**Vernier Callipers : ** An ordinary scale can be used for measuring perfect accuracy upto 1 mm . For further perfect accuracy millimeter scale has to be subdivided .

Vernier calliper is used to measure accuracy with perfection upto (1/10)th of a millimeter . It was developed by French mathematician Pierre Vernier which led to name ” Vernier Calliper ” after name of the inventor . It contains main scale and Vernier scale . The Vernier scale is attached to the movable jaw . When the jaw touch each other , the zero of Vernier scale coincides with the zero of main scale .

**Vernier Constant : **It is defined as the minimum length which may be measured with instrument . It is also called least count . It is the difference between one main scale division and one Vernier Scale division .

**Calculation of Vernier Constant : **

Vernier Constant = Least Count = 1 MSD – 1VSD

If n division of vernier scale coincides with (n-1) division of main scale then ,

n VSD = (n-1) MSD

$\displaystyle 1 VSD = \frac{n-1}{n} MSD $

Vernier Constant $\displaystyle V.C = 1 MSD – (\frac{n-1}{n}) MSD $

$\displaystyle V.C = \frac{1}{n} MSD $

$\displaystyle V.C = \frac{value \; of \; 1 div. \; main \; scale}{number \; of \; div. \; on \; vernier \; scale} MSD $

Suppose 10 VSD = 9 MSD

$\displaystyle 1 VSD = \frac{9}{10} MSD $

$\displaystyle V.C = 1 MSD – (\frac{9}{10}) MSD = \frac{1}{10} MSD $

1 MSD = 1 mm = 1/10 cm

$\displaystyle V.C = \frac{1}{10} \times \frac{1}{10} = \frac{1}{100}$

= 0.01 cm = 0.1 mm

**Determination of Zero Error :** Vernier is supposed to posses zero error . If zero of main scale doesn’t coincides with zero of Vernier of Scale when jaws are brought in touch with each other . Zero error takes place because of wear and tear of jaws and some time because of manufacturing defects .

**(i) Positive Zero Error and its correction :** The zero error is considered to be positive when the zero mark of vernier scale crosses the zero mark of main scale when jaws touch each other . since in such cases measured length would be more than the actual length , the zero error is said to be positive zero error . To calculate zero error note the division coinciding with main scale .

Zero Error = 0.00 + 5 × Vernier constant

Zero Error = 0.00 + 5 × 0.01

Zero Error = 0.05 cm

hence , for zero correction 0.05 cm needs to be subtracted from the observed value .

**(ii) Negative zero Error and its correction :** The zero error is considered to be negative when zero mark of vernier scale lies towards the left side of the zero of the main scale when jaws contact each other the length measured by this vernier calliper will be less than the actual length , hence zero error is said to be negative zero error .

Zero Error = 0.00 -(10-6) × V.C

= -4 x 0.01 = – 0.04

Zero correction = observed Reading – (-0.04)

Zero correction = observed Reading + 0.04 cm

**Use of Vernier Calliper : **

Three parts of Vernier Calliper are used to do various kinds of measurements :

(i) Main jaw to hold objects from outside and determine its thickness

(ii) Small jaw to hold objects from inside for measuring internal diameter or distance between two parts .

(iii) Pointed tips at the back of Vernier to measure depth of the objects .