Question 1

Compass surveying – definition of back bearing In routine field work, the back bearing (BB) of a line is related to its fore bearing (FB) by which relationship?

Accepted Answer

Introduction / Context: Bearings denote the direction of a line with respect to a reference meridian. In traverse work, it is common to observe both fore bearing (from the rear station to the forward station) and back bearing (from the forward station back to the rear). This item checks your recall of the fundamental angular relation between these two quantities in whole-circle or quadrantal systems when properly corrected for station errors and local attraction. Given Data / Assumptions: The same reference meridian is used for both observations. No local attraction or index error remains after correction. Bearings are expressed in degrees. Concept / Approach: Direction reversal rotates the line by a straight angle. On a plane, reversing the direction of a vector changes its bearing by exactly 180 degrees. Therefore, the back bearing equals the fore bearing plus or minus 180 degrees, adjusted into the 0°–360° range when reported as whole-circle bearings. The same principle applies for quadrantal bearings after converting appropriately. Step-by-Step Solution: Start with FB of line AB measured at A.Reverse the direction to get BA; the orientation changes by 180 degrees.Compute BB = FB ± 180°, bringing the result within 0°–360° if necessary.Confirm if expressed in quadrantal form by converting to N/S–E/W notation consistently. Verification / Alternative check: Check with a simple example: if FB = 60°, then BB should be 240°. Adding or subtracting 180° yields the correct reverse direction every time, confirming the rule. Why Other Options Are Wrong: ±90° or ±270°: correspond to perpendicular or three-quarter turn, not a direction reversal. ±360°: brings you back to the same direction, not the reverse. Common Pitfalls: Forgetting to bring the result back into the 0°–360° range; mixing up magnetic and true bearings without applying declination corrections. Final Answer: Fore bearing ± 180°

Question 2

Tacheometry – effect of an anallatic lens on stadia constants If a tacheometer is fitted with an anallatic lens (for internal focusing), what are the effective stadia constants used in the distance formula?

Accepted Answer

Introduction / Context: Tacheometry determines horizontal distances and elevations quickly by reading staff intercepts through a telescope with stadia hairs. The distance formula uses two constants: a multiplying constant (k) and an additive constant (c). Instruments are often designed to simplify this relationship. This question checks your understanding of how an anallatic lens affects the stadia constants. Given Data / Assumptions: Standard stadia distance formula: D = k * s + c, where s is the staff intercept. Internal focusing telescope with an anallatic lens to eliminate the additive term. Usual stadia interval factor adjusted to give k ≈ 100 for convenience. Concept / Approach: The anallatic lens is a special converging lens introduced into the telescope so that the additive constant c (which depends on instrument geometry and focusing) becomes zero. This makes the distance computation simply D = k * s, eliminating range-dependent offsets. Most instruments are built to yield k ≈ 100, allowing field staff to multiply the intercept by 100 mentally, greatly speeding calculations. Step-by-Step Solution: Recall D = k * s + c.With an anallatic lens, c → 0 to simplify the formula.Instrument design sets k ≈ 100 by choosing stadia hair separation and focal length.Hence, multiplying constant = 100, additive constant = 0. Verification / Alternative check: Manufacturer specifications and surveying texts list anallatic lenses as eliminating c and commonly standardizing k to 100, confirming the selection. Why Other Options Are Wrong: Additive 100, k = 0: would make distances constant regardless of staff intercept, which is nonsensical. Both 100 or both 50: do not reflect the effect of the anallatic lens and typical calibration practice. Common Pitfalls: Confusing external-focus systems (which may have a nonzero c) with anallatic setups; forgetting that k is set by stadia interval and optics, not by staff properties. Final Answer: Multiplying constant is 100, additive constant is zero

Question 3

Traverse computations – projection of a leg on the reference meridian In coordinate (latitude–departure) computations, the orthographic projection of a traverse leg upon the reference meridian is termed the:

Accepted Answer

Introduction / Context: Closed traverses are reduced by resolving each side into components along a reference meridian (north–south) and a reference parallel (east–west). The component names have long-standing conventions in surveying. This question checks your ability to assign the correct term to the north–south component used in balancing traverses and computing coordinates and areas. Given Data / Assumptions: Reference meridian is the north–south direction. Orthographic projection ignores curvature for small traverses. Sign convention: northings positive, southings negative (common practice). Concept / Approach: The component along the meridian (north–south axis) is called the latitude of the line. The component along the parallel (east–west axis) is the departure. These components are used to compute coordinate increments, check linear misclosure, and perform traverse balancing via Bowditch or transit rules. Step-by-Step Solution: Resolve a leg of length L at bearing θ into L * cos θ (north–south) and L * sin θ (east–west).Assign names: latitude = L * cos θ; departure = L * sin θ.Apply signs depending on quadrant: N positive, S negative; E positive, W negative.Use these to sum misclosures and adjust to zero for a closed traverse. Verification / Alternative check: Any traverse computation example will show “latitudes” for N–S and “departures” for E–W components, confirming the terminology. Why Other Options Are Wrong: Departure: this is the east–west component on the reference parallel. Coordinate of the leg: generic term; not the standard component name. Bearing: angular direction, not a linear projection. Common Pitfalls: Swapping sine and cosine for a given bearing definition; mixing local and true meridians; neglecting sign conventions leading to area sign errors. Final Answer: Latitude of the leg

Question 4

Chain surveying across an obstruction – effect of raised ground between stations While chaining a line between two stations A and B when a raised ground intervenes between them, which situation typically occurs?

Accepted Answer

Introduction / Context: In chain surveying and basic layout, obstacles often interrupt either visibility, chaining, or both. Raised ground (such as a ridge) between two stations is a classic case used to illustrate the choice of indirect methods for alignment and distance transfer. This question checks whether you can correctly diagnose the type of obstruction created by a raised ground between endpoints A and B. Given Data / Assumptions: Stations A and B lie on opposite sides of a ridge or mound. Line AB passes over higher intermediate ground. We consider direct intervisibility and direct chaining along AB. Concept / Approach: With a raised intermediate ground, a straight line of sight from A to B is blocked by the crest; hence intervisibility is lost. Additionally, direct chaining along the straight alignment becomes impractical because of slope, uneven footing, and absence of a straight-line path across the crest at the same elevation. Therefore, both visibility and direct chaining are obstructed, and one must resort to indirect methods (e.g., reciprocal ranging, random line and offsets, or alignment via intermediate points) to establish the distance and direction. Step-by-Step Solution: Assess visibility: the crest blocks the line of sight → vision obstructed.Assess chaining: irregular slope and lack of straight path → chaining obstructed.Conclude that both are obstructed simultaneously.Plan workarounds: choose an alternative line, use triangulation or offsets, or set intervisible intermediate stations. Verification / Alternative check: Textbook obstacle problems categorize raised ground as causing both types of obstruction in contrast to features like a pond (chaining obstructed, visibility unobstructed) or a building (visibility obstructed, chaining possibly unobstructed around it). Why Other Options Are Wrong: Only vision obstructed or only chaining obstructed: incomplete diagnosis for a raised ground crest. All of the above: includes mutually inclusive but redundant statements; the precise best choice is “both vision and chaining”. Common Pitfalls: Assuming you can still range over the crest; forgetting the distinction between visibility-only and chaining-only obstructions used in standard survey problems. Final Answer: Both vision and chaining get obstructed

Question 5

Theodolite checks – interpreting bubble behavior during horizontal rotation If, while rotating a theodolite in the horizontal plane, the bubble in the bubble tube occupies the same position throughout the rotation, what does this indicate about the …

Accepted Answer

Introduction / Context: The accuracy of angular measurements with a theodolite depends on the relationship among its principal axes: the vertical (rotation) axis, the trunnion (horizontal) axis, and the line of collimation. Bubble tube observations provide quick diagnostics of these relationships. This question asks you to interpret a stable bubble during a full horizontal rotation of the instrument. Given Data / Assumptions: The instrument is rotated 360 degrees about the vertical axis. The bubble in the level attached to the instrument maintains the same position throughout. We assume the bubble tube is aligned to indicate horizontality of the instrument base plate. Concept / Approach: If the vertical axis is perfectly vertical, the instrument’s base plane remains horizontal during rotation, and the bubble does not wander. Any tilt in the vertical axis would cause the bubble to move cyclically as the instrument turns. Therefore, a stationary bubble indicates that the rotation axis has been leveled to true vertical. Though other axis conditions are also important, this specific observation directly diagnoses the verticality of the rotation axis. Step-by-Step Solution: Rotate the instrument and observe the bubble.No change in bubble position → base plane remains horizontal.Base plane stays horizontal during rotation only if the rotation axis is vertical.Thus, the test confirms the vertical axis is truly vertical. Verification / Alternative check: Standard field checks use this observation to verify vertical axis adjustment before precise angle work; any drift indicates the need for footscrew correction or instrument servicing. Why Other Options Are Wrong: Trunnion axis horizontal: tested by level swings in vertical plane, not by this horizontal rotation bubble stability alone. Line of collimation perpendicular to vertical axis: assessed via collimation tests (face left/right), not solely by bubble stability during rotation. Common Pitfalls: Assuming bubble constancy proves all adjustments; in reality it confirms only verticality of the rotation axis. Final Answer: The rotation axis is truly vertical

Question 6

Chain surveying errors – identifying a cumulative error (positive or negative) Among the following, which source of error in chaining is cumulative in nature and may be positive or negative depending on the direction of error?

Accepted Answer

Introduction / Context: Errors in chaining are classified as cumulative or compensating. Cumulative errors add up systematically with each chain length, whereas compensating errors tend to cancel out partially due to randomness. Recognizing which errors are cumulative helps surveyors prioritize calibration and procedural controls. This question targets the classic cumulative error source in chain surveys. Given Data / Assumptions: Standard chain or tape is used to measure multiple lengths. Some errors repeat at every application of the chain length. Others vary randomly with sign and magnitude. Concept / Approach: If the chain is too long or too short relative to its nominal length (due to wear, temperature, or manufacturing tolerance), every measured segment inherits a systematic bias. Over many applications, the total measured distance will be proportionally too small (if chain is long) or too large (if chain is short). Hence, chain-length error is cumulative and can be positive or negative depending on whether the error shortens or lengthens the actual standard relative to nominal. Step-by-Step Solution: Identify systematic source: incorrect chain length repeats every time distance is laid.Determine sign: if chain is too long → measured distance too small (negative error); if too short → measured distance too large (positive error).Conclude cumulative nature: error scales with number of chain lengths.Plan correction: calibrate and apply a multiplying correction factor to all measured lengths. Verification / Alternative check: Field calibration against a standard base line reveals a constant ratio error that persists across measurements, confirming the cumulative character. Why Other Options Are Wrong: Bad ranging/straightening: predominantly compensating; signs vary with operator behavior and terrain, partially canceling out. Sag: generally produces an excess length (tape sags), thus a consistent negative correction; while systematic, it is treated per span and not strictly “±” as asked. Common Pitfalls: Ignoring temperature corrections; failing to recalibrate worn chains, leading to large positional misclosures. Final Answer: Erroneous length of chain

Question 7

Level tube design – reason bubble size stays constant in a constant-level tube In a constant level tube, the bubble length remains essentially constant during small tilts because the upper wall of the tube is made with which characteristic?

Accepted Answer

Introduction / Context: Bubble tubes in spirit levels are precision glass vials whose internal curvature governs sensitivity and bubble behavior. Two general designs exist: sensitive level tubes and constant-level tubes. The latter are shaped so that the bubble length stays nearly unchanged during small angular changes, simplifying reading and keeping the bubble steady within the graduation marks. This question examines the geometric reason behind that behavior. Given Data / Assumptions: We consider a constant-level tube (not a highly sensitive, strongly curved vial). Bubble size stability is desired across typical operating tilts. Internal surface curvature can be varied across the upper wall. Concept / Approach: Bubble length depends on the internal curvature of the vial and the volume of the gas pocket. By giving the upper wall a relatively large radius of curvature (i.e., making it very slightly curved), the cross-sectional profile changes very gently with position. Small tilts displace the bubble without appreciable change in its volume distribution along the tube, so its apparent length remains practically constant within the graduations. A smaller radius (tighter curvature) or a strongly convex profile would change the cross-sectional area more rapidly, causing bubble length variation. Step-by-Step Solution: Recognize objective: hold bubble length constant over operational tilt range.Control variable: curvature radius of the internal upper wall.Choose geometry: a relatively larger radius produces gentle curvature → minimal change in bubble length.Hence, the upper wall is made with a relatively larger radius in constant-level tubes. Verification / Alternative check: Instrument design texts describe constant-level tubes as having long radii to moderate sensitivity and stabilize bubble size, in contrast to sensitive vials where short radii increase sensitivity but change bubble length noticeably. Why Other Options Are Wrong: Smaller radius: increases curvature and sensitivity, altering bubble length more with tilt. Flat or convex downwards: do not achieve the desired constancy and would impair predictable graduations. Common Pitfalls: Confusing sensitivity with constant-length behavior; assuming all spirit levels use the same vial geometry. Final Answer: Of relatively larger radius

Question 8

Optics of telescopes – defining magnification in surveying instruments The ratio of the angle subtended at the eye by the virtual image to the angle subtended by the object itself is known as the telescope’s:

Accepted Answer

Introduction / Context: Surveying telescopes are optical systems used to sight distant targets with precision. Several performance metrics characterize their behavior, including magnification, resolving power, field of view, and image brightness. This question focuses on the formal definition of magnification as perceived by the observer’s eye when viewing the virtual image formed by the instrument. Given Data / Assumptions: The telescope forms a virtual image at or near infinity for comfortable viewing. Angles are small, and paraxial approximations hold. The observer compares angular sizes, not linear sizes at the object plane. Concept / Approach: Angular magnification M is defined as M = θ_image / θ_object, where θ denotes the angle subtended at the eye. A higher magnification makes the target appear larger angularly, improving fine pointing and reading of cross-hairs on the staff or target. This definition distinguishes magnification from resolving power (ability to separate closely spaced details), field of view (angular width of the observable scene), and brightness (related to aperture and exit pupil). Step-by-Step Solution: Identify the observed quantities: angles subtended at the eye by virtual image and by the object.Form the ratio M = θ_image / θ_object.Conclude the metric is called magnification.Relate to practice: typical surveying telescopes use magnifications around 20× to 30× for a balance of clarity and field of view. Verification / Alternative check: Optics references consistently define angular magnification this way; instrument datasheets list “magnification” as a unitless ratio (e.g., 30×), confirming the concept. Why Other Options Are Wrong: Resolving power: linked to aperture and wavelength; not a simple angular size ratio. Field of view: total angular extent observable, typically decreases as magnification increases. Brightness: influenced by exit pupil and coatings; not defined by the angular ratio. Common Pitfalls: Equating high magnification with better resolution without considering diffraction and stability; overlooking that excessive magnification narrows field and reduces brightness. Final Answer: Magnification

Question 9

Compass instruments – why a prismatic compass gives better reading accuracy A prismatic compass is generally considered more accurate than a surveyor’s compass primarily because:

Accepted Answer

Introduction / Context: Both prismatic and surveyor’s compasses are used to measure magnetic bearings in the field. However, practical accuracy differs due to mechanical design and how readings are observed. This question asks you to identify the major design features that give the prismatic compass an edge in typical surveying practice. Given Data / Assumptions: We compare reading convenience and reduction of parallax and estimation errors. We focus on scale type and viewing method. Magnetic environment and needle quality are assumed comparable. Concept / Approach: The prismatic compass uses a prism to magnify and bring the graduated circle into focus at the same time as the target is sighted, allowing the observer to read bearings directly without shifting eye position. It also uses whole-circle bearings (0°–360°), which reduce confusion between quadrants and often minimize transcription errors. These features together improve reading speed and accuracy compared with the surveyor’s compass that typically uses quadrantal bearings and separate viewing of sights and graduations. Step-by-Step Solution: Identify key differences: prism for direct, magnified reading; whole-circle graduation.Analyze impact: fewer parallax issues, less misreading of quadrants, faster booking.Conclude that features (c) and (d) are principal reasons for improved accuracy.Note that needle quality and sliding glass are secondary or unrelated to the core accuracy benefit. Verification / Alternative check: Standard surveying manuals emphasize WCB scales and prismatic reading as advantages of the prismatic compass, corroborating the selection of both (c) and (d). Why Other Options Are Wrong: Better needle: not the main differentiator; both instruments use adequate needles. Sliding glass: a protective feature, not a primary accuracy enhancer. Common Pitfalls: Confusing magnetic accuracy with reading accuracy; attributing improvements to needle magnetization instead of optical reading and scale system. Final Answer: Both (c) and (d)

Question 10

Topographic surveying concept: In relation to contour lines drawn on a map, the direction of the steepest slope (i.e., the line of maximum gradient) at any point is oriented how?

Accepted Answer

Introduction / Context: Contours are lines joining points of equal elevation on a plan. Understanding how slope directions relate to contours is essential for designing roads, drains, retaining walls, and for interpreting topographic maps in civil engineering and land surveying. The question asks for the orientation of the steepest slope relative to the local contour line at a given point. Given Data / Assumptions: Contours represent constant elevation; moving along a contour does not change elevation. Gradient is the rate of change of elevation per unit horizontal distance. We consider a smooth terrain surface where contours are well-behaved locally. Concept / Approach: A direction of maximum slope corresponds to the direction of the greatest rate of change of elevation. Since contours are level curves, the direction of the gradient of elevation is perpendicular to these level curves. Thus, the line of steepest descent (or ascent) is normal (at right angles) to the contour at the point considered. Step-by-Step Solution: Identify that a contour = locus of equal elevation.Recognize that moving along a contour changes distance but not elevation, so slope along the contour is zero.The largest change of elevation occurs in the direction where elevation increases/decreases most rapidly: the gradient direction.By definition of level curves, the gradient is normal to the curve; therefore, the steepest slope is perpendicular to the contour. Verification / Alternative check: On a plan, closely spaced contours indicate steeper ground. The shortest line crossing the maximum number of contours per unit plan distance is the line drawn perpendicular to the contours—confirming the maximum gradient direction. Why Other Options Are Wrong: Along the contour: elevation does not change; slope is zero. At 45°: an arbitrary angle; not guaranteed to be maximum slope. None of these: incorrect because a specific relationship exists (perpendicular). Common Pitfalls: Assuming the steepest line “follows” the contour spacing visually; confusing drainage flow direction with arbitrary downslope directions not checked against the perpendicular rule. Final Answer: At right angles (perpendicular) to the contour

Question 11

Levelling instruments – bubble tube filling: The liquid used to fill the spirit (bubble) level tube should have which properties?

Accepted Answer

Introduction / Context: Bubble levels in dumpy/auto levels and theodolites depend on a sealed, slightly curved tube filled with a suitable liquid and an air bubble. The fluid must allow the bubble to respond quickly and reliably under field temperatures. The question checks the desirable properties and common fluids used. Given Data / Assumptions: The bubble responds to instrument tilts by moving to the highest point. Field temperatures may be low; freezing must be avoided. Quick damping and mobility are needed for productivity and accuracy. Concept / Approach: A suitable bubble liquid typically has low viscosity (to let the bubble settle rapidly), a low freezing point (to avoid solidification in cold climates), and chemical compatibility with glass and seals. Alcohols (such as ethyl or methyl alcohol) and sometimes chloroform or ether-based mixtures have been traditionally used because they meet these requirements better than water or oils. Step-by-Step Solution: Assess mobility: choose a low-viscosity liquid to achieve fast bubble movement and stabilization.Assess low-temperature performance: select a liquid with a freezing point well below 0°C.Identify common choices: alcohols and certain solvents like chloroform have been employed historically; modern instruments may use proprietary blends.Therefore, all listed statements describe correct and desirable properties/choices. Verification / Alternative check: Instrument manuals list denatured alcohol or specialized formulations with antifreeze characteristics to maintain sensitivity and speed across temperature ranges. Why Other Options Are Wrong: Any single property alone is incomplete; optimal bubble fluids satisfy all three. Common Pitfalls: Using water (freezes easily and is too viscous at low temperatures); ignoring seal compatibility; allowing contamination that changes viscosity or creates bubbles/foaming. Final Answer: All of the above

Question 12

Astronomical surveying – meridians: The true meridian at a place is the intersection on the Earth’s surface of a plane passing through which reference line?

Accepted Answer

Introduction / Context: Meridians are essential reference lines for azimuths, bearings, and map orientation. Surveyors distinguish between the astronomical/true meridian and the magnetic meridian. The question tests the definition of the true meridian used in precise work and for control networks. Given Data / Assumptions: The Earth has geographic (true) poles defined by its axis of rotation. Magnetic poles differ in position and shift slowly over time. Meridian planes intersect the Earth’s surface along meridian lines. Concept / Approach: The true meridian is the line of intersection of the Earth’s surface with the plane that passes through the geographic North–South poles and the observation station. This line is independent of the magnetic field and is fundamental for astronomical azimuths and triangulation baselines. Step-by-Step Solution: Define the meridian plane: through the Earth’s rotational axis (true poles) and the local station.Intersect with the Earth’s surface: the curve obtained at the station is the true meridian line.Differentiate from magnetic meridian: the latter aligns with the Earth’s magnetic field direction.Hence, the correct defining reference is the geographic poles. Verification / Alternative check: True meridian direction can be established by solar observations (e.g., equal altitude method) or stellar transits, all referencing the Earth’s rotational axis, not the magnetic field. Why Other Options Are Wrong: East–West points and zenith–nadir define other great circles/vertical planes, not the true meridian plane. Magnetic poles define the magnetic meridian, which differs from the true meridian by the declination angle. Common Pitfalls: Confusing true and magnetic bearings; neglecting local magnetic disturbances; assuming fixed relation between true and magnetic meridians without applying current declination. Final Answer: The geographic (true) North and South poles

Question 13

Compass surveying – magnetism basics: Which statements about magnetic meridian, magnetic variation (declination), dip, and balancing a magnetic needle are correct?

Accepted Answer

Introduction / Context: Compass work relies on Earth’s magnetic field. To interpret bearings correctly, a surveyor must know how a magnetic needle behaves, how magnetic meridian differs from the true meridian, and how instruments compensate for dip and balance. This question validates those fundamentals. Given Data / Assumptions: A freely suspended magnet aligns with the horizontal component of Earth’s magnetic field. True and magnetic meridians generally do not coincide. The Earth’s field is inclined to the horizontal, producing dip. Compass needles are adjusted for balance and sensitivity. Concept / Approach: The magnetic needle seeks the magnetic meridian. The angle it makes from the true meridian is the magnetic declination (variation). Because the field is inclined, the needle experiences dip toward the nearer magnetic pole; counterweights or rider weights are used to balance the needle on its pivot for smooth motion without rubbing the glass cover. Step-by-Step Solution: Relate field to needle: needle aligns with magnetic meridian (statement A).Define variation: declination = angle between true and magnetic meridians (statement B).Account for dip: one end dips toward the nearer magnetic pole (statement C).Instrument balance: use a small rider weight to balance the pivoted needle (statement D).Therefore, all statements are correct together. Verification / Alternative check: Standard compass descriptions include declination adjustment scales and rider weights for balancing; dip is handled by needle design and counterbalancing for local latitude. Why Other Options Are Wrong: Selecting only one statement ignores other fundamental behaviors; all are simultaneously true in normal surveying practice. Common Pitfalls: Assuming magnetic and true meridians coincide; ignoring time-varying declination; neglecting to balance the needle after moving instruments across latitudes. Final Answer: All of the above

Question 14

Geomagnetism – diurnal variation of magnetic declination: How does the daily (diurnal) variation of magnetic declination generally change with latitude and season?

Accepted Answer

Introduction / Context: Magnetic declination (variation) is not constant: it changes with location, season, and even time of day. Surveyors should understand general trends so they can schedule compass work and apply corrections prudently. This question focuses on the broad behavior of diurnal variation with latitude and season. Given Data / Assumptions: Diurnal variation refers to the cyclic change in declination over a day. Solar heating and ionospheric currents influence the Earth’s magnetic field. We consider general trends used in classical surveying guidance. Concept / Approach: Classical surveying texts note that diurnal variation is commonly more pronounced near the magnetic equator due to stronger ionospheric current systems (e.g., the equatorial electrojet), and that it usually increases in summer daylight hours because of enhanced solar activity and atmospheric conductivity. Hence, it is generally greater at or near the equator than near the poles and is typically larger in summer than in winter. Step-by-Step Solution: Establish latitude effect: stronger daily swing near low latitudes → greater variation at/near the equator.Establish seasonal effect: higher solar input in summer → larger daytime variation.Compare statements offered: option A matches the latitude trend; options C and D contradict common observations.Therefore, select the statement indicating greater variation at the equator. Verification / Alternative check: Historical field recommendations suggest avoiding critical compass observations during midday in summer at low latitudes due to higher diurnal disturbances, reinforcing the chosen trend. Why Other Options Are Wrong: Less at equator than nearer poles: opposite of the commonly observed trend for diurnal swings. Less in summer than in winter: seasonal relationship is typically the reverse. Same at all latitudes/months: magnetic behavior is location- and season-dependent. Common Pitfalls: Confusing long-term secular change with diurnal variation; overlooking local magnetic anomalies that may superimpose site-specific effects. Final Answer: It is greater at the equator than nearer the poles.

Question 15

Plane table orientation – Bessel’s method: For orienting a plane table by three well-defined points A, B, and C, which description best states Bessel’s drill (sequence of sights and rays)?

Accepted Answer

Introduction / Context: When re-orienting a plane table without resetting on the same station mark, Bessel’s method (drill) provides a practical sequence of sights to ensure the table is correctly oriented using three known points plotted on the sheet. It is widely taught for reliability and simplicity in the field. Given Data / Assumptions: Three well-defined, intervisible points A, B, C are plotted accurately on the table. The alidade can be used to draw rays from plotted points toward others. The goal is to bring the table into the correct orientation so that plotted lines align with ground directions. Concept / Approach: Bessel’s drill uses two successive orientations and ray drawings that converge to a unique intersection on the sheet. By aligning B through A and drawing a ray toward C, then aligning A through B and drawing another ray toward C, the intersection of the two rays marks the proper plotted position through which C should be sighted to complete the orientation accurately. Step-by-Step Solution: First step: place the alidade on AB so that B is sighted through A; draw a ray from A toward C.Second step: place the alidade on BA so that A is sighted through B; draw a ray from B toward C.Third step: the intersection of these two rays identifies the proper line of sight for C; align C through this intersection to lock orientation.The table is now oriented when all three directions match the ground lines. Verification / Alternative check: Field texts present equivalent step orders as long as the logic of intersecting rays to the third point is preserved; option A states the classical sequence verbatim. Why Other Options Are Wrong: Options B and C permute roles incorrectly relative to the classical description. Option D is vague and does not specify the canonical order; Bessel’s drill is prescriptive rather than arbitrary. Common Pitfalls: Drawing rays from wrong plotted points; parallax or poor sighting; not clamping the table between steps, leading to misalignment. Final Answer: Align B through A and draw a ray toward C; align A through B and draw a ray toward C; finally, align C through the intersection of the two rays.

Question 16

Levelling fundamentals – lines of sight and staff readings: Which statements correctly describe the geometry of back sight/fore sight observations and the reference plane for staff readings?

Accepted Answer

Introduction / Context: Differential levelling establishes elevations by reading a staff from a fixed instrument set-up. Knowing how the line of collimation and staff readings relate to the horizontal reference surface prevents conceptual errors in field notes and computations. Given Data / Assumptions: An instrument is properly levelled, so the line of sight is horizontal. Back sight (BS) and fore sight (FS) are taken without moving the instrument. The level surface through the instrument axis approximates the reference horizontal plane at the set-up. Concept / Approach: With the instrument clamped, the BS and FS share the same line of collimation (horizontal plane). A staff reading is effectively the vertical distance between this plane and the staff zero at the observed point. In geometric levelling, we treat the horizontal reference as a level surface passing through the telescope axis for the small area around the instrument. Step-by-Step Solution: BS and FS from one set-up share the same horizontal line of sight.Staff reading concept: reading = HI − RL_point, i.e., vertical drop from the plane of collimation to the ground point.Local level surface approximation: coincides with the horizontal reference through the instrument axis.Therefore, all three statements are mutually consistent and correct. Verification / Alternative check: Field-book checks (sum BS − sum FS = last RL − first RL) rely on the common horizontal plane assumption for each set-up and confirm consistency when arithmetic balances. Why Other Options Are Wrong: Choosing any single statement omits the other equally essential elements of levelling geometry. Common Pitfalls: Confusing the reference plane when the instrument is moved; ignoring curvature/refraction over long sights (where refined corrections may be required); mixing instrument height with staff readings. Final Answer: All of the above

Question 17

Chaining on slopes – stepping technique: For measuring distances down a steep hillside by stepping to improve accuracy, how should the step length (distance between steps along the slope) vary with slope?

Accepted Answer

Introduction / Context: When chaining on sloping ground, direct measurement along the ground introduces slope errors. The stepping method projects the measurement into short, nearly horizontal segments. Choosing appropriate step lengths is crucial to reduce cumulative error and maintain control of the chain or tape. Given Data / Assumptions: Downhill measurement is being made using stepping with pegs or arrows. Human control, tension, and alignment become harder on steep slopes. Shorter steps improve approximation to horizontal distances and handling. Concept / Approach: As slope increases, maintaining straight alignment, correct tension, and level projection is more difficult. Shortening the step length reduces sag and alignment error, allows the chainman to hold the tape near-horizontal between points, and limits slip on the ground. Therefore, the distance between steps should decrease as the slope becomes steeper. Step-by-Step Solution: Assess terrain: steeper slope → more difficult to keep tape level and taut.Adapt step length: reduce segment length to maintain control and approximate horizontality.Measure each short horizontal projection and sum to get total distance.Thus, step length decreases with increasing slope. Verification / Alternative check: Survey practice manuals recommend short steps (even under one tape length) on steep ground, and allow longer steps on gentle slopes where control is easier. Why Other Options Are Wrong: Increase with increase of slope: opposite of good practice; it increases error risk. Decrease with decrease of slope: backward relation. Weight of chain is not the controlling parameter for step spacing. Common Pitfalls: Forgetting to keep the tape level at each step; inconsistent tension; poor alignment causing cumulative lateral error. Final Answer: Decrease with increase of slope (steeper ground → smaller steps)

Question 18

Internal focusing telescope – focusing travel: For an internal focusing surveying telescope that must focus at all distances beyond 4 m, the minimum axial sliding range required for the focusing lens is approximately how much?

Accepted Answer

Introduction / Context: Internal focusing telescopes shift a small lens group within the telescope tube to achieve focus, keeping the tube length fixed and maintaining collimation. Design guidelines specify a minimum mechanical travel to cover a practical focus range used in surveying, typically from a few meters to infinity. Given Data / Assumptions: Required focusing range: from beyond 4 m to infinity. Optical group is lightweight and moves axially by a small amount. Mechanical travel must be sufficient for the focus shift while preserving stability. Concept / Approach: The movement of the internal lens causes a change in the effective image plane position to bring objects at various distances into sharp focus at the reticle. Practical instrument designs indicate that a modest travel—on the order of a centimeter—covers from several meters out to infinity. Hence, a typical minimum travel approximates 10 mm for common magnifications and focal lengths used in levels and theodolites. Step-by-Step Solution: Relate focusing travel to focus range: nearer objects require more displacement than distant ones.Survey requirement: satisfy focus from > 4 m to infinity for staff reading.Empirical guideline: about 10 mm travel suffices for standard objective/eyepiece combinations.Select the nearest standard value: 10 mm. Verification / Alternative check: Manufacturers’ specifications and classical surveying texts often cite ~10 mm travel for internal focusing systems providing focus from a few meters to infinity without excessive mechanical complexity. Why Other Options Are Wrong: 5 mm: often insufficient to cover from ~4 m to infinity. 15–20 mm: larger than typical minimum required; may be used in special optics but not necessary as a minimum guideline. Common Pitfalls: Confusing external focusing (tube length change) with internal focusing; overlooking the need to refocus the eyepiece on the reticle first to eliminate parallax. Final Answer: 10 mm

Question 19

Surveying hand instrument – clinometer: A clinometer (Abney level/hand level variants) is primarily used for which field task?

Accepted Answer

Introduction / Context: A clinometer is a simple, portable instrument for quickly measuring vertical angles or gradients. It is widely used in reconnaissance surveys, forestry, road alignment checks, and slope staking where a full theodolite is unnecessary. The question asks for its primary function in the field. Given Data / Assumptions: Clinometers may have bubble levels and protractor scales. Some variants incorporate a small telescope (Abney level) and stadia scale. Readings yield angle of elevation, depression, or percent grade directly. Concept / Approach: By sighting a target with the clinometer and aligning the bubble, the user reads the vertical angle from the scale. This angle can be converted to slope ratio or percentage if required. The instrument is not designed to set right angles (a task for optical squares) or to correct instrument collimation; nor does it replace cartographic symbolization of features. Step-by-Step Solution: Sight the target point or staff mark through the clinometer’s view.Level the bubble to ensure the reading corresponds to the true vertical angle.Read the angle directly from the graduated arc (in degrees or percent grade).Use the angle to compute slope, height differences, or to set desired gradients on site. Verification / Alternative check: Standard field procedures use clinometers for quick checks of embankment side slopes, road grades, and tree heights via simple trigonometric relationships. Why Other Options Are Wrong: Correcting line of collimation requires instrument adjustments/tests (e.g., two-peg test) on levels and theodolites, not a clinometer. Setting out right angles uses a cross-staff or optical square. Defining natural features refers to mapping/cartography, not angle measurement. Common Pitfalls: Ignoring parallax by not focusing on the scale; reading without properly centering the bubble; using clinometer readings as precise as a theodolite without considering its lower accuracy. Final Answer: Measuring the angle of slope (angle of elevation or depression)

Question 20

Plane tabling — which procedure provides the most distinctive and accurate method of orienting the plane table at an unknown station? Read each technique and choose the one that uniquely serves accurate orientation on the job site.

Accepted Answer

Introduction / Context: Plane tabling is a rapid field-plotting method used in engineering surveying. A critical step is orientation: setting the table so that plotted lines are parallel to their corresponding ground directions. Among several procedures (radiation, intersection, traversing, resection), one is especially distinctive for obtaining accurate orientation at an unknown point without needing a prior oriented line through that station. Given Data / Assumptions: An unknown occupied station must be oriented on an existing plotted control. Visible control points around the station can be sighted. Accuracy and practicality in the field are key. Concept / Approach: Resection determines the position and orientation of the plane table by sighting two or more well-defined control points already plotted on the sheet. By solving the geometrical problem of back rays (e.g., two- or three-point resection), the orientation is fixed accurately. Other methods (radiation, intersection, traversing) either require the table to be already oriented or are primarily meant for plotting new points rather than establishing orientation at an unknown station. Step-by-Step Solution: Sight at least two (preferably three) plotted control points and draw back rays from their plotted positions.Adjust the table by rotation so the ground rays coincide with the plotted rays.Fix the station position by the intersection of back rays and lock the table orientation.Check with an additional point to confirm orientation accuracy. Verification / Alternative check: Three-point resection offers a strong geometric check; if small triangle of error forms, orientation is refined until it collapses to a point, confirming accuracy. Why Other Options Are Wrong: Radiation: Plots detail from a known, oriented station; not primarily for orientation at an unknown point. Intersection: Locates new points by intersecting rays; orientation still needed first. Traversing: Extends control but assumes prior orientation at each setup. Common Pitfalls: Using poorly distributed control points (acute angles) in resection; choose well-spread points to minimize error. Final Answer: Resection

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