Mile

Summary

The mile, sometimes the international mile or statute mile to distinguish it from other miles, is a British imperial unit and United States customary unit of distance; both are based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. The statute mile was standardised between the Commonwealth of Nations and the United States by an international agreement in 1959, when it was formally redefined with respect to SI units as exactly 1,609.344 metres.

mile
A milestone in the City of Westminster showing the distance from Kensington Road to Hounslow and Hyde Park Corner in miles
General information
Unit systemBritish imperial/US customary
Unit oflength
Symbolmi. or mi, (rarely) m
Conversions
1 mi. or mi in ...... is equal to ...
   SI units   1609.344 m
   imperial/US units   
   US survey mile   0.999998 survey mile
   nautical units   0.86898 nmi

With qualifiers, mile is also used to describe or translate a wide range of units derived from or roughly equivalent to the Roman mile (roughly 1.48 km), such as the nautical mile (now 1.852 km exactly), the Italian mile (roughly 1.852 km), and the Chinese mile (now 500 m exactly). The Romans divided their mile into 5,000 pedēs ("feet"), but the greater importance of furlongs in the Elizabethan-era England meant that the statute mile was made equivalent to 8 furlongs or 5,280 feet in 1593. This form of the mile then spread across the British Empire, some successor states of which continue to employ the mile. The US Geological Survey now employs the metre for official purposes, but legacy data from its 1927 geodetic datum has meant that a separate US survey mile (6336/3937 km) continues to see some use, although it was officially phased out in 2022. While most countries replaced the mile with the kilometre when switching to the International System of Units (SI), the international mile continues to be used in some countries, such as Liberia, the United Kingdom, the United States, and a number of countries with fewer than one million inhabitants, most of which are UK or US territories or have close historical ties with the UK or US.

Name edit

The modern English word mile derives from Middle English myle and Old English mīl, which was cognate with all other Germanic terms for miles. These derived from the nominal ellipsis form of mīlle passus 'mile' or mīlia passuum 'miles', the Roman mile of one thousand paces.[1]

The present international mile is usually what is understood by the unqualified term mile. When this distance needs to be distinguished from the nautical mile, the international mile may also be described as a land mile or statute mile.[2] In British English, statute mile may refer to the present international mile or to any other form of English mile since the 1593 Act of Parliament, which set it as a distance of 1,760 yards. Under American law, however, statute mile refers to the US survey mile.[3] Foreign and historical units translated into English as miles usually employ a qualifier to describe the kind of mile being used but this may be omitted if it is obvious from the context, such as a discussion of the 2nd-century Antonine Itinerary describing its distances in terms of miles rather than Roman miles.

Abbreviation edit

The mile has been variously abbreviated in English—with and without a trailing period—as "mi", "M", "ml", and "m".[4] The American National Institute of Standards and Technology now uses and recommends "mi" to avoid confusion with the SI metre (m) and millilitre (ml).[5] However, derived units such as miles per hour or miles per gallon continue to be abbreviated as "mph" and "mpg" rather than "mi/h" and "mi/gal". In the United Kingdom, road signs use "m" as the abbreviation for mile though height and width restrictions also use "m" as the symbol for the metre, which may be displayed alongside feet and inches.[6] The BBC style holds that "there is no acceptable abbreviation for 'miles'" and so it should be spelled out when used in describing areas.[7]

Historical edit

 
The supposed remains of the Golden Milestone, the zero-mile marker of the Roman road network, in the Roman Forum

Roman edit

The Roman mile (mille passus, lit. "thousand paces"; abbr. m.p.; also milia passuum[n 1] and mille) consisted of a thousand paces as measured by every other step—as in the total distance of the left foot hitting the ground 1,000 times.[9] When Roman legionaries were well-fed and harshly driven in good weather, they thus created longer miles. The distance was indirectly standardised by Agrippa's establishment of a standard Roman foot (Agrippa's own) in 29 BC,[10] and the definition of a pace as 5 feet. An Imperial Roman mile thus denoted 5,000 Roman feet. Surveyors and specialised equipment such as the decempeda and dioptra then spread its use.[11]

In modern times, Agrippa's Imperial Roman mile was empirically estimated to have been about 1,618 yards (1,480 m) in length, slightly less than the 1,760 yards (1,610 m) of the modern international mile.[12]

In Hellenic areas of the Empire, the Roman mile (Greek: μίλιον, mílion) was used beside the native Greek units as equivalent to 8 stadia of 600 Greek feet. The mílion continued to be used as a Byzantine unit and was also used as the name of the zero mile marker for the Byzantine Empire, the Milion, located at the head of the Mese near Hagia Sophia.

The Roman mile spread throughout Europe, with its local variations giving rise to the different units.[citation needed] Also arising from the Roman mile is the milestone. All roads radiated out from the Roman Forum throughout the Empire – 50,000 (Roman) miles of stone-paved roads. At every mile was placed a shaped stone. Originally, these were obelisks made from granite, marble, or whatever local stone was available. On these was carved a Roman numeral, indicating the number of miles from the centre of Rome – the Forum. Hence, one can know how far one is from Rome.[13]

Italian edit

The Italian mile (miglio, pl. miglia) was traditionally considered a direct continuation of the Roman mile, equal to 1000 paces,[14] although its actual value over time or between regions could vary greatly.[15] It was often used in international contexts from the Middle Ages into the 17th century[14] and is thus also known as the "geographical mile",[16] although the geographical mile is now a separate standard unit.

Arabic edit

The Arabic mile (الميل, al-mīl) was not the common Arabic unit of length; instead, Arabs and Persians traditionally used the longer parasang or "Arabic league". The Arabic mile was, however, used by medieval geographers and scientists and constituted a kind of precursor to the nautical or geographical mile. It extended the Roman mile to fit an astronomical approximation of 1 arcminute of latitude measured directly north-and-south along a meridian. Although the precise value of the approximation remains disputed, it was somewhere between 1.8 and 2.0 km.

English edit

The "old English mile" of the medieval and early modern periods varied but seems to have measured about 1.3 international miles (2.1 km).[17][18] The old English mile varied over time and location within England.[18] The old English mile has also been defined as 79,200 or 79,320 inches (1.25 or 1.2519 statute miles).[19] The English long continued the Roman computations of the mile as 5000 feet, 1000 paces, or 8 longer divisions, which they equated with their "furrow's length" or furlong.[20]

The origins of English units are "extremely vague and uncertain",[21][citation needed] but seem to have been a combination of the Roman system with native British and Germanic systems both derived from multiples of the barleycorn.[n 2] Probably by the reign of Edgar in the 10th century, the nominal prototype physical standard of English length was an arm-length iron bar (a yardstick) held by the king at Winchester;[22][21] the foot was then one-third of its length. Henry I was said to have made a new standard in 1101 based on his own arm.[21] Following the issuance of Magna Carta in 1215, the barons of Parliament directed John and his son to keep the king's standard measure (Mensura Domini Regis) and weight at the Exchequer,[21] which thereafter verified local standards until its abolition in the 19th century. New brass standards are known to have been constructed under Henry VII and Elizabeth I.[24]

Arnold's c. 1500 Customs of London recorded a mile shorter than previous ones, coming to 0.947 international miles (5000 feet) or 1.524 km.[20]

Statute edit

The English statute mile was established by a Weights and Measures Act of Parliament in 1593 during the reign of Queen Elizabeth I. The act on the Composition of Yards and Perches had shortened the length of the foot and its associated measures, causing the two methods of determining the mile to diverge.[25] Owing to the importance of the surveyor's rod in deeds and surveying undertaken under Henry VIII,[26] decreasing the length of the rod by 111 would have amounted to a significant tax increase. Parliament instead opted to maintain the mile of 8 furlongs (which were derived from the rod) and to increase the number of feet per mile from the old Roman value.[27] The applicable passage of the statute reads: "A Mile shall contain eight Furlongs, every Furlong forty Poles,[n 3] and every Pole shall contain sixteen Foot and an half."[29] The statute mile therefore contained 5,280 feet or 1,760 yards.[20] The distance was not uniformly adopted. Robert Morden had multiple scales on his 17th-century maps which included continuing local values: his map of Hampshire, for example, bore two different "miles" with a ratio of 1 : 1.23[30] and his map of Dorset had three scales with a ratio of 1 : 1.23 : 1.41.[31] In both cases, the traditional local units remained longer than the statute mile. The English statute mile was superseded in 1959 by the international mile by international agreement.

Welsh edit

The Welsh mile (milltir or milldir) was 3 statute miles and 1,470 yards long (6.17 km). It comprised 9,000 paces (cam), each of 3 Welsh feet (troedfedd) of 9 inches (modfeddi).[32] (The Welsh inch is usually reckoned as equivalent to the English inch.) Along with other Welsh units, it was said to have been codified under Dyfnwal the Bald and Silent and retained unchanged by Hywel the Good.[33] Along with other Welsh units, it was discontinued following the conquest of Wales by Edward I of England in the 13th century.

Scots edit

 
Edinburgh's "Royal Mile"—running from the castle to Holyrood Abbey—is roughly a Scots mile long.[34]

The Scots mile was longer than the English mile,[35] as mentioned by Robert Burns in the first verse of his poem "Tam o' Shanter". It comprised 8 (Scots) furlongs divided into 320 falls or faws (Scots rods).[36] It varied from place to place but the most accepted equivalencies are 1,976 Imperial yards (1.123 statute miles or 1.81 km). It was legally abolished three times: first by a 1685 act of the Scottish Parliament,[37] again by the 1707 Treaty of Union with England,[38] and finally by the Weights and Measures Act 1824.[35] It had continued in use as a customary unit through the 18th century but had become obsolete by its final abolition.

Irish edit

 
Milestone on Mountbellew Bridge, erected c. 1760. Distances are given in Irish miles.

The Irish mile (míle or míle Gaelach) measured 2,240 yards: approximately 1.27 statute miles or 2.048 kilometres.[39][40] It was used in Ireland from the 16th century plantations until the 19th century, with residual use into the 20th century. The units were based on "English measure" but used a linear perch measuring 7 yards (6.4 m) as opposed to the English rod of 5.5 yards (5.0 m).[40]

Dutch edit

 
Scalebar on a 16th-century map made by Mercator. The scalebar is expressed in "Hours walking or common Flemish miles", and includes three actual scales: small, medium and big Flemish miles.

The Dutch mile (mijl) has had different definitions throughout history. One of the older definitions was 5,600 ells. But the length of an ell was not standardised, so that the length of a mile could range between 3,280 m and 4,280 m. In the sixteenth, the Dutch had three different miles: small (kleine), medium (middelbaar/gemeen), and large (groote). The Dutch kleine mile had the historical definition of one hour's walking (uur gaans), which was defined as 24 stadia, 3000 paces, or 15,000 Amsterdam or Rhineland feet (respectively 4,250 m or 4,710 m). The common Dutch mile was 32 stadia, 4,000 paces, or 20,000 feet (5,660 m or 6,280 m). The large mile was defined as 5000 paces.[41] The common Dutch mile was preferred by mariners, equating with 15 to one degree of latitude or one degree of longitude on the equator. This was originally based upon Ptolemy's underestimate of the Earth's circumference. The ratio of 15 Dutch miles to a degree remained fixed while the length of the mile was changed as with improved calculations of the circumference of the Earth. In 1617, Willebrord Snellius calculated a degree of the circumference of the Earth at 28,500 Rijnlantsche Roeden (within 3.5% of the actual value), which resulted in a Dutch mile of 1900 rods.[42] By the mid-seventeenth century, map scales assigned 2000 rods to the common Dutch mile, which equalled around 7,535 m (reducing the discrepancy with latitude measurement to less than 2%). The metric system was introduced in the Netherlands in 1816, and the metric mile became a synonym for the kilometre, being exactly 1,000 m. Since 1870, the term mijl was replaced by the equivalent kilometer. Today, the word mijl is no longer used, except as part of certain proverbs and compound terms like mijlenver ("miles away").

German edit

 
Various historic miles and leagues from an 1848 German textbook, given in feet, metres, and fractions of a "degree of meridian"

The German mile (Meile) was 24,000 German feet. The standardised Austrian mile used in southern Germany and the Austrian Empire was 7.586 km; the Prussian mile used in northern Germany was 7.5325 km. Following its standardisation by Ole Rømer in the late 17th century, the Danish mile (mil) was precisely equal to the Prussian mile and likewise divided into 24,000 feet.[43] These were sometimes treated as equivalent to 7.5 km. Earlier values had varied: the Sjællandske miil, for instance, had been 11.13 km. The Germans also used a longer version of the geographical mile.

Breslau edit

The Breslau mile, used in Breslau, and from 1630 officially in all of Silesia, equal to 11,250 ells, or about 6,700 meters. The mile equaled the distance from the Piaskowa Gate all the way to Psie Pole (Hundsfeld). By rolling a circle with a radius of 5 ells through Piaskowa Island, Ostrów Tumski and suburban tracts, passing eight bridges on the way, the standard Breslau mile was determined.[44][45]

Saxon edit

The Saxon post mile (kursächsische Postmeile or Polizeimeile, introduced on occasion of a survey of the Saxon roads in the 1700s, corresponded to 2,000 Dresden rods, equivalent to 9.062 kilometres.[46]

Hungarian edit

The Hungarian mile (mérföld or magyar mérföld) varied from 8.3790 km to 8.9374 km before being standardised as 8.3536 km.

Portuguese edit

The Portuguese mile (milha) used in Portugal and Brazil was 2.0873 km prior to metrication.[47]

Russian edit

The Russian mile (миля or русская миля, russkaya milya) was 7.468 km, divided into 7 versts.

Croatian edit

The Croatian mile (hrvatska milja), first devised by the Jesuit Stjepan Glavač on a 1673 map, is the length of an arc of the equator subtended by 1/10° or 11.13 km exactly.[48][49] The previous Croatian mile, now known as the "ban mile" (banska milja), had been the Austrian mile given above.[50]

Ottoman edit

The Ottoman mile was 1,894.35 m (1.17709 mi), which was equal to 5,000 Ottoman foot. After 1933, the Ottoman mile was replaced with the modern Turkish mile (1,853.181 m).

International edit

The international mile is precisely equal to 1.609344 km (or 25146/15625 km as a fraction).[52] It was established as part of the 1959 international yard and pound agreement reached by the United States, the United Kingdom, Canada, Australia, New Zealand, and the Union of South Africa,[53] which resolved small but measurable differences that had arisen from separate physical standards each country had maintained for the yard.[54] As with the earlier statute mile, it continues to comprise 1,760 yards or 5,280 feet.

The old Imperial value of the yard was used in converting measurements to metric values in India in a 1976 Act of the Indian Parliament.[55] However, the current National Topographic Database of the Survey of India is based on the metric WGS-84 datum,[56] which is also used by the Global Positioning System.

The difference from the previous standards was 2 ppm, or about 3.2 millimetres (18 inch) per mile. The US standard was slightly longer and the old Imperial standards had been slightly shorter than the international mile. When the international mile was introduced in English-speaking countries, the basic geodetic datum in America was the North American Datum of 1927 (NAD27). This had been constructed by triangulation based on the definition of the foot in the Mendenhall Order of 1893, with 1 foot = 1200/3937 (≈0.304800609601) metres and the definition was retained for data derived from NAD27, but renamed the US survey foot to distinguish it from the international foot.[57][n 4] Thus a survey mile = 1200/3937 × 5280 (≈1609.347218694) metres. An international mile = 1609.344 / (1200/3937 × 5280) (=0.999998) survey miles.

The exact length of the land mile varied slightly among English-speaking countries until the international yard and pound agreement in 1959 established the yard as exactly 0.9144 metres, giving a mile of exactly 1,609.344 metres. The US adopted this international mile for most purposes, but retained the pre-1959 mile for some land-survey data, terming it the U. S. survey mile. In the United States, statute mile normally refers to the survey mile,[58] about 3.219 mm (18 inch) longer than the international mile (the international mile is exactly 0.0002% less than the US survey mile).

While most countries abandoned the mile when switching to the metric system, the international mile continues to be used in some countries, such as Liberia, Myanmar,[59] the United Kingdom[60] and the United States.[61] It is also used in a number of territories with less than a million inhabitants, most of which are UK or US territories, or have close historical ties with the UK or US: American Samoa,[62] Bahamas,[63] Belize,[64] British Virgin Islands,[65] Cayman Islands,[66] Dominica,[66] Falkland Islands,[67] Grenada,[68] Guam,[69] The N. Mariana Islands,[70] Samoa,[71] St. Lucia,[72] St. Vincent & The Grenadines,[73] St. Helena,[74] St. Kitts & Nevis,[75] the Turks & Caicos Islands,[76] and the US Virgin Islands.[77] The mile is even encountered in Canada, though this is predominantly in rail transport and horse racing, as the roadways have been metricated since 1977.[78][79][80][81] Ireland gradually replaced miles with kilometres, including in speed measurements; the process was completed in 2005.

US survey edit

The US survey mile is 5,280 US survey feet, or 1,609.347 metres and 0.30480061 metres respectively.[82] Both are very slightly longer than the international mile and international foot. In the United States, the term statute mile formally refers to the survey mile,[3] but for most purposes, the difference of less than 18 inch (3.2 mm) between the survey mile and the international mile (1609.344 metres exactly) is insignificant—one international mile is 0.999998 US survey miles—so statute mile can be used for either. But in some cases, such as in the US State Plane Coordinate Systems (SPCSs), which can stretch over hundreds of miles,[83] the accumulated difference can be significant, so it is important to note that the reference is to the US survey mile.

The United States redefined its yard in 1893, and this resulted in US and Imperial measures of distance having very slightly different lengths.

The North American Datum of 1983 (NAD83), which replaced the NAD27, is defined in metres. State Plane Coordinate Systems were then updated, but the National Geodetic Survey left individual states to decide which (if any) definition of the foot they would use. All State Plane Coordinate Systems are defined in metres, and 42 of the 50 states only use the metre-based State Plane Coordinate Systems. However, eight states also have State Plane Coordinate Systems defined in feet, seven of them in US survey feet and one in international feet.[83]

State legislation in the US is important for determining which conversion factor from the metric datum is to be used for land surveying and real estate transactions, even though the difference (2 ppm) is hardly significant, given the precision of normal surveying measurements over short distances (usually much less than a mile). Twenty-four states have legislated that surveying measures be based on the US survey foot, eight have legislated that they be based on the international foot, and eighteen have not specified which conversion factor to use.[83]

SPCS 83 legislation refers to state legislation that has been passed or updated using the newer 1983 NAD data. Most states have done so. Two states, Alaska and Missouri, and two jurisdictions, Guam and Puerto Rico, do not specify which foot to use.[83] Two states, Alabama and Hawaii, and four jurisdictions, Washington, DC, US Virgin Islands, American Samoa and Northern Mariana Islands, do not have SPCS 83 legislation.[83]

In October 2019, US National Geodetic Survey and National Institute of Standards and Technology announced their joint intent to retire the US survey foot and US survey mile, as permitted by their 1959 decision, with effect on January 1, 2023.[84][85][86]

Nautical edit

 
On the utility of the nautical mile.
Each circle shown is a great circle—the analogue of a line in spherical trigonometry—and hence the shortest path connecting two points on the globular surface. Meridians are great circles that pass through the poles.

The nautical mile was originally defined as one minute of arc along a meridian of the Earth.[87] Navigators use dividers to step off the distance between two points on the navigational chart, then place the open dividers against the minutes-of-latitude scale at the edge of the chart, and read off the distance in nautical miles.[88] The Earth is not perfectly spherical but an oblate spheroid, so the length of a minute of latitude increases by 1% from the equator to the poles. Using the WGS84 ellipsoid, the commonly accepted Earth model for many purposes today, one minute of latitude at the WGS84 equator is 6,046 feet and at the poles is 6,107.5 feet. The average is about 6,076 feet (about 1,852 metres or 1.15 statute miles).

In the United States, the nautical mile was defined in the 19th century as 6,080.2 feet (1,853.249 m), whereas in the United Kingdom, the Admiralty nautical mile was defined as 6,080 feet (1,853.184 m) and was about one minute of latitude in the latitudes of the south of the UK. Other nations had different definitions of the nautical mile, but it is now internationally defined to be exactly 1,852 metres (6,076.11548556 feet).[89]

Related units edit

The nautical mile per hour is known as the knot. Nautical miles and knots are almost universally used for aeronautical and maritime navigation, because of their relationship with degrees and minutes of latitude and the convenience of using the latitude scale on a map for distance measuring.

The data mile is used in radar-related subjects and is equal to 6,000 feet (1.8288 kilometres).[90] The radar mile is a unit of time (in the same way that the light year is a unit of distance), equal to the time required for a radar pulse to travel a distance of two miles (one mile each way). Thus, the radar statute mile is 10.8 μs and the radar nautical mile is 12.4 μs.[91]

Geographical edit

The geographical mile is based upon the length of a meridian of latitude. The German geographical mile (geographische Meile) was previously 115° of latitude (7.4127 km).[92]

Grid system edit

Cities in the continental United States often have streets laid out by miles. Detroit (e.g., Eight Mile Road), Indianapolis, Chicago, Phoenix, Philadelphia, Las Vegas, Los Angeles, and Miami, are several examples. Typically the largest streets are about a mile apart, with others at smaller intervals. In the Manhattan borough of New York City, "streets" are close to 20 per mile, while the major numbered "avenues" are about six per mile. (Centerline to centerline, 42nd Street to 22nd Street is supposed to be 5,250 feet, while 42nd Street to 62nd Street is supposed to be 5,276 ft 8 in.)[citation needed]

Metric edit

The informal term "metric mile" is used in some countries, in sports such as track and field athletics and speed skating, to denote a distance of 1,500 metres (0.932 miles). The 1500 meters is the premier middle distance running event in Olympic sports. In United States high-school competition, the term is sometimes used for a race of 1,600 metres (0.994 miles).[93]

Scandinavian edit

The Scandinavian mile (mil) remains in common use in Norway and Sweden, where it has meant precisely 10 km since metrication in 1889.[43] It is used in informal situations and in measurements of fuel consumption, which are often given as litres per mil. In formal situations (such as official road signs) only kilometres are given.

The Swedish mile was standardised as 36,000 Swedish feet or 10.6884 kilometres (6.6415 miles) in 1649; before that it varied by province from about 6 to 14.485 km.[43]

Before metrication, the Norwegian mile was 11.298 kilometres (7.020 miles).

The traditional Finnish peninkulma was translated as Swedish: mil and also set equal to 10 km during metrication in 1887, but is much less commonly used.

Comparison table edit

A comparison of the different lengths for a "mile", in different countries and at different times in history, is given in the table below. Leagues are also included in this list because, in terms of length, they fall in between the short West European miles and the long North, Central and Eastern European miles.

Length (m) Name Country used From To Definition Remarks
0500 mainland China 1984 today 1,500 chi In Chinese, this unit and the imperial mile are written using the same word (里), with a qualifier to distinguish between systems if needed
0960–1,152 Talmudic mil Land of Israel/Canaan today 2,000 amot (cubits) Biblical and Talmudic units of measurement
01,480 mille passus, milliarium Roman Empire Ancient Roman units of measurement
01,486.6 miglio[94] Sicily
01,524 London mile England
01,609.3426 (statute) mile England/UK 1592 1959 1,760 yards Over the course of time, the length of a yard changed several times and consequently so did the English, and from 1824, the imperial mile. The statute mile was introduced in 1592 during the reign of Queen Elizabeth I
01,609.344 mile some English speaking countries[citation needed] 1959 today 1,760 yards On 1 July 1959, the imperial mile was standardized to an exact length in metres. This figure corresponds to 5280 feet at 25.4 millimeters per inch.
01,609.3472 (statute) mile United States 1893 2022 1,760 yards From 1959 also called the US Survey Mile. From then, its only utility has been land survey, before it was the standard mile. From 1893, its exact length in metres was: 3600/3937 × 1760
01,807 Scots mile Scotland 1685 5,920 feet
01,820 Italy
01,852 nautical mile international today approx. 1 minute of arc Measured at a circumference of 40,000 km. Abbreviation: NM, nm
01,852.3 (for comparison) 1 meridian minute
01,853.181 nautical mile Turkey
01,855.4 (for comparison) 1 equatorial minute Although the NM was defined on the basis of the minute, it varies from the equatorial minute, because at that time the circumference of the equator could only be estimated at 40,000 km.
02,065 Portugal
02,220 Gallo-Roman league Gallo-Roman culture 1.5 miles Under the reign of Emperor Septimius Severus, this replaced the Roman mile as the official unit of distance in the Gallic and Germanic provinces, although there were regional and temporal variations.[95]
02,470 Sardinia, Piemont
02,622 Scotland
02,880 Ireland
03,780 Flanders
03,898 French lieue (post league) France 2,000 "body lengths"
03,927 Ri Japan 12,960 shaku
04,000 general or metric league
04,000 legue Guatemala
04,190 legue Mexico[96] = 2,500 tresas = 5,000 varas
04,444.8 landleuge 125° of a circle of longitude
04,452.2 lieue commune France Units of measurement in France before the French Revolution
04,513 legue Paraguay
04,513 legua Chile,[96] (Guatemala, Haiti) = 36 cuadros = 5,400 varas
04,808 Switzerland
04,828 English land league England 3 miles
04,800
04,900
Germanic rasta, also doppelleuge
(double league)
05,000 légua nova Portugal[96]
05,196 legua Bolivia[96] = 40 ladres
05,152 legua Argentina Argentina, Buenos Aires[96] = 6,000 varas
05,154 legue Uruguay
05,200 Bolivian legua Bolivia
05,370 legue Venezuela
05,500 Portuguese legua Portugal
05,510 legue Ecuador
05,510 Ecuadorian legua Ecuador
05,532.5 Landleuge
(state league)
Prussia Obsolete German units of measurement
05,540 legue Honduras
05,556 Seeleuge (nautical league) 120° of a circle of longitude
3 nautical miles
05,570 legua Spain and Chile Spanish customary units
05,572 legua Colombia[96] = 3 Millas
05,572.7 legue Peru[96] = 20,000 feet
05,572.7 legua Antigua
old league
Spain[96] = 3 millas = 15,000 feet
05,590 légua Brazil[96] = 5,000 varas = 2,500 bracas
05,600 Brazilian legua Brazil
05,685 Fersah (Turkish league) Ottoman Empire 1933 4 Turkish miles Derived from Persian parasang
05,840[97] Dutch mile Holland
06,170 milltir Wales 13thC 9,000 camau ( = 27,000 troedfeddi = 243,000 inches) Eclipsed by the conquest of Wales by Edward I
06,197 légua antiga Portugal[96] = 3 milhas = 24 estadios
06,240 Persian legue Persia
06,277 Luxembourg
06,280 Belgium
06,687.24 legua nueva
new league, since 1766
Spain[96] = 8,000 varas
06,700 Breslau mile Silesia 1630 1872 Also known as mila wrocławska in Polish
06,797 Landvermessermeile
(state survey mile)
Saxony Obsolete German units of measurement
07,400 Netherlands
07,409 (for comparison) 4 meridian minutes
07,419.2 Kingdom of Hanover Obsolete German units of measurement
07,419.4 Duchy of Brunswick Obsolete German units of measurement
07,420.4
07,414.9
Bavaria Obsolete German units of measurement
07,420.439 geographic mile 115 equatorial grads[dubious ]
07,421.6 (for comparison) 4 equatorial minutes
07,448.7 Württemberg Obsolete German units of measurement
07,450 Hohenzollern Obsolete German units of measurement
07,467.6 Russia 7 verst Obsolete Russian units of measurement
07,480 Bohemia
07,500 kleine / neue Postmeile
(small/new postal mile)
Saxony 1840 German Empire, North German Confederation, Grand Duchy of Hesse, Russia. Obsolete German units of measurement
07,532.5 Land(es)meile
(German state mile)
Denmark, Hamburg, Prussia Primarily for Denmark defined by Ole Rømer. Obsolete German units of measurement
07,585.9 Postmeile
(post mile)
Austro-Hungary Austrian units of measurement
07,850 Milă Romania
08,534.31 Mila Poland 1819 7146 meters before 1819, also equaled 7 verst[98]
08,800 Schleswig-Holstein Obsolete German units of measurement
08,888.89 Baden Obsolete German units of measurement
09,062 mittlere Post- / Polizeimeile
(middle post mile or police mile)
Saxony 1722 Obsolete German units of measurement
09,206.3 Electorate of Hesse Obsolete German units of measurement
09,261.4 (for comparison) 5 meridian minutes
09,277 (for comparison) 5 equatorial minutes
09,323 alte Landmeile
(old state mile)
Hanover 1836 Obsolete German units of measurement
09,347 alte Landmeile
(old state mile)
Hanover 1836 Obsolete German units of measurement
09,869.6 Oldenburg
10,000 metric mile, Scandinavian mile Norway, Sweden today Still commonly used today, e.g. for road distances; equates to the myriametre
10,044 große Meile
(great mile)
Westphalia Obsolete German units of measurement
10,670 Finland
10,688.54 mil Sweden 1889 In normal speech, "mil" means a Scandinavian mile of 10 km.
11,113.7 (for comparison) 6 meridian minutes
11,132.4 (for comparison) 6 equatorial minutes
11,299 mil Norway was equivalent to 3,000 Rhenish rods.

Similar units:

Idioms edit

The mile is still used in a variety of idioms, even in English-speaking countries that have moved from the Imperial to the metric system (for example, Australia, Canada, or New Zealand). These idioms include:

  • A country mile is used colloquially to denote a very long distance.
  • "A miss is as good as a mile" (failure by a narrow margin is no better than any other failure)
  • "Give him an inch and he'll take a mile" – a corruption of "Give him an inch and he'll take an ell"[99][100] (the person in question will become greedy if shown generosity)
  • "Missed by a mile" (missed by a wide margin)
  • "Go a mile a minute" (move very quickly)
  • "Talk a mile a minute" (speak at a rapid rate)
  • "To go the extra mile" (to put in extra effort)
  • "Miles away" (lost in thought, or daydreaming)
  • "Milestone" (an event indicating significant progress)

See also edit

Notes edit

  1. ^ A partitive genitive construction literally meaning "one thousand of paces".[8]
  2. ^ The c. 1300 Composition of Yards and Perches, a statute of uncertain date usually reckoned as an enactment of Edward I[22] or II,[21] notionally continued to derive English units from three barleycorns "dry and round" to the inch[22] and this statute remained in force until the 1824 Weights and Measures Act establishing the Imperial system. In practice, official measures were verified using the standards at the Exchequer or simply ignored.[23]
  3. ^ "Pole" being another name for the rod.
  4. ^ When reading the document it helps to bear in mind that 999,998 = 3,937 × 254.

References edit

Citations edit

  1. ^ OED (2002), "mile, n.1".
  2. ^ AHD (2006), "mile, 1".
  3. ^ a b Thompson (2008), B.6..
  4. ^ Weintrit, Adam (24 October 2019). "History of the Nautical Mile". Logistyka. Archived from the original on 1 March 2018. Retrieved 24 October 2019.
  5. ^ Butcher (2014), p. C-16.
  6. ^ "Road traffic: The traffic signs regulations and general directions 2015" (PDF). Government of the United Kingdom.
  7. ^ "Numbers" Archived 27 July 2018 at the Wayback Machine BBC
  8. ^ Lease (1905), p. 211.
  9. ^ Bassett, David R.; Mahar, Matthew T.; Rowe, David A.; Morrow, James R. (2008). "Walking and Measurement". Medicine & Science in Sports & Exercise. 40 (7): S529–S536. doi:10.1249/MSS.0b013e31817c699c. ISSN 0195-9131.
  10. ^ Soren (1999), p. 184.
  11. ^ Shuttleworth.
  12. ^ Smith (1875), p. 762.
  13. ^ Lesley Adkins; Roy A. Adkins; Both Professional Archaeologists Roy A Adkins (14 May 2014). Handbook to Life in Ancient Rome. Infobase Publishing. pp. 199–. ISBN 978-0-8160-7482-2.
  14. ^ a b De Morgan (12 February 1842). "XXXIV On Fernel's Measure of a Degree, in reply to Mr. Galloway's Remarks". The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science. Taylor & Francis: 230–233.
  15. ^ Zupko (1981), "Miglio".
  16. ^ Young, Norwood, ed. (1908). Handbook for Rome and the Campagna. Murray's Handbooks. E. Stanford. p. 29.
  17. ^ Andrews (2003), p. 70.
  18. ^ a b Evans (1975), p. 259.
  19. ^ Chaney (1911), p. 484.
  20. ^ a b c Klein (1988), p. 69.
  21. ^ a b c d e Chisholm (1864), p. 8.
  22. ^ a b c NPL.
  23. ^ Chisholm (1864), p. 37.
  24. ^ Chisholm (1864), p. 4.
  25. ^ Zupko (1977), pp. 10–11, 20–21.
  26. ^ Burke (1978), Ch. 9.
  27. ^ Adams (1990).
  28. ^ Statutes at large from the first year of King Edward the fourth to the end of the reign of Queen Elizabeth. Vol. II. 1763. p. 676. Retrieved 29 November 2011.
  29. ^ Act 35 Eliz. I cap. 6, s. 8.[28]
  30. ^ Norgate (1998).
  31. ^ Morden (1695).
  32. ^ Owen (1841), Book II, Ch. XVII, §5.
  33. ^ Owen (1841), Book II, Ch. XVII, §2.
  34. ^ Edinburgh 2000 visitors' guide. Collins. 1999. p. 31. ISBN 978-0-004-49017-5.
  35. ^ a b "mile". Dictionary of the Scottish Language – Scottish National Dictionary.
  36. ^ "fall, faw". Dictionary of the Scottish Language – Dictionary of the Older Scottish Tongue.
  37. ^ "Act for a standard of miles". Records of the Parliaments of Scotland. Edinburgh. 23 April 1685. APS viii: 494 c.59. Retrieved 10 March 2023.
  38. ^ "Act ratifying and approving the treaty of union of the two kingdoms of Scotland and England". Records of the Parliaments of Scotland. Edinburgh. 3 October 1706. Retrieved 10 March 2023.
  39. ^ Rowlett (2018), "Irish mile".
  40. ^ a b Ordnance Survey Ireland. "Frequently Asked Questions". Archived from the original on 28 February 2012. Retrieved 17 February 2009.
  41. ^ Apian, Petrus (1545). Cosmographie, oft Beschryvinghe der geheelder werelt. de Bonte. p. xvii. Retrieved 18 November 2023.
  42. ^ Metius, Adriaan Adriaansz (1627). Fundamentale onderwijsinghe, aengaende de fabrica en het veelvoudigh gebruyck van het Astrolabium, soo catholicum als particulier. Netherlands: gedr. bij U. Balck. p. 163. Retrieved 18 November 2023.
  43. ^ a b c Rowlett (2018), "mil 4".
  44. ^ Jan Harasimowicz; Włodzimierz Suleja, eds. (2000). Encyklopedia Wrocławia (Wyd. 1 ed.). Wrocław: Wydawn. Dolnośląskie. ISBN 83-7023-749-5. OCLC 46420892.
  45. ^ Davies, Norman (2002). Mikrokosmos : portret miasta środkowoeuropejskiego: Vratislava, Breslau, Wrocław. Roger Moorhouse, Andrzej Pawelec (Wyd. 1 ed.). Kraków: Wydawn. Znak. ISBN 83-240-0172-7. OCLC 50928641.
  46. ^ "Historie der Postsäulen" (in German). Forschungsgruppe Kursächsische Postmeilensäulen e.V. und 1. Sächsischer Postkutschenverein e.V. Archived from the original on 5 February 2017. Retrieved 5 February 2017.
  47. ^ Rowlett (2018), "milha".
  48. ^ (in Croatian) "Centuries of Natural Science in Croatia : Theory and Application". Kartografija i putopisi.
  49. ^ Viličić, Marina; Lapaine, Miljenko (2016). "Hrvatska milja na starim kartama" [The Croatian Mile on Old Maps] (PDF). Kartografija I Geoinformacije (in Croatian and English). Zagreb: Croatian Cartographic Society. 15 (25): 4–22. Retrieved 8 July 2019.
  50. ^ Opačić, Nives (23 February 2003). "Mrvice s banskoga stola". Vijenac (in Croatian). No. 232. Zagreb: Matica hrvatska. Retrieved 8 July 2019.
  51. ^ "Schedule I, Part VI", Weights & Measures Act of 1985.
  52. ^ 1,760 yards × 0.9144 m/yard.[51]
  53. ^ Barbrow (1976), pp. 16–17, 20.
  54. ^ Bigg (1964).
  55. ^ Parliament of India (8 April 1976). "The Standards of Weights and Measures Act" (PDF). Act No. 60 of 1976. Archived from the original (PDF) on 12 November 2009. Retrieved 10 March 2023.
  56. ^ Survey of India, "National Map Policy – 2005 Archived 2010-03-31 at the Wayback Machine".
  57. ^ Astin (1959).
  58. ^ Convert mile [statute] to mile [statute, US] "1 metre is equal to 0.000621371192237 mile [statute], or 0.000621369949495 mile [statute, US]. ... The U.S. statute mile (or survey mile) is defined by the survey foot. This is different from the international statute mile, which is defined as exactly 1609.344 metres. The U.S. statute mile is defined as 5,280 U.S. survey feet, which is around 1609.347219 metres."
  59. ^ File:Naypyitaw Tollbooth.jpg
  60. ^ "The Units of Measurement Regulations 1995", legislation.gov.uk, The National Archives, SI 1995/1804
  61. ^ Maximum posted speed limits Archived 23 September 2011 at the Wayback Machine (US) IIHS. Retrieved 14 September 2011
  62. ^ Hayner, Jeff (29 November 2012). "ASAA planning 1.2-mile swim in Pago Pago harbor". Samoa News. Retrieved 18 January 2014.
  63. ^ "The Nassau Guardian". 29 August 2012. Archived from the original on 29 October 2013. Retrieved 18 January 2014.
  64. ^ Jerome Williams (30 August 2013). "Pawpa Brown Race results". Amandala.com.bz. Retrieved 18 January 2014.
  65. ^ "Mt. bikers compete in Anegada". Bvibeacon.com. 8 May 2013. Retrieved 18 January 2014.
  66. ^ a b "Paddling 300 miles for NCVO". Cayman Compass. 4 June 2013. Archived from the original on 29 October 2013. Retrieved 18 January 2014.
  67. ^ "Bronze medal for Falklands football at Island Games in Bermuda". Penguin-news.com. 24 July 2013. Archived from the original on 24 September 2015. Retrieved 18 January 2014.
  68. ^ "Find the culprit!!!". Spicegrenada.com. Archived from the original on 16 September 2013. Retrieved 18 January 2014.
  69. ^ "Navy evacuates patient from cruise ship 50 miles off Guam". Pacific Daily News. 9 March 2013. Archived from the original on 16 September 2013. Retrieved 18 January 2014.
  70. ^ "Saipan Tribune". 23 September 2013. Archived from the original on 23 September 2013. Retrieved 10 March 2023.
  71. ^ "When you need to go". 23 September 2013. Archived from the original on 23 September 2013. Retrieved 10 March 2023.
  72. ^ "The Voice – The national newspaper of St. Lucia since 1885". Thevoiceslu.com. 8 February 2008. Archived from the original on 29 October 2013. Retrieved 18 January 2014.
  73. ^ "Peace Corps Volunteer runs 49 miles from Petit Bordel to Georgetown". Searchlight.vc. 16 December 2011. Archived from the original on 29 October 2013. Retrieved 18 January 2014.
  74. ^ "And I would walk 50 miles..." Sthelenaonline.org. 7 October 2012. Archived from the original on 22 March 2014. Retrieved 18 January 2014.
  75. ^ "104 Square Miles, but is it ours?". The St. Kitts-Nevis Observer. 28 September 2012. Archived from the original on 1 February 2013. Retrieved 18 January 2014.
  76. ^ "Provo has a new club". Suntci.com. 15 July 2009. Retrieved 18 January 2014.
  77. ^ AARON GRAY (Daily News Staff) (27 February 2012). "Butler outduels archrival to win 8 Tuff Miles". Virgin Islands Daily News. Archived from the original on 16 September 2013. Retrieved 18 January 2014.
  78. ^ Branch, Legislative Services (19 April 2021). "Consolidated federal laws of Canada, Weights and Measures Act". laws-lois.justice.gc.ca. Retrieved 10 March 2023.
    Act current to 18 January 2012. 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).
  79. ^ Weights and Measures Act Archived 16 October 2012 at the Wayback Machine
  80. ^ Government of Canada, Transportation Safety Board of Canada (26 October 2011). "Railway Investigation Report R10E0096 - Transportation Safety Board of Canada". www.tsb.gc.ca. Retrieved 10 March 2023.
    February 2012, Rail Report – 2010 – Report Number R10E0096. Other Factual Information (See Figure 1). 2. Assignment 602 travelled approximately 12 car lengths into track VC-64 and at a speed of 9 mph struck a stationary cut of 46 empty cars (with the air brakes applied) that had been placed in the track about 2+12 hours earlier. Canadian railways have not been metricated and therefore continue to measure trackage in miles and speed in miles per hour.
  81. ^ Hastings Racecourse Fact Book Archived 18 April 2012 at the Wayback Machine Like Canadian railways, Canadian race tracks have not been metricated and continue to measure distance in miles, furlongs, and yards (see page 18 of the fact book).
  82. ^ "Appendix E. General Tables of Units of Measurement". Retrieved 14 January 2020. (links to a Microsoft Word document)
  83. ^ a b c d e US National Geodetic Survey. "What are the 'official' conversions that are used by NGS to convert 1) metres to inches, and 2) metres to feet?". Frequently Asked Questions about the National Geodetic Survey. Retrieved 16 May 2009.
  84. ^ "NGS and NIST to Retire U.S. Survey Foot after 2022". National Geodetic Survey. 31 October 2019. Retrieved 4 March 2020.
  85. ^ "U.S. Survey Foot: Revised Unit Conversion Factors". NIST. 16 October 2019. Retrieved 4 March 2020.
  86. ^ "Federal Register :: Request Access".
  87. ^ Maloney (1978), p. 34.
  88. ^ Maloney (1978), pp. 34–35.
  89. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 127, ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021.
  90. ^ Rowlett (2018), "data mile".
  91. ^ Rowlett (2018), "radar mile".
  92. ^ Rowlett (2018), "meile".
  93. ^ Rowlett (2018), "mile".
  94. ^ Leopold Carl Bleibtreu: Handbuch der Münz-, Maß- und Gewichtskunde und des Wechsel-Staatspapier-, Bank- und Aktienwesens europäischer und außereuropäischer Länder und Städte. Verlag von J. Engelhorn, Stuttgart, 1863, p. 332
  95. ^ R. C. A. Rottländer (January 2006). "Hierarchische Gliederung der vormetrischen Längeneinheiten". vormetrische-laengeneinheiten.de. Archived from the original on 22 February 2006. Retrieved 10 March 2023.
  96. ^ a b c d e f g h i j k Helmut Kahnt (1986), BI-Lexikon Alte Maße, Münzen und Gewichte, Leipzig: VEB Bibliographisches Institut, p. 380
  97. ^ IKAR-Altkartendatenbank[permanent dead link] der Staatsbibliothek zu Berlin, Kartenabteilung.
  98. ^ Gloger, Zygmunt (1898). Ksiega rzeczy polskich. Druk W.L. Anczyca i Sp. OL 23442814M.
  99. ^ Concise Oxford English Dictionary (5th edition; 1964). Oxford University Press.
  100. ^ John Heywood (1562). The proverbs, epigrams, and miscellanies of John Heywood ... Print. for subscribers, by the Early English Drama Society. pp. 95–. Retrieved 1 December 2011.

Bibliography edit

  • Adams, Cecil (1990), "What's the origin of miles and yards?", The Straight Dope, retrieved 6 April 2015.
  • The American Heritage Dictionary of the English Language (4 ed.), Boston: Houghton Mifflin Co., 2006 [Originally published 2001], ISBN 978-0-618-70172-8.
  • Andrews, J.H. (15 September 2003), "Sir Richard Bingham and the Mapping of Western Ireland" (PDF), Proceedings of the Royal Irish Academy, vol. 103C, No. 3, Dublin: Royal Irish Academy, archived from the original (PDF) on 17 February 2012, retrieved 27 October 2011.
  • Astin, A.V.; et al. (25 June 1959), Doc. 59-5442: Refinement of values for the yard and the pound (PDF), Washington, D.C.: National Bureau of Standards.
  • Barbrow, Louis E.; et al. (1976), Weights and Measures Standards of the United States—A Brief History (PDF), National Institute of Standards and Technology, doi:10.6028/NBS.SP.447.
  • Bigg, P.H.; et al. (1964), "The United Kingdom Standards of the Yard in Terms of the Metre", British Journal of Applied Physics, vol. 15, No. 3, pp. 291–300, Bibcode:1964BJAP...15..291B, doi:10.1088/0508-3443/15/3/308.
  • Burke, James (1978), Connections, Little, Brown, & Co., ISBN 0-316-11685-8.
  • Butcher, Tina, ed. (2014), "Appendix C", NIST Handbook 44: Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices.
  • Chaney, Henry James (1911). "Weights and Measures" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 28 (11th ed.). Cambridge University Press. pp. 477–494.
  • Chisholm, Henry Williams (11 March 1864), "No. 115: Letter from the Comptroller General of the Exchequer to the Treasury, Dated 3d June 1863, Transmitting a Report on the Exchequer Standards of Weight and Measure, Dated 27th April 1863", Accounts and Papers: Session 4 February — 29 July 1864, vol. LVIII, London: Milner Gibson, p. 621
  • Evans, I. M. (1975), "A Cartographic Evaluation of the Old English Mile", The Geographical Journal, 141 (2): 259–264, doi:10.2307/1797211, JSTOR 1797211
  • Klein, Herbert Arthur (1988) [Originally published 1974], The Science of Measurement: A Historical Survey, New York: Dover Publications (Previously published by Simon & Schuster as The World of Measurements: Masterpieces, Mysteries and Muddles of Metrology).
  • Livy (1905), Lease, Emory Bair (ed.), Ab Urbe Condita, vol. I, XXI, & XXII, New York: University Publishing.
  • Maloney, Elbert S. (1978), Dutton's Navigation and Piloting (13 ed.), Annapolis: Naval Institute Press.
  • Morden, Robert (1695), Dorsetshire, retrieved 17 August 2011.
  • "History of Length Measurement", Factsheets, Teddington: National Physical Laboratory.
  • Norgate, Martin; et al. (1998), "Morden's Hampshire 1695", Old Hampshire Mapped, Hampshire County Council, ISBN 1-85975-134-2, retrieved 17 August 2011.
  • Owen, Aneurin, ed. (1841), "The Venedotian Code", Ancient Laws and Institutes of Wales; Comprising Laws Supposed to be Enacted by Howel the Good, Modified by Subsequent Regulations under the Native Princes prior to the Conquest by Edward the First: And Anomalous Laws, Consisting Principally of Institutions which by the Statute of Ruddlan were Admitted to Continue in Force: With an English Translation of the Welsh Text, to which are Added A few Latin Transcripts, Containing Digests of the Welsh Laws, Principally of the Dimetian Code, London: Commissioners on the Public Records of the Kingdom. (in Welsh) & (in English)
  • Oxford English Dictionary, 3rd ed., Oxford: Oxford University Press, 2002.
  • Rowlett, Russ (2018), How Many? A Dictionary of Units of Measurement, Chapel Hill: University of North Carolina, retrieved 5 November 2019.
  • Shuttleworth, M., Building Roman roads, Experiment Resources, archived from the original on 21 April 2011, retrieved 2 May 2011.
  • Smith, William, ed. (1875), Dictionary of Greek and Roman Antiquities, London: John Murray.
  • Soren, D.; et al. (1999), "A Roman villa and a late Roman infant cemetery : excavation at Poggio Gramignano, Lugnano in Teverina", Bibliotheca Archaeologica, Rome: L'Erma di Bretschneider.
  • Thompson, Ambler; et al. (2008), Special Publication 811: Guide for the Use of the International System of Units (SI) (PDF), Gaithersburg: National Institute of Standards and Technology.
  • Zupko, Ronald Edward (1977), British weights & measures: a history from antiquity to the seventeenth century, University of Wisconsin Press, ISBN 978-0-299-07340-4, retrieved 26 November 2011.
  • Zupko, Ronald Edward (1981), Italian Weights and Measures from the Middle Ages to the Nineteenth Century, Philadelphia: American Philosophical Society, ISBN 0-87169-145-0.

Further reading edit

  • NIST General Tables of Units of Measurement, United States National Institute of Standards and Technology, archived from the original on 10 December 2011
  • "Tafel zur Vergleichung und Bestimmung der Wegemaasse", Naturhistorische und chemischtechnische Notizen nach den neuesten Erfahrungen zur Nutzanwendung für Gewerbe, Fabrikwesen und Landwirthschaft, Expedition der Medicinischen Centralzeitung, 1856, pp. 320–326 (Item notes: Sammlung5-6 (1856–57) Original from Harvard University Digitized 9 January 2008)
  • Smits, Jan (15 February 2013) [1996], Mathematical data for bibliographic descriptions of cartographic materials and spatial data, Personal page on website ICA Commission on Map Projections, archived from the original on 12 February 2014
  • Wigglesworth Clarke, Frank (1875), Weights, measures, and money, of all nations, New York, D. Appleton & Company, p. 91