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#### Old Methods of Measurement of a Length

- To measure lengths units used were a finger, palm, span, cubit, foot, yard, fathom, furlong etc.
- The length of an inch was originally decided by Edward-II of England in the early 1300’s as the length of three grains of barley laid end to end. Inch was divided into three parts called barley.

#### Measurement of Length:

- The length is a fundamental quantity, it is used to measure a distance between two points in space. S.I. unit of length is a metre (m) and c.g.s. unit of length is centimetre (cm).
- Other practical units of measurement of length are micrometer (mm), millimetre (mm), kilometre (km), Angstrom (A°) etc.
- Length of accessible objects can be measured directly using a metre scale, vernier callipers, micrometer screw gauge, measuring tapes, travelling microscopes etc. Length of non-accessible objects is measured indirectly.

#### Metre Scale:

- one metre is divided into 100 equal parts, each part is called centimetre. Each centimetre is divided into 10 equal parts, each part is called millimetre.
- Least count is the smallest measurement that can be taken accurately with an instrument or device. The least count of a metre scale is 1 mm or 0.1 cm.
- Engineering metre scale has centimetres marked on one edge and inches marked on another edge. Centimetres have decimal divisions while inches have fractional divisions.
- metre scale may have bevelled edges to avoid errors due to parallax.

#### Linear Measurements (Direct Method):

- Place the metre scale along the object so that the ‘0’ mark on the metre scale coincides with one end of the object and reading at the other end of the scale indicates the length of the object.
- To avoid wear and tear off the end of the scale, sometimes the scale is placed along the object and readings at the ends of the object are taken. The length of the object is obtained by subtracting higher reading from lower reading.
- The eye must be kept vertically above the end of the object so that the corresponding graduation can be read clearly. If the eye is not kept exactly vertically above the end of the object, it leads into error called parallax error.

- In case, the end of the object lies between the two small divisions of the scale, the correct length is reported by noting the marking nearer to the end of the object.
- Limitation of metre scale is that it cannot measure the length of an object smaller than 1 mm or 0.1 cm.

#### Measurement of Length of a Curve

#### A) Thread Ruler Method (Direct Method):

- In this case, a thread is laid along the curve
- Then the length of the thread is measured using a metre scale.

#### Divider Ruler Method (Direct Method):

- In this method, the curve is divided into small straight segments.
- Length of each such segment is measured using divider and scale.
- Then the total length of the curve can be obtained by adding lengths of all individual segments.

#### External diameter of cylinder or sphere

#### Blocks Ruler Method (Direct Method):

- A cylinder or sphere whose external diameter is to be measured is placed between two blocks.
- The reading on the scale corresponding to inner edge is x cm while that corresponding to outer edge is y cm.
- then the diameter is the absolute value of (x-y) cm.

#### Caliper Ruler Method (Direct Method):

- To measure external diameter of sphere or cylinder, an external calliper is used.
- In this method, the cylinder or sphere whose external diameter is to be measured is placed between two jaws of the calliper.
- The position of the calliper is fixed by tightening the screw.
- The distance between the jaws gives the external diameter of the cylinder or the sphere.
- To measure internal diameter of the cylinder, an internal calliper is used.

#### External Diameter of Thin Wire: (Indirect Method):

- A known number of turns of the wire whose diameter is to be measured are wound on a scale or on a rod of uniform diameter.
- The length of turns on the scale or the rod is measured.
- The diameter of the wire is calculated by dividing the length of turns by the number of turns.

#### External Diameter of Cylinder: (Indirect Method):

- A known number of turns (N) of a thin wire are wound on a cylinder whose diameter is to be measured.
- Then the wire is unwounded and straightened. Then its length is measured.
- Diameter of the rod can be obtained by the formula

#### Next Topic: Measurement of Length Using Vernier Callipers

#### Previous Topic:: Basic Concept of Measurement

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