inch

An inch (plural: inches; abbreviation or symbol: in or ″ – a double prime) is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot. Corresponding units of area and volume are the square inch and the cubic inch.

Usage

The inch is a commonly used customary unit of length in the United States,^[1] Canada,^[2][3] and the United Kingdom.^[4] For the United Kingdom, guidance on public sector use states that since 1 October 1995, without time limit, that the inch (along with the mile, yard and foot) is to be used as a primary unit for road signs and related measurements of distance and speed and may continue to be used as a secondary or supplementary indication following a metric measurement for other purposes.^[4]

Measuring tape calibrated in 32nds of an inch

International inch

From July 1, 1959, the United States and countries of the British Commonwealth defined the length of the international yard to be exactly 0.9144 metres.^[5][6] Consequently, the international inch is defined as exactly 25.4 millimetres. This creates a slight difference between the international units and American surveyor's units which are described in the article on the foot.

The international standard symbol for inch is in (see ISO 31-1, Annex A). In some cases, the inch is denoted by a double prime, which is often approximated by double quotes, and the foot by a prime, which is often approximated by an apostrophe.

Equivalence to other units of length

Mid-19th century tool for converting between different standards of the inch

1 international inch is equal to:

• 1,000 thou (also known as mil) (1 mil = 1 thou = 0.001 inches)
• 1,000,000 microinches (1 μin is one millionth of an inch.)

• ≈ 0.02778 yards (1 yard is equal to 36 inches.)
• 2.54 centimetres (1 centimetre ≈ 0.3937 international inches.)

Historical origin

The English word inch comes from Latin uncia meaning "one twelfth part" (in this case, one twelfth of a foot); the word ounce (one twelfth of a troy pound) has the same origin. The vowel change from u to i is umlaut; the consonant change from c (pronounced as k) to ch is palatalization (see Old English phonology).

In some other languages, the word for "inch" is similar to or the same as the word for "thumb"; for example, French: pouce inch/thumb; Italian: pollice inch/thumb; Spanish: pulgada inch, pulgar thumb; Portuguese: polegada inch, polegar thumb; Swedish: tum inch, tumme thumb; Dutch: duim inch/thumb; Sanskrit: angulam inch, anguli finger; Slovak: palec inch/thumb; Hungarian: hüvelyk inch/thumb, Danish and Norwegian: tomme / tommer inch/inches and tommel thumb. Given the etymology of the word "inch", it would seem that the inch is a unit derived from the Foot unit in Latin in Roman times.

King David I of Scotland in his Assize of Weights and Measures (c. 1150) is said to have defined the Scottish inch as the width of an average man's thumb at the base of the nail, even including the requirement to calculate the average of a small, a medium, and a large man's measures.^[7] However, the oldest surviving manuscripts date from the early 14 century and appear to have been altered with the inclusion of newer material.^[8]

The earliest known reference to the inch in England is from the Laws of Æthelberht dating to the early 7th century, surviving in a single manuscript from 1120.^[9] Paragraph LXVII sets out the fine for wounds of various depths: one inch, one shilling, two inches, two shillings, etc. "Gif man þeoh þurhstingð, stice ghwilve vi scillingas. Gife ofer ynce, scilling. æt twam yncum, twegen. ofer þry, iii scill."^[10][11]

An Anglo-Saxon unit of length was the barleycorn. After 1066, 1 inch was equal to 3 barleycorn, which continued to be its legal definition for several centuries, with the barleycorn being the base unit.^[12] One of the earliest such definitions is that of 1324, where the legal definition of the inch was set out in a statute of Edward II of England, defining it as "three grains of barley, dry and round, placed end to end, lengthwise".^[12]

Similar definitions are recorded in both English and Welsh medieval law tracts.^[13] One, dating from the first half of the 10th century, is contained in the Laws of Hywel Dda which superseded those of Dyvnwal, an even earlier definition of the inch in Wales. Both definitions, as recorded in Ancient Laws and Institutes of Wales (vol i., pp. 184,187,189), are that "three lengths of a barleycorn is the inch".^[14]

Charles Butler, a mathematics teacher at Cheam School, in 1814 recorded the old legal definition of the inch to be "three grains of sound ripe barley being taken out the middle of the ear, well dried, and laid end to end in a row", and placed the barleycorn, not the inch, as the base unit of the English Long Measure system, from which all other units were derived.^[15] John Bouvier similarly recorded in his 1843 law dictionary that the barleycorn was the fundamental measure.^[16] Butler observed, however, that "[a]s the length of the barley-corn cannot be fixed, so the inch according to this method will be uncertain", noting that a standard inch measure was now (by his time) kept in the Exchequer chamber, Guildhall, and that was the legal definition of the inch.^[15] This was a point also made by George Long in his 1842 Penny Cyclopædia, observing that standard measures had since surpassed the barleycorn definition of the inch, and that to recover the inch measure from its original definition, in the event that the standard measure were destroyed, would involve the measurement of large numbers of barleycorns and taking their average lengths. He noted that this process would not perfectly recover the standard, since it might introduce errors of anywhere between one hundredth and one tenth of an inch in the definition of a yard.^[17]

Before the adoption of the international inch (see above), the United Kingdom and most countries of the British Commonwealth defined the inch in terms of the Imperial Standard Yard. But Canada had its own, different, definition of the inch, defined in terms of metric units. The Canadian inch was defined to be equal to 25.4 millimetres, the amount later accepted as the international inch.

Metric or decimal inch

A metric inch (25 mm instead of 25.4 mm) was the equivalent of an inch under a former proposal for the metrification and unification of the English system of measures.

In Sweden, between 1855 to 1863, the existing Swedish "working inch" of ≈24.74 mm was replaced by a "decimal inch" of ≈29.69 mm which was one tenth of the Swedish foot. Proponents argued that a decimal system simplifies calculations. However, having two different Swedish inch measures (and the English inch on top of that) proved to be complicated. So in a transition period between 1878 and 1889 the metric units were introduced as the overall standard measures. However, the various inches survived some time in building and construction trades.

Scottish inch

A Scottish inch (Scottish Gaelic: òirleach) was a Scottish measurement of length. It equals 1/12 ft in Scottish measures, and 1.0016 inches in imperial units (about 2.5441 cm).^[18] It was used in the popular expression Gie 'im an inch, an he'll tak an ell, in English "Give him an inch and he'll take an ell", first published as "For when I gave you an inch, you tooke an ell," by John Heywood in 1546.^[19] (The ell, equal to 37 inches or about 94 cm, was in use in England until 1685.)^[20] A Scottish square inch was equivalent to 1.0256 imperial square inches and 6.4516 square centimetres.

See also

• Anthropic units
• English units
• Gry
• Guz
• Imperial unit
• Pyramid inch
• United States customary units
• UCUM

References

1. ^ Corpus of Contemporary American English (Brigham Young University, accessed December 2011) lists 24,302 instances of inch(es) compared to 1548 instances of centimeter(re)(s) and 1343 instances of millimeter(re)(s).
2. ^ Weights and Measures Act
3. ^ Weights and Measures Act, accessed January 2012, Act current to 2012-01-18. Canadian units (5) The Canadian units of measurement are as set out and defined in Schedule II, and the symbols and abbreviations therefor are as added pursuant to subparagraph 6(1)(b)(ii).
4. ^ ^{a b} Guidance Note on the use of Metric Units of Measurement by the Public Sector. Department for Business Innovation and Skills. Crown copyright 2011. Accessed December 2011.
5. ^ Lasater, Brian (31 January 2008). The Dream of the West, Pt II. Lulu.com. p. 256. ISBN 978-1-4303-1382-3. http://books.google.com/books?id=_BQHPD0RNe4C&pg=PA256. Retrieved 14 May 2012. 
6. ^ "On what basis is one inch exactly equal to 25.4 mm? Has the imperial inch been adjusted to give this exact fit and if so when?". National Physical Laboratory. http://www.npl.co.uk/reference/faqs/on-what-basis-is-one-inch-exactly-equal-to-25.4-mm-has-the-imperial-inch-been-adjusted-to-give-this-exact-fit-and-if-so-when-(faq-length). Retrieved 2010-07-13. 
7. ^ Lord John Swinton (1789). A proposal for uniformity of weights and measures in Scotland. printed for Peter Hill. p. 134. http://books.google.com/books?id=kHhbAAAAQAAJ&pg=PA134. Retrieved 27 February 2012. 
8. ^ Elizabeth Gemmill; Nicholas Mayhew (22 June 2006). Changing Values in Medieval Scotland: A Study of Prices, Money, and Weights and Measures. Cambridge University Press. p. 113. ISBN 978-0-521-02709-0. http://books.google.com/books?id=t1hmrzOSEagC&pg=PA113. Retrieved 27 February 2012. 
9. ^ Goetz, Hans-Werner; Jarnut, Jörg; Pohl, Walter (2003). Regna and Gentes: The Relationship Between Late Antique and Early Medieval Peoples and Kingdoms in the Transformation of the Roman World. BRILL. p. 33. ISBN 978-90-04-12524-7. http://books.google.com/books?id=RovRlJkrncEC&pg=PA33. Retrieved 14 May 2012. 
10. ^ Wilkins, David (1871). Councils and Ecclesiastical Documents Relating to Great Britain and Ireland: English church during the Anglo-Saxon period: A.D. 595-1066. 1871. Clarendon Press. p. 48. http://books.google.com/books?id=XGUAAAAAMAAJ&pg=PA48. Retrieved 27 November 2011. 
11. ^ Duncan, Otis Dudley (1984). Notes on social measurement: historical and critical. Russell Sage Foundation. p. 87. ISBN 978-0-87154-219-9. http://books.google.com/books?id=5c459mDugI0C&pg=PA87. Retrieved 27 November 2011. 
12. ^ ^{a b} H. Arthur Klein (1974). The world of measurements: masterpieces, mysteries and muddles of metrology. New York: Simon and Schuster. 
13. ^ Jane Hawkes and Susan Mills (1999). Northumbria's Golden Age. Sutton. pp. 310. ISBN 978-0-7509-1685-1. 
14. ^ John Williams (1867). "The civil arts — mensuration". The Traditionary Annals of the Cymry. Tenby: R. Mason. pp. 243–245. 
15. ^ ^{a b} Charles Butler (1814). An Easy Introduction to the Mathematics. Oxford: Bartlett and Newman. pp. 61. 
16. ^ John Bouvier (1843). "Barleycorn". A Law Dictionary: With References to the Civil and Other Systems of Foreign Law. Philadelphia: T. & J. W. Johnson. pp. 188. 
17. ^ George Long (1842). "Weights & Measures, Standard". The Penny Cyclopædia of the Society for the Diffusion of Useful Knowledge. London: Charles Knight & Co.. p. 436. 
18. ^ "Dictionary of the Scots Language". Edinburgh: Scottish Language Dictionaries. http://www.dsl.ac.uk/getent4.php?plen=333&startset=1811889&query=INCH&fhit=inch&dregion=form&dtext=snds#fhit. Retrieved 2011-05-21. 
19. ^ Heywood, John (1546). A dialogue conteinying the nomber in effect of all the prouerbes in the englishe tongue, compacte in a matter concernyng two maner of mariages, etc.. London: Thomas Berthelet.  Full text of 1874 reprint
20. ^ Gibson, A. J. S.; Smout, T. C. (19 July 2007). Prices, Food and Wages in Scotland, 1550-1780. Cambridge University Press. p. 371. ISBN 978-0-521-03780-8. http://books.google.com/books?id=PHtKW4hPqBYC&pg=PA371. Retrieved 11 March 2012. 

• Collins Encyclopedia of Scotland
• Weights and Measures, by D. Richard Torrance, SAFHS, Edinburgh, 1996, ISBN 1-874722-09-9 (NB book focusses on Scottish weights and measures exclusively)
• This article incorporates text from "Dwelly's [Scottish] Gaelic Dictionary" (1911).
• Scottish National Dictionary and Dictionary of the Older Scottish Tongue