and 1.25 cm deep fig. 3.11 (a). It is protected by a metal cover fig. 3.11. (b) which can slide round the box as so as to cover the openings and thus prevents the interior from dust, moisture, etc. when the instrument is not in use. Fig. 3.12 (a) shows the sectional plan of the important parts of the instrument.

H and I are two mirrors placed at an angle of 45° to each other. The mirror H, known as the horizon mirror, is half silvered and half unsilvered and is rigidly attached to the base plate of the box. The mirror I, called the index mirror, is wholly silvered and is attached to the box in such a way that it can be adjusted to any position. In some forms of the instrument, the index mirror is also permanently fixed to the base plate.

Three openings are made in the rims of the box: a is a small hole for the eye ; b is a small rectangular slot for the horizon sight placed diametrically opposite to the eye-hole ; and c is a large rectangular slot for index sight placed at right angles to the line joining a and b.

Three similar openings are also made in the rims of the cover such that each of them is brought over the corresponding opening in the rims of the box when the instruments is in use. A small circular hole is also provided on the top of the cover for inserting the key by means of which the index mirror is adjusted.

The lines ab and cl are called the horizon and the index sights respectively both being at right angles to each other. The horizon mirror makes an angle of 120° to the horizon sight while the index mirror makes an angle of 105° to the index sight, the angle between both the mirror being 45°.

A ray of light from the object or ranging rod O strikes the index mirror (I) and is reflected along IH. Thus reflected ray again strikes the silvered portion of the horizon mirror (H) and is then reflected along HE. Thus the observer, looking through the eye-hole, can see the ranging rod at the far end B of the chain line directly through the unsilvered portion of the horizon mirror and at the same time he can see the image of the ranging rod at O in the silvered portion of the horizon mirror.

If the ranging rod at O is at right angles to the horizon sight (chain line) exactly, then the ranging rod at B and the image of O are exactly coincident as in fig. 3.12 (b) otherwise they do not coincide as in fig. 3.12 (c).

**Principle of Optical Square:**

If there are two plane mirrors whose reflecting surfaces make a given angle with each other and if a ray of light is reflected successively from both of them, then the angle between the first incident ray and the last reflected ray is twice the angle between the two mirrors.

Since we want to set out right angles with the optical square, it follows that the two mirrors in it must make an angle with each other equal to half the right angle i.e 90°/2 = 45°

**The principle underlying the construction of the optimal square can be explained as follows (fig 3.13):**

EB is a chain line and O is an object on the line OI which is at right angles to EB.

A ray of light from O strikes the index mirror (I) and is reflected along (IH). The reflected ray again strikes the horizon mirror (H) and is then reflected towards Eye (E) of the observer.

i.e. the angle between the two mirrors (∠ILH)=45°=1/2 of 90°, which is the angle between the index sight and the horizon sight (chain line).

**Use:**

To find out the foot of the perpendicular from any object upon the chain line, place the eye opposite to the eye-hole so that the small slot (aperture) and the large slot (object-hole) are towards the far end of the chain line and the object respectively.

Then walking forward and backward along the chain line, the point where the reflection of the object as seer on the silvered portion of the horizon mirror appears to be coincident with the ranging rod at the farther extremity of the chain line as seen through the plane portion of the same mirror (fig. 3.12b) is the required point.

**Note: **

If the object lies on the left hand side of the chain line, the instrument is held in the right hand and vice-versa.

To set out a perpendicular from any point on the chain line, stand on the chain line holding the instruments exactly above the point. Now place the small slot (aperture) towards farther end of the chain line and the large slot (object-hole) towards the direction in which perpendicular is to be set out. Sight the end ranging rod through the aperture.

Then instruct the assistant to move to and fro until image of his ranging rod seen through the silvered portion of the horizon mirror appears to be coincident with the ranging rod at the farther end of the chain line as seen through the plane portion of the same mirror. The assistant is then directed to fix the ranging rod in that position. The line joining this position of the ranging rod and the point below the optical square is at right angles to the chain line.

**(ii) Indian Optical Square (Fig 3.14): **

It is a brass wedge shaped hollow box of about 5 cm sides and about 3 cm deep with a handle about 8 cm long fixed underneath, m_{1} and m_{2} are two mirrors fixed to the inclined sides of the box at an angle of 45°; ab and cd are two rectangular openings above these mirrors. PQRS is the open face which is to be turned towards the object to which the offset is to be taken.

**Use (Fig. 3.15):**

In taking an offset from an object say O, the observer holding the instrument in his hand stands on the chain line AB and turns the open face towards the object. He then sights the ranging rod B at the forward station by looking through the openings in the direction cb or ad, according as the object is to his left or right and moves along the chain line forward or backward until the image of the object appears exactly in line with the ranging rod B. The point vertically under the instrument is foot of the perpendicular from the object O and OC is perpendicular to the chain line AB.

In using the instrument, hold it quite erect and always apply the eye to the lower corner of the opening which is nearer the open face PQRS and look diagonally to the forward ranging rod. Thus if the object is to the left of the chain line, apply the eye at c and look in the direction of cb and if to the right, apply it at a and look in the direction of ad.

For setting out a right angle from any point ‘C’ on the chain line, stand on the chain line holding the instrument exactly above the point and turn the open face of the optical square towards the direction in which right angle is to be set out. Sight the end ranging rod ‘B’ through the openings.

Then instruct the assistant to move to and fro until image of his ranging rod ‘O’ seen through the mirror appears to be coincident with the ranging rod at the farther end of the chain line as seen through the openings as in fig. 3.16. (b). The line joining this position of the ranging rod and the point below the optical square is a right angles to the chain line.

It is based upon the same principle as that of the optical square. It is more reliable and bright than the optical square. It requires no adjustment since the angle of 45° between the reflecting surfaces of the prism is fixed.

It using the instrument hold it in your hand and see directly over the prism a ranging rod at B. Then walk along the chain line until the image of the object ‘O’ seen in the prism appears to coincide with the ranging rod at B.

When it is used for taking the offset, the perpendicular direction is first ascertained by judgement and then the offset rod is turned over end for end as many times consecutively as may be required to reach the object. This method of offsetting is not preferable as errors accumulate rapidly. This is used only for taking small offsets.

When measuring tape is to be used for taking the offset hold its zero end at the point to which an offset is to be taken and swing the other end on the chain line and note the point of minimum reading on it, which denotes the length of the offset.

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]]>1. The graduated ring being attached to the magnetic needle remains stationary when the compass-box and the sight vane is rotated.

2. The graduations are marked on the ring in a clock-wise direction with 0° or 360″ at South end of the needle so that 90° is marked at the West. 108° at the North and 270° at the Fast (Fig. 5.3 (a)]. The figures are written upside down as shown in [Fig. 5.3 (b)].

3. The sighting of an object and reading of the bearing are done simultaneously.

4. This can be used without a stand.

1. The graduated ring being attached to the compass-box moves with the sights and the needle remains stationary when the box is moved.

2. The graduations are marked both in the clockwise and counter clockwise directions dividing the graduated ring into four quadrants and the graduations are numbered from 0° to 90° in each quadrant. The zero points are marked at north and south and 90° at east and west (Fig. 5.4). The east and west have been inter-changed from their true positions.

3. An object is sighted first and the bearing is then read with the naked eye by going vertically over the middle point.

4. This cannot be used without a stand.

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]]>A compass is a small instrument which consists essentially of a magnetic needle, a graduated circle and a line of sight. When the line of sight is directed towards a line, the magnetic needle points towards magnetic meridian and the angle which the line makes with the magnetic meridian is read at the graduated circle.

The compass cannot measure the angle between the two lines directly. If it is desired to find out angle between two lines, firstly their angles with the magnetic meridian are determined separately and then the difference of the two values is found which is equal to angle between the lines.

It is very valuable instrument and is commonly used for rough surveys where speed and not the accuracy is main consideration. It was invented by Captain Kater in 1814. Fig. 5.1 shows its sectional elevation.

It consists of cylindrical metal box** **of about 8 cm to 12 cm. diameter, in the centre of which is a pivot carrying a magnetic needle which is already attached to the graduated aluminium ring with the help of an agate cap.

The ring is graduated to half a degree and is read by a reflecting prism which is protected from dust moisture etc. by the prism cap. Diametrically opposite to the prism is the object vane hinged to the box side and carrying a horse hair with which an object in the field is bisected.

The eye is applied at the eye-hole below the sighting slit. The graduations on the ring can be observed directly by the eye after they are reflected from the diagonal of the prism. The graduations can be made clearly visible by adjusting the prism to the eye sight by the focussing screw. Both the horizontal and vertical side faces of the prism are made convex to give magnified readings.

To prevent undue wear of the pivot point, the object vane is brought down on the face of the glass cover which presses against a lifting pin and the needle is then automatically lifted off the pivot by the lifting lever.

To damp the oscillations of the needle before taking a reading and to bring it to rest quickly, the light spring brake attached to the inside of the box is brought in contact with the edge of the ring by gently pressing inward the brake pin.

If the bearings of very high or very low objects are to be taken, the reflecting mirror which slides on the object vane is tilted and image obtained in it is bisected by the horse hair. A pair of the object glasses shell have to be interposed between the slit and the coloured vane when the Sun or some other luminous object is to be bisected. A metal cover fits over the glass cover as well as the object vane when the compass is not in use.

**Working of the Prismatic Compass:**

This can be used while holding it in hand, but for better accuracy, it is usually mounted on a light tripod which carries a vertical spindle in the ball and socket arrangement to which the compass is screwed. By means of this arrangement the compass can be placed in position easily.

**Its working involves the following three steps. **

(i) Centering

(ii) Levelling, and

(iii) Observing the bearing.

**(i) ****Centering:**

The centre of the compass is placed vertically over the station-point by dropping a small piece of stone below the centre of the compass so that it falls on the top of the peg marking that station.

**(ii) ****Levelling:**

By means of ball and socket arrangement, the compass is then levelled so that the graduated ring swings quite freely. It may be tested by rolling a round pencil on the compass box.

**(iii) ****Observing the bearing:**

Having centered the instrument over the station and levelled it, raise or lower the prism until the graduations- on the ring are clearly visible when looked through the prism. Turn the compass-box until the ranging rod at the forward station is clearly visible. Use the brake-pin and bring the ring at rest and then take the reading at which the hair line appears to cut the graduated ring. Readings are usually estimated up to nearest 15 minutes.

It may be noted that with this compass, the sighting, of the object and reading of the graduated ring are done simultaneously.

It was formerly much used for land surveys but now-a-days, it is little used. It is similar to a prismatic compass except that it has another plain sight having a narrow vertical slit in place of the prism and that it carries an edge bar needle.(Fig. 5.2. (a)] in place of broad form needle [Fig. 5.2. (b)].

**Note: **

(i) Why Zero is marked at South in the Prismatic Compass. Since the bearing of the North direction is zero, therefore when the North end of the needle and object vane point towards North, the reading under the prism should be zero.

But since the prism is placed exactly opposite to the object vane, the south end will be under the prism. Hence, the zero graduation of the ring must be placed at South end of the needle. In this way bearings are obtained clockwise from North.

(ii) Why East and West are interchanged in the Surveyor’s Compass. The letters E and W are interchanged from their true positions in order to read the bearings in the proper quadrants. Supposing, the bearing of a line is N 30°E.

Since the graduated ring is attached to the box, therefore, it moves with the sights when the box is rotated while the magnetic needle remains stationary. The N and S points on the ring and the sights move through 30° from left to right when the point P is bisected (Fig. 5.5).

Thus the actual East of the compass moves away from the North end of the needle while the actual west comes near it. Therefore, if the letters E and W are interchanged from their natural positions, only then the reading N 30°E can be read otherwise the reading observed will be N 30° W, which is wrong.

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]]>1. The glass cover of the compass box gets charged with electricity when dusted off with a handkerchief or by the influence of electric charge in the atmosphere. Consequently, the needle adheres to the glass. This may be avoided by applying a moist finger or cloth to the glass.

2. To avoid local attraction, nothing made of iron or steel such as bunch of keys, iron-buttons etc. should be carried by the surveyor. The instrument should not, as far as possible, be set up near telegraph poles, rails, other steel structures and currents carrying wires etc.

3. Set up and level the compass properly.

4. Stop the vibrations of the needle by gently pressing the brake-pin so that it may come to rest soon.

5. Always look along the needle and not across it, thus avoiding parallax. In Surveyor’s compass always read the north end of the needle.

6. For important lines, take duplicate readings at each station. After having taken the first reading, displace the needle and take the second reading and then take the mean of the two.

7. To detect local attraction, take fore and back bearings of the lines.

8. The pivot sharp edge should be protected by keeping the needle off the pivot when compass is not in use or when it is shifted from one station to another.

**The compass should be tested and adjusted as explained below before putting it to use: **

1. When the compass is levelled the needle or compass ring should be horizontal, if not, slide the rider on the higher end of the needle to make it horizontal.

2. The needle in the compass should be straight and the pivot should be at the centre of the graduated circle. To test this, read two or three sets of the end readings of the needle.

**The difference for each set shall be exactly 180° for the needle being straight and pivot in the centres, otherwise, there may be any of the following two cases: **

(i) The difference being constant for all sets.

(ii) The difference not being constant for all sets.

In the first case, the pivot is in the centre, only bend the needle straight. But in the second case, the correction is made by bending the pivot as well as by straightening the needle.

3. The needle should be sensitive so that it may not come to rest in a direction other than the magnetic meridian. To ascertain if the needle is sluggish, take reading in any position of the needle being in rest. Then displace the needle by bringing near it a piece of steel or bunch of keys etc. and let it come to rest and then again take the reading.

The reading will be the same if there is no friction on the pivot and the needle is not sluggish. If reading is not the same, then the pivot-point should be sharpened by a fine oilstone and the needle should be remagnetised by a bar magnet.

4. To find if the sights are vertical when the compass is levelled, suspend a plumb-line in front of the compass and sight it. If the sights are vertical, the eye-vane, the object-vane, and the string will be parallel and in the same vertical line. If not, then either file one side of the bottom of the vane where it rests on the plate or insert a paper packing. Repeat the test and adjustment until the error is eliminated.

5. To see if the sights are fixed diametrically opposite to each other, stretch a fine horse-hair between the sights. It will pass over the N and S marks (zeros if the sights are fixed exactly opposite to each other).

6. To detect if there be any error due to careless working or external influence, take the fore and back bearings of a line. These will differ exactly by 180° if the work is correct and there is no external influence.

**Sources of Error in Compass Work: **

**The errors may be due to faulty instruments or bad observations or natural and other causes and accordingly they are classified as follows:**

**1. Instrumental Errors: **

(i) The needle not being perfectly straight.

(ii) The needle being sluggish either by having lost its magnetism or due to dip, or friction on the pivot-point.

(iii) The pivot not being in the centre of the graduated ring.

(iv) The graduated ring not being horizontal.

(v) The sight vanes not being truly vertical.

(vi) The line of sight not passing through the centre of the graduated circle.

(vii) The horse hair being too thick or loose.

**2. Observational or Personal Errors: **

(i) Inaccurate centering of the compass over the station-point.

(ii) Inaccurate levelling of the compass.

{iii) Imperfect bisection of the object sighted.

(iv) Carelessness in reading and booking of the bearings.

**3. Errors Due to External Influences: **

(i) Local attraction due to presence of magnetic substances nearby the compass.

(ii) Magnetic changes in the atmosphere.

(iii) Regular and irregular magnetic variations.

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]]>The angular error of 10 minutes corresponds to lateral deviation of 1 in 344.

**Closing Error and Its Graphical Adjustment:**

While plotting a closed traverse, the starting and the ending points seldom coincide, and this discrepancy by which the ending point fails to meet with the starting one is called the closing error or error of closure. The error occurs due to wrong measurement of lengths and bearings of lines in the field and due to faulty plotting.

When the closing error exceeds the permissible limit, the fieldwork, should invariably by repeated.

**But when the error is found to be within the permissible value, the traverse may be adjusted graphically by one of the following two methods: **

**First Method: **

This method is the graphical application of Bowditch’s rule.

In this method, the correction is applied to the lengths as well us to the bearings of the lines in proportion to their lengths Therefore, this method is also known as proportionate method. Here each station is shifted proportionately according to the length and direction of the closing error. This method is used when the angular and linear measurements are equally precise.

**It is explained as follows: **

For example, AB’C’D’E’A’ [fig. 5.28 (a)] is a traverse as plotted from the bearings and lengths of the lines, where AA’ is the amount of closing error which is to be adjusted.

To adjust it, draw a line AA’ (Fig. 5.28 b) equal in length to the perimeter of the traverse to any convenient scale and set off along it the distances AB’, B’C’, C’D’, D’E’ and E’A’ equal to the lengths of the sides of the traverse. The scale need not be the same as that of the plan but is usually kept much smaller, At A’, draw a line A’ a parallel and equal to the closing error A’A. Join Aa and from B’, C’, D’ and E’ draw lines B’b, C’c, D’d and E’e parallel to A’ A meeting the line Aa at b, c, d and e respectively.

The intercepts B’b, C’c, D’d and E’e give distances through which the stations B’, C’, D’ and E’ are to be shifted. In this case, it will be noticed, that the stations will have to be shifted downwards. To do this, draw lines parallel to the closing error at each of the stations B’, C, D’, E’ and set off along them the respective intercepts on the proper side. Joining the points having shifted positions is obtained an adjusted traverse ABCDEA.

When only the magnitude of correction to be applied at each station is required, draw A’a perpendicular to A A’ and equal in length to the closing error [fig. 5.28 (c)]. Then the intercepts B’b, C’c, D’d and E’e represent the corrections at B’, C, D’ and E’ in magnitude only but not in direction.

**Second Method:**

In this method, the correction is applied only to the lengths of the sides of the traverse without changing their bearings. This method is suitable when the angular measurements are more precise than the linear measurements.

**It is explained as follows: **

Let A’BC’D’E’A’ ‘Fig. 5 .29 be a traverse as plotted from the bearings and lengths of the lines, where A’A” is the amount of closing error which is to be adjusted. To do this , produce AA” to meet any side of the traverse. In the figure, Å, A’ produced meets the produced line D’E’ at O .From this point O, draw lines to all the angular points as shown. Bisect the length of the closing error at A. From A, themed-point of A’A” draw AB parallel to A’B’ to meet OB’ at B. Also from A, draw AE parallel to A”E’ to meet OE at E. Similarly, from B and C draw lines BC ad CD parallel to B’C” and CD’ to meet OC and OD’ at C and D respectively. Then ABCDIZA in an adjusted traverse.

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]]>Bearing of a line is the horizontal angle which a line makes with some reference direction also known as meridian.

**The reference direction may be any of the following: **

1. A true meridian

2. A magnetic meridian

3. An assumed meridian

**1. True Meridian:**

True meridian of a place is a direction indicated by an imaginary circle passing round the earth through that place and the two (north and south) geographical poles. The horizontal angle between a line and the true meridian is called true bearing of the line. It is also known as azimuth.

**2. Magnetic Meridian:**

The direction indicated by a freely suspended and properly balanced magnetic needle unaffected by local attractive forces is called the magnetic meridian. The horizontal angle which a line makes with this meridian is called magnetic bearing or simply bearing of the line.

**3. An Assumed or Arbitrary Meridian:**

For small surveys, any convenient direction may be taken as a meridian. It is usually the direction of the first line of survey of the direction from a station to some well- defined permanent object. Such a meridian also has the advantage of being invariable and its direction can be recovered whenever required if the stations defining it are permanently marked or fixed by the measurements from permanent objects.

The horizontal angle between a line and this meridian is called assumed or arbitrary bearing of the line.

**The bearings are expressed in the following two ways: **

A. Whole circle bearings

B. Quadrantal bearings

**A. Whole Circle Bearings:**

The horizontal angle which a line makes with the north direction of the meridian measured in the clockwise direction and can value upto 360° i.e. the whole circle, is known as whole circle bearing (W.C.B.) of the line.

The prismatic compass measures the bearings of lines in the whole circle system.

**B. Quadrantal Bearings:**

The horizontal angle which a line makes with the north or south direction of the meridian whichever is nearer the line measured in the clockwise or counter clockwise direction towards east or west and can value upto 90° i.e. one quadrant of a circle is known as quadrantal bearing of the line.

The surveyor’s compass measures the bearings of lines in the quadrantal system.

**Reduced Bearings:**

The whole circle bearing when exceeds 90° may be converted or reduced into the corresponding bearing in the quadrantal system, which has the same numerical values of the trigonometrical functions. The bearing thus obtained is known as the reduced bearing (R.B.).

**The following table may be referred to convert the whole circle bearings to the reduced bearings:**

**Fore and Back ****Bearings: **

Every line has two bearings one, observed at each of the line. The bearing of a line taken in the progress of the survey or in the forward direction is the fore or forward bearing (F B.) of the line; while its bearing taken in the reverse or opposite direction is known as reverse or back bearing (B.B.)

The bearing of a line AB (Fig. 5.6) expressed in the direction A to B, (observed at A by sighting towards B) F.B. of AB. The bearing of AB / when recorded in the opposite / direction i.e. from B to A is B.B. of AB or F.B. of BA.

In the whole circle system, the fore and back bearing of a line differ exactly by 180°.

.** ^{.}**.B.B. of a line = F.B ± 180° …………………………………….. (Eqn 5.1)

Use Plus sign if the given F.B. is less than 180°; and minus sign if it exceeds 180°.

In the quadrantal system, fore and back bearings are numerically equal but with opposite cardinal points. Back bearings of a line may, therefore, be obtained by simply substituting N for S, or S for N; and E for W or W for E in its fore bearing. Supposing F.B. of a line is N 30°E, then its B.B. is equal to S 30°W.

**Examples on Bearings****: **

**Example 1: **

Convert the following whole circle bearings to reduced bearings.

(i) 65° – 30°; (ii) 140° – 20′ ; (iii) 255° – 10′ ; (iv) 336° – 40′.

**Solution: **

Applying the rules given in the table 5.1.

(i) W.C.B. = 65° – 30′; which is less than 90°

.** ^{.}**.R.B. = N (the same as W.C.B.) E = N 65° – 30′ E (Ans.)

(ii) W.C.B. = 140° – 20’; which is between 90° and 180°

.** ^{.}**.R.B. = S (180° – 140° 20′) E = S 39° 40′ E (Ans.)

(iii) W.C.B. = 255° – 10′: which is between 180° and 270°

.** ^{.}**.R.B. = S (255°10′ – 180°) W = S75° – 10′ W (Ans.)

(iv) W.C.B. = 336° – 40′; which is between 270° and 360°

.** ^{.}**.R.B. = N (360° – 336″40′) W = N 23° – 20′ W (Ans.)

**Example 2: **

Convert the following reduced bearings to the whole circle bearings:

(i) N 56° – 30′ E ; (ii) S 32° – 15’E ; (iii) S 85° – 45’W ; (iv) N 15°- 10′ W.

**Solution: **

(i) R.B. = N 56° – 30 E &, which is in the NE quadrant,

.** ^{.}**.W.C.B. = the same as R.B. = 56° – 30′ (Ans.)

(ii) R.B. = S 32° – 15′ E, which is in the SE quadrant,

.** ^{.}**.W.C.B. = 180° – 32° 15′ = 147° – 45′ (Ans.)

(iii) R.B. = S 85° – 45′ W, which is in the SW quadrant,

.** ^{.}**.W.C.B. = 180° + 85° 45′ = 265° – 45′ (Ans.)

(iv) R.B. = N 15° – 10′ W, which is in the NW quadrant,

.** ^{.}**.W.C.B. = 360° – 15° 10′ = 344° – 50′ (Ans.)

**Example 3:**

Find back bearings of the following observed fore hearings of lines AB, 63° – 30′; BC, 112° – 45′ ; CD, 203° – 45′ ; DE, 320′ – 30′.

**Solution:**

From the Eqn 5.1., B.B. = F.B ± 180°

F.B. of AB = 63°- 30′, which is less than 180°

.** ^{.}**. B.B. of AB = 63° 30′ + 180° = 243° – 30′ (Ans.)

F.B. of BC =112° – 45′, which is less than 180°

.** ^{.}**. B.B. of BC = 112°45′ + 180° = 292° – 45′ (Ans.)

F.B. of CD = 203° – 45′, which is less than 180°

.** ^{.}**. B.B. of CD = 203°-45′-180° =23°-45′ (Ans.)

F.B. of DE = 320° – 30′, which is more than 180°

.** ^{.}**. B.B. of DE = 320° 30′ – 180° = 140 – 30′ (Ans.)

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]]>The post Calculation of Angles from Bearings | Compass Surveying | Surveying appeared first on Engineering Notes India.

]]>Bearing of a line = given bearing + included angle.

**Note:**

**In a closed traverse, where local attraction is not suspected i.e. difference between F.B. and B.B of all lines is exactly 180°, we can find the angles and bearings in a shorter way as follows: **

Let ‘a’ be the interior angle required at a station, ‘P’ be the F.B. of the line coming from the previous station and ‘F’ be the F.B. of the next or forward line. Then,

**(i) For a Clockwise Traverse [Fig. 5.8. (a)]: **

a = P – F ± 180° ………….. (Eqn. 5.2.)

.** ^{.}**.F = P – a ± 180° (Eqn. 5.3.)

**(ii) For an Anti-Clockwise Traverse[Fig. 5.8. (b)]: **

a = F – P ± 180° … … … (Eqn. 5.4.)

F = P + a ± 180° ………… (Eqn. 5.5)

The signs (+) or (-) in the above equations are to be used according as (P – F) or (F – P) is less or more than 180°.

**Important:**

Unless and otherwise stated or apparent from the bearings, a traverse should be considered as an anti-clockwise one.

The ordinary compass cannot read directly the angle between two lines. The angles can be determined by observing the bearings of the two lines from their point of convergence. When the two lines meet at a point, two angles (interior and exterior) and formed. The sum of these two angles is equal to 360°. The following rules may be employed to find the angles between the lines whose bearings are given.

**The bearings of lines may be given in:**

(i) The whole circle system, or

(ii) The quadrantal system.

**(i) Given the Bearings of the Lines in the Whole Circle System: **

**There may further be two cases: **

(a) When bearings of the two lines measured from their point of section are given.

**Rule:**

Subtract the smaller bearing from the greater one. The difference will give the interior angle if it is less than 180°. But if the difference exceeds 180°, It will be exterior angle. Then obtain the interior angle by subtracting the difference from 360°.

(b) When bearings of the two lines measured not from their point of intersection, are given.

**Rule: **

Express both the bearings as if they are measured from the point where the lines intersect and then apply the above rule.

For example, if the bearings of the lines BA and AC are given, then to find angle at A, the bearings of AB must be obtained. The bearing of AB is the back bearing of BA and is equal to bearing of BA±180°. The angle BAC can then be obtained by the application of the above rule.

**(ii) Given the Bearings of the Lines in the Quadrantal System: **

In this case, to avoid unnecessary labour, firstly draw a rough sketch showing the directions of the lines and then proceed as follows.

**Rule:**

(a) If the lines are on the same side of the meridian and in same quadrant (Fig. 5.7, a) the included angle = the difference of the two reduced bearings.

∠AOB = difference of bearings OA and OB.

(b) If the lines are on the same side of the meridian and in the different quadrants (Fig. 5.7, b), the included angle = 180° – sum of the two reduced bearings.

.** ^{.}**. ∠AOB =180°- sum of the reduced bearings of OA and OB

(c) If the lines are not in the same side of the meridian but they are in the adjacent quadrants (Fig. 5.7, c).the included angle = sum of the two reduced bearings.

.** ^{.}**.∠AOB = sum of the bearings of OA and OB.

(d) If the lines are not on the same side of the meridian and also not in the adjacent quadrants (Fig 5.7. d) the included angle = 180° – difference of the bearings OA and OB.

**Example 1:**

**Find the angle between the lines OA and OB if their respective bearings are: **

(i) 25° – 30′ and 160° – 30′

(ii) 25° – 30’and 340° – 15′.

(iii) 126°- 0′ and 300° – 15′.

**Solution: **

Since the lines are meeting at the same point O, the included angle will be the difference of the two bearings.

**(i) ∠AOB = bearing of OB – bearing of OA: **

= 160° 30′ – 25° 30′ = 135° – 0′ (Ans.)

**(ii) ∠AOB = bearing of OB – bearing of OA: **

= 340 15′ -25° 30’= 314°-45′

Since the difference is greater than 180°, it is an exterior angle; and to obtain the interior angle it must be subtracted from 360°.

.** ^{.}**. interior angle AOB = 360° – 314° 45′

= 45°-15′ (Ans.)

**(iii) ∠AOB = bearing of OB – bearing of OA: **

= 300° 15′- 126° 0′

174°- 15′ (Ans.)

**Example 2: **

The bearing of a line AB is 164° – 15′ and the angle ABC is 117° – 30′. What is the bearing of BC?

**Solution: **

Bearing of AB = 164° – 15′

Bearing of BA = 164° 15′ + 180° = 344° – 15′

Now bearing of BC = bearing of BA + ∠ABC

= 344° 15′ + 117° 30′

= 461°- 45′

Since it is more than a complete circle, deduct 360°.

.** ^{.}**.Bearing of BC = 461° 45′ -360°= 101° -45′ (Ans.)

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]]>The post Field-Work in Compass Surveying | Compass Surveying |Surveying appeared first on Engineering Notes India.

]]>**1. ****Field-Party:**

**It will consist of four persons: **

(i) Surveyor for taking bearings of the lines, recording field-notes and imparting instructions to other party members.

(ii) Two chainmen for chaining the survey lines.

(iii) One flagman, cum pegman to fix stations, pegs and ranging rods as directed by the surveyor.

**2. ****Equipment:**

The equipment in compass surveying consists of a prismatic compass with tripod stand along with all the instruments as required in chain surveying.

**3. ****Traverse:**

A series of connected survey lines of known lengths and directions is called a traverse.

**It is of two types, viz:**

(a) Closed, and

(b) Unclosed or open.

**(a) Closed Traverse:**

A traverse is said to be closed when a complete circuit is made i.e. when it returns to the starting point forming a closed polygon as ABCDEA [fig. 5. 18(a)], or when it starts and ends at points whose positions on plan are known, as ABCDE [fig. 5.18 (b)].

The survey work in a closed traverse can be checked and adjusted. It is suitable for the survey of moderately large areas such as small towns and big villages etc., and for locating boundaries of forests, lakes etc.

**(b) Unclosed or Open Traverse:**

A traverse is said to be unclosed or open when it does not form a closed polygon as ABCDEF (fig 5.19). It consists of series of lines extending in the same general direction and not returning to the starting point.

It is suitable for the survey of long narrow strips e.g., a road, railway, river, coast-line etc.

**4. Surveying a Closed Traverse:**

After performing reconnaissance and preparing a rough sketch as usual, the station-points (A, B, C, D, etc. fig.5.20) are marked by fixing pegs and ranging rods all visible from another and as near the boundary of the field as possible.

The compass is set up at the starting station (A) and bearings towards the back forwards stations (D and B) are taken and recorded. The length of the first line (AB) is chained and offsets on both sides of the chain line are taken in the same way as in chain surveying. Having arrived at the 2nd station (B), the length of the first line (AB) is recorded in the field-book.

The compass is then set up there, bearings towards back and forward stations (A and C) are recorded, the length of the 2nd line (BC) measured and offsets are taken as before. The work is continued in the same way until the whole circuit is complete. For rough work and rapid performance, the compass may be set up at alternate stations. The traverse may be run in the clockwise or in the anti-clockwise direction.

The positions of the objects which are out of reach of an offset are fixed by radiation. To do this, bearings of such objects are observed, and the lengths of the radial lines from the instruments are measured. More distant points such as comers of buildings may be located by the intersection of two bearings.

**Field-Check on Closed Traverse:**

In traversing with the compass, described above, the compass is set up at each of the successive stations and fore and back bearings of each of the lines are observed. Each bearing being observed independently of the others, the errors do not accumulate, but tend to compensate.

The fore and back bearings of a line should differ exactly by 180°. If the error between the fore and back bearings of a line exceeds the permissible error of reading (generally 15′), then they should be measured again ; and if on checking, the error is still found to exist, then either one or both the stations are affected by local attraction provided there is not other source of error. The bearing should then be corrected. For better accuracy, the survey lines should be as few in number as possible and as long as possible.

In addition to taking bearings towards the following and the preceding stations from a station of observation, bearings are also taken to some more conspicuous stations, such as towards C while at A (Fig.5.20). On arriving at C, bearing CA will be observed and if this bearing differs from the fore bearing AC as taken at A by 180°, then the accuracy of the work is ascertained and we can proceed safely.

**5. Surveying an Open Traverse:**

After performing preliminary steps and marking the station-points say A, B, C, D etc. (Fig. 5.21), the compass is set up over the starting station A and bearing taken towards the next station B. The compass is then set up at B and bearings taken towards A and C.

The line BC is then chained and offsets recorded as before. The work in continued is the same way till the end-station is reached from where only the back bearing towards the back station is taken.

**6. Field-Notes:**

The field-book for a compass survey is booked in the same way as in chain surveying, the only addition being of the bearings. Therefore bearing of the first line is written in the central column above the starting station and that of the following lines, to the right or left of the central column according as each of them turns towards the right or left of the preceding line. The back bearings are entered in the central column at the end of each line.

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]]>The post Local Attraction (With Remedies) | Compass Surveying | Surveying appeared first on Engineering Notes India.

]]>The magnetic needle is disturbed from its normal position if it is under the influence of external attractive forces called the sources of local attraction. Such a disturbing influence is known as local attraction. The term is also used to denote the amount of deviation of the needle from its normal position.

The local attractive sources may be neutral such as the masses of magnetic rock or iron ore etc. and artificial such as proximity of steel structures, rails, iron-pipes, current carrying wires etc. The iron made instruments such as chains, arrows, ranging rods and other things such as bunch of keys, knife, iron-buttons etc. should also be kept away from the compass at a safe distance apart.

Local attraction at a place can be detected by observing bearings, from both ends, of a line in the area. If the fore and back bearings of the line differ exactly by 180°, there is no local attraction at either station provided instrumental and observational errors are eliminated. But if this difference is not equal to 180°, then local attraction exists there either at one or at both ends of the line.

**Remedies for Local Attraction:**

**There are the following two methods of correcting the observed bearings of the lines taken in the area affected by the local attraction: **

(i) The error due to local attraction being same for each of the bearings observed at an affected station, the included angle calculated from the bearings taken at the same station will be correct, even though, the station is affected by the local attraction. Starting from the unaffected line and using these included angles, the correct bearings of the successive lines are calculated as already explained.

(ii) The observed bearings are corrected by applying correction to the stations affected by the local attraction. For this, error at each of the station is found and then starting from an unaffected bearing, the bearings of the successive lines are adjusted by applying corrections to them.

**Note: **

The magnitude and nature of error at a station due to local attraction can be determined by drawing a sketch of the observed and correct bearings of a line at that station. If the error is negative then the correction is positive, and vice versa, the magnitude of the two remaining equal to each other.

**If the bearings are given in the whole circle system, then remember the following rule for finding the nature of error: **

**Rule: **

If at a station, observed bearing of a line is more than that of its correct one, then the error at that station is +ve and the correction is -ve and vice versa.

**Examples on Local Attraction****: **

**Example 1:**

**The following are the observed bearings of the lines of a traverse ABCD taken with a compass in a place where local attraction was suspected: **

Find the correct bearing of the lines.

**Solution:**

On examining, it is found that fore and back bearings of line AB differ exactly by 180°. Stations A and B are, therefore free from local attraction. Consequently, the bearing observed at A and B are correct.

As the observed back bearing of BC is less than the corrected one, therefore, the error at C is -ve and the correction is +ve.

As the observed back bearing of CD is more than the corrected one, therefore, the error at D is +ve and the correction is -ve.

**The result may be tabulated as shown below:**

**Example 2:**

**The following are the observed fore and back bearings of lines of a closed traverse. Correct them where necessary for local attraction: **

**Solution: **

On examining, it is found that fore and back bearings of line BC differ exactly by 180°. Stations B and C are therefore, free from local attraction. Consequently, bearings taken at B and C are correct.’

As the observed back bearing of CD is less than the corrected one, therefore, the error at D is -ve and the correction is +ve.

**The result may be tabulated as shown below:**

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]]>The post Magnetic Declination: Meaning and Variation | Compass Surveying |Surveying appeared first on Engineering Notes India.

]]>Except in few places, the magnetic meridian at a place does not coincide with the true meridian at that place. The horizontal angle which the magnetic mariotion makes with the true meridian is known as the magnetic declination or simply declination of the needle at that place.

When the needle is deflected towards east of the true meridian, it is said east declination, and west declination when it is deflected towards west of the true meridian. Since the magnetic meridian varies from place to place and from time to time on the earth’s surface, the amount and direction of the declination is different at different places and at different times.

If the true bearing of a line is determined by the astronomical method, the declination at that place can be found by observing the magnetic bearing of that line and finding their difference. The declination can also be obtained approximately from isogonic charts published from time to time through government agencies.

The lines joining the places of equal declination at the same time are called isogonic lines, and the charts showing these lines are called isogonic charts. The lines joining the places of zero declination are known as agonic lines.

The declination at any place is not constant, but is subjected to fluctuations or variations which may be regular or irregular.

**1. Regular or Periodic Variations:**

This class of variation may itself be analysed into several components of different periods and amplitudes.

**They are:**

(i) Secular,

(ii) Annual, and

(iii) Diurnal or Daily.

**(i) Secular Variation:**

The magnetic meridian swings like a pendulum. It swings in one direction for a long time (100 to 200 years) and gradually comes to rest and then swings in the opposite direction.

**(ii) ****Annual Variation: **

The change produced annually by secular variation amounts in different places from 0 to ± 12 minutes but does not remain constant at any place.

**(iii) ****Diurnal Variation:**

It is an oscillation of’ the needle from its mean position during the day. The amount of this variation varies from 1 minute to about 12 minutes at different places. This is greater in high latitudes than near the equator, and more in summer than in the winter at the same place.

**2. Irregular Variations:**

These are caused by magnetic storms such as earthquakes or volcanic eruptions and their amount may be even 1° or 2° at a time.

Of the above variations, secular and diurnal are sufficiently pronounced and be kept in view by the surveyor. When magnetic bearings are taken in a survey, it is always desirable to note on the plan, the date of the survey and the magnetic declination on that date and its annual variation. Any survey line can easily be retraced if magnetic declination when the survey, was made and the present declination are known.

**Calculation of True Bearings: **

All survey maps which are to form a permanent record such as revenue survey maps are plotted with reference to the true meridian. And if the survey is made with a compass, the observed magnetic bearings shall have to be converted to the true bearings.

**The magnetic bearings can be converted to the true bearings by the following rule: **

**Rule 1:**

True bearing of a line = Magnetic bearing of the line ± declination.

Use (+) sign, when the declination is east as in fig. 5.13. (a) and (-) sign when it is west as in fig. 5.13 (b).

**On the other hand, the magnetic bearing of a line can be deduced from its bearing by the following rule: **

**Rule 2:**

Magnetic bearing of a line = True bearing of the line ± declination. Use (□-) sign, when the declination is east, and (+) sign then it is west.

**Note: **

The above rules apply only to the W.C.B.

**Examples on Declination****: **

**Example 1:**

The magnetic bearing of a line is 197°. Find its true bearing, it the magnetic declination is 3° W.

**Solution: **

Since the magnetic meridian is deflected towards west of the true meridian, true bearing of the line, = the magnetic bearing – declination = 197° – 3° = 194° (Ans.)

**Example 2:**

If the magnetic hearing of a line is N 37° W and the magnetic declination is 2° E find the true bearing.

**Solution: **

(Fig. 5.14) Magnetic, bearing of the line = N 37° W

Magnetic declination = 2° E

True bearing = Magnetic bearing-Declination.

= N (37° – 2°) W = N 35° W (Ans.)

**Example 3:**

True bearing of a line is 217° and magnetic declination is 2°W. Find the magnetic bearing.

**Solution: **

Since the magnetic meridian is deflected towards west of the true meridian, magnetic bearing of the line

= True bearing of the line + declination

= 217°+ 2° = 219° (Ans.)

The post Magnetic Declination: Meaning and Variation | Compass Surveying |Surveying appeared first on Engineering Notes India.

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