After reading this article you will learn about the levelling for finding distance above earth, explained with the help of suitable diagrams.
Meaning of Levelling:
Levelling is the art of finding the relative heights and depths of the objects on the surface of the earth. It is that part of surveying which deals with the measurements in vertical plane.
Levelling is of prime importance to an engineer for the purpose of planning, designing and executing the various engineering projects such as roads, railways, canals, dams, water supply and sanitary schemes etc. The success of any engineering project is based upon the accurate and complete levelling work of the project.
The principle of levelling lies in furnishing a horizontal………sight and finding the vertical distances of the points above………..this line. This is done with the help of a level and a level…………respectively.
The Level:
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Level consists essentially of a telescope and a level tube to provide a horizontal line of sight, both fitted above the levelling head.
It is supported on a tripod-stand when in use parts of a level and the tripod stand are explained below:
Parts of a Level: (fig 7.1): It consists of the following parts:
1. Levelling head.
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2. Telescope.
3. Eye-piece.
4. Diaphragm screws.
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5. Focussing screw.
6. Ray-shade.
7. Level tube.
8. Level tube nuts.
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9. Cross-bubble tube.
10. Magnetic compass plate
1. Levelling Head:
It consists of a tribarch plate having three arms each carrying a levelling screw in the ball and socket arrangement and an outer hollow vertical axis into which fits the inner solid vertical axis of the upper works. The upper and the lower works are connected together by a clamping screw.
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2. Magnetic Compass Plate:
The level is usually provided with a compass of the prismatic type with the only difference that the sighting is done with the telescope and the reading are observed through the prism placed at west end of the compass. To take reading in the usual way as in the ordinary prismatic compass, the graduations are turned clockwise through 90°so that 0° or 360° is marked at the west, 90° at the north, 180° at the east and 270° at the south.
3. Telescope:
There are two types of telescope of levels:
(i) External focussing telescope, and
(ii) Internal focussing telescope.
The first type was much used in the older type of levels while the later is used in the modern type instruments.
(i) External Focussing Telescope:
The principal parts of the external focussing telescope are:
(a) The body,
(b) The object -glass,
(c) The eye -piece, and
(d) The diagram.
The body consists of two tubes, one of which slides within the other. One tube carries the object -glass while the other carries eye -piece and diagram. The object glass forms the real and inverted image of the object in the plane of the cross-hairs at the diagram.
The eye-piece magnifies body the image and the cross-hairs. The diagram consists of a brass ring carrying cross-hairs and is held in position by means of two vertical screws known as diagram screws which are used while making the permanent adjustments of the instrument.
The other parts of the telescope are the rack and pinion arrangement actuated by a focussing screw and a ray -shade etc.
The main disadvantage of this type of the telescope is greater length for the given power.
(ii) Internal Focussing Telescope:
It mainly differs from the above type in that the slide carries an additional double concave lens and is moved by the focussing screw and that the object glass and the eye-piece are fixed at opposite ends of the same tube. Other arrangement is similar to dial of the first type.
The main advantages of this type of the telescope are:
(a) Both ends being closed, the interior of the telescope is prevented from dust and moisture etc., and
(b) Well balanced length for the given power. But on the other hand the addition of lenses reduces the brilliancy of the image by about 15%.
4. Bubble or Level Tube (Fig. 7.2):
It is a curved and sealed glass tube nearly filled with alcohol, ether or a mixture of the two, the remaining space being occupied by the bubble of air, which always remains at the highest part of the tube. The tube is graduated on both the directions from the centre so that the bubble may be centred when so desired.
The length of one division is usually 2mm. The tube is attached to the top of the telescope by means of capstan headed nuts. The line tangential to the circular arc at its highest point (middle of the tube) is called the axis of the bubble tube. It is also known as the bubble line. The bubble line is horizontal when the bubble is in the centre. The bubble shortens in length due to rise in temperature.
The Tripod Stand (Fig. 7.3):
The level is supported on a tripod stand when in use. The tripod consists of three legs which may be solid or sometimes framed for lightness. The legs are usually made of mahogany wood and fitted at their lower ends with pointed steel shoes in order that they may be firmly pressed into the ground. It is absolutely necessary that the tripod should be rigid.
If there is any looseness in the joints, it will disturb the position of the instrument and lead to inaccurate work. The tripod head carries at its upper surface external threads to which the internal threads of the instrument are fitted when desired. When the tripod is not in use, the cap is screwed to its top to project the external threads from dust, moisture, wear and tear etc.
Accessories of a Level:
(i) Capstan bars,
(ii) Screw driver,
(iii) Wrench or spanner,
(iv) Brush,
(v) Lubricating oil, and
(vi) Spare eyepiece which is generally kept in the box.
Kinds of a Level:
The different kinds of level in use are:
1. Dumpy level.
2. Wye level.
3. Cook’s reversible level.
4. Cushing’s level.
5. Modern tilting level such as India Office Pattern (I.O.P).
1. Dumpy Level (Fig.7.1):
It has the vertical spindle and the telescope barrel cast in one piece and therefore is termed as Solid Dumpy. It is simple, compact and stable. The telescope being rigidly fixed to its supports can neither be rotated about its longitudinal axis nor can it be removed from its supports and changed end for end.
It has greater stability of a adjustments than the Wye level but its permanent adjustment involves long procedure and takes much time and is necessarily done outdoors. It is generally used for field works.
2. Wye (y) Level (Fig. 7.4):
The telescope can be removed from the Y- supports (3) and reversed end for end. It can also be removed about its longitudinal axis in the Ys. It is very delicate and non – compact instrument. It has many loose and open parts which are subjected to frictional wear.
1. Levelling screws.
2. Level tube.
3. Y-supports.
4. Clips.
5. Telescope.
6. Eye-piece.
7. Diaphragm screws.
8. Focussing screw.
9. Ray shade.
3. Cooke’s Reversible Level (7.5):
M/S York combined good features of both dumpy and wye levels in one by providing a stop flange screw for reversibility of the telescope and named the level as Cooke’s reversible level. By slackening the stop -screw (3), the telescope can be rotated about its longitudinal axis in the sockets (4) and can also be withdrawn from the sockets and replaced end for end.
1. Levelling head.
2. Limb nuts.
3. Stop-screws.
4. Socket.
5. Telescope.
6. Eye-piece.
7. Diaphragm screws.
8. Focusing screw.
9. Ray-shade.
10. Level tube.
11. Level tube nuts.
12. Cross-bubble tube.
4. Cushing’s Level:
Mr. Cushing, inspector of instruments to the India Office Calcutta made the eye and the object ends interchangeable by providing slot and pin arrangement and the level is named after him as Cushing’s level. The end collars are exactly similar. Therefore, the eyepiece and the object-glass ends can be interchanged to reverse the telescope end for end also fixed after the desired rotation in its filings.
Note:
The permanent adjustments in case of Wye, Cooke’s and Cushing’s level can bez-tested easily and rapidly and the same can made indoors.
5. Modern Tilting Level (India Office Pattern) (Fig. 7.6):
The telescope of this level has a small motion about a horizontal axis just below it. It is, therefore known as the tilting level. In the above type of levels, since the line of collimation is at right angles to the vertical axis if the instrument is in permanent adjustment, therefore when the bubble is centered, the line of collimation is made horizontal and the vertical axis is made truly vertical.
1. Levelling screws.
2. Micrometer screw.
3. Cross Levels.
4. Scale.
5. Milled head.
6. Clamp screw.
7. Prism.
8. Reflector.
9. Telescope.
10. Ray-shade.
But in the case of this instrument, the telescope along with its bubble tube can be levelling by a micrometer screw without using the foot-screws of the instrument i.e. the line of collimation can be made horizontal independent of the vertical axis, therefore, the line of collimation may not be at right angles to the vertical axis.
In addition to providing easy means for bringing the bubble in the centre of its run, the micrometer screw is also used for laying out grades and measuring distances. The permanent adjustment of this level can be made easily since there is only one condition for the same. This is commonly used for precise levelling work.
The Levelling – Staff:
It is a graduated rod used for measuring the vertical distances of the points above or below the horizontal line of sight.
Levelling staves are divided into two classes:
(i) Self -reading staves, and
(ii) Target staves
The former are so called as they can be read directly by the level – man through the telescope while the latter are provided with a movable target. The target is equipped with vernier which is adjusted, by the staff- man as directed by the level-man until its centre line coincides with the horizontal cross – hair of the diagram. The reading is then taken and recorded by the staff man. Target staves are used when the sights are long, say more than 100m. Their use is rare in India.
Self-Reading Staves:
The self – reading staves were previously marked in feet, tenths and hundredths but now -a -days they are marked in the metric units such as metres, decimetres etc.
There are several types of the levelling staves available but only few important ones are describe here.
Sop with Telescopic Staff (Fig. 7.7):
It is commonly used type of the levelling staff. It is usually arranged in three telescopic lengths and is 4m long when fully extended. The solid top length of 1.25m, slides into the central box of 1.25m long, which again as a whole slide into the bottom box of 1.5m length. Each length is held in extended position by a brass spring catch. Carelessness in not extending the parts to the full length may spoil the whole work.
The smallest division marked on this staff shown in the Fig. 7.7 is 5mm. The metre numerals are on the left and are marked in red, while decimetre numerals are on the right and marked in black. The graduations are marked erect and are seen inverted when viewed through the telescope.
2. Folding Metric Staff (Fig. 7.8):
The Indian Standards Institution has discarded the telescope type levelling staff and has adopted the folding type because it is lighter, more convenient to handle and gives more accurate readings.
It is made of well-seasoned timber such as deodar, blue pine or cypruss. It is 75 mm wide, 18 mm thick and 4m long arranged in two lengths each being 2m and connected at the middle. The folding joint of the staff is of detachable type with a locking device at the back.
It is joined together in such a way:
(i) It can be folded to a 2m length,
(ii) The two pieces can be detached from each other, when required to facilitate easy handling and using one piece, and
(iii) When the two portion are looked together, the two pieces become rigid and straight. It is provided with a circular bubble of 25-minutes sensitivity fitted at the back and two foldings.
Each metre length is divided into 200 divisions, each being 5mm thick, spaces indicating the decimetre readings are marked in red while all other spaced are marked in black against a white back ground. Each decimetre length is figured with the corresponding numeral in black and marked to the left. The metre numerals are marked to the right in red. The graduations are inverted so that when seen through the telescope they appear erect.
3. One Length Staff:
It is usually 3m long in one solid length and is graduate to 5mm in the same way as the telescopic metric staff. It is used for precise levelling work.
4. Invar Precision Staff:
It is usually 3m long. As invar band graduated to a millimetre is fitted to a wooden staff, tightly fastened at the lower end and by a spring at the upper end. Thus any extension of the staff has no effect on the invar band. It is used for the most precise levelling work.
History Sheet of a Level:
Each level has got its history sheet in which is recorded the history of the level i.e. its number and type the name of the maker, the date of its purchase, its cost and subsequent repairs and transfers etc.
The proforma of the history sheet used for recording transfers of the instrument is given below:
Terms used in Levelling:
1. Level Surface:
This is a surface parallel to the mean spheroidal surface of the earth, e. g. the surface of still water in a lake. Every point on this surface of the earth, is equidistant from the centre of the earth. It is normal to the plumb line at all points. Any line lying in the level surface is known as a level line.
2. Horizontal Surface:
A horizontal surface through any point is a surface tangential to the level surface at that point, it is perpendicular to the plumb line. Any line lying in the horizontal surface is called a horizontal line. It is tangential to the level line.
3. Vertical Surface:
A vertical surface through any point is a surface normal to the level surface at that point. Any line lying in the vertical surface is called a vertical line. It is normal to the level line.
4. Datum Surface or Line:
It is an imaginary level surface or line from which vertical distance of the points above or below this line are measured. In India the datum adopted for Great Trigono-Metrical Survey (G.T.S.) of India department is mean sea level at Karachi.
5. Reduced Level (R.L.):
Reduced level of any point is the height or depth of that point above or below any datum. It is also known as elevation of the point. The elevation is positive or negative according as point lies above or below the datum.
6. Line of Collimation:
It is an imaginary straight line joining the intersection of the cross- hairs at diagram to the optical centre of the object- glass and its continuation. It is also called the line of sight. It is horizontal when the bubble is in the centre.
7. Axis of the Telescope:
It is an imaginary line joining the centre of the eye- piece and the optical centre of the object- glass.
8. Axis of the Bubble Tube:
It is an imaginary line tangential to the longitudinal curve of the level or bubble tube at its middle point (fig.7.2). It is also known as bubble line. It is horizontal when the bubble lies in the centre of its run.
9. Back Sight (B.S.) or Back Sight Reading:
It is a staff reading taken on a point of known R.L. as on a bench mark or a change point. It is the first staff reading taken after the level is set up and levelled. It is considered to be positive.
In fig. 7.11, the readings 2. 640 at the bench mark and 3.055 at the change point are back sight reading.
10. Fore Sight (F.S.) or Fore Sight Reading:
It is a staff reading taken on a point whose R.L. is to be determined. It is the last staff reading taken before shifting of the level to another position. It is considered to be negative. In fig. 7.11, the reading 1.280 is the fore sight reading.
11. Intermediate Sight (I.S.) or Inter Sight Reading:
It is any reading other than foresight and back sight taken on a point of unknown R.L. from the same set up of the level. All readings taken between the back and fore sight readings are called inter sight readings. In fig. 7.11, the readings 2.380, 1.735, 1.600 are inter sight readings.
Note:
In one setting of a level, there is only one back sight and one fore sight, but there can be any number of intermediate sights.
12. Height of Instrument (H.I.):
It is the R.L. of the line of collimation when the instrument is correctly levelled.
Note:
The height of instrument does not mean the height of the centre of the telescope above the ground where the level is set up.
13. A Station:
Any point where the staff is held and the reading taken during the process of levelling is called a station. It may be noted that it is a point where the stall is held and not a point where the level is set up.
14. Back sight and fore sight distance if kept approximately equal to eliminator the instrumental error.
15. Change Point (C.P) (Fig. 7.11):
It is an intermediate staff station on which two sights F, S. and B.S. are taken and is used for the purpose of changing the position of the instrument. Its elevation should be accurately determined as it is used for future reference, and the error in it affects every succeeding R.L. Any firm point which can be easily located should be selected as a change point such as a rail, rock, plinth, parapet etc. On soft ground, a steel- foot plate or steel pin may be used as a change point. A bench mark may also be used as a change point.
16. Bench Mark (B.M.):
It is a fixed reference point of known elevation. The R.L. of a B.M. above a certain assumed datum is determined and recorded together with its sketch and description for the future reference.
These may be classified as:
(i) G.T.S. (Great Trigonmetrical Survey) bench marks,
(ii) Permanent bench marks,
(iii) Arbitrary bench marks, and
(iv) Temporary bench marks.
(i) G.T.S Bench Marks:
These are established by the Great Trigonometrical Survey of India department. These have been set up at intervals all over the country with very high precision with reference to the mean sea level at Karachi as the datum. Their positions and reduced levels are shown on G.T.S. maps.
(ii) Permanent Bench Marks:
The G.T.S. bench marks are located far away from one another. To facilitate survey work, Government agencies such as P.W.D., M.E.S. etc. have established bench marks between the G.T.S. bench marks at closer intervals. These are called permanent bench marks. These are marked on well-defined and permanent points such as km-stones, plinths of buildings, top of parapets of bridges or culverts etc.
(iii) Arbitrary Bench Marks:
In small levelling operations, the reduced level of a well- defined reference point is arbitrarily assumed. These are called arbitrary bench marks.
(iv) Temporary Bench Marks:
These are the reference points, which are established when there is a break in the work i.e. the whole levelling work cannot be completed at a stretch. The survey work is closed at this point and restarted from the same when it is resumed.
17. Focussing:
Focussing means to set the eye- piece and the object – glass at the proper distance apart for the clear vision of the object sighted. The function of the object- glass is to focus the object on to the diagram while that of the eye- piece is to magnify the cross-hairs and the image as projected on the diagram.
The focus of the object- glass and of the eyepiece must coincide with the cross-hairs of the diagram as it is placed at the common focus. This can be done by first focussing the eye- piece and then the object- glass.
To focus the eye-piece, hold a piece of white paper in front of the telescope and move the eye-piece gently in and out with a screw motion until the cross- hairs appear distinct and clear. To focus the object – glass, direct the telescope to the object and turn the focussing screw until the image appears clear and sharp. Now if the eye is moved up and down and there is no movement of the image with respect to the cross-hairs, then the focussing is correct otherwise not.
18. Parallax:
It is the relative motion of the image with respect to the cross hairs when the image formed by the object- glass does not fall in the plane of the diagram. It is due to faulty focussing of the object- glass, it can be tested by moving the eye up or down. If the focussing is correct, the image seems to be fixed to the cross-hair when the eye is moved up or down.
But if the image appears to move relatively to the cross-hairs when the eye is moved up or down, that means parallax exists. It is a source of error in observations and must, therefore, be eliminated by focussing the objective correctly. This can be done by first focussing the eye- piece for the distinct vision of the cross hairs and then focussing the objective by the focussing screw.
Adjustments of the Level:
There are two types of the adjustments:
1. Permanent, and
2. Temporary.
The permanent adjustments are made to establish the fixed relationship between the fundamental lines of an instrument. Once made, the permanent adjustments last for a long time depending on the type of the instrument. The temporary adjustments are made at each set up of the instrument before starting to take the various staff readings.
The temporary adjustments are described here as follows:
Temporary Adjustments of the Level:
These are performed to make die axis of rotation vertical and to eliminate the parallel every time when the instrument is shifted and set up in a new position.
It is also known as ‘Setting Up’ of the instrument and is made in the following steps:
1. Fixing the instrument on stand.
2. Levelling up of the instrument.
3. Focussing.
1. Fixing the Instrument on Stand:
Release the clamp screw of the instrument, hold it in the right hand and fix it on the tripod stand by turning round only the lower part with left hand. Then screw the instrument firmly.
2. Levelling up of the Instrument:
It is done approximately by legs and correctly by the levelling screws:
(i) Levelling by Legs:
Bring all the foot- screws in the centre of their run and place the instrument in a desired position at a convenient height with the tribrach plate as nearly horizontal as possible. Fix any two firmly into the ground by pressing them with hand and turn the telescope to be nearly parallel to the line joining the feet of these two legs. Then move -the third leg to right or left and in or out to bring the long and cross bubbles respectively in their central positions. Much time is saved if nearly all the levelling is done by the tripod legs.
(ii) Levelling by Foot-Screws:
Place the telescope parallel to any pair of the foot-screws and bring the long bubble to the centre of its run by turning these screws equally either both inwards or both out-wards. To move the bubble to the right turn the screws inwards and to move it to the left turn the screws outwards (right in and left out).
Then turn the third foot screw to bring the cross bubble to its central position. Repeat this until both the bubbles are centered. If the instrument is in permanent adjustment, then the bubbles will traverse for all directions of the telescope.
Note:
(a) The instrument should, as far as possible, be set up on a solid ground to avoid its settlement in the course of observation in a setting. However, if such stable ground is not available, the tripod legs should be pressed firmly into the ground.
(b) While setting the instrument on a pucca floor, the shoes of the tripod should, as far as possible, be placed in the joints to prevent the legs from spreading out through slipping.
(c) When setting on a sloping ground, two legs should be kept down slope and the third up slope.
3. Focussing:
This is done in two steps viz:
(i) Focussing the eyepiece for distinct vision of the cross- hairs at diagram, and
(ii) Focussing the object- glass for bringing the image of the object into the plane of the diagram.
(i) Focusing the Eye-Piece:
point the telescope towards the sky or hold a piece of white paper in front of the telescope. Move the eye- piece in and out until a distinct and sharp black image of the cross-hairs is seen.
(ii) Focussing the Object-Glass:
Direct the telescope towards the staff and turn the focussing screw until a clear and sharp image of the staff graduations is obtained it may be noted that the parallax is completely eliminated if there is no change in the staff reading when the eye is moved up and down.
Note:
The focussing of the eye- piece when once made need not be changed provided only one person is using the instrument since it depends upon the eye sight of the observer, whereas the object- glass must be focussed whenever the distance of the staff from the level is changed.
Temporary Adjustments of a Tilting Level:
These are made in the following steps:
(i) Set up the level on firm ground. Bring the circular bubble or the two small cross bubbles (which ever arrangement is provided in the level) to the centre in the usual way. The vertical axis is thus made approximately vertical.
(ii) If the level is of reversible type, bring the main level tube on its left face. Set the tilting or micrometer screw to zero. The end of the main bubble then appears in prism.
(iii) Direct the telescope towards the staff and focus it. Turn the tilting screw to make the end of the bubble coincident with its index line (fig 7.12). Thus the bubble is exactly centered. In another pattern of the instruments, the halves of the two ends of the bubble appear in the prism as shown in fid 7.13(a). Adjust the tilting screw such that the two halves of the bubble appear coincident as shown in fig 7.13(b)
(iv) Take the Staff Reading:
Note:
The approximate levelling as in step:
(i) Has to be done only once for setting of the instrument but the final levelling as in step
(ii) Has to be repeated before every staff reading is taken.
Instructions for a Staff-Man:
The following points should be kept in view while holding a levelling staff:
1. The staff should be held vertical and upright.
2. Ground for the staff should be stable.
3. When working with a telescopic staff, care should be taken to stretch it fully by the spring catches.
4. The bottom of the shoe of the staff should be quite clean and there should be no mud sticking.
5. The staff man should not wear flat shoes in the survey of hilly area.
Instructions for a Level-Man:
The following points should be observed while conducting levelling work by a level man:
1. Levelling should always commence from a permanent bench mark and end on a permanent bench mark.
2. Position of the Level:
The level should be set up on a firm ground and at some convenient place from where the greatest number of sights can be taken. It should not be too high or too low. To avoid errors due to imperfect adjustment of the instrument, it is necessary to keep the lengths of the back sight and fore sight nearly equal i.e. The instrument should be set up approximately midway between the change points.
3. Observing the Staff-Readings:
(i) Set up the level at the desired position and perform the temporary adjustment.
(ii) Turn the telescope to bring the staff approximately in the line of sight.
(iii) Move the telescope laterally by gentle tapping to bring the staff exactly between the vertical hairs and focus it.
(iv)The staff- man should be directed to wave the staff until it is vertical i.e. exactly parallel to be the vertical hairs and focus it.
(v) Bring the bubble exactly in the centre of its run either by turning that foot- screw which is nearest to the telescope or by turning the micrometer drums if it is fitted with the telescope.
(vi) Read the staff where the horizontal hair of the diagram appears to cut it.
(vii) Check the bubble for its central position. If it is out of centre, bring it in (he center and retake the reading and then record the correct reading.
(viii) The hand should not be put on telescope while taking reading.
4. It may be noted that on looking through the telescope, the staff is seen inverted. It should, therefore, always be read from above downwards and not upwards.
5. When a party of levellers is working, one’s own staff should be carefully recognised.
Taking Bearings with the Compass Attached to the Level:
The bearing of a line may be taken in the following steps:
1. If the compass is separate, attach it to the level in its place.
2. Release the clamping screw of the compass- needle and allow it to come to rest.
3. Raise or lower the prism to focus the circular scale.
4. Direct the telescope towards the ranging rod or the staff and bring it correctly in the centre of the two vertical hairs of the diagram.
5. Take the reading through the prism which is the required bearing of the line joining the instrument – station and the ranging rod or the staff.
6. Clamp the compass needle by clamping screw.
Finding the Difference of Level of Two Points:
There may be two cases:
Case I:
When the two points are so situated that both of them are visible from a single position of the level. The level in this case, is set tip approximately mid-way between the two points the readings on the staff held at each point are observed, the difference of the two readings being the difference of level of the two points. The operation of finding the difference of level in this case being so simple is known as Simple Levelling.
Let A and B be the two points (Fig. 7.14) whose difference of level is required. The leveller sets the instrument at a suitable position say ‘0’ on firm ground, approximately midway between A and B and performs the temporary adjustment. The staff – man hold the staff vertically upon the first point, say A.
The level-man directs the telescope towards it and takes the reading as already explained. The staff is then held on the second point B and a second reading taken as before. The difference between these readings gives the difference of level between A and B which is equal to 3.285-1.125 = 2.160 m.
If the R.L. of A above any particular datum= 100.000, the R.L. Of B. may be found as below.
H.L. at O= 100 + 1.125 = 101.125
R.L. of B= 101.125-3.285 = 97.840
It may be noted here that when the point is higher, the staff reading is smaller; while when the point is lower, the staff reading is greater.
Case II.
When the two points are so situated that:
(i) The distance between them being too large to permit reading of the staff with the limited optical power of the telescope.
(ii) They cannot be sighted from a single position of the instrument due to intervening obstacle.
(iii) The difference of their level being too large.
In such a case, it is necessary to set up the level in several positions and to work in series of stages. The method of simple levelling is employed to each of the successive stages. This process is known as Continuous or Compound Levelling. Let A and B be the two points (fig.7.15) whose difference of level is required. This difference of level is determined by observing that from A to a convenient point C and then proceeding similarly from C to D etc. and from D to B. 
The instrument is, therefore, first set up in such a position as (1), from where a staff held at A can be read and a clear forward view obtained. After the back sight on A is taken, the staff- man selects a firm point C on which he hold the staff and the fore reading is taken. Thus the level difference of A and C can be found out. Then the instrument is transferred to position (2), the staff in the meantime being held at C.
After the instrument so levelled, the staff at C is again shifted, so that level of C may be compared with that of a convenient point D in the same manner as before. The process is repeated till the end point is reached. In this particular case, three settings of the instrument suffice to reach the end station B.
The difference of level between A and B is equal to the algebraic sum of the difference of level of points A & C, C & D, D& B, or equals the difference between the sum of the back sights and the sum of the fore sights i.e. (Σ B.S. – Σ F. S.). If the difference is positive, it indicates that the point B is higher than the point A; while if negative, the point B is lower than the point A.
Thus if the R.L. of A is known, the R.L. of B may be found out by the relation:
R.L. of B = R.L. of A + Σ B.S. – Σ F.S.