View source for Nonius (device)

{{Short description|Measuring tool used in navigation and astronomy}}
{{Use dmy dates|date=March 2021}}
[[File:Nonio originale.jpg|thumb|190px|right|[[Pedro Nunes]] '''Nonius''' model]]

'''Nonius''' is a measuring tool used in navigation and astronomy named in honour of its inventor, [[Pedro Nunes]] (Latin: Petrus Nonius),<ref>{{cite web|url=http://www.infopedia.pt/$pedro-nunes|title=Pedro Nunes|publisher=Infopédia [em linha]. Porto: Porto Editora|year=2015}}</ref> a Portuguese author, mathematician and navigator. The nonius was created in 1542 as a system for taking finer measurements on circular instruments such as the [[astrolabe]]. The system was eventually adapted into the [[Vernier scale]] in 1631 by the French mathematician [[Pierre Vernier]].<ref name="Poelje">{{cite journal|last1=Poelje|first1=Otto van|title=Diagonals and Transversals: Magnifying the Scale|journal=Journal of the Oughtred Society|date=25 July 2004|pages=22–28|url=https://eeuwen.home.xs4all.nl/images/Pics/Kombuispraat/Pleinschaal/200410%20Diagonals%20and%20Transversals%20V13-2.pdf|accessdate=2 May 2017}}</ref>

== Technical features ==
[[File:Nónio.gif|thumb|right|Nonius method of measuring an angle with higher precision]]
The nonius was used to improve the [[astrolabe]]'s accuracy. This consisted of a number of [[concentric]] circles traced on an instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. On a standard scale of 90 degrees, there are an additional 44–45 concentric circles, with each divided into a specific unit size such that a scale unit on position <math>n</math> had an arc of <math>90/n</math> degrees.<ref name="Poelje"/><ref name="Eisele">{{cite web |last1=Eisele |first1=Margarete |title=The Nonius |url=http://www.maths-in-europe.eu/ru/2-uncategorised/684-the-nonius |website=Mathematics in Europe |accessdate=2 May 2017 |language=ru-ru }}{{dead link|date=June 2021}}</ref> Thus, the outermost [[Quadrant (circle)|quadrant]] would comprise 90° in 90 equal divisions, the next inner would have 89 divisions, the next 88 and so on. When an angle was measured, the circle and the division on which the [[alidade]] fell was noted. A table was then consulted to provide the exact measure.<ref>{{cite web |url=http://www.cienciaviva.pt/latlong/anterior/nonio2.asp |title=O conceito de nónio |author=António Estácio dos Reis |lang=pt |publisher=Ciência Viva |trans-title=The concept of Nonius |access-date=17 January 2015 |archive-url=https://web.archive.org/web/20150414094509/http://www.cienciaviva.pt/latlong/anterior/nonio2.asp |archive-date=14 April 2015 |url-status=dead}}</ref>

== Applications ==
The [[astronomer]] [[Tycho Brahe]] applied the nonius to the astronomic [[Quadrant (instrument)|quadrant]].<ref>{{cite web|url=http://www.cienciaviva.pt/latlong/anterior/nonio3.asp|title=Tycho Brahe recorre ao nónio de Pedro Nunes|author=António Estácio dos Reis|publisher=Ciência Viva|trans-title=Tycho Brahe betakes Pedro Nunes' Nonius|access-date=17 January 2015|archive-url=https://web.archive.org/web/20150414093623/http://www.cienciaviva.pt/latlong/anterior/nonio3.asp|archive-date=14 April 2015|url-status=dead}}</ref><ref name="Eisele"/>

In [[numerical control|numerically controlled]] machines, the nonius is part of several [[Linear encoder#Absolute code|absolute encoders]], that measure linear or rotational displacements.<ref>{{cite web|url=http://www.sensorsmag.com/sensors/position-presence-proximity/the-vernier-scale-goes-digital-1541|title=Nonius interpolation provides excellent differential linearity and higher resolution for linear displacement measurement systems or rotary encoders}}</ref>

==See also==
* [[Transversal (instrument making)]]
* {{ill|Nonius connector|de|Noniusverbinder}}<!-- more related to Vernier than Nonius. Either way: red link with possibilities -->

==References==
{{Reflist}}

{{Measuring and alignment tools}}
{{Authority control}}

[[Category:Portuguese inventions]]
[[Category:Navigational equipment]]
[[Category:Historical scientific instruments]]