Talk:History of measurement/Archive 1


 * Archive I
 * Unified theory of ancient measurement
 * Archive III
 * Archive IV
 * Archive V
 * Archive VI

Miles

 * While inches and feet have remained pretty constant, the riddle that puzzles me is to trace the history of the various miles. There seem to be at least 4 species:
 * The ~10 km Egyptian mile, carried on in the Greek scoinios. No Roman equivalent? Must surely be the origin of the ~10 km Norwegian and Swedish land miles.
 * The ~6-7 km mile. Why the change? Presumably to get it in accordance with degrees. When did this happen? Did the Greeks do this at some stage? The German geographical mile and Nordic sea miles at ~7.5 km must be related? Is Goethe connected to this (he was a pioneer of land measurement)? For navigation at sea, it was significant to have a measure which related directly to the degree. On land, not so important.

" The ~1.6 km UK/US mile, with origins from the 1000 paces is a pure Roman invention. " The ~1.8 Nautical mile, based on the ~1.8 km geograpical miles. Why two different equatorial miles? Which came first?

Short answer

 * Miles
 * The Greek Milos of 4800 pous and
 * the Roman Milliare of 5000 pes and
 * The English Myle of c 49 BC - 1593 AD
 * are 8 stadions, stadiums, furlongs of 185 m.


 * Stadions
 * The ordinary Mesopotamian sos or side at 6 iku and 180 meters
 * was the basis for the Egyptian minute of march
 * the Egyptian minute of march at 183 m and 350 royal cubits
 * was the basis for the stadion of the Greek Milos
 * The stadion of the Greek Milos at 6 plethrons or 100 orguia and
 * 600 Atic pous of 308.4 mm at 185 m
 * was the basis for the stadium of the Roman milliare
 * The stadium of the Roman Milliare at 625 pes of 296 mm
 * was also 185 m and at 1000 passus of 5 pes
 * was the basis for the furlong of 625 fote of the English Myle


 * Leauges
 * 3 Milos of 4800 pous = 24 stadions = 14,400 pous = 1 leauge = 4440 m
 * 3 Milliare of 5000 pes = 24 stadiums = 15,000 pes = 1 leauge = 4440 m
 * 3 Myles of 5000 fote = 24 furlongs = 15,000 fote = 9375 English cubits = 1 leauge = 4440 m
 * 3 Miles of 5280 feet = 24 furlongs = 15,840 feet = 9900 English cubits = 1 leauge = 4828 m


 * 7.5 milliare = 1 schoeni = 1 kapsu = 2 parasang = 60 furlongs = 11.1 km = 1/10 degree
 * 1 degree (eec) = 1 itrw = 10 schoeni = 20 parasangs = 600 furlongs = 21,000 royal cubits

Divisions of the Milos, Milliare, Myle and Mile into areas

 * Milos
 * 1 square Milos of side 4800 pous = 1 Knights fee
 * 64 square stadions of 360,000 square pous,
 * 34,225 square meters, 368,554 SF
 * 576 aroura of 40,000 square pous, 3802.78 square m, 40,950.46 SF
 * each aroura had a side of 200 pous divisible into 2 plethrons
 * each of the 2304 plethron in a square Milos had a side of 100 pous
 * 2304 square plethrons of 10,000 square pous,
 * 950.6 square meters 10,237.64 SF
 * 640,000 square orquia of 36 square pous, 3.4 square meters, 36.85 SF
 * Milliare
 * 1 square Milliare of side 5000 pes
 * 64 square stadiums of 390,625 square pes,
 * 34,225 square meters, 368,554 SF
 * 25 square actus of side 1000 pes with 25 acres or 20 heridia
 * 1 Heridia was 1.25 Roman acres so there were
 * 20 Heridis to a square Actus
 * 625 areas of 40,000 square pes, 3802.78 m, 40,950.46 SF
 * 1.25 Roman acres is 50,000 pied = side 217.15 Ft area 47,154.54 SF
 * Each Jugerum was half a Heridium and Half a Jugerum was an acuna.
 * A Centuria was 100 Heredia or 125 acres or 5 square Actus
 * Myle
 * 1 square Myle of side 5000 fote or 8 furlongs
 * 64 square furlongs of side 625 square feet
 * in a square acre there were 40,000 square feet or fote
 * each acre had a side of 200 fote
 * In Roman Europe The Bodelian manuscript tells us
 * 14 acres maketh a yerde of land
 * If those are Roman acres of 40,000 pied then
 * the yerde is 12 English acres
 * 5 yerdis maketh a hyde of land which is 70 acres 60 English acres
 * 8 hydis maketh a knights fee which is 560 acres of land
 * 8 hydis = 480 English acres

The Confusion

 * the redefinition of the Greek Milos by the Romans and
 * The redefinition of the Milliare by the Elizabeathans, and
 * The redefinition of the Mile by the Metric system

Old English or Anglo Saxon units derived from the Greeks and Romans

 * The Virgate - "An old English unit of area" is actually Roman in origin
 * equal to one quarter of a hide = 1.25 yerdis = 17.5 acres
 * The amount of land needed to support a person.
 * The hide is at its root a German word for household, but
 * the hide is a Roman derived unit
 * We are told that in the Saxon counties of southern England,
 * it referred to the land sufficient to support one family,
 * which equaled what the family plowed in a year.
 * We are told that depending on the fertility of the land, the hide varied
 * from as little as 60 to as many as 240 acres, half a knights fee
 * but it was typically between 80 and 120 acres, 1/4 knights fee
 * Its actually 60 modern English, and 70 old Roman acres
 * We are told that the bovate is 1/8 of a carucate,
 * which also appears in the Domesday Book originated as a Danish measure
 * and it is found in the northeastern English counties
 * constituting the Danelaw.
 * Lets allow a carucata or carucate, like
 * 1 hide, is approximately 120 acres and
 * like the bovate was found in the Danish counties.
 * Lets allow A Plowland or plowgate is equal to a carucate or
 * an area eight oxen can plow
 * sufficient for a free family to support itself;
 * its origins precede 1100. (see definitions of Sumerian areas)
 * We are told the plowland compares with the knight’s fee
 * which we have established originates with the Milos
 * which was a larger area sufficient to support a knight’s family
 * (perhaps to allow pasture for animal husbandry).
 * Sulung is a Kentish term for two hides.
 * Its 120 modern English, 140 Roman acres
 * A yoke in Kent is 1/4 of a sulung.
 * A virgate is a rod in linear measure and 1/4 of a hide
 * (or 30 acres) used as a measure of area in Saxon counties.
 * 30 acres is 1/4 sulong
 * We have the Arpent AS a unit of length =~ 191.8 feet and
 * the (square) arpent used as a unit of area, area
 * (180 old French 'pied', or foot) used in France, Louisiana, and Canada.
 * approximately .845 acres, or 36,802 SF
 * Clearly derived from 1000 square orguia = 36,850 SF
 * which is itself derived from 1 sos = 10,000 square orguia.
 * We have the Morgen a unit of area =~ .6309 acres. or 27, 482 SF
 * used in Germany, Holland and South Africa, as 3/4 the Arpent
 * derived from the German word Morgen ("morning").
 * It represented the amount of land that could be plowed in a morning.

Ancient Definitions of Medieval Units

 * Mesopotamia
 * 1 square iku = 10,000 SF
 * 1 square great iku = 14,400 SF
 * 1 square sos = 360,000 SF


 * Egypt
 * 1 square khet = 21,780 SF
 * 1 square st3t of remen = 15,064.64 SF
 * 1 square st3t = 29,526.69 SF


 * Greece
 * 1 square aroura = 40,950.46 SF
 * 1 square plethron 10,237.64 SF
 * 1 square orquia 36.85 SF


 * Rome
 * 1 square actus 943,090.78 SF
 * 1 square Centuria 4,715,454 SF
 * 1 square Heridia 47,154.54 SF
 * 1 square area 40,950.46 SF
 * 1 square Jugerum 23,577.27 SF
 * 1 square acuna 11788.63 SF

Anglo - Saxon use of Roman and Greek Units

 * 1 Myle of 5000 fote became 1 Mile of 5280 feet in 1593
 * 1 square Mile of side 5280 feet was now divided into 8 furlongs of 220 yards
 * where before it had been 8 stadium/furlongs of 625'
 * 1 acre = 43,560 SF because it was increased by Queen Elizabeth
 * The side of each square furlong was increased 35'
 * The area that had been 8 Heridia of 1.25 acres or 9 acres was now divided into 10 acres
 * each acre measured a perch by a furlong
 * Each square furlong was half a square Actus
 * Each Jugerum was half a Heridium and Half a Jugerum was an acuna.
 * Each Furlong was 16 Jugerum and 32 acuna
 * A Centuria was 100 Heredia, 12.5 square furlongs
 * 125 acres was 5 square Actus
 * in a square acre there were 40,000 square feet or fote
 * each square acre had a side of 200 feet

Longer Discussion
Stadios
 * The Greek root stadios means "to have standing"
 * "to have standing" means to be a landowner.
 * Land measures including both
 * length and area are based on the size of fields
 * The base units are the remen, pace, yard, orguia,
 * fathom, rod, cord, perche and furlong.
 * Body measures fingers, thumbs, palms, hands, fists, feet, forearms
 * are related and worked into the system as multiples of the foot.
 * Different classes of citizen and occupation are apportioned
 * different amounts of land by the community

Ancient Degree Based Stadia Standards of Measure

 * Ancient stadia measures were always divisions of the degree
 * Systemized standards of measure derived from this common standard
 * Mesopotamia used 600 sos of 180 m = 108 km
 * Egypt used 10 itrw = 700 "3ht or fields" (of 3 kht of 100 royal cubits) = 110.25 km
 * Persia used 20 parasangs of 30(furlongs = 185 m) = 111 km
 * Phoenicia used 500 stadions (of 750 feet = 185 m) = 111 km
 * Ptolomy and Marinus of Tyre measured in the Persian/Phoenician stadia
 * Eratosthenes measured in the 700 3ht of Egypt.
 * The Greeks used 600 stadions (of 600 pous of 308.4 mm) = 111 km
 * The Romans used 600 stadiums of 625 pes (of 296 mm = 111 km
 * All of those are accurate divisions of a degree as defined by Ptolomy
 * Ancient Europe used the same standards because it did business with the same people


 * The credit for the first systemized collection and standardization
 * probably goes to the empire builders of Mesopotamia and Egypt
 * but the international commerce of the people who benefited
 * by those great empires, the Greeks and Persians and the Romans
 * who followed them is what really required the system
 * be standardized over such vast areas.


 * The important thing to recognize is that you can identify the original source
 * as Mesopotamian or Egyptian depending on whether the system is sexigesimal
 * or septenary and whether the divisions are by palms or feet or both.

Egyptian Itrw and Atur

 * The Itrw is an hour of travel on the river = 21,000 royal cubits
 * The Atur is an hour of march on the land = 21,000 royal cubits
 * The minute of march is a unit of 1 minutes travel = 350 royal cubits
 * 21,000 royal cubits = 36,085 English feet = 6.83 modern miles
 * It equaled 7.22 miles prior to the time of Queen Elizabeth
 * That was 11 km or 7.43 Roman milliare.
 * 75 Roman milliare are a pretty good value for a degree
 * The Egyptian value for 10 itrw is a little less accurate
 * and that probably explains the correction.

Conversions between Mesopotamian and Other Systems

 * Much of the Egyptian system of measurement is based on the Mesopotamian.
 * The Egyptian system in its turn formed the basis of the later Greek and Roman systems
 * while they in turn influenced European Systems.


 * The Egyptians took a sexigesimal Mesopotamian system and converted it to a septenary Egyptian system by taking an ordinary cubit of five gat measuring 30 sheshi 25 uban(500 mm) and a great cubit of 6 gat measuring 30 uban (600 mm)and making the first 6 Šsp (6 palms with 24 db<= 450 mm) and the second 7 Šsp (palms with 28 db< = 525 mm).


 * There are generally two or more divisions by size of finger and thumb

and different cultures have a preference for different unit fractions but basically all of it is part of the same system.


 * Mesopotamian;
 * 1 (little finger) = 1 "shusi" = 15 mm = 0.05 feet or podes
 * Greek;
 * 1 (ring finger)= 1 daktylos = 19.275 mm = 0.06 feet or podes
 * Roman;
 * 1.33 finger = 1 (thumb or inch)= 1 uncia = 25.64 mm = 0.08 feet or podes
 * Greek;
 * 2 (daktylos)= 1 condylos = 38.55 mm = 0.13 feet or podes
 * Roman
 * 4 (daktylos)= 1 palaiste = 77.10 mm = 0.25 feet or podes =(1 palm)
 * 8 (daktylos)= 1 dichas = 154.20 mm = 0.51 feet or podes =(2 palms)
 * 12 (daktylos)= 1 spithame = 231.30 0.76 feet or podes =(3 palms)
 * Greek;
 * 16 (daktylos)= 1 pous = 308.40 mm =1.01 podes =(4 palms)
 * 20 (daktylos)= 1 pygon = 385.50 mm =1.26 podes =(5 palms = 1 remen)
 * Roman
 * 24 daktylos = 1 pechya = 462.60 mm = 1.52 podes =(6 palms = 1 cubit)
 * English;
 * 25 (daktylos )= 1 English cubit = 493.44 mm = 1.62 podes;
 * Egyptian;
 * 28 (daktylos )=~ 1 Egyptian royal cubit = 539.70 = 1.77 podes =(7 palms)

Land cubits and tenure, the Feudal system

 * The Mesopotamians measured their arable land in garden plots or sar and combined them into fields or iku of 100 cubits to a side. The Egyptians measured out the irrigation ditches that bounded their 3ht or fields as strips a cubit wide and 100 cubits long known as kht. Their st3t which was a field 100 cubits to a side is said to have become the Greek Aroura or thousand but when you run the numbers the Aroura seems more likely to have derived from the iku.


 * Its probable that farmers measured out the land their community allowed them to plow in return for digging the ditch by pacing it off and built up an enclosure for it with the stones they found in their furrows.


 * The community would give the fields out in pairs, one to be plowed and one to remain fallow which were planted in rotation. As beasts of burden were domesticated and yoked to the plow the amount of land under cultivation increased, and a third field was added to be planted in hay or fodder for the plow animal. The side of this cluster of fields became standardized at 350 cubits or one minute of march.

Where the Metric System came from

 * In 1670 Abbe Mouton suggested a primary length standard
 * equal to 1 minute of arc on a great circle of the earth.
 * For this basic length Mouton offered the name milliare.
 * This was to be subdivided by seven sub units with each one
 * to be 1/10 the length of the one preceeding or


 * Milliare = 1 minute of arc = 36524 English feet = 1.11 km
 * Centuria =.1 minute of arc = 3652.4 English feet = .111 km
 * Decuria = .01 minutes of arc = 365.24 English feet = 111.1 m
 * Virga = .001 minutes of arc = 36.524 English feet =11.1 m
 * Virgula = .0001 minutes of arc = 3.6524 English feet = 1.11 m
 * Decima = .00001 minute of arc = .36524 English feet = .111 m
 * Centesima = .000001 minute of arc .36524 = English feet = 113.25 mm
 * Millesima = .0000001 minute of arc .036524 = English feet = 11.325 mm


 * Abbe Mouton may or may not have known that
 * The Milos was based on a stadion equivalent to the Egyptian minute of march.
 * Sir Issac Newton who attempted to restablish the measures of the ancient world
 * from the math problems in Kings 1 may not have known that


 * But its certain that Jomard, one of the French savants accompanying Napoleon
 * to Egypt entrusted with the measurement of ancient architecture to attempt
 * to restablish the correct value of ancient measures by measurement
 * knew that because he cites the Greeks who knew that


 * "In 1798, Edme-Francois Jomard visited the Great Pyramid
 * as a young savant on Napoleon's expedition.
 * The French had the debris cleared away from
 * the two northern corners of the Pyramid and discovered the corner sockets
 * where the corner casing stones had apparently originally been placed.
 * These were ten by twelve foot mortises, perfectly level,
 * and perfectly level with each other, cut twenty inches into the limestone bedrock.


 * Although, there were still piles of rubble between them,
 * Jomard was able to measure the north side of the base to be 230.902 meters (757.5 feet).
 * For the height, he measured each step. They added up to a total of 144 meters (481 feet).
 * By means of trigonometry Jomard calculated a slope of 51* 19' 14", and
 * an apothem of 184.722 meters. Because the casing stones were missing,
 * these figures were both estimates, but the length of the apothem
 * looked virtually perfect in light of various ancient classical texts
 * which Jomard was familiar with."


 * Diodorus Siculus and Strabo both claimed that the apothem of the Great Pyramid
 * was one stadium long. The Olympic stadium was 600 Greek feet, and
 * was supposed to be related to the size of the earth.


 * Jomard found the stadium of Eratosthenes and Hipparchus to be 185.5 meters,
 * and thus within one meter of his figure for the apothem. He also found that
 * distances quoted by the ancients in stadia matched the distances found by
 * Napoleon's surveyors, if a stadium was taken to be 185 meters.


 * The ancient stadium was also reported to have been 1/600 of a degree.
 * When Jomard took the length of a degree at what he believed to be
 * the mean latitude of Egypt, 110,827.68 meters, and divided it by 600,
 * he arrived at a stadium of 184.712 meters, which was
 * within ten centimeters of his figure for the length of the apothem!


 * In addition, several Greek authors had reported that the perimeter
 * of the base was equal to half a minute of a degree.


 * This would mean that a degree of latitude divided by 480 should
 * equal the length of one side of the base.


 * Again Jomard used the length of a degree at his mean latitude of Egypt,
 * 110,827 meters, and dividing by 480 arrived at 230.8 meters,
 * again within 10 centimeters of his measured base.

The Egyptian Minute of March as Stadion, Stadium, Furlong

 * In Egypt the minute of march was 350 royal cubits long and
 * an hour of march or itrw was 21,000 royal cubits long.
 * The Greeks tell us they noted their measures of 6 plethrons and 8 stadions,
 * were both the equivalent of the Apothem or slant side of the Great Pyramid.
 * The modern pre Euro nautical mile was ten times the length of that Apothem.


 * Using unit measures like the Stadion, Stadium and Furlong, which
 * were originally used to lay out fields and only gradually became defined as areas
 * like the Aroura or thousand square royal cubits, the empire builders
 * measured out their roads.


 * The Greek Milos was originally 8 stadions or 600 Greek pous x 8 = 4800 pous
 * The Pous came in long short and median variations so depending on which one
 * you used the number of pous would vary even as the length of the stadion and
 * Milos remained the same.
 * 600 Attic pous were equal to 625 Ionian pous but
 * both stadions were 185 meters long


 * The Romans standard pes was the Ionian pous of 296 mm so
 * they made their stadium of 185 meters egual to 625 pes or 1000 passus and
 * that made their Milliare 5000 pes


 * What makes that a great system for empire builders is that
 * the passus is now a measure of the pace at which the army moves.
 * If such standards of measure are well suited to
 * controlling the movements of armies with milestones
 * related to how much distance can be covered in a set period of time
 * they are equally servicable to the needs of commerce.


 * Just as the farmer can use the stone walls that border his field
 * to help him restablish its boundaries after a flood,
 * the community can establish its bounds in terms of
 * how much land it needs to irrigate to sustain its population and
 * the lugal or narmr (chief farmer)can determine
 * how many men he needs to dig the irrigation system and
 * how much land to alot to each oinkos, gene and phratre
 * in return for their service. Its all very feudal.


 * The city state is based on a market or agora that
 * serves a number of communities which are
 * spaced about as far apart as a man can walk in a day
 * driving a team of oxen pulling a cart.


 * When it takes more days to get the goods to market
 * than it takes for the crops to spoil you need a new market.

Leauges and the Vestigal Remnant of ther English Cubit on the Stanley Tape Measure

 * The various leagues at ~4km also enters the picture, but these seem to have
 * a simple, pedestrian origin. The French league later connects it to the meridian.


 * Pull out your standard everyday run of the mill Stanly tape measure and you should
 * see a diamond at 19.2" That is the ancient ordinary English cubit and its
 * the basis of the English League of three modern miles or
 * anciently in the time when a mile was 8 furlongs of 600 feet,
 * 14,400 ft and 9,000 diamonds.

Egil 13:49 Feb 13, 2003 (UTC)


 * I don't know about Goethe, but
 * Ole Rømer was a big player in the 4-minute geographical mile.
 * Elizabeth I added the 280 ft to make an 8-furlong mile.

Gene Nygaard 17:52, 4 Feb 2005 (UTC)

iku, 3kr, 3ht, kht, st3t, aroura, area, are, acre

 * She added the 280 feet to make a mile of 8 furlongs of 660 feet
 * be a mile of 80 perche instead of a mile of 8 furlongs of 625 feet.
 * The perche was not a Roman measure.
 * Trying to lay out a knights fee with a mile that measured 75.75 perche to a side
 * was what led to the confusion as to how many acres were in a hyde and yerde.
 * In a modern square mile there are 640 acres making 10 acres to a square furlong.


 * In the ancient square Milos there were 576 Aroura.
 * Greek Aroura would be measured with a side of 200 Attic pous of 308.4 mm.
 * That means there would have been 9 Aroura to a square stadion and
 * 576 to a square Milos of 23040000 square pous.


 * Those would have been derived from
 * a Mesopotamian iku of 100 cubits of 600 mm rather than
 * a st3t with side 100 Egyptian royal cubits of +/- 525 mm.


 * An iku of side 100 great cubits of 600 mm has
 * a side of 196.85 modern English feet and
 * an area of 38750 SF. It would have had
 * a side of 202.7 Ionian pous or Roman pes of 296 mm


 * An Egyptian st3t with side 100 royal cubits
 * would measure 171.83 modern English feet to a side and
 * contain 29526.69 SF. While thats about half of a modern acre and
 * anciently fields were farmed in pairs that's 169.83 Attic pous and
 * With 28841.37 square pous not enough square pous in an Aroura
 * to multiply out to a square mile of 4800 pous to a side.


 * When people began to harness domestic animals to the plow
 * they added a third field which probably became
 * the basis for the Roman jugerum.


 * The above questions are very old, and I have found some answers
 * I have yet found no clear connection between
 * the Egyptian mile (river measure) and anything else,


 * The Egyptian minute of march is 350 royal cubits.
 * The itrw is 60 minutes of march or a one hour river journey and
 * measures 21,000 royal cubits.
 * The key to understanding Egyptian measures is that they are septenary
 * and based on multiples of the palm rather than multiples of the hand.


 * but the Persian parasang is also interesting.

Herodotus on the length of ancient measures

 * For that you go to Herodotus (and Ptolomy)
 * Herodotus explains that the Persian stadia are 500 to a degree
 * rather than 600 so their stadion is 222 meters rather than 185 and
 * based on 750 Persian feet rather than 600 Greek feet.


 * The geographical ~7.5 km mile, land and sea, is the brainchild of Ole Rømer - the Prussian king later adopting it.


 * VI. Further, the length of the seacoast of Egypt itself is sixty “schoeni”1 --of Egypt, that is, as we judge it to be, reaching from the Plinthinete gulf to the Serbonian marsh, which is under the Casian mountain--between these there is this length of sixty schoeni. [2] Men that have scant land measure by feet; those that have more, by miles; those that have much land, by parasangs; and those who have great abundance of it, by schoeni. [3] The parasang is three and three quarters miles, and the schoenus, which is an Egyptian measure, is twice that.


 * VII. By this reckoning, then, the seaboard of Egypt will be four hundred and fifty miles in length. Inland from the sea as far as Heliopolis, Egypt is a wide land, all flat and watery and marshy. From the sea up to Heliopolis is a journey about as long as the way from the altar of the twelve gods at Athens to the temple of Olympian Zeus at Pisa. [2] If a reckoning is made, only a little difference of length, not more than two miles, will be found between these two journeys; for the journey from Athens to Pisa is two miles short of two hundred, which is the number of miles between the sea and Heliopolis.


 * IX. From Heliopolis to Thebes is nine days' journey by river, and the distance is six hundred and eight miles, or eighty-one schoeni. [2] This, then, is a full statement of all the distances in Egypt: the seaboard is four hundred and fifty miles long; and I will now declare the distance inland from the sea to Thebes : it is seven hundred and sixty-five miles. And between Thebes and the city called Elephantine there are two hundred and twenty-five miles.


 * 81 schoeni = 608 miles
 * 1 schoeni = 7.5miles = 1/10 degree = 11.1 km

Parasan = 30 furlongs


 * The British nautical mile may have been due to a want of having a sea mile in the same order of magnitude as their land mile? The relationship between the Roman and British land miles are, as you note, well documented. -- Egil 08:48, 9 Feb 2005 (UTC)