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The Cubit: A History and Measurement Commentary

The Cubit: A History and Measurement Commentary Hindawi Publishing Corporation Journal of Anthropology Volume 2014, Article ID 489757, 11 pages http://dx.doi.org/10.1155/2014/489757 Review Article Mark H. Stone Aurora University, Aurora, Illinois, USA Correspondence should be addressed to Mark H. Stone; markhstone2@sbcglobal.net Received 20 August 2013; Accepted 7 November 2013; Published 30 January 2014 Academic Editor: Kaushik Bose Copyright © 2014 Mark H. Stone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Historical dimensions for the cubit are provided by scripture and pyramid documentation. Additional dimensions from the Middle East are found in other early documents. Two major dimensions emerge from a history of the cubit. The first is the anthropological or short cubit, and the second is the architectual or long cubit. The wide geographical area and long chronological period suggest that cubit dimensions varied over time and geographic area. Greek and Roman conquests led to standardization. More recent dimensions are provided from a study by Francis Galton based upon his investigations into anthropometry. The subjects for Galton’s study and those of several other investigators lacked adequate sample descriptions for producing a satisfactory cubit/forearm dimension. This finding is not surprising given the demise of the cubit in today’s world. Contemporary dimensions from military and civilian anthropometry for the forearm and hand allow comparison to the ancient unit. Although there appears no pressing need for a forearm-hand/cubit dimension, the half-yard or half-meter unit seems a useful one that could see more application. 1. Introduction a distance located between the outstretched thumb and little n fi ger, or from the elbow to the tip of the middle nge fi r. If we know anything of the cubit today, it probably comes These alternate descriptions further complicate the matter of from acquaintance with Hebrew Scripture and/or the Old and determining a specific unit measure of the cubit. Hereaer ft , NewTestaments. People have heardorreadabout thedimen- thelatterdescription,elbow to thetip of themiddlefinger, sionsofNoah’sArk or Solomon’sTemple. Acquaintance with will signify the common unit. Egyptian history might have brought some awareness from The human gur fi e (typically male) has been the basis for the dimensions given for pyramids and temples. The cubit many dimensions. eTh foot is immediately recognized as an was a common unit in the early East. It continues today in example [1]. Less commonly heardisonyx(nail), butonyx some locations, but with less prominence having been remains a medical term. The Old English ynche, ynch, unce, replaced by modern day units. Early employment of the cubit or inch was a thumb-joint breadth. eTh anthropomorphic throughout the Near East showed varied dimensions for this basisfor many standardssupportsthe statement“manisthe unit. Some variants can be examined easier with reference measure of all things” attributed to Protagoras according to to biblical passages. Additional variants can also be found in Plato in the Theaetetus [2]. Small wonder the cubit was numerous secular documents, but these are less known and initially employed for measurement given its omnipresent less accessible than scripture. availability for use. We always possess the unit. Human gfi ure The word cubit ( kyu-b ¨ Jt) in English appears derived units are arbitrary but universal are especially effective by from the Latin cubitum for elbow. It was𝜋 𝜂𝜒𝜐𝜍 ́ (pay -kus) in their bodily reference producing a crude standard that is Greek. eTh cubit is based upon a human characteristic—the immediately accessable. length of the forearm from the tip of the middle nge fi r to end The cubit provides a convenient middle unit between the of the elbow. Many den fi itions seem to agree on this aspect foot andthe yard.TheEnglish yard couldbeconsidered a of theunit, yetitdoesnot produceauniversalstandardfor double cubit said to measure 12 palms, about 90 cm, or 36 there are many ways to determine a cubit. It can be measured inches measured from the center of a man’s body to the tip from theelbow to thebaseofthe hand,fromthe elbowto of the nge fi rs of an outstretched arm [ 3]. This is a useful way 2 Journal of Anthropology Table 1: eTh relative lengths of four common dimensions. Meter Yard Cubit Foot of measuring cloth held center body to an outstretched hand whoseheightwas sixcubitsand aspan. (1 Samuel (two cubits), or across the body to both outstretched hands 17:2–4 RSV) (four cubits as specified in Exodus 26: 1-2, 7-8). eTh English (5) In the four hundred and eightieth year after the people ellisalargervariantofthecubitconsistingof15palms,114cm, of Israel came out of the land of Egypt, in the fourth or 45 inches. It is about equal to the cloth measure ell of year of Solomon’s reign over Israel, in the month of early Scotland. A man’s stride, defined as stepping left-right, Ziv, which is the second month, he began to build the produces a double cubit, or approximately a yard [1]. houseofTheLord. eTh housewhich King Solomon The dimensions in Table 1 give the (approximate) relative built for The Lord was sixty cubits long, twenty cubits lengths for meter, yard, cubit, and foot. wide, and thirty cubits high. (1 Kings 6:1-2 RSV) The cubit was a basic unit in early Israel and the surround- The cubit determined a measure for many aspects of life ingNearEastcountries.ItisĎĹĂ in Hebrew (pronounced in Biblical history. A Sabbath day’s journey measured 2,000 am-mah ), which can be interpreted “the mother of the cubits (Exodus 16:29). This statue proscribed a limit to travel arm” or the origin, that is, the forearm/cubit. Selected biblical on the Sabbath. eTh distance between the Ark of the Covenant references [4]for thecubit includethese vfi eratherwell- and the camp of the Israelites during the exodus is estimated known selections. at about 914 meters, 1,000 yards, or 2,000 cubits [5]. Biblical citations and historical archeology suggest more (1) And GodsaidtoNoah, Ihavedeterminedtomake than one standard length for the cubit existed in Israel. In an end of all flesh; for the earth is filled with violence II Chronicles 3:3 the citation may imply cubits of the old through them; behold, I will destroy them with the standard. Ezekiel 40:5; 43:13 may be indicating the cubit plus earth. Make yourself an ark of gopher wood; make a hand. Archeological evidence from Israel [6]suggeststhat rooms in the ark, and cover it inside and out with 52.5 cm = 20.67 and 45 cm = 17.71 constitute the long and pitch. Thisishow youare to make it:the length of the short cubits of this time and location. To some scholars, the ark three hundred cubits, its breadth ftfiy cubits, and Egyptian cubit was the standard measure of length in the its height thirty cubits. (Genesis 6:13–15 RSV) Biblical period. eTh Biblical sojourn/exodus, war, and trade (2) eTh y shall make an ark of acacia wood; two cubits and areprobablereasons forthislengthtohavebeenemployed a half shall be its length, a cubit and a half its breadth, elsewhere. andacubitand ahalfits height.And youshall overlay The Tabernacle, the Temple of Solomon, and many other it with pure gold, within and without shall you overlay structures are described in the Bible by cubit measures. These it, and you shall make upon it a molding of gold round also occur with two different cubits dimensions, the long or about. (Exodus 25:10-11 RSV) royal (architectural) cubit and the short (anthropological) cubit. Scholars have used various means to determine the (3) And he made the court; for the south side the hang- length of these cubits with some success. eTh long cubit is ings of thecourt were of nfi etwinedlinen,ahundred given as approximately 52.5 centimeters and the short cubit cubits; their pillars were twenty and their bases as about 45 centimeters [4, 5]. twenty,ofbronze,butthehooksofthepillarsandtheir eTh Israelite long cubit corresponds to the Egyptian cubit fillets were of silver. And for the north side a hundred of 7 hands with 6 hands for shorter one. Eerdman’s Dictionary cubits, their pillars twenty, their bases twenty, of of the Bible [7,page1373] states “... archeology and literature bronze,but thehooks of thepillars andtheir fillets suggests an average length for the common cubit of 44.5 cm were of silver. And for the west side were hangings of (17.5 in.).” This citation also gives a range of 42–48 cm (17– fifty cubits, their pillars ten, and their sockets ten; the 19 in) for the cubit. Range is an important parameter because hooks of the pillars and their fillets were of silver. And it indicates the variation operating on this measure. Variation for the front to the east, ftfiy cubits. (Exodus 38:9–13 indicates multiple influences. RSV) The English use of cubit is difficult to determine. eTh (4) And Saul and the men of Israel were gathered, and exact length of this measure varies depending upon whether encamped in the valley of Elah, and drew up in line it included the entire length from the elbow to the tip of the of battle against the Philistines. And the Philistines longest n fi ger or by one of the alternates described earlier. stood on themountainonthe oneside, andIsrael Some scholars suggest that the longer dimension was the stood on the mountain on the other side, with a valley original cubit making it 20.24 inches for the ordinary cubit, between them. And there came out from the camp of and 21.88 inches for the sacred one, or a standard cubit from the Philistines a champion named Goliath, of Gath, theelbow to endofmiddlefinger (20 )and alower forearm 󸀠󸀠 Journal of Anthropology 3 Table 3 Table 2: Hebrew linear measures. Great Pyramid at Gizeh, Khufu 20.620±−005 Common scale Ezekiel’s scale Measure Millimeters Inches Millimeters Inches Second Khafra 20.64±−03 Granite temple 20.68±−02 Cubit 444.25 17.49 518.29 20.405 Span 222.12 8.745 259.14 10.202 Third Pyramid Menkaura 20.71±.02 Peribolus walls 20.69±−02 Handbreadth 74.04 2.91 74.04 2.91 Finger 18.51 0.72 18.51 0.72 Great Pyramid of Dahshur (?) 20.58±−02 Pyramid at Sakkara Pepi 20.51±−02 Fourth to sixthdynasty,meanofall 20.63±−02 cubit from the elbow to base of the hand (12 ). These are the Table 4 same dimensions for Egyptian measurements according to Easton’s Illustrated Bible Dictionary [9]. The Interpreter’s Bible Egyptian common cubit 18.24 inches [10, page 154] gives the Common Scale length as 444.25 mm Egyptian royal cubit 20.64 inches or 17.49 inches and Ezekial’s Scale as 518.29 mm or 20.405 Great Assyrian cubit 25.26 inches inches for the two cubit lengths. Inasmuch as the Romans Beladi ´ cubit 21.88 inches colonizedEngland theshorter cubitpreviouslymentioned Black cubit 20.28 inches may have been the standard. Arod or staff is called ČŐĆ (gomedh) in Judges 3:16, which means a cut, or something cut off. The LXX (Septu- result from strong disagreement over the dimension of the agint) and Vulgate render it “span” which in Hebrew Scripture cubit. Kaufman [11] argues against the “central location or the Old Testament is defined as a measure of distance (the theory” defending a cubit measuring 0.437 meters (1.43 feet). forearm cubit), roughly 18 inches (almost 0.5 of a meter). David [12] argues for a Temple cubit of 0.56 meters (1.84 feet). Among the several cubits mentioned is the cubit of a man or Differences in the length of the cubit arise from various common cubitinDeut. 3:11and thelegal cubitorcubit of the historical times and geographical locations in the biblical sanctuary described in Ezra 40.5 [6]. period. es Th e very long time periods and varied geographical Barrios [5] gives a summary of linear Hebrew measures locations frustrate determining a more exact length to the (see Table 2). cubit. Israel’s location between Egypt and Mesopotamia Barrois [5] indicates the dimension of the cubit can only suggest that many influences came into play over the space be determined by deduction and not directly because of of hundreds and hundreds of years in this well-traveled area. conflicting information. He reports the aqueduct of Hezekiah These influences probably contributed to the varied dimen- was 1,200 cubits according to the inscription of Siloam. sions encountered over this long time frame. Stories, myths, Its length is given as 5333.1 meters or 1,749 feet. Absolute and drama add their share. certainty for the length of a cubit cannot be determined, and eTh earliest written mention of the cubit occurs in the there are great differences of opinion about this length fos- Epic of Gilgamesh. eTh incomplete text is extant in twelve tering strong objections and debates. Some writers make the tablets written in Akkadian found at Nineveh in the library cubit eighteen inches and others twenty, twenty-one inches, of Ashurbanipal, king of Assyria (669–630? BCE). Other or greater. This appears critically important for those seeking fragments dated from 1800 BCE contain parts of the text, to determine the exact modern equivalent of dimensions and still more fragments mentioning this epic have been taken from scripture. Taking 21 inches for the cubit, the ark found dating from the 2nd millennium BCE. The cubit is Noah built would be 525 feet in length, 87 feet 6 inches in specifically mentioned in the text when describing a flood breadth, and 52 feet 6 inches in height. Using the standard as remarkably similar and predating the flood mentioned in cubit and 9 span, Goliath’s height would be 6 cubits plus Genesis. Obviously, the cubit was an early and important unit a span for about 10 feet and 9 inches. With a cubit of 18 of the Middle East fundamental to conveying linear measures his height is 9 feet 9 inches. The Septuagint, LXX, suggests 4 as showninTables 2, 3,and 4. cubits plus a span, or a more modest 6 feet and 9 inches. er Th e are many implications depending upon which dimension is selected [7]. The story requires young David to slay a giant 2. Egypt and not simply an above average sized man! Likewise for many other dimensions and description found in early writ- The Egyptian hieroglyph for the cubit shows the symbol of ings,the larger thedimensions, thebetterthe story. Sacred a forearm. However, the Egyptian cubit was longer than a dimensions require solemn, awe inspiring ones, but this frus- typical forearm. It seems to have been composed of 7 palms trates an exact determination. of 4 digits each totaling 28 parts and was about 52.3-52.4 cm Rabbi David ben Zimra (1461–1571) claimed the Founda- in length according to Arnold [13]. tion Stone and Holy of Holies were located within the Dome of The earliest attested standard measure is from the Old theRockonthe Temple Mount. Thisviewiswidelyaccepted, KingdompyramidsofEgypt.Itwas theroyal cubit(mahe). but with differences of opinion over the exact location known The royal cubit was 523 to 525 mm (20.6 to 20.64 inches) in as the “central location theory,” some of these differences length: and was subdivided into 7 palms of 4 digits each, for 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 4 Journal of Anthropology a 28-part measure in total. eTh royal cubit is known from Nichholson [20]in Men and Measures devoted a chapter Old Kingdom architecture dating from at least as early as the to The story of the cubit .His summary(page 30)provided construction of the Step Pyramid of Djoser around 2,700 BCE comparative lengths to vfi e cubits as shown in Table 4. [13–15]. Nichholson proposes a long history of the cubit beginning Petrie [15] begins Chapter XX the following. Values of the before thetimeofthe GreatPyramid of Kufu c. 2600BCE. Cubit and Digit writing. He claims a measure of 500 common cubits for the base side indicating only a six-inch difference from the base measure eTh measurements which have been detailed in the made by Flinders Petrie. He fixes the date of the royal cubit foregoing pages supply materials for an accurate at about 4000 BCE. eTh great Assyrian cubit is dated c. 700 determination of the Egyptian cubit. From such a BCE. eTh Bel adic ´ cubit is dated c. 300 BCE. Nichholson xfi es mass of exact measures, not only may the earliest the Black cubit as fully realized at around the ninth century valueofthe cubitbeascertained,but also the of this era which suggests a parallel to the growth and spread extent of its variations as employed by dier ff ent of Islam. While his measures for these variants of the cubit architects. appear to dovetail with some of the other estimates given in this paper, there are serious questions about the chronological Petrie’s methods and findings are so clearly and precisely sequence associated with these variants. Nichholson oer ff s no described they can best be quoted as follows. evidence or support for this sequence. His estimates of the common and royal cubits conform to other estimates, but the For the value of the usual cubit, undoubtedly the other values are less conforming. most important source is the King-s Chamber in the Great Pyramid; that is the most accurately wrought, thebestpreserved,and themostexactly 4. Greek/Roman Periods measured, of all the data that are known. The Greek 𝜋 𝜂𝜒𝜐𝜍̃ (pay -kus) was a 24-digit cubit. The Arranging the examples chronologically, the cubit used Cyrenaica cubit measured about 463.1 mm with the middle was as shown in Table 3. cubitabout 474.2mmmakingthemroughly 25/24and 16/15 Petrie writes the following. Romancubits. OtherGreek cubits basedondieff rentdigit measures from other Greek city-states were also used. The For the cubit I had deduced ([16,page50])from Greek 40-digit-measure appears to correspond to the Latin a quantity of material, good, bad, and indieff r- gradus, the step, or half-a-pace [21]. ent, 20–64±.02asthe best result thatIcould It shows that the Greeks and Romans inherited the foot get; about a dozen of the actual cubit rods from theEgyptians.TheRoman foot wasdivided into both that are known yield 20–65±−01; and now 12 unciae (inches) and 16 digits. The uncia was a twelfth fromtheearliestmonumentswenfi dthatthecubit part of the Roman foot or pes of 11.6 inches. An uncia was first used is 20–62, and the mean value from 2.46 cm or 0.97 of our inch. The cubitas was equal to 24 the seven buildings named is 20–63=𝑏 .02-. digiti or 17.4 inches. eTh Romans also introduced their mile ... On the whole we may take 20–62±−01 as the of 1000 paces or double steps, with the pace being equal to original value and reckon that it slightly increased five Roman feet. eTh Roman mile of 5000 feet was introduced on an average by repeated copyings in course of into England during the occupation. Queen Elizabeth, who time. (pages 178-179). reigned from 1558 to 1603, changed the statute mile to 5280 feet or 8 furlongs, with a furlong being 40 rods of 5.5 yards 3. Greek and Roman Comparisons each. eTh furlong continues today as a unit common in horse racing. In the writings of Eratosthenes, the Greek oˆı]o𝜍 eTh introduction of the yard as a unit of length came later, (schoe nus) was 12,000 royal cubits assuming a 0.525 meter. but its origin is not definitely known. Some believe the origin The stade was 300 royal cubits or 157.5 meters or 516.73 was the double cubit. Whatever its origin, the early yard was feet. Eratosthenes gave 250,000 stadia for circumference of divided by the binary method into 2, 4, 8, and 16 parts called the earth. Strabo and Pliny indicated 252,000 stadia for the the half-yard, span, finger, and nail. The yard is sometimes circumference and 700 stadia for a degree [13, 17]. Reports associated with the “gird” or circumference of a person’s waist, of Egyptian construction indicate only a 0.04 inch dieff rence or with the distance from the tip of the nose to the end of between cubit of Snefru and Khufu pyramids according to the thumb on the body of Henry I. Units were frequently Arnold [13] and Gillings [17]. “standardized” by reference to a royal gfi ure. Lelgemann [18, 19] reported the investigation of nearly 870 metrological yard sticks whose lengths represent 30 dif- eTh distance between thumb and outstretched nge fi r to ferent units. He argues for the earliest unit, the Nippur cubit, the elbow is a cubit sometimes referred to as a “natural cubit” to be 518.5 mm. Lelgemann gives the ancient stadion =600 of about 1.5 feet. This standard seems to have been used in feet and reports the stadionat Olympiaat192.27meterswhich the Roman system of measures as well as in different Greek he believes is based on the Remen or old Egyptian trade cubit systems. eTh Roman ulna, a four-foot cubit (about 120 cm), derived from theEgyptianroyal cubit(523.75mm) andold was common in the empire. This length is the measure from a trade cubit = 448.9 mm. man’s hip to the n fi gers of the outstretched opposite arm. The 𝜎𝜒 Journal of Anthropology 5 Table 5: Middle East names and dimensions for the cubit and related measures. Egypt Digit, zebo 1/28 royal cubit 0.737 18.7 mm Palm, shep 1/7 2.947 75 mm Royal foot 2/3 13.95 254 mm Royal cubit unit 20.62 524 Ater, skhoine 12,000 royal cubits 3.9 miles 6.3 km Hebrew Finger, ezba 1/24 cubit 0.74 19 mm Palm, tefah 4 fingers, 1/6 cubit 2.9 75 mm Span, zeret 3 palms, 1/2 cubit 8.8 225 mm Royal cubit 7/6 standard cubit 20.7 525 mm Pace 2 cubits 35.4 900 mm Stadion 360 cubits 528 162 meters Greek Palm 4 fingers 3.0 77 mm Span 12 fingers 9.1 231 Cubit 24 fingers 18.2 463 mm Stade 604 feet 185 meter Roman cubitus is a six-palm cubit of about 444.5 mm about 0.68 inch). The Arabic Hashimi cubit of about 650.2 mm (25.6 17.49 inches [17]. inches) is considered to measure two French feet. Since the established ratio between the French and English foot is about 16 to 15, it produces the following ratios: 5 Hashimi cubits≈ 5. Other Near East Dimensions 10 French feet≈ 128 English inches. Also, the length of 256 Over time and the geographic areas of the Middle East Roman cubits and the length of 175 Hashimi cubits are nearly variouscubitsandvariationsonthecubithavebeenrecorded: equivalent [16]. 6palms =24digits, that is,∼45.0 cm or 18 inches (1.50 ); ft The guard cubit (Arabic) measured about 555.6 mm; 5/4 7palms =28digits, that is,∼52.5 cm or 21 inches (1.75 ); ft of the Roman cubit producing 96 guard cubits≈ 120 Roman 8palms =32digits, that is,∼60.0 cm or 24 inches (2.00 ); ft cubits≈ 175 English feet. eTh Arabic nil cubit (or black cubit) and 9 palms = 36 digits, that is,∼67.5 cm or 27 inches (2.25 )ft measured about 540.2 mm. Therefore 28 Greek digits of the [1]. Oates [22, page 186] writing of mesopotamian archeology Cyrenaica cubit≈ 25/24ofaRomanfootor308.7mm, and states “measures of length were based on the cubit or “elbow” 175 Roman cubits ≈ 144 black cubits. eTh mesopotamian (very approximately 0.5 m).” cubit measured about 533.4 mm, 6/5 Roman cubit making 20 The Histories of Herodotus [23, page 21] described the Mesopotamian cubits≈ 24 Roman cubits≈ 35 English feet. walls surrounding the city of Babylon as “ftyfi royal cubits eTh Babylonian cubit (or cubit of Lagash) measured about wide andtwo hundredhigh(theroyal cubitisthree inches 496.1 mm. A Babylonian trade cubit existed which was nine- longer than the ordinary cubit).” An accompanying note to tenths of the normal cubit, that is, 446.5 mm. eTh Babylonian the text provides the information given in parentheses, and cubit is 15/16 of the royal cubit making 160 Babylonian trade the end note reports these values as “exceedingly high” raising cubits≈ 144 Babylonian cubits≈ 135 Egyptian royal cubits. questions about the height of these walls which would be eTh Pergamon cubit 520.9 mm was 75/64 of the Roman cubit. well over three-hundred feet high if the royal cubit of 20 eTh Salamiscubit 484.0mmwas 98/90ofthe Romancubit. inches is implied, or 100 meters if the royal cubit is 50 cm. For eTh Persia cubitofabout 500.1mmwas 9/8ofthe Roman comparison, the great pyramid of Khufu is listed as originally cubit and 9/10 of the guard cubit. Extending the geographic 146.59 meters [24,page895]. eTh credibilityofHerodotus area still further produces more names and values for the has often been questioned, and these dimensions might be cubit [16, 18, 19, 25, 26]. suspect also or subject to the same exaggerations found From the Encyclopedia Britannica [24] section on elsewhere in his reportings. Weights and Measures given in Volume 23, the unit specifi- In 1916, during the last years of Ottoman Empire and cations for the Middle East cubit are shown in Table 5. during WWI, the German Assyriologist Eckhard Unger From a table in A. E. Berriman’s Historical Metrology [8] found a copper-alloy bar during excavation at Nippur from c. we n fi d his summary of cubit standards in Table 6. If one assumes the values from Berriman’s table to be 2650 BCE. He claimed it to be a measurement standard. This bar, irregular in shape and irregularly marked, was claimed reasonable estimates, then the descriptive statistics from the to be a Sumerian cubit of about 518.5 mm or 20.4 inches. A data in Table 7 oer ff a summary of these varied dimensions. 30-digit cubit has been identified from the 2nd millennium The estimates in Berriman’s table for Greek and Roman BCEwithadigitlengthofabout 17.28mm(slightly more than cubits align reasonably well with the Egyptian short cubit 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 6 Journal of Anthropology Table 6: Cubit dimensions from Berriman [ 8]. Table 8: Human dimensions relative to the six-foot male. Unit Inches Cubit Inches Meter Finger 0.75 Roman 17.48 0.444 Palm 3 Egyptian (short) 17.72 0.450 Foot 12 Greek 18.23 0.463 Cubit 18 Assyrian 19.45 0.494 Height 72 Sumerian 19.76 0.502 Pace 72 Egyptian (royal) 20.62 0.524 Talmudist 21.85 0.555 Palestinian 25.24 0.641 Table 7: Descriptive statistics for A. E. Berriman’s table. Inches Meter Flemish ell Yard Cubit English ell Mean 20.04 0.51 Span French ell Median 19.61 0.50 Fathom Standard deviation 2.57 0.07 Range 7.76 0.20 18 handbreadths Minimum 17.48 0.44 Maximum 25.24 0.64 6 feet suggesting an average of approximately 18 inches. This dimen- sion is about two inches shorter than the overall mean in Table 7. eTh full range of values is about eight inches from 17.5 to 25. eTh varied origins for these data and previous values Figure 1: Vitruvian Man. suggest considering a family of cubits accumulated from many geographic areas over many different times rather than view these differences as suspects of one exact dimension. Figure 1 gives the famous picture associated with these Such variants may not be simple differences, or differences dimensions. eTh unit given shows one more example of the around an exact unit, but rather a composite of dimensions dimension of the cubit [1]. accumulated over a large chronological period from many eTh gfi ure of the Vitruvian Man by Leonardo da Vinci geographical locations that cannot be disentangled. These depicts nine historical units of measurement: the yard, the multiple dimensions suggest local applications rather than span, the cubit, the Flemish ell, the English ell, the French simply differences about a single standard which frustrates ell, the fathom, the hand, and the foot. eTh units depicted greater accuracy. are displayed with their historical ratios. In this gfi ure the Arounded valueof18 seems common for this period. cubit is 25% of the 6 individual and about 18 inches. We are The Hellenistic cubit appears in line with what has been iden- reminded once more of the importance of the human gfi ure tiefi d as the short cubit. Standardization of the cubit began for establishing units of measure. during Hellenism coinciding with Alexander’s conquests in the Middle East. Its standardization was probably increased Another example from this period comes from the Auto- greatly under the Roman Empire from the inu fl ences of war, biography [27] of Benvenuto Cellini (1500–1571). In describ- travel, and trade. eTh se inu fl ences contributed to bringing ing his casting of Medusa, Cellini’s narration uses cubit to the cubit into a more standard operational unit. Roman illustrate length as casually as we might use foot or yard. At engineers in viaduct, bridge, and road construction brought least in this context, if not others, the cubit appears of com- standardization throughout the empire. mon usage. How more generalized a cubit dimension pre- Cubits were employed through Antiquity to the Middle vailed through this time period is not known exactly. By the Ages and continue even today in some parts of the East. time of the French Revolution the Committee of Weights and Continued usage prevailed for measuring textiles by the span Measures had abandoned the cubit among other dimensions of arms with subdivisions of the hand and cubit in less in favor of the metric system. industrialized countries. Moving forwardtoDaVinci (1452–1519)wehavehis 6. The Human Cubit specicfi ations and commentary on Vitruvius Pollio (1st cen- tury BCE) for the human gur fi e and its dimensions [ 1]. They The history of metrology provides interesting data on the can be summarized as fractions of a 6-foot man as given in varied dimensions of the cubit. Metrology rfi st utilized the Table 8. human gfi ure in establishing dimensions. History to this 󸀠󸀠 Journal of Anthropology 7 Table 9: Frequency of left cubit measure by inches. Stature by inches Under 16.5 Under 17 Under 17.5 Under 18 Under 18.5 Under 19 Under 19.5 Above 19.5 71+ 000 1 3 4 15 7 30 70 0 0 0 1 5 13 11 0 30 69 0 1 1 2 25 15 6 0 50 68 0 1 3 7 14 7 4 2 38 67 0 1 7 15 28 8 2 0 61 66 0 1 7 18 15 600 47 65 0 4 10 12 8 2 0 0 36 64 0 5 11 2 3 0 0 0 21 −64 9 12 10 3 1 0 0 0 35 Total 925 49 61 102 55 38 9 348 Inches 16.5 17 17.5 18 18.5 19 19.5 19.5 Frequency 9 25 49 61 102 55 38 9 point suggests that a value of about 17-18 seems average and most common. Sir Francis Galton (1822–1911) offers data gathered from the investigations he conducted. Galton deserves recognition as one of the rfi st investigative anthropometrists. He was a scientist producing some of the first weather maps for recording changes in barometric pressure [28]and strategies for categorizing n fi gerprints [ 29]. Galton stands out for his investigations involving thousands of subjects. Some investigations were conducted at the International Health Exhibition in London held 1884-85 and at other eld fi loca- tions. Galton had earlier made an analysis of famous families 16.5 17 17.5 18 18.5 19 19.5 20 from which he compiled Hereditary Genius [30]and laterin Cubit frequency by inches Natural Inheritance [31]. He maintained a life-long interest in Frequency determining the physical and mental characteristics of groups of individuals. Figure 2: Cubit frequency by inches for 348 subjects. Not only did Galton collect data from his laboratory on human subjects, he investigated statistical techniques for analyzing tables, graphs, and plots of data. In doing so he created the origins for what is now recognized as correlation Figure 2 indicates the modal category of forearm/cubit and regression analysis. Correlation became more formally measures for Galton’s sample was 18.5 inches. eTh frequency developed by Pearson [32] as the product moment correlation distribution of forearm measurements is somewhat balanced. coefficient. It has become the most known and used statistical This might be expected given that these measures would be procedure of our time. Other statisticians, especially Sir determined by chance through heredity. This was Galton’s Ronald Fisher [33–35]and Tukey[36], have criticized the viewpoint and emphasis. Consequently, his attention derived correlation coefficient for its abuse arising from simplistic from this data and other data moved his interest to eugenics. applications and dubious interpretations. Nevertheless, the Many other English scientists and statisticians shared this correlation coefficient remains a popular analytic technique. interest; Fisher, Pearson, Haldane, Cattell, and others [40]. Pearson [37]alsoproducedthree volumesonthe life,letters, Galton (and the others) received considerable criticism for and works of Galton. taking this position. However, it was as a scientist and com- Galton’s data for the cubit of his day is given in Table 9.It piler of human data that led Galton to draw his inferences. was taken from Stigler [38,page319] The History of Statistics . His pronouncements [30, 31, 41] concerning eugenics do not Its original source is Galton [39] whose investigation gives smack of a political or personal agenda. One may disagree, data gathered from about 130 years ago on the forearm or butitisimportant to understandthatGalton’sworkwas cubit. Stigler [38,page319]indicated threeofGalton’srow focused upon data and methodology as the basis for forming totals were summed incorrectly. eTh se sums were corrected his conclusions. in Table 9. The mean for the Galton sample of 348 persons in Table 9 Figure 2 summarizes the relative frequency of fore- was almost 18 inches bringing estimates of a center location arm/cubit lengths from Galton’s data on 348 subjects given (i.e., mode, median, and mean) in sync with an approximate in Table 9. normal distribution as shown in Table 10. 󸀠󸀠 Stature by inches 8 Journal of Anthropology Table 10: Millimeters and inches of the left cubit. Left cubit to stature y = 0.2546x + 0.7623 Millimeters Inches R = 0.5715 Mean 67.06609 17.83621 Standard error 0.126798 0.042699 Median 67 18 Mode 67 18 Standard deviation 2.365384 0.796541 16 Sample variance 5.595043 0.634478 Kurtosis −0.9142 −0.42833 62 64 66 68 70 72 Stature in inches Skewness −0.09243 −0.16653 Range 8 3.5 Figure 4: Plot of left cubit to stature. Minimum 63 16 Maximum 71 19.5 Sum 23339 6207 analytic methods. These matters are not directly connected Count 348 348 to the issues of cubit length and therefore not discussed here. However, the relationship of cubit to stature is useful and it canbecomparedtoDaVinci’s estimate. Galton’s data on cubit length by inches Stigler [38,page319]indicated “Galton’sadhoc semi- graphical approach gave the correlation value𝑟=0.8 .” This was Galton’s approach prior to the Pearson product moment correlation which when calculated for his data gave𝑟=0.75 . Figure 4 is a plot of data from Table 9 with a linear regres- 20 sion line and showing the variation in forearm/cubit at each level of stature. It is very important to note the wide variation of left cubit measures (vertical) for each indication of stature (horizontal). Individual differences in the cubit/forearm are clearlyevidentateachpoint of staturethwarting anything more specific than a generalized indication for the fore- 19.5 arm/cubit from Galton’s data. eTh shared variance between 0 18 1 stature and cubit is about 57% suggesting these two variables +71 71 70 70 6 69 9 68 68 16.5 16 5 67 67 are related but not completely. 66 66 −64 Several questions emanate from Galton’s data regarding forearm length or the cubit. Figure 3: A three-dimensional view of Galton’s data. (1) How representative is this sample of the general pop- ulation? (2) How much change, if any, in human dimensions has From Galton’s data summarized in Figure 2 and Tables occurred from ancient times and over the one hun- 9 and 10 about 2% had forearms at 16.5 or less and 2% dred plus years from Galton’s sample to the present had forearms greater than 19.5 .Approximately 63%or218 day? personsand closetotwo-thirdsofthe 348personsampleare within one-half inch + or− themeanof18.3inchesoralmost (3) Is there any gender difference or other sources of 18.5 if rounded o.ff About 95% vary less than an inch above influence and bias? andbelow themeanestimate. Rounding from thesefrequen- cies makes these values approximate, but they still provide From what we know of Galton’s methods there appears no a generally useful summary from his sample. Skewness and indication of outright bias. Stigler [38]inchapters8,9,and 10 kurtosis appear as minimal influences on the distribution of his book raised no questions when describing Galton’s data further confirming a balanced distribution. andmethods foranalysing data.Galton’ssamples were large Figure 3 provides a three-dimensional view of Galton’s andoeft ninthe thousands. Thiscubit sample is moderatein data. It usefully shows the clustering of values along the scope. Galton was aware of gender differences and utilized center diagonal from the upper left to lower right. Galton’s 1.08 as a correction factor for male/female differences [ 38]. figures were not shown as three-dimensional, but he recorded However, there is little information regarding sample the frequencies at each intersection of his two-way table representation. It appears that Galton was generally fastidious which were used to produce this three-dimensional gur fi e. in his investigations. He utilized gatherings of the general Pondering his data gave rise to Galton’s work on association/ population from which to procure his samples and make his correlation for which the word regression has now evolved measurements. Given that right handedness predominates, being derived from his eo ff rts to interpret what this and other Galton measured the left hand to avoid what might result data express. See Stigler [38] for more details on Galton’s from possible environmental influences upon the mostly Cubit by inches Frequency Left cubit in inches 󸀠󸀠 󸀠󸀠 󸀠󸀠 Journal of Anthropology 9 Table 11: Forearm percentiles for an unidentified British population. Table 12: Elbow-fingertip length percentile distribution in millime- ters. Percentile 5 50 95 (a) Male 440 475 516 1st 2.5th 5th 10th25th50th75th90th95th97.5th99th Female 400 430 460 435 442 448 455 468 483 499 515 523 532 542 (b) Mean 484.04 (19.05 inches) Standard error 0.55 dominant right hand. Volunteering could be a potential source of bias, but volunteering probably allowed a larger Median 483 (19.01 inches) sample of individuals. He paid individuals a modest amount Mode 472 (18.58 inches) to participate not unlike what is sometimes done today. Standard deviation 23.32 Johnson et al. [42]reviewedand reanalyzed Galton’s Sample variance 544.09 original data. eTh y report on mean scores, correlations of Kurtosis 0.43 the measures with age, correlations among measures, occu- Skewness 0.22 pational differences in scores, and sibling correlations. A cor- Range 192 relation of cubit/forearm to stature indicated the former Minimum 386 was about 25–27% of stature. Nothing further is added to a knowledge of forearm/cubit dinemsion by their work. Maximum 578 Relevance of the forearm/cubit length in more recent Count 1774 times comes from anthropometric dimensions utilized in industrial psychology and applications to the clothing indus- try. Data from Mech [43] gives more recent data of human dimensions including the forearm. Forearm lengths reported 7. Discussion for percentiles 5, 50, and 95 are given in Table 11. eTh varied dimensions forthe historical cubitofancient eTh se percentiles are from an unidentiefi d British sample times and places speak to a variation in the dimension itself. ages 19 to 65. Lacking more information one can only Two major units predominate; one estimate centers around compare and contrast these dimensions to previous samples 18 inches and the other around 20 inches. There are other discussed earlier. es Th e males had a median cubit measure variations, some smaller and some much greater. er Th e is too of 475 mm or ∼18.7 inches. Females measured a slightly wide ageographicalareaand toogreat achronological time shorter median measure of 430 mm or∼16.9 inches. Mech period to consider any of these latter variations normative. [43] indicated a median value close to that given in Table 9 Each variant was more likely to be locally relevant rather for Galton’s data or∼18.7 to∼18.3. than widely prominent. Only in the Greek and Roman The Lean Manufacturing Strategy reports a forearm empires through war, trade, and construction did these values 󸀠 󸀠 󸀠 mean = 18.9 ,standarddeviation =0.81 , minimum = 15.4 , coalesce to somewhat of a standard. and maximum = 22.1 based on data from McCormick [45]. How has the human physique changed over time? Roche Nothing further is given regarding this sample and its char- [48] reported that rates of growth during childhood have acteristics. increased considerably during the past 50–100 years. He There are numerous sites and organizations providing indicated increases in rates of growth and maturation for all carefully determined dimensions for the human body. How- developed nations, but not evident in many other countries. ever, these dimensions are developed to serve the clothing eTh re were recorded increases in length at birth in Italy and industry and furniture design adding nothing to a knowledge France, but little change in the United States. An increase in of the contemporary forearm/cubit dimension [46]. childhood stature was given for about 1.5 cm/decade for 12- The anthropometry database ANSUR [ 47]obtainedfrom year-old children. eTh increase in stature for youth was about http://www.openlab.psu.edu/ gives a table of percentiles for 0.4 cm/decade in most developed countries. eTh changes in the horizontal measure made “from the back of the elbow to body proportions during recent decades were reported as less the tip of the middle n fi ger with the hand extended,” that is, marked than those in body size. Leg length increased more cubit. eTh sample was comprised of unidentiefi d male army than stature in men but not in women. Roach further indi- recruits. cated that changes in nutrition alone could not account for the eTh ANSURdatasample[ 47]in Table 12 provides trends which exceed the original socioeconomic differentials. In the United States, Roach reported there have been per descriptive statistics for the right male forearm plus extended hand in millimeters. The mean for this quite large contem- capita increases in the intake of protein and fat from animal sources, decreases in carbohydrates and fat from vegetable porary sample is about one inch greater than the short cubit reported much earlier. So is the median although the mode is sources, and some changes in caloric intake. It is not clear slightly less. eTh sample appears reasonably balanced, but the that these changes constitute better nutrition stimulating growth. eTh trends could reflect environmental improve- variation indicated by the standard error, standard deviation, and range show this human dimension to vary. Variation has ments, specifically changes in health practices and living been encountered before in the reporting of earlier samples. conditions leading to improvements for mortality rates and 10 Journal of Anthropology life expectancy [44].Nutritionvariesevenindevelopedcoun- [2] F.M.Cornford, Plato’s eor Th y of Knowledge: Theaetetus and Sophist, Liberal Arts Press, New York, NY, USA, 1957. tries. Roche [48] reported genetic factors play a small role in causing trends. However, the data speaks to considerable [3] E. Zupko, Revolution in Measurement; Western European Weights and Measures Since the Age of Science,TheAmerican variation among contemporary samples as also noted in Philosophical Society, Philadelphia, Pa, USA, 1990. Galton’s data. [4] Revised Standard Version of the Bible: RSV,NationalCouncil of Overall, it seems unwise to be overly fastidious about the Churches of Christ in the United States of America, New any contemporary value for the cubit when such samples York, NY, USA, 1952. are vaguely described. For any comparison of contemporary [5] G. A. Barrois, Chronology and Metrology. the Interpreter’s Bible, dimensions reported there are few characteristics given by vol. 1, Abington Press, New York, NY, USA, 1952. which to judge sample representation. eTh contemporary [6] G. Barkay, “Measurements in the Bible: evidence at St. Etienne estimates appear somewhat close together and suggest at least for the length of the cubit and reed,” Biblical Archeological forthesesamplesnogreat changehasoccurredovertheyears, Review,vol.12, no.2,article 37,1986. butwecannotbesurelacking validdata. Withoutmoresam- [7] D.N.Freedman, Eerdman’s Dictionary of the Bible,Eerdmans, ple definition, any fastidious analysis appears unwarranted. Grand Rapids, Mich, USA, 2000. eTh Galton values are likely to have been local and relevant to [8] A.D.Berriman, Historical Metrology,Dent, London,UK, 1953. a British sample. Nowadays samples are more likely to reflect [9] M. G. Easton, Illustrated Bible Dictionary, om Th as Nelson, the role of immigration with whatever additional effects this Knoxville, Tenn, USA, 3rd edition, 1897. might bring to bear on determining national human dimen- [10] G. A. Buttrick, The Interpreter’s Bible ,vol.I,AbingtonPress,New sions. In general, Europeans are taller than Asian/Middle East York, NY, USA, 1952. peoples and Americans are taller than Europeans. eTh se are [11] A. S. Kaufman, The Temple of Jerusalem , Har Year’ah Press, Jer- generalizations from gross estimates. Komlos and Baten [49] usalem, Palestinian, 2004. have made a comprehensive analysis of stature over centuries. [12] A. B. David, “Ha-midda ha-Yerushalmit,” Israel Exploration The striking feature of their tables is the intravariation of Journal,vol.19, pp.159–169,1969. values for each time period. Individual variation was also [13] D. Arnold, Building in Egypt: Pharaonic Stone Masonry,Oxford observed in Galton’s data. However, systematic sampling and University Press, Oxford, UK, 1991. sample details must accompany any data before estimates can [14] J. P. Lauer, “Etude sur quelques monuments de la IIIe dynastie be more than gross general indications. (pyramide ad ` egres ´ de Saqqarah),” Annales du Service des A variety of circumstances address the cubit, but most Antiquites de L’Egypte, IFAO,vol.31, no.60, article59, 1931. of them offer little specicfi information beyond what has [15] W.M.F.Petrie, The Pyramids and Temples of Gizeh , Field and already been presented. es Th e biased sites typically serve Tuer, London, UK, 1883. some agenda, oeft n religious or personal. Overall, even these [16] W. M. F. Petrie, Inductive Metrology, Saunders, London, UK, sites typically report the two major dimensions for the cubit at 18 inches or 20 inches. [17] R. J. Gillings, Mathematics in the Time of the Pharaohs, MIT The cubit as a dimension remains useful. We take the Press, Cambridge, Mass, USA, 1972. cubit (hand and foot) wherever we travel. Knowing personal [18] D. Lelgemann, Eratosthenes von Kyrene Und die Messtechnik der dimensions can sometimes prove useful for making quick Alten Kulturen, Chmielorz, Wiesbaden, Germany, 2001. albeit gross estimates. eTh 18 ruler is a very handy device [19] D. Lelgemann, Recovery of the Ancient System of Length Units, whenever measures just beyond a foot ruler are required, Institute for Geodesy and Geo-Information Technology, Berlin, especially when it is necessary to draw straight lines for a Germany, 2004. length just beyond twelve inches. Tape measures are a boon, [20] E. Nichholson, Men and Measures, Smith, Elder & Co, London, but not for drawing lines. UK, 1912. It appearsthatwemight contentourselves with acubit [21] J. L. E. Dreyer, A History of Astronomy from al Th es to Kepler , length of 18 inches as a somewhat consistent dimension for Dover, New York, NY, USA, 1953. the cubit. Even as the foot evolved from a specific albeit arbi- [22] J. Oates, Babylon, aTh mes and Hudson, London, UK, 1986. trary personage, any assemblage of them leads to an abstract [23] Herodotus, eTh Histories. (Trans. Aubrey De S el ´ incourt; Notes dimension, so the cubit could justify more application as a 0.5 John Marincola), Penguin books, London, UK, 1954. yard and/or a 0.5 meter. Further prominence of either or both [24] “Weights and measures,” in Encyclopedia Britannica,vol.23, pp. these units might prove more useful than rfi st surmised. 371–372, Encyclopedia Britannica, Chicago, Ill, USA, 1971. [25] M. A. Powell, “Metrology and mathematics in ancient Mesopo- tamia,” in Civilizations of the Ancient Near East III,Sasson, Ed., Conflict of Interests Scribners, New York, NY, USA, 1995. eTh author declares that there is no conflict of interests [26] D. Arnold, The Encyclopaedia of Ancient Egyptian Architecture , regarding the publication of this paper. Princeton University Press, Princeton, NJ, USA, 2003. [27] B. Cellini, Autobiography: the Life of Benvenuto Cellini (Trans. J. Symonds),P.F.Collier &Son,New York,NY, USA, 1906. References [28] F. Galton, Meteorgraphia: Methods of Mapping the Weather, Macmillan, London, UK, 1863. [1] H. A. Klein, The Science of Measurement ,Dover,New York,NY, USA, 1974. [29] F. Galton, Fingerprints, Macmillan, London, UK, 1892. 󸀠󸀠 Journal of Anthropology 11 [30] F. Galton, Hereditary Genius: An Inquiry Into Its Laws and Con- sequences, Macmillan, London, UK, 1869. [31] F. Galton, Natural Inheritance, Macmillan, London, UK, 1889. [32] K. Pearson, “Notes on the history of correlation,” Biometrika, vol. 13, pp. 25–45, 1920. [33] R. Fisher, On the Mathematical Foundtions of eor Th etical Statis- tics, eTh Philosophical Transactions of the Royal Society, Lon- don, UK, 1922. [34] R. Fisher, The Design of Experiments , Hafner, New York, NY, USA, 1951. [35] R. Fisher, Statistical Methods for Research Workers,Hafner, New York, NY, USA, 1958. [36] J. Tukey, “Analyzing data: sanctification or detective work?” American Psychologist,vol.24, pp.83–91,1969. [37] K. Pearson, eTh Life,Letters andLabours of FrancisGalton(3 Vols.), Cambridge University Press, Cambridge, UK, 1914. [38] S. Stigler, The History of Statistics , Harvard University Press, Cambridge, Ma, USA, 1986. [39] F. Galton, “Co-relations and their measurement chiefly from anthropometric data,” Proceedings of the Royal Society of Lon- don, vol. 45, pp. 135–145, 1888. [40] J. Waller, “Ideas of heredity, reproduction and eugenics in Britain 1800–1875,” Studies in History and Philosophy of Science C,vol.32, no.3,pp. 457–489, 2001. [41] F. Galton, “Kinship and correlation,” North American Review, vol. 150, pp.419–431,1890. [42] R. C. Johnson, G. E. McClearn, S. Yuen, C. T. Nagoshi, F. M. Ahern, and R. E. Cole, “Galton’s data a century later,” American Psychologist,vol.40, no.8,pp. 875–892, 1985. [43] Mech, 2010, http://mech.utah.edu/ergo/p. [44] R. Steckel, “Research project: a history of health in Europe from the late paleolithic era to the present,” Economics & Human Biology,vol.1,pp. 139–142, 2003. [45] B. McCormick, Human Engineering, Industrial Design Institute, Warsaw, Poland, 1964. [46] E. Grandjean, Fitting the Task to the Man,Taylor&Francis, New York, NY, USA, 1989. [47] ANSUR: Open Design Lab at PSU, 1988, http://openlab.psu.edu/. [48] A. F. Roche, “Secular trends in human growth, maturation, and development,” Monograph Social Research in Child Devel- opment,vol.44, no.3-4,pp. 1–120, 1979. [49] J. Komlos and J. Baten, “Height and the standard of living,” Journal of Economic History, vol. 58, no. 3, pp. 866–870, 1998. 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The Cubit: A History and Measurement Commentary

Stone, Mark H.
Journal of Anthropology , Volume 2014 – Jan 30, 2014
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Hindawi Publishing Corporation
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Copyright © 2014 Mark H. Stone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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10.1155/2014/489757
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Hindawi Publishing Corporation Journal of Anthropology Volume 2014, Article ID 489757, 11 pages http://dx.doi.org/10.1155/2014/489757 Review Article Mark H. Stone Aurora University, Aurora, Illinois, USA Correspondence should be addressed to Mark H. Stone; markhstone2@sbcglobal.net Received 20 August 2013; Accepted 7 November 2013; Published 30 January 2014 Academic Editor: Kaushik Bose Copyright © 2014 Mark H. Stone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Historical dimensions for the cubit are provided by scripture and pyramid documentation. Additional dimensions from the Middle East are found in other early documents. Two major dimensions emerge from a history of the cubit. The first is the anthropological or short cubit, and the second is the architectual or long cubit. The wide geographical area and long chronological period suggest that cubit dimensions varied over time and geographic area. Greek and Roman conquests led to standardization. More recent dimensions are provided from a study by Francis Galton based upon his investigations into anthropometry. The subjects for Galton’s study and those of several other investigators lacked adequate sample descriptions for producing a satisfactory cubit/forearm dimension. This finding is not surprising given the demise of the cubit in today’s world. Contemporary dimensions from military and civilian anthropometry for the forearm and hand allow comparison to the ancient unit. Although there appears no pressing need for a forearm-hand/cubit dimension, the half-yard or half-meter unit seems a useful one that could see more application. 1. Introduction a distance located between the outstretched thumb and little n fi ger, or from the elbow to the tip of the middle nge fi r. If we know anything of the cubit today, it probably comes These alternate descriptions further complicate the matter of from acquaintance with Hebrew Scripture and/or the Old and determining a specific unit measure of the cubit. Hereaer ft , NewTestaments. People have heardorreadabout thedimen- thelatterdescription,elbow to thetip of themiddlefinger, sionsofNoah’sArk or Solomon’sTemple. Acquaintance with will signify the common unit. Egyptian history might have brought some awareness from The human gur fi e (typically male) has been the basis for the dimensions given for pyramids and temples. The cubit many dimensions. eTh foot is immediately recognized as an was a common unit in the early East. It continues today in example [1]. Less commonly heardisonyx(nail), butonyx some locations, but with less prominence having been remains a medical term. The Old English ynche, ynch, unce, replaced by modern day units. Early employment of the cubit or inch was a thumb-joint breadth. eTh anthropomorphic throughout the Near East showed varied dimensions for this basisfor many standardssupportsthe statement“manisthe unit. Some variants can be examined easier with reference measure of all things” attributed to Protagoras according to to biblical passages. Additional variants can also be found in Plato in the Theaetetus [2]. Small wonder the cubit was numerous secular documents, but these are less known and initially employed for measurement given its omnipresent less accessible than scripture. availability for use. We always possess the unit. Human gfi ure The word cubit ( kyu-b ¨ Jt) in English appears derived units are arbitrary but universal are especially effective by from the Latin cubitum for elbow. It was𝜋 𝜂𝜒𝜐𝜍 ́ (pay -kus) in their bodily reference producing a crude standard that is Greek. eTh cubit is based upon a human characteristic—the immediately accessable. length of the forearm from the tip of the middle nge fi r to end The cubit provides a convenient middle unit between the of the elbow. Many den fi itions seem to agree on this aspect foot andthe yard.TheEnglish yard couldbeconsidered a of theunit, yetitdoesnot produceauniversalstandardfor double cubit said to measure 12 palms, about 90 cm, or 36 there are many ways to determine a cubit. It can be measured inches measured from the center of a man’s body to the tip from theelbow to thebaseofthe hand,fromthe elbowto of the nge fi rs of an outstretched arm [ 3]. This is a useful way 2 Journal of Anthropology Table 1: eTh relative lengths of four common dimensions. Meter Yard Cubit Foot of measuring cloth held center body to an outstretched hand whoseheightwas sixcubitsand aspan. (1 Samuel (two cubits), or across the body to both outstretched hands 17:2–4 RSV) (four cubits as specified in Exodus 26: 1-2, 7-8). eTh English (5) In the four hundred and eightieth year after the people ellisalargervariantofthecubitconsistingof15palms,114cm, of Israel came out of the land of Egypt, in the fourth or 45 inches. It is about equal to the cloth measure ell of year of Solomon’s reign over Israel, in the month of early Scotland. A man’s stride, defined as stepping left-right, Ziv, which is the second month, he began to build the produces a double cubit, or approximately a yard [1]. houseofTheLord. eTh housewhich King Solomon The dimensions in Table 1 give the (approximate) relative built for The Lord was sixty cubits long, twenty cubits lengths for meter, yard, cubit, and foot. wide, and thirty cubits high. (1 Kings 6:1-2 RSV) The cubit was a basic unit in early Israel and the surround- The cubit determined a measure for many aspects of life ingNearEastcountries.ItisĎĹĂ in Hebrew (pronounced in Biblical history. A Sabbath day’s journey measured 2,000 am-mah ), which can be interpreted “the mother of the cubits (Exodus 16:29). This statue proscribed a limit to travel arm” or the origin, that is, the forearm/cubit. Selected biblical on the Sabbath. eTh distance between the Ark of the Covenant references [4]for thecubit includethese vfi eratherwell- and the camp of the Israelites during the exodus is estimated known selections. at about 914 meters, 1,000 yards, or 2,000 cubits [5]. Biblical citations and historical archeology suggest more (1) And GodsaidtoNoah, Ihavedeterminedtomake than one standard length for the cubit existed in Israel. In an end of all flesh; for the earth is filled with violence II Chronicles 3:3 the citation may imply cubits of the old through them; behold, I will destroy them with the standard. Ezekiel 40:5; 43:13 may be indicating the cubit plus earth. Make yourself an ark of gopher wood; make a hand. Archeological evidence from Israel [6]suggeststhat rooms in the ark, and cover it inside and out with 52.5 cm = 20.67 and 45 cm = 17.71 constitute the long and pitch. Thisishow youare to make it:the length of the short cubits of this time and location. To some scholars, the ark three hundred cubits, its breadth ftfiy cubits, and Egyptian cubit was the standard measure of length in the its height thirty cubits. (Genesis 6:13–15 RSV) Biblical period. eTh Biblical sojourn/exodus, war, and trade (2) eTh y shall make an ark of acacia wood; two cubits and areprobablereasons forthislengthtohavebeenemployed a half shall be its length, a cubit and a half its breadth, elsewhere. andacubitand ahalfits height.And youshall overlay The Tabernacle, the Temple of Solomon, and many other it with pure gold, within and without shall you overlay structures are described in the Bible by cubit measures. These it, and you shall make upon it a molding of gold round also occur with two different cubits dimensions, the long or about. (Exodus 25:10-11 RSV) royal (architectural) cubit and the short (anthropological) cubit. Scholars have used various means to determine the (3) And he made the court; for the south side the hang- length of these cubits with some success. eTh long cubit is ings of thecourt were of nfi etwinedlinen,ahundred given as approximately 52.5 centimeters and the short cubit cubits; their pillars were twenty and their bases as about 45 centimeters [4, 5]. twenty,ofbronze,butthehooksofthepillarsandtheir eTh Israelite long cubit corresponds to the Egyptian cubit fillets were of silver. And for the north side a hundred of 7 hands with 6 hands for shorter one. Eerdman’s Dictionary cubits, their pillars twenty, their bases twenty, of of the Bible [7,page1373] states “... archeology and literature bronze,but thehooks of thepillars andtheir fillets suggests an average length for the common cubit of 44.5 cm were of silver. And for the west side were hangings of (17.5 in.).” This citation also gives a range of 42–48 cm (17– fifty cubits, their pillars ten, and their sockets ten; the 19 in) for the cubit. Range is an important parameter because hooks of the pillars and their fillets were of silver. And it indicates the variation operating on this measure. Variation for the front to the east, ftfiy cubits. (Exodus 38:9–13 indicates multiple influences. RSV) The English use of cubit is difficult to determine. eTh (4) And Saul and the men of Israel were gathered, and exact length of this measure varies depending upon whether encamped in the valley of Elah, and drew up in line it included the entire length from the elbow to the tip of the of battle against the Philistines. And the Philistines longest n fi ger or by one of the alternates described earlier. stood on themountainonthe oneside, andIsrael Some scholars suggest that the longer dimension was the stood on the mountain on the other side, with a valley original cubit making it 20.24 inches for the ordinary cubit, between them. And there came out from the camp of and 21.88 inches for the sacred one, or a standard cubit from the Philistines a champion named Goliath, of Gath, theelbow to endofmiddlefinger (20 )and alower forearm 󸀠󸀠 Journal of Anthropology 3 Table 3 Table 2: Hebrew linear measures. Great Pyramid at Gizeh, Khufu 20.620±−005 Common scale Ezekiel’s scale Measure Millimeters Inches Millimeters Inches Second Khafra 20.64±−03 Granite temple 20.68±−02 Cubit 444.25 17.49 518.29 20.405 Span 222.12 8.745 259.14 10.202 Third Pyramid Menkaura 20.71±.02 Peribolus walls 20.69±−02 Handbreadth 74.04 2.91 74.04 2.91 Finger 18.51 0.72 18.51 0.72 Great Pyramid of Dahshur (?) 20.58±−02 Pyramid at Sakkara Pepi 20.51±−02 Fourth to sixthdynasty,meanofall 20.63±−02 cubit from the elbow to base of the hand (12 ). These are the Table 4 same dimensions for Egyptian measurements according to Easton’s Illustrated Bible Dictionary [9]. The Interpreter’s Bible Egyptian common cubit 18.24 inches [10, page 154] gives the Common Scale length as 444.25 mm Egyptian royal cubit 20.64 inches or 17.49 inches and Ezekial’s Scale as 518.29 mm or 20.405 Great Assyrian cubit 25.26 inches inches for the two cubit lengths. Inasmuch as the Romans Beladi ´ cubit 21.88 inches colonizedEngland theshorter cubitpreviouslymentioned Black cubit 20.28 inches may have been the standard. Arod or staff is called ČŐĆ (gomedh) in Judges 3:16, which means a cut, or something cut off. The LXX (Septu- result from strong disagreement over the dimension of the agint) and Vulgate render it “span” which in Hebrew Scripture cubit. Kaufman [11] argues against the “central location or the Old Testament is defined as a measure of distance (the theory” defending a cubit measuring 0.437 meters (1.43 feet). forearm cubit), roughly 18 inches (almost 0.5 of a meter). David [12] argues for a Temple cubit of 0.56 meters (1.84 feet). Among the several cubits mentioned is the cubit of a man or Differences in the length of the cubit arise from various common cubitinDeut. 3:11and thelegal cubitorcubit of the historical times and geographical locations in the biblical sanctuary described in Ezra 40.5 [6]. period. es Th e very long time periods and varied geographical Barrios [5] gives a summary of linear Hebrew measures locations frustrate determining a more exact length to the (see Table 2). cubit. Israel’s location between Egypt and Mesopotamia Barrois [5] indicates the dimension of the cubit can only suggest that many influences came into play over the space be determined by deduction and not directly because of of hundreds and hundreds of years in this well-traveled area. conflicting information. He reports the aqueduct of Hezekiah These influences probably contributed to the varied dimen- was 1,200 cubits according to the inscription of Siloam. sions encountered over this long time frame. Stories, myths, Its length is given as 5333.1 meters or 1,749 feet. Absolute and drama add their share. certainty for the length of a cubit cannot be determined, and eTh earliest written mention of the cubit occurs in the there are great differences of opinion about this length fos- Epic of Gilgamesh. eTh incomplete text is extant in twelve tering strong objections and debates. Some writers make the tablets written in Akkadian found at Nineveh in the library cubit eighteen inches and others twenty, twenty-one inches, of Ashurbanipal, king of Assyria (669–630? BCE). Other or greater. This appears critically important for those seeking fragments dated from 1800 BCE contain parts of the text, to determine the exact modern equivalent of dimensions and still more fragments mentioning this epic have been taken from scripture. Taking 21 inches for the cubit, the ark found dating from the 2nd millennium BCE. The cubit is Noah built would be 525 feet in length, 87 feet 6 inches in specifically mentioned in the text when describing a flood breadth, and 52 feet 6 inches in height. Using the standard as remarkably similar and predating the flood mentioned in cubit and 9 span, Goliath’s height would be 6 cubits plus Genesis. Obviously, the cubit was an early and important unit a span for about 10 feet and 9 inches. With a cubit of 18 of the Middle East fundamental to conveying linear measures his height is 9 feet 9 inches. The Septuagint, LXX, suggests 4 as showninTables 2, 3,and 4. cubits plus a span, or a more modest 6 feet and 9 inches. er Th e are many implications depending upon which dimension is selected [7]. The story requires young David to slay a giant 2. Egypt and not simply an above average sized man! Likewise for many other dimensions and description found in early writ- The Egyptian hieroglyph for the cubit shows the symbol of ings,the larger thedimensions, thebetterthe story. Sacred a forearm. However, the Egyptian cubit was longer than a dimensions require solemn, awe inspiring ones, but this frus- typical forearm. It seems to have been composed of 7 palms trates an exact determination. of 4 digits each totaling 28 parts and was about 52.3-52.4 cm Rabbi David ben Zimra (1461–1571) claimed the Founda- in length according to Arnold [13]. tion Stone and Holy of Holies were located within the Dome of The earliest attested standard measure is from the Old theRockonthe Temple Mount. Thisviewiswidelyaccepted, KingdompyramidsofEgypt.Itwas theroyal cubit(mahe). but with differences of opinion over the exact location known The royal cubit was 523 to 525 mm (20.6 to 20.64 inches) in as the “central location theory,” some of these differences length: and was subdivided into 7 palms of 4 digits each, for 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 4 Journal of Anthropology a 28-part measure in total. eTh royal cubit is known from Nichholson [20]in Men and Measures devoted a chapter Old Kingdom architecture dating from at least as early as the to The story of the cubit .His summary(page 30)provided construction of the Step Pyramid of Djoser around 2,700 BCE comparative lengths to vfi e cubits as shown in Table 4. [13–15]. Nichholson proposes a long history of the cubit beginning Petrie [15] begins Chapter XX the following. Values of the before thetimeofthe GreatPyramid of Kufu c. 2600BCE. Cubit and Digit writing. He claims a measure of 500 common cubits for the base side indicating only a six-inch difference from the base measure eTh measurements which have been detailed in the made by Flinders Petrie. He fixes the date of the royal cubit foregoing pages supply materials for an accurate at about 4000 BCE. eTh great Assyrian cubit is dated c. 700 determination of the Egyptian cubit. From such a BCE. eTh Bel adic ´ cubit is dated c. 300 BCE. Nichholson xfi es mass of exact measures, not only may the earliest the Black cubit as fully realized at around the ninth century valueofthe cubitbeascertained,but also the of this era which suggests a parallel to the growth and spread extent of its variations as employed by dier ff ent of Islam. While his measures for these variants of the cubit architects. appear to dovetail with some of the other estimates given in this paper, there are serious questions about the chronological Petrie’s methods and findings are so clearly and precisely sequence associated with these variants. Nichholson oer ff s no described they can best be quoted as follows. evidence or support for this sequence. His estimates of the common and royal cubits conform to other estimates, but the For the value of the usual cubit, undoubtedly the other values are less conforming. most important source is the King-s Chamber in the Great Pyramid; that is the most accurately wrought, thebestpreserved,and themostexactly 4. Greek/Roman Periods measured, of all the data that are known. The Greek 𝜋 𝜂𝜒𝜐𝜍̃ (pay -kus) was a 24-digit cubit. The Arranging the examples chronologically, the cubit used Cyrenaica cubit measured about 463.1 mm with the middle was as shown in Table 3. cubitabout 474.2mmmakingthemroughly 25/24and 16/15 Petrie writes the following. Romancubits. OtherGreek cubits basedondieff rentdigit measures from other Greek city-states were also used. The For the cubit I had deduced ([16,page50])from Greek 40-digit-measure appears to correspond to the Latin a quantity of material, good, bad, and indieff r- gradus, the step, or half-a-pace [21]. ent, 20–64±.02asthe best result thatIcould It shows that the Greeks and Romans inherited the foot get; about a dozen of the actual cubit rods from theEgyptians.TheRoman foot wasdivided into both that are known yield 20–65±−01; and now 12 unciae (inches) and 16 digits. The uncia was a twelfth fromtheearliestmonumentswenfi dthatthecubit part of the Roman foot or pes of 11.6 inches. An uncia was first used is 20–62, and the mean value from 2.46 cm or 0.97 of our inch. The cubitas was equal to 24 the seven buildings named is 20–63=𝑏 .02-. digiti or 17.4 inches. eTh Romans also introduced their mile ... On the whole we may take 20–62±−01 as the of 1000 paces or double steps, with the pace being equal to original value and reckon that it slightly increased five Roman feet. eTh Roman mile of 5000 feet was introduced on an average by repeated copyings in course of into England during the occupation. Queen Elizabeth, who time. (pages 178-179). reigned from 1558 to 1603, changed the statute mile to 5280 feet or 8 furlongs, with a furlong being 40 rods of 5.5 yards 3. Greek and Roman Comparisons each. eTh furlong continues today as a unit common in horse racing. In the writings of Eratosthenes, the Greek oˆı]o𝜍 eTh introduction of the yard as a unit of length came later, (schoe nus) was 12,000 royal cubits assuming a 0.525 meter. but its origin is not definitely known. Some believe the origin The stade was 300 royal cubits or 157.5 meters or 516.73 was the double cubit. Whatever its origin, the early yard was feet. Eratosthenes gave 250,000 stadia for circumference of divided by the binary method into 2, 4, 8, and 16 parts called the earth. Strabo and Pliny indicated 252,000 stadia for the the half-yard, span, finger, and nail. The yard is sometimes circumference and 700 stadia for a degree [13, 17]. Reports associated with the “gird” or circumference of a person’s waist, of Egyptian construction indicate only a 0.04 inch dieff rence or with the distance from the tip of the nose to the end of between cubit of Snefru and Khufu pyramids according to the thumb on the body of Henry I. Units were frequently Arnold [13] and Gillings [17]. “standardized” by reference to a royal gfi ure. Lelgemann [18, 19] reported the investigation of nearly 870 metrological yard sticks whose lengths represent 30 dif- eTh distance between thumb and outstretched nge fi r to ferent units. He argues for the earliest unit, the Nippur cubit, the elbow is a cubit sometimes referred to as a “natural cubit” to be 518.5 mm. Lelgemann gives the ancient stadion =600 of about 1.5 feet. This standard seems to have been used in feet and reports the stadionat Olympiaat192.27meterswhich the Roman system of measures as well as in different Greek he believes is based on the Remen or old Egyptian trade cubit systems. eTh Roman ulna, a four-foot cubit (about 120 cm), derived from theEgyptianroyal cubit(523.75mm) andold was common in the empire. This length is the measure from a trade cubit = 448.9 mm. man’s hip to the n fi gers of the outstretched opposite arm. The 𝜎𝜒 Journal of Anthropology 5 Table 5: Middle East names and dimensions for the cubit and related measures. Egypt Digit, zebo 1/28 royal cubit 0.737 18.7 mm Palm, shep 1/7 2.947 75 mm Royal foot 2/3 13.95 254 mm Royal cubit unit 20.62 524 Ater, skhoine 12,000 royal cubits 3.9 miles 6.3 km Hebrew Finger, ezba 1/24 cubit 0.74 19 mm Palm, tefah 4 fingers, 1/6 cubit 2.9 75 mm Span, zeret 3 palms, 1/2 cubit 8.8 225 mm Royal cubit 7/6 standard cubit 20.7 525 mm Pace 2 cubits 35.4 900 mm Stadion 360 cubits 528 162 meters Greek Palm 4 fingers 3.0 77 mm Span 12 fingers 9.1 231 Cubit 24 fingers 18.2 463 mm Stade 604 feet 185 meter Roman cubitus is a six-palm cubit of about 444.5 mm about 0.68 inch). The Arabic Hashimi cubit of about 650.2 mm (25.6 17.49 inches [17]. inches) is considered to measure two French feet. Since the established ratio between the French and English foot is about 16 to 15, it produces the following ratios: 5 Hashimi cubits≈ 5. Other Near East Dimensions 10 French feet≈ 128 English inches. Also, the length of 256 Over time and the geographic areas of the Middle East Roman cubits and the length of 175 Hashimi cubits are nearly variouscubitsandvariationsonthecubithavebeenrecorded: equivalent [16]. 6palms =24digits, that is,∼45.0 cm or 18 inches (1.50 ); ft The guard cubit (Arabic) measured about 555.6 mm; 5/4 7palms =28digits, that is,∼52.5 cm or 21 inches (1.75 ); ft of the Roman cubit producing 96 guard cubits≈ 120 Roman 8palms =32digits, that is,∼60.0 cm or 24 inches (2.00 ); ft cubits≈ 175 English feet. eTh Arabic nil cubit (or black cubit) and 9 palms = 36 digits, that is,∼67.5 cm or 27 inches (2.25 )ft measured about 540.2 mm. Therefore 28 Greek digits of the [1]. Oates [22, page 186] writing of mesopotamian archeology Cyrenaica cubit≈ 25/24ofaRomanfootor308.7mm, and states “measures of length were based on the cubit or “elbow” 175 Roman cubits ≈ 144 black cubits. eTh mesopotamian (very approximately 0.5 m).” cubit measured about 533.4 mm, 6/5 Roman cubit making 20 The Histories of Herodotus [23, page 21] described the Mesopotamian cubits≈ 24 Roman cubits≈ 35 English feet. walls surrounding the city of Babylon as “ftyfi royal cubits eTh Babylonian cubit (or cubit of Lagash) measured about wide andtwo hundredhigh(theroyal cubitisthree inches 496.1 mm. A Babylonian trade cubit existed which was nine- longer than the ordinary cubit).” An accompanying note to tenths of the normal cubit, that is, 446.5 mm. eTh Babylonian the text provides the information given in parentheses, and cubit is 15/16 of the royal cubit making 160 Babylonian trade the end note reports these values as “exceedingly high” raising cubits≈ 144 Babylonian cubits≈ 135 Egyptian royal cubits. questions about the height of these walls which would be eTh Pergamon cubit 520.9 mm was 75/64 of the Roman cubit. well over three-hundred feet high if the royal cubit of 20 eTh Salamiscubit 484.0mmwas 98/90ofthe Romancubit. inches is implied, or 100 meters if the royal cubit is 50 cm. For eTh Persia cubitofabout 500.1mmwas 9/8ofthe Roman comparison, the great pyramid of Khufu is listed as originally cubit and 9/10 of the guard cubit. Extending the geographic 146.59 meters [24,page895]. eTh credibilityofHerodotus area still further produces more names and values for the has often been questioned, and these dimensions might be cubit [16, 18, 19, 25, 26]. suspect also or subject to the same exaggerations found From the Encyclopedia Britannica [24] section on elsewhere in his reportings. Weights and Measures given in Volume 23, the unit specifi- In 1916, during the last years of Ottoman Empire and cations for the Middle East cubit are shown in Table 5. during WWI, the German Assyriologist Eckhard Unger From a table in A. E. Berriman’s Historical Metrology [8] found a copper-alloy bar during excavation at Nippur from c. we n fi d his summary of cubit standards in Table 6. If one assumes the values from Berriman’s table to be 2650 BCE. He claimed it to be a measurement standard. This bar, irregular in shape and irregularly marked, was claimed reasonable estimates, then the descriptive statistics from the to be a Sumerian cubit of about 518.5 mm or 20.4 inches. A data in Table 7 oer ff a summary of these varied dimensions. 30-digit cubit has been identified from the 2nd millennium The estimates in Berriman’s table for Greek and Roman BCEwithadigitlengthofabout 17.28mm(slightly more than cubits align reasonably well with the Egyptian short cubit 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 󸀠󸀠 6 Journal of Anthropology Table 6: Cubit dimensions from Berriman [ 8]. Table 8: Human dimensions relative to the six-foot male. Unit Inches Cubit Inches Meter Finger 0.75 Roman 17.48 0.444 Palm 3 Egyptian (short) 17.72 0.450 Foot 12 Greek 18.23 0.463 Cubit 18 Assyrian 19.45 0.494 Height 72 Sumerian 19.76 0.502 Pace 72 Egyptian (royal) 20.62 0.524 Talmudist 21.85 0.555 Palestinian 25.24 0.641 Table 7: Descriptive statistics for A. E. Berriman’s table. Inches Meter Flemish ell Yard Cubit English ell Mean 20.04 0.51 Span French ell Median 19.61 0.50 Fathom Standard deviation 2.57 0.07 Range 7.76 0.20 18 handbreadths Minimum 17.48 0.44 Maximum 25.24 0.64 6 feet suggesting an average of approximately 18 inches. This dimen- sion is about two inches shorter than the overall mean in Table 7. eTh full range of values is about eight inches from 17.5 to 25. eTh varied origins for these data and previous values Figure 1: Vitruvian Man. suggest considering a family of cubits accumulated from many geographic areas over many different times rather than view these differences as suspects of one exact dimension. Figure 1 gives the famous picture associated with these Such variants may not be simple differences, or differences dimensions. eTh unit given shows one more example of the around an exact unit, but rather a composite of dimensions dimension of the cubit [1]. accumulated over a large chronological period from many eTh gfi ure of the Vitruvian Man by Leonardo da Vinci geographical locations that cannot be disentangled. These depicts nine historical units of measurement: the yard, the multiple dimensions suggest local applications rather than span, the cubit, the Flemish ell, the English ell, the French simply differences about a single standard which frustrates ell, the fathom, the hand, and the foot. eTh units depicted greater accuracy. are displayed with their historical ratios. In this gfi ure the Arounded valueof18 seems common for this period. cubit is 25% of the 6 individual and about 18 inches. We are The Hellenistic cubit appears in line with what has been iden- reminded once more of the importance of the human gfi ure tiefi d as the short cubit. Standardization of the cubit began for establishing units of measure. during Hellenism coinciding with Alexander’s conquests in the Middle East. Its standardization was probably increased Another example from this period comes from the Auto- greatly under the Roman Empire from the inu fl ences of war, biography [27] of Benvenuto Cellini (1500–1571). In describ- travel, and trade. eTh se inu fl ences contributed to bringing ing his casting of Medusa, Cellini’s narration uses cubit to the cubit into a more standard operational unit. Roman illustrate length as casually as we might use foot or yard. At engineers in viaduct, bridge, and road construction brought least in this context, if not others, the cubit appears of com- standardization throughout the empire. mon usage. How more generalized a cubit dimension pre- Cubits were employed through Antiquity to the Middle vailed through this time period is not known exactly. By the Ages and continue even today in some parts of the East. time of the French Revolution the Committee of Weights and Continued usage prevailed for measuring textiles by the span Measures had abandoned the cubit among other dimensions of arms with subdivisions of the hand and cubit in less in favor of the metric system. industrialized countries. Moving forwardtoDaVinci (1452–1519)wehavehis 6. The Human Cubit specicfi ations and commentary on Vitruvius Pollio (1st cen- tury BCE) for the human gur fi e and its dimensions [ 1]. They The history of metrology provides interesting data on the can be summarized as fractions of a 6-foot man as given in varied dimensions of the cubit. Metrology rfi st utilized the Table 8. human gfi ure in establishing dimensions. History to this 󸀠󸀠 Journal of Anthropology 7 Table 9: Frequency of left cubit measure by inches. Stature by inches Under 16.5 Under 17 Under 17.5 Under 18 Under 18.5 Under 19 Under 19.5 Above 19.5 71+ 000 1 3 4 15 7 30 70 0 0 0 1 5 13 11 0 30 69 0 1 1 2 25 15 6 0 50 68 0 1 3 7 14 7 4 2 38 67 0 1 7 15 28 8 2 0 61 66 0 1 7 18 15 600 47 65 0 4 10 12 8 2 0 0 36 64 0 5 11 2 3 0 0 0 21 −64 9 12 10 3 1 0 0 0 35 Total 925 49 61 102 55 38 9 348 Inches 16.5 17 17.5 18 18.5 19 19.5 19.5 Frequency 9 25 49 61 102 55 38 9 point suggests that a value of about 17-18 seems average and most common. Sir Francis Galton (1822–1911) offers data gathered from the investigations he conducted. Galton deserves recognition as one of the rfi st investigative anthropometrists. He was a scientist producing some of the first weather maps for recording changes in barometric pressure [28]and strategies for categorizing n fi gerprints [ 29]. Galton stands out for his investigations involving thousands of subjects. Some investigations were conducted at the International Health Exhibition in London held 1884-85 and at other eld fi loca- tions. Galton had earlier made an analysis of famous families 16.5 17 17.5 18 18.5 19 19.5 20 from which he compiled Hereditary Genius [30]and laterin Cubit frequency by inches Natural Inheritance [31]. He maintained a life-long interest in Frequency determining the physical and mental characteristics of groups of individuals. Figure 2: Cubit frequency by inches for 348 subjects. Not only did Galton collect data from his laboratory on human subjects, he investigated statistical techniques for analyzing tables, graphs, and plots of data. In doing so he created the origins for what is now recognized as correlation Figure 2 indicates the modal category of forearm/cubit and regression analysis. Correlation became more formally measures for Galton’s sample was 18.5 inches. eTh frequency developed by Pearson [32] as the product moment correlation distribution of forearm measurements is somewhat balanced. coefficient. It has become the most known and used statistical This might be expected given that these measures would be procedure of our time. Other statisticians, especially Sir determined by chance through heredity. This was Galton’s Ronald Fisher [33–35]and Tukey[36], have criticized the viewpoint and emphasis. Consequently, his attention derived correlation coefficient for its abuse arising from simplistic from this data and other data moved his interest to eugenics. applications and dubious interpretations. Nevertheless, the Many other English scientists and statisticians shared this correlation coefficient remains a popular analytic technique. interest; Fisher, Pearson, Haldane, Cattell, and others [40]. Pearson [37]alsoproducedthree volumesonthe life,letters, Galton (and the others) received considerable criticism for and works of Galton. taking this position. However, it was as a scientist and com- Galton’s data for the cubit of his day is given in Table 9.It piler of human data that led Galton to draw his inferences. was taken from Stigler [38,page319] The History of Statistics . His pronouncements [30, 31, 41] concerning eugenics do not Its original source is Galton [39] whose investigation gives smack of a political or personal agenda. One may disagree, data gathered from about 130 years ago on the forearm or butitisimportant to understandthatGalton’sworkwas cubit. Stigler [38,page319]indicated threeofGalton’srow focused upon data and methodology as the basis for forming totals were summed incorrectly. eTh se sums were corrected his conclusions. in Table 9. The mean for the Galton sample of 348 persons in Table 9 Figure 2 summarizes the relative frequency of fore- was almost 18 inches bringing estimates of a center location arm/cubit lengths from Galton’s data on 348 subjects given (i.e., mode, median, and mean) in sync with an approximate in Table 9. normal distribution as shown in Table 10. 󸀠󸀠 Stature by inches 8 Journal of Anthropology Table 10: Millimeters and inches of the left cubit. Left cubit to stature y = 0.2546x + 0.7623 Millimeters Inches R = 0.5715 Mean 67.06609 17.83621 Standard error 0.126798 0.042699 Median 67 18 Mode 67 18 Standard deviation 2.365384 0.796541 16 Sample variance 5.595043 0.634478 Kurtosis −0.9142 −0.42833 62 64 66 68 70 72 Stature in inches Skewness −0.09243 −0.16653 Range 8 3.5 Figure 4: Plot of left cubit to stature. Minimum 63 16 Maximum 71 19.5 Sum 23339 6207 analytic methods. These matters are not directly connected Count 348 348 to the issues of cubit length and therefore not discussed here. However, the relationship of cubit to stature is useful and it canbecomparedtoDaVinci’s estimate. Galton’s data on cubit length by inches Stigler [38,page319]indicated “Galton’sadhoc semi- graphical approach gave the correlation value𝑟=0.8 .” This was Galton’s approach prior to the Pearson product moment correlation which when calculated for his data gave𝑟=0.75 . Figure 4 is a plot of data from Table 9 with a linear regres- 20 sion line and showing the variation in forearm/cubit at each level of stature. It is very important to note the wide variation of left cubit measures (vertical) for each indication of stature (horizontal). Individual differences in the cubit/forearm are clearlyevidentateachpoint of staturethwarting anything more specific than a generalized indication for the fore- 19.5 arm/cubit from Galton’s data. eTh shared variance between 0 18 1 stature and cubit is about 57% suggesting these two variables +71 71 70 70 6 69 9 68 68 16.5 16 5 67 67 are related but not completely. 66 66 −64 Several questions emanate from Galton’s data regarding forearm length or the cubit. Figure 3: A three-dimensional view of Galton’s data. (1) How representative is this sample of the general pop- ulation? (2) How much change, if any, in human dimensions has From Galton’s data summarized in Figure 2 and Tables occurred from ancient times and over the one hun- 9 and 10 about 2% had forearms at 16.5 or less and 2% dred plus years from Galton’s sample to the present had forearms greater than 19.5 .Approximately 63%or218 day? personsand closetotwo-thirdsofthe 348personsampleare within one-half inch + or− themeanof18.3inchesoralmost (3) Is there any gender difference or other sources of 18.5 if rounded o.ff About 95% vary less than an inch above influence and bias? andbelow themeanestimate. Rounding from thesefrequen- cies makes these values approximate, but they still provide From what we know of Galton’s methods there appears no a generally useful summary from his sample. Skewness and indication of outright bias. Stigler [38]inchapters8,9,and 10 kurtosis appear as minimal influences on the distribution of his book raised no questions when describing Galton’s data further confirming a balanced distribution. andmethods foranalysing data.Galton’ssamples were large Figure 3 provides a three-dimensional view of Galton’s andoeft ninthe thousands. Thiscubit sample is moderatein data. It usefully shows the clustering of values along the scope. Galton was aware of gender differences and utilized center diagonal from the upper left to lower right. Galton’s 1.08 as a correction factor for male/female differences [ 38]. figures were not shown as three-dimensional, but he recorded However, there is little information regarding sample the frequencies at each intersection of his two-way table representation. It appears that Galton was generally fastidious which were used to produce this three-dimensional gur fi e. in his investigations. He utilized gatherings of the general Pondering his data gave rise to Galton’s work on association/ population from which to procure his samples and make his correlation for which the word regression has now evolved measurements. Given that right handedness predominates, being derived from his eo ff rts to interpret what this and other Galton measured the left hand to avoid what might result data express. See Stigler [38] for more details on Galton’s from possible environmental influences upon the mostly Cubit by inches Frequency Left cubit in inches 󸀠󸀠 󸀠󸀠 󸀠󸀠 Journal of Anthropology 9 Table 11: Forearm percentiles for an unidentified British population. Table 12: Elbow-fingertip length percentile distribution in millime- ters. Percentile 5 50 95 (a) Male 440 475 516 1st 2.5th 5th 10th25th50th75th90th95th97.5th99th Female 400 430 460 435 442 448 455 468 483 499 515 523 532 542 (b) Mean 484.04 (19.05 inches) Standard error 0.55 dominant right hand. Volunteering could be a potential source of bias, but volunteering probably allowed a larger Median 483 (19.01 inches) sample of individuals. He paid individuals a modest amount Mode 472 (18.58 inches) to participate not unlike what is sometimes done today. Standard deviation 23.32 Johnson et al. [42]reviewedand reanalyzed Galton’s Sample variance 544.09 original data. eTh y report on mean scores, correlations of Kurtosis 0.43 the measures with age, correlations among measures, occu- Skewness 0.22 pational differences in scores, and sibling correlations. A cor- Range 192 relation of cubit/forearm to stature indicated the former Minimum 386 was about 25–27% of stature. Nothing further is added to a knowledge of forearm/cubit dinemsion by their work. Maximum 578 Relevance of the forearm/cubit length in more recent Count 1774 times comes from anthropometric dimensions utilized in industrial psychology and applications to the clothing indus- try. Data from Mech [43] gives more recent data of human dimensions including the forearm. Forearm lengths reported 7. Discussion for percentiles 5, 50, and 95 are given in Table 11. eTh varied dimensions forthe historical cubitofancient eTh se percentiles are from an unidentiefi d British sample times and places speak to a variation in the dimension itself. ages 19 to 65. Lacking more information one can only Two major units predominate; one estimate centers around compare and contrast these dimensions to previous samples 18 inches and the other around 20 inches. There are other discussed earlier. es Th e males had a median cubit measure variations, some smaller and some much greater. er Th e is too of 475 mm or ∼18.7 inches. Females measured a slightly wide ageographicalareaand toogreat achronological time shorter median measure of 430 mm or∼16.9 inches. Mech period to consider any of these latter variations normative. [43] indicated a median value close to that given in Table 9 Each variant was more likely to be locally relevant rather for Galton’s data or∼18.7 to∼18.3. than widely prominent. Only in the Greek and Roman The Lean Manufacturing Strategy reports a forearm empires through war, trade, and construction did these values 󸀠 󸀠 󸀠 mean = 18.9 ,standarddeviation =0.81 , minimum = 15.4 , coalesce to somewhat of a standard. and maximum = 22.1 based on data from McCormick [45]. How has the human physique changed over time? Roche Nothing further is given regarding this sample and its char- [48] reported that rates of growth during childhood have acteristics. increased considerably during the past 50–100 years. He There are numerous sites and organizations providing indicated increases in rates of growth and maturation for all carefully determined dimensions for the human body. How- developed nations, but not evident in many other countries. ever, these dimensions are developed to serve the clothing eTh re were recorded increases in length at birth in Italy and industry and furniture design adding nothing to a knowledge France, but little change in the United States. An increase in of the contemporary forearm/cubit dimension [46]. childhood stature was given for about 1.5 cm/decade for 12- The anthropometry database ANSUR [ 47]obtainedfrom year-old children. eTh increase in stature for youth was about http://www.openlab.psu.edu/ gives a table of percentiles for 0.4 cm/decade in most developed countries. eTh changes in the horizontal measure made “from the back of the elbow to body proportions during recent decades were reported as less the tip of the middle n fi ger with the hand extended,” that is, marked than those in body size. Leg length increased more cubit. eTh sample was comprised of unidentiefi d male army than stature in men but not in women. Roach further indi- recruits. cated that changes in nutrition alone could not account for the eTh ANSURdatasample[ 47]in Table 12 provides trends which exceed the original socioeconomic differentials. In the United States, Roach reported there have been per descriptive statistics for the right male forearm plus extended hand in millimeters. The mean for this quite large contem- capita increases in the intake of protein and fat from animal sources, decreases in carbohydrates and fat from vegetable porary sample is about one inch greater than the short cubit reported much earlier. So is the median although the mode is sources, and some changes in caloric intake. It is not clear slightly less. eTh sample appears reasonably balanced, but the that these changes constitute better nutrition stimulating growth. eTh trends could reflect environmental improve- variation indicated by the standard error, standard deviation, and range show this human dimension to vary. Variation has ments, specifically changes in health practices and living been encountered before in the reporting of earlier samples. conditions leading to improvements for mortality rates and 10 Journal of Anthropology life expectancy [44].Nutritionvariesevenindevelopedcoun- [2] F.M.Cornford, Plato’s eor Th y of Knowledge: Theaetetus and Sophist, Liberal Arts Press, New York, NY, USA, 1957. tries. Roche [48] reported genetic factors play a small role in causing trends. However, the data speaks to considerable [3] E. Zupko, Revolution in Measurement; Western European Weights and Measures Since the Age of Science,TheAmerican variation among contemporary samples as also noted in Philosophical Society, Philadelphia, Pa, USA, 1990. Galton’s data. [4] Revised Standard Version of the Bible: RSV,NationalCouncil of Overall, it seems unwise to be overly fastidious about the Churches of Christ in the United States of America, New any contemporary value for the cubit when such samples York, NY, USA, 1952. are vaguely described. For any comparison of contemporary [5] G. A. Barrois, Chronology and Metrology. the Interpreter’s Bible, dimensions reported there are few characteristics given by vol. 1, Abington Press, New York, NY, USA, 1952. which to judge sample representation. eTh contemporary [6] G. Barkay, “Measurements in the Bible: evidence at St. Etienne estimates appear somewhat close together and suggest at least for the length of the cubit and reed,” Biblical Archeological forthesesamplesnogreat changehasoccurredovertheyears, Review,vol.12, no.2,article 37,1986. butwecannotbesurelacking validdata. Withoutmoresam- [7] D.N.Freedman, Eerdman’s Dictionary of the Bible,Eerdmans, ple definition, any fastidious analysis appears unwarranted. Grand Rapids, Mich, USA, 2000. eTh Galton values are likely to have been local and relevant to [8] A.D.Berriman, Historical Metrology,Dent, London,UK, 1953. a British sample. Nowadays samples are more likely to reflect [9] M. G. Easton, Illustrated Bible Dictionary, om Th as Nelson, the role of immigration with whatever additional effects this Knoxville, Tenn, USA, 3rd edition, 1897. might bring to bear on determining national human dimen- [10] G. A. Buttrick, The Interpreter’s Bible ,vol.I,AbingtonPress,New sions. In general, Europeans are taller than Asian/Middle East York, NY, USA, 1952. peoples and Americans are taller than Europeans. eTh se are [11] A. S. Kaufman, The Temple of Jerusalem , Har Year’ah Press, Jer- generalizations from gross estimates. Komlos and Baten [49] usalem, Palestinian, 2004. have made a comprehensive analysis of stature over centuries. [12] A. B. David, “Ha-midda ha-Yerushalmit,” Israel Exploration The striking feature of their tables is the intravariation of Journal,vol.19, pp.159–169,1969. values for each time period. Individual variation was also [13] D. Arnold, Building in Egypt: Pharaonic Stone Masonry,Oxford observed in Galton’s data. However, systematic sampling and University Press, Oxford, UK, 1991. sample details must accompany any data before estimates can [14] J. P. Lauer, “Etude sur quelques monuments de la IIIe dynastie be more than gross general indications. (pyramide ad ` egres ´ de Saqqarah),” Annales du Service des A variety of circumstances address the cubit, but most Antiquites de L’Egypte, IFAO,vol.31, no.60, article59, 1931. of them offer little specicfi information beyond what has [15] W.M.F.Petrie, The Pyramids and Temples of Gizeh , Field and already been presented. es Th e biased sites typically serve Tuer, London, UK, 1883. some agenda, oeft n religious or personal. Overall, even these [16] W. M. F. Petrie, Inductive Metrology, Saunders, London, UK, sites typically report the two major dimensions for the cubit at 18 inches or 20 inches. [17] R. J. Gillings, Mathematics in the Time of the Pharaohs, MIT The cubit as a dimension remains useful. We take the Press, Cambridge, Mass, USA, 1972. cubit (hand and foot) wherever we travel. Knowing personal [18] D. Lelgemann, Eratosthenes von Kyrene Und die Messtechnik der dimensions can sometimes prove useful for making quick Alten Kulturen, Chmielorz, Wiesbaden, Germany, 2001. albeit gross estimates. eTh 18 ruler is a very handy device [19] D. Lelgemann, Recovery of the Ancient System of Length Units, whenever measures just beyond a foot ruler are required, Institute for Geodesy and Geo-Information Technology, Berlin, especially when it is necessary to draw straight lines for a Germany, 2004. length just beyond twelve inches. Tape measures are a boon, [20] E. Nichholson, Men and Measures, Smith, Elder & Co, London, but not for drawing lines. UK, 1912. It appearsthatwemight contentourselves with acubit [21] J. L. E. Dreyer, A History of Astronomy from al Th es to Kepler , length of 18 inches as a somewhat consistent dimension for Dover, New York, NY, USA, 1953. the cubit. Even as the foot evolved from a specific albeit arbi- [22] J. Oates, Babylon, aTh mes and Hudson, London, UK, 1986. trary personage, any assemblage of them leads to an abstract [23] Herodotus, eTh Histories. (Trans. Aubrey De S el ´ incourt; Notes dimension, so the cubit could justify more application as a 0.5 John Marincola), Penguin books, London, UK, 1954. yard and/or a 0.5 meter. Further prominence of either or both [24] “Weights and measures,” in Encyclopedia Britannica,vol.23, pp. these units might prove more useful than rfi st surmised. 371–372, Encyclopedia Britannica, Chicago, Ill, USA, 1971. [25] M. A. Powell, “Metrology and mathematics in ancient Mesopo- tamia,” in Civilizations of the Ancient Near East III,Sasson, Ed., Conflict of Interests Scribners, New York, NY, USA, 1995. eTh author declares that there is no conflict of interests [26] D. Arnold, The Encyclopaedia of Ancient Egyptian Architecture , regarding the publication of this paper. Princeton University Press, Princeton, NJ, USA, 2003. [27] B. Cellini, Autobiography: the Life of Benvenuto Cellini (Trans. J. Symonds),P.F.Collier &Son,New York,NY, USA, 1906. References [28] F. Galton, Meteorgraphia: Methods of Mapping the Weather, Macmillan, London, UK, 1863. [1] H. A. Klein, The Science of Measurement ,Dover,New York,NY, USA, 1974. [29] F. Galton, Fingerprints, Macmillan, London, UK, 1892. 󸀠󸀠 Journal of Anthropology 11 [30] F. Galton, Hereditary Genius: An Inquiry Into Its Laws and Con- sequences, Macmillan, London, UK, 1869. [31] F. Galton, Natural Inheritance, Macmillan, London, UK, 1889. [32] K. Pearson, “Notes on the history of correlation,” Biometrika, vol. 13, pp. 25–45, 1920. [33] R. Fisher, On the Mathematical Foundtions of eor Th etical Statis- tics, eTh Philosophical Transactions of the Royal Society, Lon- don, UK, 1922. [34] R. Fisher, The Design of Experiments , Hafner, New York, NY, USA, 1951. [35] R. Fisher, Statistical Methods for Research Workers,Hafner, New York, NY, USA, 1958. [36] J. Tukey, “Analyzing data: sanctification or detective work?” American Psychologist,vol.24, pp.83–91,1969. [37] K. Pearson, eTh Life,Letters andLabours of FrancisGalton(3 Vols.), Cambridge University Press, Cambridge, UK, 1914. [38] S. Stigler, The History of Statistics , Harvard University Press, Cambridge, Ma, USA, 1986. [39] F. Galton, “Co-relations and their measurement chiefly from anthropometric data,” Proceedings of the Royal Society of Lon- don, vol. 45, pp. 135–145, 1888. [40] J. Waller, “Ideas of heredity, reproduction and eugenics in Britain 1800–1875,” Studies in History and Philosophy of Science C,vol.32, no.3,pp. 457–489, 2001. [41] F. Galton, “Kinship and correlation,” North American Review, vol. 150, pp.419–431,1890. [42] R. C. Johnson, G. E. McClearn, S. Yuen, C. T. Nagoshi, F. M. Ahern, and R. E. Cole, “Galton’s data a century later,” American Psychologist,vol.40, no.8,pp. 875–892, 1985. [43] Mech, 2010, http://mech.utah.edu/ergo/p. [44] R. Steckel, “Research project: a history of health in Europe from the late paleolithic era to the present,” Economics & Human Biology,vol.1,pp. 139–142, 2003. [45] B. McCormick, Human Engineering, Industrial Design Institute, Warsaw, Poland, 1964. [46] E. Grandjean, Fitting the Task to the Man,Taylor&Francis, New York, NY, USA, 1989. [47] ANSUR: Open Design Lab at PSU, 1988, http://openlab.psu.edu/. [48] A. F. Roche, “Secular trends in human growth, maturation, and development,” Monograph Social Research in Child Devel- opment,vol.44, no.3-4,pp. 1–120, 1979. [49] J. Komlos and J. Baten, “Height and the standard of living,” Journal of Economic History, vol. 58, no. 3, pp. 866–870, 1998. 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References

  • Measurements in the Bible: evidence at St. Etienne for the length of the cubit and reed,
    G. Barkay
  • Ha-midda ha-Yerushalmit,
    A. B. David
  • Étude sur quelques monuments de la IIIe dynastie (pyramide à degrés de Saqqarah),
    J. P. Lauer
  • Metrology and mathematics in ancient Mesopotamia,
    M. A. Powell
  • Notes on the history of correlation,
    K. Pearson
  • Analyzing data: sanctification or detective work?
    J. Tukey
  • Co-relations and their measurement chiefly from anthropometric data,
    F. Galton
  • Ideas of heredity, reproduction and eugenics in Britain 1800–1875,
    J. Waller
  • Kinship and correlation,
    F. Galton
  • Galton’s data a century later,
    R. C. Johnson, G. E. McClearn, S. Yuen, C. T. Nagoshi, F. M. Ahern, and R. E. Cole
  • Research project: a history of health in Europe from the late paleolithic era to the present,
    R. Steckel
  • Secular trends in human growth, maturation, and development,
    A. F. Roche
  • Height and the standard of living,
    J. Komlos and J. Baten