Lesson 3: Measuring Instruments

3.1 From the body to the instrument

• Early humans used parts of their bodies and natural events as measuring tools: the arm, hand and foot for length, and the sunrise, sunset and cycles of the moon for time.
• Because every person's arm is a different length, these units differed from one country (even one town) to another.
• With the growth of industry people needed agreed standards and better instruments, so instruments developed greatly and helped us describe phenomena more accurately.

3.2 Examples of instruments, old and modern

A sensible choice of instrument is the first step to an accurate result: you would not use a metre tape to measure the thickness of a coin, nor a kitchen balance to weigh a gold ring (see sources of error, Lesson 7).

3.3 The vernier caliper — measuring length precisely

Why do we need it?

• A ruler graduated in millimetres cannot give a reading better than about 1 mm.
• The vernier caliper allows a reading to 0.1 mm.

Parts. A vernier caliper has

• a fixed main scale (graduated in mm), and
• a sliding vernier scale that moves along it,
• jaws between which the object is placed.

The principle. The main scale is divided into millimetres: one main-scale division = 1 mm. The vernier scale has 10 divisions that together are exactly as long as 9 main divisions (9 mm). So each vernier division is 9 mm ÷ 10 = 0.9 mm, which is 0.1 mm shorter than a main-scale division. Therefore:

Vernier reading = (number of the vernier line that coincides with a main-scale line) × 0.1 mm

and the smallest length the instrument can measure (its precision, or least count) is 0.1 mm.

Procedure for measuring a length

1. Place the object between the jaws and close them gently (do not squeeze hard — you would bend the object or the jaws).
2. Read the main scale at the point just before the zero of the vernier scale. (Example: 29 mm.)
3. Look along the vernier scale for the line that lines up exactly with some line of the main scale. Multiply its number by 0.1 mm. (Example: the 6th line coincides → 6 × 0.1 = 0.6 mm.)
4. Add the two: 29 mm + 0.6 mm = 29.6 mm.
5. Repeat the measurement several times and take the average to reduce random error.

Worked example 1 (new numbers). The zero of the vernier lies just after the 41 mm mark of the main scale, and the 3rd vernier line coincides with a main-scale line. Reading = 41 + 3 × 0.1 = 41.3 mm = 4.13 cm.

Worked example 2. Four repeated readings of the diameter of a steel ball were 12.7 mm, 12.8 mm, 12.7 mm and 12.6 mm. The best value is the mean: (12.7 + 12.8 + 12.7 + 12.6) ÷ 4 = 50.8 ÷ 4 = 12.7 mm.