Surveying Master Class Part 1 : All Topic Cover in One Place

Surveying ek aisi art hai jisme kisi fixed point ke sapeksh (with respect to) dusre points ki relative position nirdharit ki jati hai. Iske liye distances aur angles ko mapa jata hai. Civil engineering exams mein iska weightage lagbhag 7-8% hota hai.

Surveying ke Mukhya Prakar (Primary Types)

Prithvi ki golai (curvature) ko dhyan mein rakhne ke aadhar par surveying do tarah ki hoti hai:

Plane Surveying:
- Isme Earth ke curvature ko neglect kiya jata hai aur surface ko flat plane mana jata hai.
- Yeh chhote areas ke liye upyog hota hai (Area < $260\text{ km}^2$ ).
Geodetic Surveying:
- Isme high precision ke liye Earth ke curvature ko consider kiya jata hai.
- Yeh bade areas ke liye upyog hota hai (Area > $260\text{ km}^2$ ).

Mukhya Technicallangauge

Linear Difference: $12\text{ km}$ lambi line ke liye, Geodetic (arc length) aur Plane (chord length) ke beech ka antar sirf $1\text{ cm}$ hota hai.
Spherical Excess: $195.5\text{ km}^2$ area wale spherical triangle ke interior angles ka jod $180^\circ 0' 1''$ hota hai.
Angle Sum: Plane surveying mein triangle ke angles ka jod hamesha exactly $180^\circ$ hota hai.
Units: $1^\circ = 60\text{ minutes}$ aur $1\text{ minute} = 60\text{ seconds}$ hote hain.

Surveys ka Classification

Objective ya field ke aadhar par surveys ko aise banta jata hai:

Topographic Survey: Natural aur man-made features (nadi, pahad, imarate) ko map karne ke liye.
Cadastral Survey: Property lines aur boundary lines nirdharit karne ke liye.
City Survey: Urban infrastructure jaise roads aur sewers ki planning ke liye.
Hydrographic Survey: Water bodies ke andar ke features janne ke liye.
Astronomical Survey: Celestial bodies (Suraj, tare, satellites) ki position janne ke liye.

Scale ko Samajhna (Understanding Scale)

Scale map ki doori aur zameen ki asli doori ka anupat (ratio) hota hai.

Linear Distance ke liye Scale: Ise Representative Fraction (R.F.) ke roop mein likha jata hai.
- Udaharan: Agar map par $1\text{ cm}$ zameen ke $10\text{ m}$ ko darshata hai, toh R.F. $= 1/1000$ hoga.
Area ke liye Scale: Area ke mamle mein relationship squared ho jati hai:
$S^2 = \frac{\text{Map Area}}{\text{Ground Area}}$

Shrunk Scale aur Shrinkage Factor

Jab koi map waqt ke saath physicaly sikud (shrink) jata hai, toh purana scale galat ho jata hai. Ise sudharne ke liye niche diye gaye sutra (formulas) upyog hote hain:

Shrinkage Factor (S.F.) = $\frac{\text{Shrunk length}}{\text{Actual (original) length}}$
Shrunk Scale = S.F. $\times$ Old R.F.

Udaharan: Agar actual length $10\text{ cm}$ thi aur ab woh $8\text{ cm}$ ho gayi hai, toh S.F. $= 0.8$ hoga. Is factor ka upyog karke sahi ground area nikala jata hai.

Vernier Scale: Ek Parichay

Vernier scale ek sahayak scale (auxiliary scale) hota hai jo main scale ki sabse chhoti division ke hisso ko bariki se padhne ke liye upyog kiya jata hai. Yeh mukhya scale par slide karta hai aur adhik sateek (accurate) map deta hai.

Vernier Scale ke Mukhya Prakar

Surveying mein mukhya roop se char prakar ke vernier scales hote hain:

Direct Vernier: Sabse zyada upyog hone wala scale..
Retrograde Vernier: Ulti disha mein calibration wala scale.
Double Vernier: Dono taraf se reading lene ke liye.
Extended Vernier: Bahut bariki se napne ke liye.

Direct aur Retrograde Vernier mein Antar

Visheshta	Direct Vernier	Retrograde Vernier
Calibration	Main scale ki disha mein hi hota hai.	Main scale ki vipreet (opposite) disha mein hota hai.
Division ka Rishta	$(n-1)$ main scale divisions = $n$ vernier divisions.	$(n+1)$ main scale divisions = $n$ vernier divisions.
Division ka Size	Main scale division ( $s$ ), vernier division ( $v$ ) se badi hoti hai ( $s > v$ ).	Vernier scale division ( $v$ ), main scale division ( $s$ ) se badi hoti hai ( $v > s$ ).

Least Count (L.C.) ki Ganana

Least Count wo sabse chhoti map hai jo scale se li ja sakti hai.

Direct Vernier ke liye: $L.C. [cite_start]= s - v$ .
Retrograde Vernier ke liye: $L.C. [cite_start]= v - s$ .
Common Formula: Dono ke liye mukhya formula $L.C. [cite_start]= \frac{s}{n}$ hota hai.

Udaharan:

Agar main scale division ( $s$ ) $1\text{ mm}$ hai aur vernier divisions ( $n$ ) $10$ hain, toh:

Least Count: $\frac{1\text{ mm}}{10} = 0.1\text{ mm}$ .
Direct Vernier division ( $v$ ): $1 - 0.1 = 0.9\text{ mm}$ .
Retrograde Vernier division ( $v$ ): $1 + 0.1 = 1.1\text{ mm}$ .

Surveying ke Siddhant (Principles of Surveying)

Surveying do mukhya siddhanto par adharit hai:

Working from Whole to Part: Isme poore kshetra ko pehle bade hisso mein aur phir chhote-chhote bhago mein banta jata hai. Iska sabse bada fayda yeh hai ki kisi ek part ki galti (error) usi tak seemit rehti hai aur poore survey ko kharab nahi karti.
Relative Position nirdharit karna: Kisi bhi naye point ki sthiti ko kam se kam do pehle se nirdharit fixed points ki madad se jana jata hai.

Vernier ke Anya Prakar

Extended Vernier: Isme main scale ki $(2n-1)$ divisions, vernier scale ki $n$ divisions ke barabar hoti hain.
Double Vernier: Jab vernier scale par dono dishao mein calibration ho, toh ise double vernier kehte hain.

Chain Surveying ki Mukhya Lines

Chain survey mein alag-alag tarah ki lines ka upyog hota hai:

Main Line: Woh line jo mukhya survey stations ko aapas mein jodti hai.
Base Line: Yeh survey ki sabse badi aur mukhya line hoti hai jo pure area ko do bhago mein banti hai.
Tie Line: Iska upyog nakshe mein barikiya (detailing) dikhane ke liye kiya jata hai.
Check Line: Survey ki shuddhata (accuracy) ko janchne ke liye iska upyog hota hai.

Offsets ke Prakar

Offsets ka upyog chain line se kisi object ki doori mapne ke liye hota hai:

Perpendicular Offset: Yeh chain line se $90^\circ$ ke kon par hota hai.
Oblique Offset: Yeh $90^\circ$ ke alawa kisi bhi anya kon (angle) par ho sakta hai.

In methods ko nirdharit karne ke liye Chain method, Compass method, aur Offset/Traverse methods ka upyog kiya jata hai.

Chain Survey mein Upyog hone wale Upkaran (Instruments)

Chain survey mein alag-alag kamo ke liye vishesh upkarano ka upyog hota hai:

1. Station aur Ranging Devices

Peg aur Arrow: Inka upyog mukhya stations (Main Stations) aur beech ke stations (Intermediate stations) ko mark karne ke liye hota hai.
Ranging Rod aur Offset Rod: Inka upyog ek seedhi rekha (ranging) nirdharit karne ke liye kiya jata hai.

2. Angle Measurement ( $90^\circ$ ) ke liye Upkaran

Lamba (Perpendicular) ya kon mapne ke liye niche diye gaye upkaran upyog hote hain:

Cross Staff: Yeh mukhya roop se $90^\circ$ ke kon ke liye hota hai.
French Cross Staff: Isse $45^\circ$ , $90^\circ$ , aur $135^\circ$ ke kon mape ja sakte hain.
Optical Square aur Prism Square: Yeh Double Reflection ke siddhant par kaam karte hain. inme do darpan (mirrors) ke beech ka kon $45^\circ$ hota hai.

Slope aur Length Measurement

Clinometer: Iska upyog zameen ki dhalan (ground slope) mapne ke liye kiya jata hai.
Chain aur Tape: Inka upyog lambai mapne ke liye hota hai.

Chains ke Prakar

Metric Chain: Yeh $20\text{ m}$ ( $100$ links) aur $30\text{ m}$ ( $150$ links) ki lambai mein aati hai. Do links ke beech ki doori $20\text{ cm}$ hoti hai.
Gunter's Chain: Iski lambai $66\text{ ft}$ hoti hai aur isme $100$ links hote hain.
Engineer's Chain: Iski lambai $100\text{ ft}$ hoti hai aur isme $100$ links hote hain.
Revenue Chain: Iski lambai $33\text{ ft}$ hoti hai aur isme $16$ links hote hain.

Tapes ke Prakar

Cloth/Linen Tape: Yeh nami (moisture) se prabhavit hoti hai aur isme mudne (twisting) ki samasya hoti hai.
Metallic Tape: Yeh Brass, Copper aur Bronze se bani hoti hai.
Steel Tape: Yeh taapman (temperature) se prabhavit hoti hai.
Invar Tape: Yeh Nickel ( $36\%$ ) aur Steel (Iron) ke mishran (alloy) se bani hoti hai. Iska thermal expansion coefficient ( $\alpha$ ) bahut kam hota hai, isliye isme taapman ke karan galti (error) bahut kam hoti hai. Iska upyog Base Line mapne ke liye kiya jata hai..

Aapai

Error aur Correction ke Mukhya Siddhant

Surveying mein koi bhi nap lete samay galti (error) hona sambhav hai, jise sudharne ke liye correction lagaya jata hai:

Correction (C): Yeh True Value aur Measured Value ka antar hota hai ( $C = \text{True value} - \text{Measured value}$ ).
Error (E): Yeh correction ka bilkul ulta hota hai ( $E = -C$ ya $E = \text{Measured value} - \text{True value}$ ).

Chain ya Tape ki Lambai mein Correction

Agar upyog ki ja rahi chain ya tape ki lambai asliyat mein galat hai, toh niche diye gaye sutra ka upyog kiya jata hai:

Sutra: $L \times l = L' \times l'$ .
- Jahan $L$ asli lambai hai aur $L'$ galat lambai hai.
- $l$ asli line ki lambai (True length) hai aur $l'$ mapi gayi lambai (Measured length) hai.
Niyam: Agar chain ki lambai badh gayi hai, toh correction positive hota hai, aur agar ghat gayi hai, toh correction negative hota hai.

Udaharan: Agar $4000\text{ m}$ ki line $20\text{ m}$ ki chain se mapi gayi jo $2\text{ link}$ chhoti ( $19.6\text{ m}$ ) thi, toh asli lambai $3920\text{ m}$ hogi ( $20 \times l = 19.6 \times 4000$ ).

Slope Correction ( $C_s$ )

Jab zameen dhalan (slope) par ho, toh mapi gayi lambai hamesha asli horizontal doori se zyada hoti hai.

Sutra: $C_s = -l' (1 - \cos \theta)$ ya $C_s = -\frac{h^2}{2l'}$ .
Visheshtha: Slope correction hamesha negative hota hai.

Temperature Correction ( $C_{Temp}$ )

Taapman mein badlav ke karan chain ya tape sikud ya phail sakti hai.

Sutra: $C_{Temp} = L \alpha (T_m - T_0)$ .
- $T_m$ : Measurement ke samay ka taapman.
- $T_0$ : Standard taapman jab chain design ki gayi thi.
Niyam: Agar $T_m > T_0$ , toh correction positive hoga; aur agar $T_m < T_0$ , toh correction negative hoga.

Pull Correction ( $C_{pull}$ )

Jab measurement ke samay lagaya gaya khinchav (pull), standard pull se alag hota hai, toh pull correction lagaya jata hai:

Sutra: $C_{pull} = \frac{(P_m - P_0)L}{AE}$ .
- $P_m$ : Measurement ke samay ka pull.
- $P_0$ : Standard pull.
- $A$ : Chain/Tape ka cross-section area.
- $E$ : Young's modulus.
- $L$ : Mapi gayi lambai.
Niyam: Agar $P_m > P_0$ , toh correction positive hota hai; aur agar $P_m < P_0$ , toh correction negative hota hai.

Sag Correction ( $C_{sag}$ )

Jab tape ko do points ke beech latka kar (suspended) nap liya jata hai, toh tape apne vajan ke karan niche ki taraf jhuk jati hai, jise sag kehte hain.

Sutra: $C_{sag} = \frac{-W^2L}{24P_m^2}$ ya $\frac{-w^2L^3}{24P_m^2}$ .
- $W$ : Tape ka kul vajan (Total weight).
- $w$ : Per unit length ka vajan.
Visheshtha: Sag correction hamesha negative hota hai.

Normal Tension

Normal Tension woh pull ( $P_m$ ) hai jis par pull correction aur sag correction ek dusre ke barabar ho jate hain, jisse kul correction zero ho jata hai ( $C_{pull} + C_{sag} = 0$ ).

Numerical Udaharan

1. Temperature Correction ka Sawal

Deta: $L = 30\text{ m}$ , $T_m = 35^\circ\text{C}$ , $T_0 = 25^\circ\text{C}$ , $\alpha = 12 \times 10^{-6}/^\circ\text{C}$ .
Solution: $C_{Temp} = 30 \times (12 \times 10^{-6}) \times (35 - 25) = +0.0036\text{ m}$ ya $+3.6\text{ mm}$ .

2. Sag Correction ka Sawal

Deta: $P_m = 36\text{ kg}$ , $w = 30\text{ gm/m}$ , $L = 30\text{ m}$ .
Solution: Sutra mein values rakhne par sag correction $-0.78\text{ mm}$ aata hai.

Bearing aur Meridian

Bearing: Yeh ek horizontal kon (angle) hota hai jo kisi fixed direction ke sapeksh (with respect to) mapa jata hai.
Meridian: Us fixed direction ko Meridian kehte hain jise reference mana jata hai.

Bearing ki Pranaliyan (Systems of Bearing)

Bearing ko mapne ke do mukhya tarike hote hain:

1. Whole Circle Bearing (WCB)

Is system mein angle hamesha North (Uttar) se mapa jata hai.

Disha: Yeh hamesha clockwise (ghadi ki disha mein) hota hai.
Range: Iska maan $0^\circ$ se $360^\circ$ ke beech hota hai.

2. Reduced Bearing (RB) ya Quadrantal Bearing (QB)

Is system mein angle North ya South dono mein se jo bhi paas ho, wahan se mapa jata hai.

Disha: Yeh clockwise aur anti-clockwise dono ho sakta hai.
Range: Iska maan hamesha $0^\circ$ se $90^\circ$ ke beech hota hai.
Likhne ka Tarika: Ise hamesha directions ke saath likha jata hai, jaise $N\theta E$ , $S\theta E$ , $S\theta W$ , ya $N\theta W$ .

WCB se RB mein Badalne ke Udaharan

Agar aapko WCB diya gaya ho, toh RB nikalne ke liye quadrant (chaturthansh) ko dekhna hota hai:

WCB Angle	Quadrant	RB Conversion	Udaharan (RB)
$89^\circ$	$NE$	$N~89^\circ~E$	$N~89^\circ~E$
$95^\circ$	$SE$	$180^\circ - \text{WCB}$	$S~85^\circ~E$
$171^\circ$	$SE$	$180^\circ - \text{WCB}$	$S~9^\circ~E$
$272^\circ$	$NW$	$\text{WCB} - 180^\circ$ (error in note) $\rightarrow$ $360^\circ - \text{WCB}$	$N~88^\circ~W$
$351^\circ$	$NW$	$360^\circ - \text{WCB}$	$N~9^\circ~W$

RB se WCB mein Badalne ke Kuch Sawal

$S~10^\circ~E$ : Yeh dusre quadrant mein hai, iska WCB $180^\circ - 10^\circ = 170^\circ$ hoga.
$S~79^\circ~W$ : Yeh teesre quadrant mein hai, iska WCB $180^\circ + 79^\circ = 259^\circ$ hoga.
$N~81^\circ~W$ : Yeh chauthe quadrant mein hai, iska WCB $360^\circ - 81^\circ = 279^\circ$ hoga.
$N~4^\circ~E$ : Yeh pehle quadrant mein hai, iska WCB seedha $4^\circ$ hoga.

Meridian ke Prakar

Surveying mein reference ke liye do mukhya meridians ka upyog hota hai:

True Meridian: Prithvi ke asli uttar (True North) aur asli dakshin (True South) se guzarne wali rekha.
Magnetic Meridian: Prithvi ke magnetic flux ki disha mein Magnetic North aur Magnetic South se guzarne wali rekha.

Magnetic Declination aur Variations

Magnetic Declination True Meridian aur Magnetic Meridian ke beech ka horizontal kon (angle) hota hai. Kyunki Magnetic Meridian lagatar badalta rehta hai, isliye declination bhi sthir nahi hota. Declination mein hone wale badlav ko Variation kehte hain.:

Diurnal Variation: Rozana hone wala badlav.
Yearly Variation: Ek saal mein hone wala badlav.
Secular Variation: Lagbhag $150$ saalo ke antral mein hone wala badlav.
Irregular Variation: Kisi bhi samay bhookamp ya tsunami jaise prakritik apdao ke karan hone wala badlav.

Declination ke Prakar aur Calculations

Calculations karte samay Declination ko do bhago mein banta jata hai:

1. Eastern Declination (Positive)

Jab Magnetic North, True North ke East (Poorv) ki taraf hota hai, toh ise positive mana jata hai.

Sutra (Formula):
$TB = MB + \delta_E$
(Yahan $TB$ = True Bearing, $MB$ = Magnetic Bearing, aur $\delta_E$ = Eastern Declination hai)

2. Western Declination (Negative)

Jab Magnetic North, True North ke West (Pashchim) ki taraf hota hai, toh ise negative mana jata hai.

Sutra (Formula):
$TB = MB - \delta_W$
(Yahan $\delta_W$ = Western Declination hai)

Dhyan dein: Yeh dono formulas hamesha WCB (Whole Circle Bearing) system mein hi upyog kiye jate hain.

Magnetic Declination ke Udaharan

Compass survey mein True Bearing ( $TB$ ) nikalne ke liye Magnetic Bearing ( $MB$ ) aur Declination ( $\delta$ ) ka upyog kiya jata hai:

Sawal 1: Agar kisi line ki Magnetic Bearing $S~70^\circ~W$ hai aur Declination $6^\circ~West$ hai, toh True Bearing kya hogi?
- Calculation: Pehle $MB$ ko $WCB$ mein badlenge: $180^\circ + 70^\circ = 250^\circ$ .
- Formula: $TB = MB - \delta_W = 250^\circ - 6^\circ = 244^\circ$ .
- Result: Isse wapas $RB$ mein badalne par $S~64^\circ~W$ aayega.
Sawal 2: Agar $TB = 140^\circ$ aur $MB = 172^\circ$ hai, toh Declination kya hogi?
- Calculation: Dono ke beech ka antar $172^\circ - 140^\circ = 32^\circ$ hai.
- Result: Kyunki $MB > TB$ , isliye Declination $32^\circ~West$ hai.

Angle of Dip

Angle of Dip magnetic flux ki disha aur horizontal satah (plane) ke beech ka vertical kon hota hai.

Equator (Bhumadhya Rekha) par Dip ka maan $0^\circ$ hota hai.
Poles (Dhruvo) par Dip ka maan $90^\circ$ hota hai.

Fore Bearing (FB) aur Back Bearing (BB)

Surveying ki disha ke anusar bearing ko do bhago mein banta jata hai:

Fore Bearing (FB): Survey ki disha mein pehle point se agle point ki taraf li gayi bearing.
Back Bearing (BB): Survey ki vipreet (opposite) disha mein agle point se pichle point ki taraf li gayi bearing.

Line	Fore Bearing (FB)	Back Bearing (BB)
AB	Point A par mapi gayi $(\theta_A)$	Point B par mapi gayi $(\theta_B)$

Line

Fore Bearing (FB)

Back Bearing (BB)

Point A par mapi gayi $(\theta_A)$

Point B par mapi gayi $(\theta_B)$

Dhyan rahe ki $WCB$ pranali mein FB aur BB ke beech hamesha $180^\circ$ ka antar hota hai.

FB aur BB ke Beech ka Rishte

Kisis bhi ek line ke liye, uske Fore Bearing aur Back Bearing ka antar hamesha $180^\circ$ hota hai.

Sutra (Formula): $|FB - BB| [cite_start]= 180^\circ$ .
Pehchan: Survey ki disha mein li gayi bearing FB hai aur uske vipreet li gayi bearing BB hai.

BB nikalne ke Niyam (Calculation Rules)

WCB (Whole Circle Bearing) system mein BB nikalne ke liye niche diye gaye niyam upyog hote hain:

Rule 1: Agar FB ka maan $180^\circ$ se kam hai ( $FB < 180^\circ$ ), toh $BB = FB + 180^\circ$ .
Rule 2: Agar FB ka maan $180^\circ$ se zyada hai ( $FB > 180^\circ$ ), toh $BB = FB - 180^\circ$ .

Internal aur External Angles

Kisi bhi station par, pichli line ki Back Bearing (BB) aur agli line ki Fore Bearing (FB) ka antar nikalne se wahan ka internal ya external angle pata chalta hai.

Station B par: Line AB ki BB aur line BC ki FB ka antar wahan ka kon (angle) darshata hai.

Numerical Udaharan

Sawal 1: Agar line AB ki FB $290^\circ$ hai, toh BB kya hogi?
- Solution: Kyunki $290^\circ > 180^\circ$ , isliye $290^\circ - 180^\circ = 110^\circ$ .
Sawal 2: Agar line BA ki FB $60^\circ$ hai, toh line AB ki FB kya hogi?
- Hint: Line BA ki FB asal mein line AB ki BB hoti hai.
- Solution: $60^\circ + 180^\circ = 240^\circ$ .
Sawal 3: Agar line BA ki BB $N~30^\circ~W$ hai, toh line AB ki BB kya hogi?
- Calculation: Pehle WCB mein badlenge ( $330^\circ$ ), phir $330^\circ - 180^\circ = 150^\circ$ .

Bearing Conversion (RB System)

Reduced Bearing (RB) system mein Fore Bearing (FB) se Back Bearing (BB) nikalna bahut saral hai. Isme sirf cardinal directions ( $N, S, E, W$ ) ko badal diya jata hai, jabki numerical value wahi rehti hai.

Niyam: $N$ ko $S$ mein, $S$ ko $N$ mein, $E$ ko $W$ mein aur $W$ ko $E$ mein badlein.
Udaharan: Agar FB $S~30^\circ~E$ hai, toh BB $N~30^\circ~W$ hogi.

Internal Angle nikalne ka Sutra

Kisi bhi station par do lines ke beech ka internal angle nikalne ke liye niche diye gaye sutra ka upyog kiya jata hai:

Internal Angle = Agli line ki Fore Bearing (FB) - Pichli line ki Back Bearing (BB)

Numerical Udaharan

1. Bearing Calculation

Sawal: Agar line BA ki BB $210^\circ$ hai, toh line AB ki BB kya hogi?
Solution: $210^\circ - 180^\circ = 30^\circ$ . (Dhyan dein ki line BA ki BB asal mein line AB ki FB hoti hai).

2. Angle ABC nikalna (Example 1)

Data: Line AB ki FB $= 60^\circ$ aur line BC ki FB $= 95^\circ$ .
Step 1: Line AB ki BB nikalein $\rightarrow 60^\circ + 180^\circ = 240^\circ$ .
Step 2: Diagram ke anusar calculations karne par $(\angle ABC)$ ka maan $145^\circ$ aata hai.

3. Angle ABC nikalna (Example 2)

Data: Line AB ki FB $= 200^\circ$ aur line BC ki BB $= 30^\circ$ .
Step 1: Line AB ki BB $= 200^\circ - 180^\circ = 20^\circ$ .
Step 2: Line BC ki FB $= 180^\circ + 30^\circ = 210^\circ$ .
Step 3: Angle ABC $= FB_{BC} - BB_{AB} = 210^\circ - 20^\circ = \mathbf{190^\circ}$ .

Local Attraction Kya Hai?

Local attraction ek aisi galti (error) hai jo magnetic needle par aati hai jab survey area mein koi local magnetic object (jaise bijli ke khambe, steel ki imarate, ya lohe ke upkaran) maujood ho.

Pehchan: Agar kisi line ke Fore Bearing (FB) aur Back Bearing (BB) ka antar $180^\circ$ nahi aata ( $|FB - BB| \neq 180^\circ$ ), toh iska matlab hai ki stations local attraction se prabhavit hain.
Shuddh Station: Agar $|FB - BB| [cite_start]= 180^\circ$ hota hai, toh dono readings sahi hain aur stations local attraction se mukt (free) hain.

Local Attraction ka Prabhav

Ek dilchasp baat yeh hai ki bhale hi stations local attraction se prabhavit hon, lekin unke beech ka internal ya external angle galat nahi hota.

Karan: Kyunki local attraction dono readings ( $\theta_1$ aur $\theta_2$ ) ko ek hi barabar matra ( $x$ ) se badalta hai, isliye jab hum unka antar nikalte hain, toh woh error ( $x$ ) cancel ho jata hai.
Sutra: $\Delta = (\theta_1 + x) - (\theta_2 + x) = \theta_1 - \theta_2$ .

Numerical Udaharan

1. Included Angle nikalna

Data: Line AB ki FB $= N~20^\circ~W$ ( $340^\circ$ ) aur line BC ki BB $= S~50^\circ~E$ ( $130^\circ$ ).
Step 1: AB ki BB nikalein $\rightarrow S~20^\circ~E$ ( $160^\circ$ ).
Step 2: BC ki FB nikalein $\rightarrow N~50^\circ~W$ ( $310^\circ$ ).
Step 3: Angle B $= FB_{BC} - BB_{AB} = 310^\circ - 160^\circ = \mathbf{150^\circ}$ .

2. Error aur Correction Calculation

Sawal: Agar point A par $2^\circ$ ka local attraction hai aur FB $40^\circ$ mapi gayi hai, toh sahi BB kya hogi?.
Solution:
- Measured Value (MV) $= 40^\circ$ , Error (E) $= +2^\circ$ .
- True Value (TV) $= MV - E = 40 - 2 = 38^\circ$ .
- Corrected BB $= 38^\circ + 180^\circ = \mathbf{218^\circ}$ .

3. Local Attraction ki matra nikalna

Sawal: Line AB ki FB $= N~20^\circ~W$ hai aur BB $= S~23^\circ~E$ hai. Station B par local attraction kitna hai?.
Solution:
- True BB honi chahiye $= S~20^\circ~E$ ( $160^\circ$ ).
- Measured BB (MV) $= S~23^\circ~E$ ( $157^\circ$ ).
- Error (E) $= MV - TV = 157^\circ - 160^\circ = \mathbf{-3^\circ}$ .

Closed Traverse ki Bearing nikalne ki Vidhiya

Traverse mein bearings ko sahi karne ke do mukhya tarike hote hain:

Direct Method: Yeh tab upyog hota hai jab traverse ki kam se kam ek line puri tarah sahi ho aur internal angles mein koi galti na ho.
Internal Angle Method: Is vidhi mein internal ya external angles ki madad se bearings ko correct kiya jata hai.

Latitude aur Departure

Traversing mein kisi line ke coordinates ko Latitude aur Departure mein banta jata hai:

Latitude (L): Kisi line ka North-South axis par projection.
- Iska sutra hai: $L = l \cos \theta$ .
- North ki taraf yeh positive (+ive) aur South ki taraf negative (-ive) hota hai.
Departure (D): Kisi line ka East-West axis par projection.
- Iska sutra hai: $D = l \sin \theta$ .
- East ki taraf yeh positive (+ive) aur West ki taraf negative (-ive) hota hai.

Closed Traverse ke Niyam

Ek perfect closed traverse ke liye niche di gayi sharte poori honi chahiye:

Sabhi Latitudes ka jod zero hona chahiye: $\Sigma L = 0$ .
Sabhi Departures ka jod zero hona chahiye: $\Sigma D = 0$ .

Closing Error ( $e$ )

Agar $\Sigma L$ aur $\Sigma D$ ka jod zero nahi aata, toh iska matlab hai ki traverse mein "Closing Error" hai.

Sutra (Formula): $e = \sqrt{e_L^2 + e_D^2}$ .
- Yahan $e_L$ ( $\Sigma L$ ) latitude mein error hai.
- Yahan $e_D$ ( $\Sigma D$ ) departure mein error hai.

Closing Error ko Correct karne ki Vidhiyan

Traverse mein aane wali galti (closing error) ko theek karne ke liye niche di gayi char mukhya vidhiyan hain:

Bowditch Method
Transit Method
Graphical Method
Axis Method

Bowditch aur Transit Method mein Antar

Visheshta	Bowditch Method	Transit Method
Precision	Isme linear (line) aur angular (angle) dono measurements ko ek hi precision se mapa jata hai.	Isme angular measurement, linear measurement ki tulna mein adhik sateek (precise) hoti hai.
Latitude Correction ( $C_L$ )	$C_L = - \frac{\text{length of that side}}{\text{perimeter of traverse}} \times e_L$.	$C_L = - \frac{\text{latitude of that line}}{\text{sum of all latitudes (magnitude)}} \times e_L$.
Departure Correction ( $C_D$ )	$C_D = - \frac{\text{length of that side}}{\text{perimeter of traverse}} \times e_D$.	$C_D = - \frac{\text{departure of that line}}{\text{sum of all departures (magnitude)}} \times e_D$.