1.4. RT CI [VernierScale - BHANGAR MAHAVIDYALAYA

1.4. RT CI [VernierScale

10 o.10 eie 1 fa U TA tT| eis,|tTA (Pierre Vernier-1580-1637) tATCA 9T

3.501 3.60I TI AoADN TRTS 11 TI f NRe (Definition) CRIT ATTEta A 1 , 3.50 3.60-9 ATAS A AR 3.57 19 31 A

9 0.10 AA JA (TN 0.01, 0.025, 0.06, TRAT1 T [Vernier Scale is a small and sliding

scale attached along the edge of the Main Scale to

measure the fractional part of one division ie. least

count of the main scale very accurately]|

1.4 SA CATA RIAA [Description of Vernier Scale]

s41 1 7 (Main scale -M) TYI EATR CAT| I 9T4 FfFRTS 1 *01 (n) 7°p1 TST

1 7R3U (n-1) 9*T I foa 1.23 TT (

10 Vernier Scale Dlvisions Vernier Scale 10

5

10

9

10 5 10

Main Scale 9 Main Scale Divisions

34 1 2 TRRfA yTi7 (R)

1.4 2Ats caTN afE [Features of Vernier Scalel

TCS PT T (6 (Index mark) et o

(zero) fA

1 AIR (rectilinear) 33PTa(curvilinear) I

1.43GtANTI CATFIE UR [Uses of Vernier Scale] TAI CoH E 3RI |ao fReTURT (Transit Theodolite)

DT (Sextant) cafaa (Planimeter TaDIA (Barometer) TRA FTT (Abney Level) Ji I

1.44 SiAta CAT TG [Principle of Vernier Scale]

S T Ra (Vernier Constant VC)I TER

A 3 (Definition)

1, VC = d-vl

14 utAA C(OS 4PI(GH [Types of Vernier Scale]

Oat3 ao u (According to Vernier Principle) 11 Ra DE AI (Direct or Positive Vernier) :

DIRECT VERNIER SCALE RETROGRADE VERNIER SCALE

Vernier Scale Vernier Scale 10

10 5

LLU (TTTITTTTtHT TTTTTTTTTTH T

2

INCH Main Scale INCH Main Scale

T5 1.24 (a): RaT UAAIS CH 6 1.24 (b): ATITAU EAA CA7

2 CHCRTCATG 1 AUDE N (Retrograde or Negative Vernler)

NR * TT (According to Method of Uses) 1 3 BRTR (Double Vernier): 4nT qTART 3 rotaME 5TATR (Double Folded Vernier)

(Counter-clockwise) e NCE (Clockwise) NCCI KTC CPTa RA AKPiTTAR ATATION

2 A (Extended Vernier):

14 uRNS DE UAtI CH [Direct or Positive Vernier Scale]

5tfAuta fate f Determination of Vernier Constant 1.4.6.1

VC = d- v 4P .-(1)

36 1 F RAT FT (A)

(n-1)d K

= (n - 1)d p

= (n-1)d n

vC = d-(n-1)d = d-(nd-d) = d-nd,d n n n n

- 31, VC = n n

1.462 stffra caTo Function of Vernier Scale

9 :10 9:1 10

Vernier Scale Vernier Scale 10

10 5 5

LLL

T 0 1 2

1 2 Main Scale Main Scale

oa 1.25(a) : 73 (AA 1R HTIS TI

Vernier Scale 10 20 Point of

coincidence - -- 3.665".-

ITITIT TITITTIITITTTTTIIUTITI|TIT|TT|I 3.60" 1 2 3 5

INCH Main Scale

FRTA R EARA CATR 13 -9 PID TI count of Main Scale) I TIR FA T I I

CI 7AC 0.10 31 AA T 15' T 30 G A 13 x 0.0051 o.065 1 AR,

HT RTE UAIA CAA 1 R (b) x VC |

1.4.63 Total Total Scale Reading-TSR .

1 TA ID (Main Scale Reading-MSR)

3.6019)I

2 AT A (Vernier Scale Reading-VsR): CAT Cj *D (TSR) = MSR+ VSR

= MSR+ (b x VC)

-bxVC MSR+(bx VC) = TSR

1, bxVC = TSR- MSR 1, b = SR-MSR VC

1.4.6.4 Method of Construction

(n-1)d 7AIA T 7R n **U I1 Main Scale-4 T49 TA AA (d)

a

1.465 Points to be remembered

VC), E* E (n), 8RISE

R AA Ui R 5, 10

1.46.6 Examples

Example-1 Draw a Vernier Scale to read 3.58 when 9 m.s.d. coincide with 10 v.s.d. and value of one

main scale d�ivision is 0.1. [3.58" A1 T SAA C7 dITI TA 9 m.s.d. TNA 10 vs.d. R

Solution

Step-1 vc Where, VC = Vernier Constant, d = Least count of Main Scale,

0.1" n = No.of Vernier Scale division = = 0.01" 10

Step-2 Length of Venier Scale = (n-1)d = (10-1)0.1" = 0.9"

Step-3 Coincident point of v. s. division with any forward division of main scale

Total Scale Reading-Main Scale Reading VC

3.58-3.50 = 08 = 8th d sion 0.01 01 8th d

TAb 7, �7J 3 CEAP7 °A1 39

Step-4 Drawing of Scale

cONSTRUCTION OF A VERNIER SCALE 0.90"

4 -----

Vernier Scale Divisions (o Vernier Scale 10 5 Point of

3.58" Coincidence LLLL TTTTTT|TIJT|TTTTTTTTT|TTTTTD

0 2 5

INCH Main Scale

Example-2 main scale is 0.2". [2.46" TACE G fAT za diet T 9 m.s.d. 10 v.s.d. R AA

STI NA 0.2"

Draw a Vernier Scale to read 2.46" when 9 m.s.d. represent 10 v.s.d. and least count of

Solution Step-1 Least count of main scale 0.2 = 0.02"

No. of vernier scale division Vernier Constant

10

Step-2 Length of Vernier Scale = (n-1)d Where,n = No. ofv. s. d. , d = least count of m. s.

= (10-1) x 0.2"

= 1.8"

Coincident Point of v. s. d. with the any forward division of main scale Total Scale Reading -Main Scale Reading

Step-3 VC

0.06 3rd division 0.02"

2.46"-2.40" 02"

Step-4 Drawing of Scale:

CONSTRUCTION OFA VERNIER SCALE 1.80 9:10

Vernier Scale Divisions

Vernier Scale 10 5 Point of

Coincidence 2.46".--.

2 4 5

INCH Main Scale

oa 1.28:1Y UANIS MAN TA

40 4012I TRRtar yi (A)

Example-3 Draw a Vernier Scale to read 16°41' where 29 main scale divisions coincide with 30

Vernier Scale divisions and main scale is divided into degrees and half a degrees. [16°41'13 PAa3

Solution

Vernier constant (VC) = Least count of main scale(d) - 30 1

No. of vernier scale divisions (n) Step-1 30 1

30

Step-2 Length of Vernier Scale = (n-1)d

let d be 0.1" which represents angular value of one division of main scale = (30-1) x .1" = 2.90"

Step-3 nth division of V.S. which coincide with any forward division of main scale

16° 41'-16°30 = 11th division

Step-4 Drawing of Scale:

cONSTRUCTION OF A VERNIER SCALE Vernier Scale Divisions

- - 2.90".

29 30

Vernier Scale

10 20 30 Point of

5 15 25 Coincidence --- 16° 41'--J T TTTTTT --

TTTTTTTTTTTTT 5 15 25 35

20 30 DEGREES Main Scale