A vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale. It is a sliding secondary scale that is used to indicate where the measurement lies when it is in between two of the marks on the main scale.

Verniers are common on sextants used in navigation, scientific instruments and machinists' measuring tools (all sorts, but especially calipers and micrometers) and on theodolites used in surveying.

When a measurement is taken by mechanical means using one of the above mentioned instruments, the measure is read off a finely marked data scale (the "fixed" scale, in the diagram). The measure taken will usually be between two of the smallest graduations on this scale. The indicating scale ("vernier" in the diagram) is used to provide an even finer additional level of precision without resorting to estimation.

History

It was invented in its modern form in 1631 by the French mathematician Pierre Vernier (1580–1637). In some languages, this device is called a nonius. It was also commonly called a nonius in English until the end of the 18^th century. Nonius is the Latin name of the Portuguese astronomer and mathematician Pedro Nunes (1502–1578) who in 1542 invented a related but different system for taking fine measurements on the astrolabe that was a precursor to the vernier.

Construction

In the following, N is the number of divisions the maker wishes to show at a finer level of measure.Direct vernier:Direct verniers are the most common. The indicating scale is constructed so that when its zero point is coincident with the start of the data scale, its graduations are at a slightly smaller spacing than those on the data scale and so none but the last graduation coincide with any graduations on the data scale. N graduations of the indicating scale would cover N-1 graduations of the data scale.Retrograde vernier:Retrograde verniers are found on some devices, including surveying instruments. A retrograde vernier is similar to the direct vernier except its graduations are at a slightly larger spacing. N graduations of the indicating scale would cover N+1 graduations of the data scale. The retrograde vernier also extends backwards along the data scale.

Direct and retrograde verniers are read in the same manner.

Use

When a length is measured the zero point on the indicating scale is the actual point of measurement, however this is likely to be between two data scale points. The indicator scale measurement which corresponds to the best-aligned pair of indicator and data graduations yields the value of the finer additional precision digit.

Examples

On instruments using decimal measure, as shown in the diagram below, the indicating scale would have 10 graduations covering the same length as 9 on the data scale. Note that the vernier's 10th graduation is omitted.

On an instrument providing angular measure, the data scale could be in half-degrees with an indicator scale providing 30 1-minute graduations (spanning 29 of the half-degree graduations).

Why a vernier scale works

The vernier scale is constructed so that it is spaced at a constant fraction of the fixed main scale. So for a decimal measuring device each mark on the vernier would be spaced nine tenths of those on the main scale. If you put the two scales together with zero points aligned then the first mark on the vernier scale will be one tenth short of the first main scale mark, the second two tenths short and so on up to the ninth mark which would be misaligned by nine tenths. Only when a full ten marks have been counted would there be an alignment because the tenth mark would be ten tenths, that is a whole main scale unit, short and will therefore align with the ninth mark on the main scale.

Now if you move the vernier by a small amount, say, one tenth of its fixed main scale, the only pair of marks which come into alignment will be the first pair since these were the only ones originally misaligned by one tenth. If we had moved it 2 tenths then the second pair and only the second would be in alignment since these are the only ones which were originally misaligned by that amount. If we had moved it 5 tenths then the fifth pair and only the fifth would be in alignment. And so on for any movement, only one pair of marks will be in alignment and that pair will show what is the value of the small displacement.

Vernier Acuity

Vernier acuity is the ability by a person to detect the proper alignment of two line segments. In most persons, Vernier acuity is particularly acute. This allows one to differentiate the aligned and misaligned marks on a Vernier scale.

See also

• Micrometer
• Transversal (instrument making) - technique in use prior to vernier scales.

Notes

References

• Animated Vernier caliper
• Instrumentos de Medición Vernier y Calculadoras Texas Instruments
• The VERNIER Scale Open Door Web Site reference source for both students and teachers.
• How to use the vernier caliper Clemson University Physics On-line Laboratories