# Vernier scale

A vernier scale lets one read more precisely from a linear measurement scale. 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, which is the latin name of the Portuguese astronomer and mathematician Pedro Nunes (1492-1578) who invented the principle.

Verniers are common on sextants, machinists' measuring tools (all sorts, but especially calipers and micrometers) and on theodolites.

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 gradations 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.

## Construction

The indicating scale is constructed with its zero point coincident with the start of the data scale. Its gradations are at a slightly smaller spacing than those on the data scale: N gradations of the indicating scale would cover N-1 gradations of the data scale (where N is the number of divisions the maker wishes wishes to show at the finer level). The indicator scale measurement corresponding to the best-aligned pair of indicator & data gradations yields the value of the finer additional precision.

## Examples

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

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

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy