Inch

• 1. Introduction

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  The inch began with a thumb. In many European languages, the very word for inch is borrowed from the word for thumb, because a man's thumb measures about an inch across the base. That bodily measure was once even used to define the unit itself. But a thumb varies from person to person, and so does a grain of barley, and so does the foot it belongs to. How do you pin down something that started as a part of the human body? The story of the inch is a long argument over precision. It runs from the fines listed in early English law, through grains of dried barley laid end to end, to a single number agreed across the world. Along the way, two great nations defined the same inch slightly differently, and a Swedish gauge-block maker quietly settled the matter for everyone. What follows asks how a humble unit became a measurement accurate to a few parts per million, and why one country still kept an older inch for surveying its own land.

• 2. A Word From Latin

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  The Latin uncia meant one-twelfth, and it gave English two different words. "Inch" came in early, borrowed as ynce, while "ounce" arrived later through Anglo-Norman unce and ounce. That is why the two words sound and look so different despite sharing one root. The shift from the Latin u sound to the English short i is a process called umlaut. The change from the Latin c sound to the English ch sound is called palatalisation. Both were features of Old English phonology. The same Latin source explains why an inch is one-twelfth of a foot, just as the Roman uncia was one-twelfth of its larger unit. Across Europe the unit took a more bodily name instead. The Dutch term engelse duim means english thumb, and pairs like pulgada and pulgar, or polegada and polegar, set the word for inch beside the word for thumb. In Swedish, tum means inch and tumme means thumb. The unit carried the body inside its name, which made it intuitive and imprecise at the same time.

• 3. Where The Inch Still Rules

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  On road signs in the United Kingdom, the inch is not a relic but a requirement. Since the 1st of October 1995, guidance on public sector use states that the inch, alongside the foot, is to be used as a primary unit for road signs and related measurements of distance. Clearance heights and widths are a possible exception, and for other purposes the inch may follow a metric figure as a secondary indication. The unit also remains common in the United States and Canada. The inch travels even into countries that otherwise run entirely on the metric system. It measures the screens of televisions and computer monitors worldwide. It is the official Japanese standard for electronic parts, especially display screens, and the industry standard for display screens throughout continental Europe. Countries such as France, Germany and Turkey often pair it with centimetres in advertisements, catalogues and packages. The inch also sizes the metal you ride on. It specifies the diameter of vehicle wheel rims, and the matching inner diameter of tyres written into tyre codes. A unit named for a thumb now defines the wheels of cars and the faces of screens.

• 4. Marks On The Page

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  Three feet, two inches can be written without a single letter. The foot is marked by a prime, often approximated by an apostrophe, and the inch by a double prime, often approximated by a double quote. The same prime and double prime mark the first and second cuts of an hour, and of a degree, so the symbols carry across geometry and time. The international standard symbol, though, is simply the letters in, as set out in ISO 31-1, Annex A. When the inch is divided, the fractions follow an old habit. Subdivisions are typically written as dyadic fractions with odd numerators, so two and three-eighths of an inch appears as a fraction rather than as the decimal 2.375. Engineering keeps its own convention. For engineering purposes the inch has long been given to three or four decimal places, a precision that fractions of barley grains could never have promised.

• 5. Fines And Barley Grains

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  A wound an inch deep cost the offender one shilling. The earliest known reference to the inch in England comes from the Laws of Æthelberht, dating to the early 7th century. The text survives in a single manuscript, the Textus Roffensis, copied in 1120. Its paragraph LXVII sets the fine by depth: one inch, one shilling; two inches, two shillings, and so on up the scale. After 1066 the inch was tied to grain. One inch was set equal to three barleycorns, and the barleycorn, an Anglo-Saxon unit of length, became the base from which the inch was derived. A statute of Edward II of England in 1324 fixed it as three grains of barley, dry and round, placed end to end, lengthwise. Wales recorded much the same idea, and earlier. The Laws of Hywel Dda, from the first half of the 10th century, hold that three lengths of a barleycorn is the inch. Those laws superseded a still older Welsh definition attributed to Dyfnwal. In Scotland the body returned. King David I, in his Assize of Weights and Measures around 1150, is said to have defined the Scottish inch as the width of an average man's thumb at the base of the nail. The rule even asked for the average of a small, a medium and a large man's measure, though the surviving manuscripts date only from the early 14th century and appear to have been altered.

• 6. The Trouble With Barley

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  "As the length of the barley-corn cannot be fixed, so the inch according to this method will be uncertain." That warning came from Charles Butler, a mathematics teacher at Cheam School, who in 1814 recorded the old definition: three grains of sound ripe barley, taken from the middle of the ear, well dried, and laid end to end in a row. Butler still placed the barleycorn, not the inch, as the base unit of the English Long Measure system. John Bouvier agreed in his 1843 law dictionary, calling the barleycorn the fundamental measure. Yet Butler noted that a standard inch was by then kept in the Exchequer chamber at Guildhall, and that physical object was the legal definition. George Long made the same point in his 1842 Penny Cyclopædia. He observed that standard measures had surpassed the barleycorn, and that rebuilding the inch from grains alone, if the standard were destroyed, would mean measuring large numbers of barleycorns and averaging them. Long warned that the process could introduce errors of between one hundredth and one tenth of an inch in a yard. The grain that once anchored the inch had become its weakest link.

• 7. Two Inches, One Metre

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  For decades, the United States and the United Kingdom did not share the same inch. The United States adopted the conversion factor of one metre equal to 39.37 inches by an act in 1866. In 1893, Mendenhall ordered the physical inch to be based on the international prototype metres numbers 21 and 27, received from the CGPM, with that conversion factor. The result was a U.S. inch of 25.4000508 mm, referenced at 68 degrees Fahrenheit. The UK inch, defined against the Imperial Standard Yard, came out at 25.399977 mm, referenced at 62 degrees Fahrenheit. The two definitions differed by a tiny but real amount. The man who reconciled them sold gauge blocks. When Carl Edvard Johansson began making gauge blocks in inch sizes in 1912, he chose a nominal size of 25.4 mm at 20 degrees Celsius, accurate to within a few parts per million of both official inches. His blocks were so popular that they became the de facto standard, and rival manufacturers copied his ratio. Officialdom caught up. In 1930 the British Standards Institution adopted an inch of exactly 25.4 mm, and the American Standards Association followed in 1933. By 1935 industry in 16 countries had taken up this industrial inch, endorsing Johansson's pragmatic choice.

• 8. Settling The Number

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  In 1946 the Commonwealth Science Congress recommended a yard of exactly 0.9144 metres for the British Commonwealth. The recommendation spread by stages. Canada adopted it in 1951, the United States on the 1st of July 1959, Australia in 1961 with effect from the 1st of January 1964, and the United Kingdom in 1963, also effective on the 1st of January 1964. The new yard fixed the inch at exactly 25.4 mm. That figure sat 1.7 millionths of an inch longer than the old imperial inch and 2 millionths of an inch shorter than the old US inch. One inch survived the change unaltered. The United States kept the older metre-based definition for surveying, leaving a 2 millionth part difference between standard and US survey inches. That gap is about one inch per mile, so that 12.7 kilometres equals an exact, but different, count of standard inches and survey inches. The difference grows serious in State Plane Coordinate Systems, where values reach into the hundreds of thousands or millions of feet. Even that exception has now closed. In 2020 the National Institute of Standards and Technology announced that the U.S. survey foot would be phased out on the 1st of January 2023, replaced by the international foot of 0.3048 metres exactly. The Scottish inch, the òirleach, did not survive. About 1.0016 imperial inches, it is now obsolete, one more local measure absorbed into a single agreed number.