vernier scale

An enlarged view of the above caliper showsit has a resolutionor precisionof0.02 mm. The reading is 3.58 mm. The3 mm is read off from the upper (fixed) datascale. The 0.58 mm is obtained from thelower (sliding) indicating scale at the pointof closest alignment between the two scales.The caliper has two external and twointernal jaws, which are used to measurerespectively the external and the internaldiameter of a cylinder. The tail is used tomeasure the internal depth.

Mechanical displacement gauges with vernier scaleson wall cracks (Moika Palace, Saint Petersburg).

Vernier scaleFrom Wikipedia, the free encyclopedia

A vernier scale is a device that lets the user measure more precisely than could be done unaided when readinga uniformly divided straight or circular measurement scale. It is a scale that indicates where the measurementlies in between two of the marks on the main scale. Verniers are common on sextants used in navigation,scientific instruments used to conduct experiments, machinists' measuring tools (all sorts, but especially calipersand micrometers) used to work materials to fine tolerances, and on theodolites used in surveying.

Contents1 History2 Construction3 Use4 Least Count of Vernier scale5 Examples6 How a vernier scale works7 Vernier acuity8 Zero error9 See also10 External links11 References

HistoryCalipers without a vernier scale originated in ancient Chinaas early as the Qin dynasty (9 AD).[1][2] The secondaryscale, which contributed extra precision, was invented in1631 by French mathematician Pierre Vernier (15801637).Its use was described in detail in English in NavigatioBritannica (1750) by mathematician and historian JohnBarrow.[3] While calipers are the most typical use of Vernierscales today, they were originally developed for angle-measuring instruments such as astronomical quadrants.

In some languages, the Vernier scale is called a nonius. Itwas also commonly called a nonius in English until the endof the 18th century.[4] Nonius is the Latin name of thePortuguese astronomer and mathematician Pedro Nunes (15021578), who in 1542 invented a different systemfor taking fine angular measurements. Nunes' nonius was not widely adopted, being difficult to make and alsodifficult to read. Tycho Brahe used it on at least one instrument.[4][5][6]

The name "vernier" was popularised by the French astronomer Jrme Lalande (17321807) through his Traitd'astronomie (2 vols) (1764).[7]

Vernier scale - Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Vernier_scale

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Vernier scale direct vernier

Animation of a caliper measurementusing a vernier scale. Click to enlarge

Vernier scale use 0.02 scalemeasurement is 19.44 mm

ConstructionIn the following, N is the number of divisions the maker wishes to show at a finer level of measure.

Direct verniers are the most common. The indicating scale is constructedso 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 datascale and so none but the last graduation coincide with any graduationson the data scale. N graduations of the indicating scale cover N1graduations of the data scale.

Retrograde verniers are found on some devices, including surveyinginstruments.[8] A retrograde vernier is similar to the direct vernier, exceptits graduations are at a slightly larger spacing. N graduations of theindicating scale cover N+1 graduations of the data scale. The retrogradevernier also extends backwards along the data scale.

Direct and retrograde verniers are read in the same manner.

UseThe main use of the vernier caliper is to measure the internal and theexternal diameters of an object. To measure using a vernier scale, theuser first reads the finely marked "fixed" scale (in the diagram). Thismeasure is typically between two of the scale's smallest graduations. Theuser then reads the finer vernier scale (see diagram), which measuresbetween the smallest graduations on the fixed scaleproviding muchgreater accuracy.

It is also used in measuring an object to its lowest decimal point.

Least Count of Vernier scaleLet the measure of the smallest main scale reading, that is the distancebetween two consecutive graduations (also called its pitch) be S and thedistance between two consecutive Vernier scale graduations be V suchthat the length of (n-1) main scale divisions is equal to n Vernier scaledivisions.Then,

the length of (n-1) main scale divisions = the length of n vernier scaledivisions

or, (n-1)S = nV

or, nS-S = nV

or, S = nS - nV

or, S/n = (S-V)


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Vernier scale How a vernier scaleworks

or (Pitch)/(Number of Vernier scale divisions) = (Length of one main scale division - Length of one Vernierscale division)

S/n and (S-V) are both equal to the least count of Vernier Caliper, and are also termed as "Vernier constant".

ExamplesOn decimal measuring instruments, as in the diagram below, the indicating scale has 10 graduations that coverthe same length as 9 on the data scale. Note that the vernier's 10th graduation is omitted.

On an angular measurement instrument, the data scale might be in half-degrees, with an indicator scale thatprovides 30 1-minute graduations (that span 29 of the half-degree graduations).

How a vernier scale worksThe vernier scale is constructed so that it is spaced at a constant fractionof the fixed main scale. So for a decimal measuring device each mark onthe vernier is spaced nine tenths of those on the main scale. If you putthe two scales together with zero points aligned, the first mark on thevernier scale is one tenth short of the first main scale mark, the secondtwo tenths short, and so on up to the ninth markwhich is misaligned bynine tenths. Only when a full ten marks are counted is there alignment,because the tenth mark is ten tenthsa whole main scale unit short, andtherefore aligns with the ninth mark on the main scale.

Now if you move the vernier by a small amount, say, one tenth of itsfixed main scale, the only pair of marks that come into alignment are thefirst pair, since these were the only ones originally misaligned by onetenth. If we move it two tenths, the second pair aligns, since these arethe only ones originally misaligned by that amount. If we move it fivetenths, the fifth pair alignsand so on. For any movement, only one pairof marks aligns and that pair shows the value between the marks on the fixed scale.

Vernier acuityVernier scales work so well because most people are especially good at detecting which of the lines is alignedand misaligned, and that ability gets better with practice, in fact far exceeding the optical capability of the eye.This ability to detect alignment is called 'Vernier acuity'.[9] Historically, none of the alternative technologiesexploited this or any other hyperacuity, giving the Vernier scale an advantage over its competitors.[6]

Zero errorZero error is defined as such a condition when a measuring instrument registers a reading when there should notbe any reading. In case of vernier calipers it occurs when a zero on main scale does not coincide with a zero onvernier scale. Rather the zero error may be of two types i.e. when the scale is towards numbers greater than zeroit is positive else negative. The method to use a vernier scale or caliper with zero error is to use the formula:actual reading = main scale + vernier scale (zero error). Zero error may arise due to knocks that cause thecalibration at the 0.00 mm when the jaws are perfectly closed or just touching each other.


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When the jaws are closed and if thereading is 0.10mm, the zero error isreferred to as +0.10mm. The methodto use a vernier scale or caliper withzero error is to use the formula 'actualreading = main scale + vernier scale (zero error)' thus the actual reading is19.00 + 0.54 (0.10) = 19.44 mm

Positive zero error refers to the fact that when the jawsof the vernier caliper are just closed, the reading is apositive reading away from the actual reading of0.00mm. If the reading is 0.10mm, the zero error isreferred to as +0.10 mm.

Negative zero error refers to the fact that when the jawsof the vernier caliper are just closed, the reading is anegative reading away from the actual reading of0.00mm. If the reading is 0.08mm, the zero error isreferred to as 0.08mm. If positive,the error issubtracted from the mean reading the instrumentreads.Thus if the instrument reads 4.39 cm and the erroris +0.05,the actual length will be 4.39-0.05=4.34 cm. Ifnegative, the error is added from the mean reading theinstrument reads.Thus if the instrument reads 4.39 cmand as above the error is -0.05 cm, the actual length willbe 4.39+0.05=4.44 cm. (Considering that,The quantity iscalled zero correction which should always be addedalgebraically to the observed reading to the correctvalue.)

Zero Error (Z.E) = + or- n* Least Count(L.C).

See alsoMicrometerNonius device invented by Pedro NunesTransversal (instrument making) technique inuse prior to vernier scales

External linksUse of vernier scale in inch - simulator of measurement andinterpretation (http://stefanelli.eng.br/en/vernier-caliper-inch-fractional-measures-use.html)How to read a vernier caliper (http://www.miniphysics.com/how-to-read-a-vernier-caliper.html)Calculation of Least Count in Metric & Imperial Scales of VernierCaliper (http://vernierscaliper.com/vernier-caliper-calculation-of-least-count-in-metric-imperial-scales-213.html)

Classroom activity on the Vernier scale at Wikiversity


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When the jaws are closed and if thereading is 0.08mm, the zero error isreferred to as 0.08 mm. The methodto use a vernier scale or caliper withzero error is to use the formula 'actualreading = main scale + vernier scale (zero error)' thus the actual reading is19.00 + 0.36 (0.08) = 19.44 mm

ReferencesColin A. Ronan; Joseph Needham (24 June 1994). The Shorter Science and Civilisation in China: 4. CambridgeUniversity Press. p. 36. ISBN 978-0-521-32995-8. "adjustable outside caliper gauge... self-dated at AD 9". Anabridged version.

1.

"Bronze Caliper of the Wang Mang Regime". Retrieved 26 November 2013.2. Barrow called the device a Vernier scale. See: John Barrow, Navigatio britannica: or a complete system ofnavigation (London, England: W. and J. Mount and T. Page, 1750), pp. 140142 (http://books.google.com/books?id=u5CBsgTxtIMC&pg=PA140#v=onepage&q&f=false), especially page 142.

3.

Daumas, Maurice, Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers, PortmanBooks, London 1989 ISBN 978-0-7134-0727-3

4.

1911 Encyclopaedia Britannica article on Navigation (http://www.1911encyclopedia.org/Navigation). AccessedApril 2008

5.

Kwan, A. (2011). "Vernier scales and other early devices for precise measurement". American Journal of Physics79 (4): 368. doi:10.1119/1.3533717.

6.

Lalande, Jrme (1746), Astronomie, vol. 2 (Paris, France: Desaint & Saillant), pages 859-860(http://books.google.com/books?id=Z6I-AAAAcAAJ&pg=PA859#v=onepage&q&f=false).

7.

Davis, Raymond, Foote, Francis, Kelly, Joe, Surveying, Theory and Practice, McGraw-Hill Book Company, 1966LC 64-66263

8.

Vernier acuity definition (http://cancerweb.ncl.ac.uk/cgi-bin/omd?Vernier+acuity) at the Online Medical Dictionary9.

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Categories: Measurement Scales Chinese inventions

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vernier scale

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