Vernier scale
Encyclopedia
Verniers are common on sextant
Sextant
A sextant is an instrument used to measure the angle between any two visible objects. Its primary use is to determine the angle between a celestial object and the horizon which is known as the altitude. Making this measurement is known as sighting the object, shooting the object, or taking a sight...
s used in navigation
Navigation
Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
, scientific instrument
Scientific instrument
A scientific instrument can be any type of equipment, machine, apparatus or device as is specifically designed, constructed and often, through trial and error, ingeniously refined to apply utmost efficiency in the utilization of well proven physical principle, relationship or technology to...
s used to conduct experiments, machinist
Machinist
A machinist is a person who uses machine tools to make or modify parts, primarily metal parts, a process known as machining. This is accomplished by using machine tools to cut away excess material much as a woodcarver cuts away excess wood to produce his work. In addition to metal, the parts may...
s' measuring tools (all sorts, but especially caliper
Caliper
A caliper is a device used to measure the distance between two opposing sides of an object. A caliper can be as simple as a compass with inward or outward-facing points...
s and micrometer
Micrometer
A micrometer , sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw used widely for precise measurement of small distances in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier,...
s) used to work materials to fine tolerances and on theodolite
Theodolite
A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...
s used in surveying
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...
.
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
The vernier scale was invented in its modern form in 1631 by the FrenchFrance
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician Pierre Vernier
Pierre Vernier
Pierre Vernier was a French mathematician and instrument inventor. He was inventor and eponym of the vernier scale used in measuring devices....
(1580–1637). Its use was described in detail in English in Navigatio Britannica (1750) by John Barrow
John Barrow (historian)
John Barrow was an English mathematician, naval historian and lexicographer.Nothing is known of Barrow's family. He was initially a teacher of mathematics and navigation aboard ships of the Royal Navy. He retired before 1750 and devoted himself to writing and compiling dictionaries and other works...
, the mathematician and historian. In some languages, this device is called a nonius. It was also commonly called a nonius in English until the end of the 18th century. Nonius is the Latin name of the Portuguese
Portugal
Portugal , officially the Portuguese Republic is a country situated in southwestern Europe on the Iberian Peninsula. Portugal is the westernmost country of Europe, and is bordered by the Atlantic Ocean to the West and South and by Spain to the North and East. The Atlantic archipelagos of the...
astronomer and mathematician Pedro Nunes
Pedro Nunes
Pedro Nunes , was a Portuguese mathematician, cosmographer, and professor, from a New Christian family. Nunes, considered to be one of the greatest mathematicians of his time , is best known for his contributions in the technical field of navigation, which was crucial to the Portuguese period of...
(1502–1578) who in 1542 invented a related but different system for taking fine measurements on the astrolabe
Astrolabe
An astrolabe is an elaborate inclinometer, historically used by astronomers, navigators, and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets, and stars, determining local time given local latitude and longitude, surveying, triangulation, and to...
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 graduation
Graduation (instrument)
-Linear graduation:Linear graduation of a scale occurs on a straight instrument. The graduation can identify linear measures, such as inches or millimetres on a rule. They can also be non-linear such as logarithmic or other transcendental scales....
s 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
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).
How 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 scales can be read because the human eye can detect whether two line segments are aligned or if they are slightly off alignment. Vernier acuity is the ability by a person to detect the proper alignment of two line segments. In most people, Vernier acuity is particularly high, allowing one to accurately differentiate between aligned and misaligned marks on a Vernier scale.Zero error
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 the calibration at the 0.00 mm when the jaws are perfectly closed or just touching each other.
Positive zero error refers to the fact that when the jaws of the vernier caliper are just closed, the reading is a positive reading away from the actual reading of 0.00mm. If the reading is 0.10mm, the zero error is referred to as +0.10mm.
Negative zero error refers to the fact that when the jaws of the vernier caliper are just closed, the reading is a negative reading away from the actual reading of 0.00mm. If the reading is -0.08mm, the zero error is referred to as -0.08mm.
See also
- MicrometerMicrometerA micrometer , sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw used widely for precise measurement of small distances in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier,...
- Transversal (instrument making)Transversal (instrument making)Transversals are a geometric construction on a scientific instrument to allow a graduation to be read to a finer degree of accuracy. Transversals have been replaced in modern times by vernier scales.-History:...
– technique in use prior to vernier scales.
External links
- Animated Vernier caliper
- The VERNIER Scale Open Door Web Site reference source for both students and teachers.
- How to use a Vernier scale Clemson University Physics On-line Laboratories
- Reading and interpretation simulator: Vernier scale or Nonius millimetric scale, decimal precision