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"Nonius" redirects here. For the Roman grammarian, see Nonius Marcellus:"Vernier" redirects here. For the village, see Vernier, Switzerland A vernier scale lets one read more precisely from an evenly divided straight or circular measurement scale. It is fitted with 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. 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. Another theory is that this name is from the Latin "nona" meaning "9" and therefore "nonius" means a "ninth" of the main scale. Verniers are common on sextants, scientific instuments and 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 so that when its zero point is coincident with the start of the data scale, its gradations are at a slightly smaller spacing than those on the data scale and so do not coincide with any 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 to show at the finer level). 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 gradations 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 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). Why a vernier scale works
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